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Formula when i know the GST total 2017-10-31
From Duncan:
HI - I've added up the GST from a pile of receipts and would like to know what the total cost of goods would be without GST. I don't want to add up 100's of receipts again with the cost before GST but I do need this total cost. i.e.) I know I paid $400 GST, what would the formula be to find out the cost of what I purchased before taxes? Your help is much appreciated!
Answered by Penny Nom.
formula when i know the GST total 2017-10-31
From Duncan:
HI - I've added up the GST from a pile of receipts and would like to know what the total cost of goods would be without GST. I don't want to add up 100's of receipts again with the cost before GST but I do need this total cost. i.e.) I know I paid $400 GST, what would the formula be to find out the cost of what I purchased before taxes? Your help is much appreciated!
Answered by Penny Nom.
A tangent to a curve 2017-10-22
From Jasem:

Suppose that
f(x)=(3x-3)^1/2.

(A) Find an equation for the tangent line to the graph of f(x) at x=2

(B) Find all values of xx where the tangent line is horizontal, and enter them as a comma-separated list (e.g., 2,-3,6). If there are none, enter none.

Values of x


Answered by Penny Nom.
The distance between the origin and a moving point on a graph 2017-10-16
From Paulina:
Find the rate of change of the distance between the origin and a moving point on the graph of y=x^2 +1 if dx/dt=2 centimeters per second
Answered by Penny Nom.
An enclosure for some remote control boats 2017-10-03
From Roberto:
I am trying to build a "ring" for our remote control boats, using irrigation pipe. I'd like to use full 20' long sticks for the long sides and use eight of what we call 45s, which are actually 135' fittings to make the six short sides. If I know the length of the two long sides, what would be the formula to find the exact lengths of the short sides?

Thank you.

Answered by Penny Nom.
The volume of a cone without calculus 2017-10-02
From Akash:
How to find the volume of a cone without the knowledge of calculus?
Answered by Penny Nom.
Four multiples of 10 2017-09-23
From Laudacir:
Four multiples of 10 are added together.the total is a 3 digit number with three consecutive digits. What could the four number be?
Answered by Penny Nom.
Simultaneous equations with fractions 2017-09-09
From Farah:
Hi, my name is Farah. I hope you can help me with this question . X/2 + g/5= 3 and 2g - f = 10
Answered by Penny Nom.
The volume of an attic 2017-09-07
From paul:
trying to determine volume of an attic base is rectangular 29 ft by 37 ft peak runs parallel to longest base side and is 7 ft long roof lines run from each end of the peak to the respective corners the peak is 3.5 ft above the base
(so seen from above there are 5 visible lines: the peak and 1 line to each of the 4 corners)

Answered by Harley.
Simultaneous equations 2017-09-02
From keto:
x-y=2,x^2+xy=12
Answered by Penny Nom.
A rectangle and a circle 2017-08-12
From Ramzan:
a diagram shows the shape of rectangular framework with length (2x+20)cm and with (y+10)cm . The outline is made of wire . If a circle with diameter 56 cm is to be made from the wire and the area of the rectangle is 420 square centimeter ,find the possible lengths and width of the rectangle
Answered by Penny Nom.
An arched window 2017-07-24
From Gerry:
Looking to make a full size template for an arched window. Need increments every 16". The radius is 138' 0 9/16" , the chord is 226" and the rise at center of chord is 43"
Answered by Penny Nom.
3 consecutive multiples of 11 2017-07-22
From nisha:
using the multiples formula shown at ypur site how can we solve finding 3 consecutive multiples of 11 whose sum is 363
Answered by Penny Nom.
Parallel and Perpendicular lines 2017-07-17
From Karen:
Find an equation for the line with the given properties. Perpendicular to the line 7x + 2y = -6; containing the point (-2, -1)

Find an equation for the line with the given properties. Parallel to the line 5x - 3y =-6; x intercept = 3

Answered by Penny Nom.
Simultaneous equations with fractions 2017-06-02
From Jamal:
1/x + 1/y =5 and 1/y - 1/x =-1
Answered by Penny Nom.
What is the regular price? 2017-05-11
From Saira:
If the sale price is 55.50$ and the discount is 12% what is the regular price
Answered by Penny Nom.
Canada's population as a percentage 2017-05-11
From bethmarie:
What percentage of the world population (7.5 billion) is Canada's population (36 million). Thank you very much!
Answered by Penny Nom.
Why does 10x10x10 give 1,000.0000000000001? 2017-04-12
From Randolph:
Hi, On your calculator I found that a box 10 by 10 by 10 inches has a volume of 1,000.0000000000001 cubic inches. Can you explain the numeral 1 thirteen places past the decimal? Thanks, Randy
Answered by Penny Nom.
Quadratic Equations 2017-03-28
From Natalie:

Hi Maths Central,

I am having trouble with quadratic equations. The question is:

Calculate the length 'l' of a rectangular pool by creating and solving a quadratic equation.

1. The rectangular pool is of equal area to a square pool, and a circular pool (5.70m^2).
2. The length of the rectangular pool must be 2m longer than the width 'w'.

Thank you so, so much for your help, Maths Central!


Answered by Penny Nom.
Differentiate y = x^x^x 2017-03-19
From Nafis:
differentiate y = x^x^x
Answered by Penny Nom.
A regular tetrahedron 2017-03-12
From Jeramie:
When we have a regular tetrahedron, is it always true that all the angles of the triangles measure 60 degrees?
Answered by Penny Nom.
A block base for a plywood rectangle 2017-02-18
From Joe:
How many cinder blocks 16x8 would i need to build a solid base for a plywood base 54inches wide and 30 inches deep Thank you
Answered by Penny Nom.
Vinculum 2017-01-27
From Dick:
What is the line or bar over a Roman Numeral called?

Eg. V with the bar over it representing 5,000 .

Answered by Penny Nom.
The volume of a slab 2017-01-21
From Russell:
Working with a segment of a circle. The O.D. is 3.440" the length of the chord is 3.130 I need information on the volume of the largest area. I would like to know (in thousands of an inch) how tall would the largest area need to be to equal .1143 cubic inches If you need more info I can send it Thanks in advance
Answered by p.
Angular speed 2017-01-21
From Kenzi:
A wheel of radius 14 inches is rotating 45°/sec. What is the linear speed in in/sec and the angular speed in RPM? (Round your answers to three decimal places)

I already found the linear speed. I got 10.996 in/sec. I don't know how to find the angular speed.

Answered by Penny Nom.
The average rate of change of cot(t) 2017-01-18
From Brianna:
Hello! It's been a while since I've taken a math course, and I'm stuck on a problem in my calculus course.
The question is this:

Find the average rate of change of the function over the given interval.
h(t)=cot(t) a) [5pi/4, 7pi/4]

Answered by Penny Nom.
Five equations 2017-01-16
From Muhammed:
A x 4 = E
B ÷ 4 = E
C + 4 = E
D - 4 = E
___________
& A + B + C + D = 100
what is the value of E

Answered by Penny Nom.
8^3/2(2+2) 2017-01-13
From Mary:
8^3/2(2+2)
Answered by Penny Nom.
Simultaneous equations with fractions 2016-12-21
From Kimi:
I am stuck on this,can someone please help me????

1/2x+1/3y=11
8x+2/5y=102
Can someone please explain how to solve questions like these?? Or else I will never learn...
Thank you

Answered by Penny Nom.
Two concentric circles 2016-12-21
From shrestha:
Two concentric circles have radii of 14 cm and 7 cm respectively. Find the area of space between them.
Answered by Penny Nom.
Two boys on the same route 2016-12-06
From Abbey:
Starting from the same spot, one boy completed a route in 9 minutes and another boy completed it in 15 minutes. When will both boys be at the same starting point at the same time again?
Answered by Penny Nom.
Simultaneous equations 2016-11-25
From Rohan:
x-2/3 + y - 1/4 = 13/12
2-x/2 + 3 + y/3 = 11/6

Answered by Penny Nom.
Multiplication and repeated addition 2016-11-23
From Anandmay:
Hello I was looking closely at early arithmetic where I found how we discovered properties of Arithmetic. Like:2 x 3 = 3 x 2. This can be proved by considering a 2-D figure(actually,quadrilateral) having length consisting of 2 boxes of 1-by-1 dimensions and breadth of 3 boxes of the same dimensions. Now,consider it again,but,this time,length of 3,and breadth of 2 of such 1 by 1 boxes. We now notice that we can fit the 2 types of rectangles formed on each other precisely. So the multiplicative property of commutativity is true for all natural numbers as we can generalize the result(in our mind,for self satisfaction).

Now,can you find me a nice satisfactory reason of why a fraction times a natural number equals the number times the fraction? I mean, for example,i can understand the meaning of 3 x 2/3 to be three times 2-3rd,that is, 2/3+2/3+2/3.Fair enough. But here is the problem:By definition and actual meaning of multiplication, a x b means the repeated sum of b,done 'a' times. So what is the meaning of doing 2/3 x 3?The repeated addition of 3 how many times??2/3 times??Not making sense,right?And even we have not proved yet the commutative property of numbers INCLUDING fractions.So how can we resolve this problem and make these things meaningful?
Thanks

Answered by Penny Nom.
Volume of liquid remaining in a tilted cylinder 2016-11-08
From Brian:
I am trying to determine the amount of a liquid remaining in a 55 gallon drum when it is tilted at 45 degrees and the liquid level is low enough so that the liquid does not completely cover the bottom of the drum.

Your help is greatly appreciated.

Answered by Harley Weston.
A pattern rule for a sequence 2016-10-28
From Grace:
Here's a Grade 7 question, we need to find the pattern rule:

1 - 1
2 - 3
3 - 6
4 - 10
......
It may involve exponents, but we can't seem to figure it out.
thank you.
Grace.

Answered by Penny Nom.
An airplane schedule 2016-10-14
From Stephanie:
Starting at 8:00a.m., a passenger plane leaves from an airport every 6 minutes and a cargo plane leaves every 7 minutes. When is the next time these kinds of planes will leave at the same time?
Answered by Penny Nom.
Hexagonal pyramid bevel angles 2016-09-30
From Peter:
I have seen your response to a similar question from Steve which Chris and Harley responded to, however I am not familiar with some of the terms. Is there a formula that I can enter my details in which will give me the specific angles I require. The item I am constructing is much larger than the one you responded to previously. Thank you for any assistance you are able to provide.
Answered by Penny Nom.
2,006-1-2-3-4-...-48-49-50 2016-09-24
From Mimi:
Compute the following:

2,006-1-2-3-4-…-48-49-50

Answered by Penny Nom.
The width of a 300 foot long rectangular acre 2016-09-21
From Debbie:
If 2 sides of a 1 acre plot is 300 feet each what are the other 2 sides? The acre is a rectangle.
Answered by Penny Nom.
The distance around a warehouse 2016-09-21
From Chuck:
How far do I walk when I walk around a 751,000 sq. ft. warehouse?
Answered by Penny Nom.
Integrate (x^2 - 4x + 4) ^4/3 2016-09-15
From Ifah:
Hi i have questions please answer
Integral 2 sampai 3 dari (x² - 4x + 4) ^4/3 dx

Answered by Penny Nom.
The modulus of a complex number 2016-07-29
From Cheyenne:
There's a question on my Summer Assignment I cant figure out. Here it is:

Find the absolute Value of the complex number. -5i

Please help?

Answered by Penny Nom.
Two equations with fractions 2016-07-22
From kanesh:
p/2+q/3=3

p/4+2q/3=3

Answered by Penny Nom.
Simultaneous equations 2016-06-25
From sena:
2x/3+3y/2=-1
4x-5y=22

simultaneous equation

Answered by Penny Nom.
The difference between the ares of two rectangles 2016-06-09
From Ingrid:
I am trying to help my son with an area question.
I have the answer, from the solutions, but I cannot figure out how to teach him.

Question:

Two rectangles have lengths 13cm and 19cm respectively.
Their total area is 376cm squared.
If both their widths are whole numbers, what is the difference in their areas?

I know that this is solvable once I determine the widths of the rectangles ,
but how do I go about finding that?

Thanks for your help

Answered by Chris Fisher and Harley Weston.
Implicit differentiation 2016-06-06
From Pranay:
Is a circle x^2+y^2=2 a function? If it is not a function, why is it possible to do implicit differentiation on it?
Thanks.

Answered by Penny Nom.
A barn roof 2016-05-29
From Joe:
Is it possible to build a barn roof (irregular pentagon?) with a 12' base and the other 4 sides 4' each? Thanks.
Answered by Penny Nom.
Two pieces of rope 2016-05-21
From Render:
Fred cuts a 12- inch piece of rope. Then he cuts a second piece of rope that is 3/2 longer than the first piece. Is the second piece shorter or longer than the first piece? Explain.
Answered by Penny Nom.
A trough with a triangular cross section 2016-05-21
From Clarice:
A trough having an equilateral triangle end sections has sides equal to 0.4 m and 7m long.what is the volume of the liquid in the container if the depth of the water is one half the depth of the trough?
Answered by Penny Nom.
Euler's polyhedron formula 2016-05-20
From Antonia:
why does not cylinders follow Euler's polyhedron formula ( V-E+F=2) ?? if a cylinder has 3 faces, 2 edges and 0 vertices it doesn't follow Euler's formula???
Answered by Penny Nom.
The volume of a truncated rectangular pyramidal pond 2016-05-13
From Paul:
How do you calculate a partially filled truncated rectangular pyramid if you always know the bottom rectangle, the maximum height top rectangle perimeter, but have a varying height. Similar to filling up a pond you know the current height and dimensions at the max rectangle how do you calculate it half full i.e. 10x30 outside perimeter with a 2x8 base and a max height of 6ft how do you calculate it at 3ft without re-measuring the top perimeter. Thanks, Paul
Answered by Harley Weston.
A pair of equations with fractions 2016-05-11
From tiya:
hello, i want to know how to solve this question.

m/6+2n/3=6
-m/10=2n/5=2

Answered by Penny Nom.
A rectangular field 2016-05-07
From Jan:
A rectangular field is 63m long and 21m wide. A fence of 2m in height is needed to fence the field and fencing is also required to divide the field in three square sections. There are three wooden gates measuring at 1.5m to the three sections of the field. What is the total surface area of the fence needed for fencing and diving the field?
Answered by Penny Nom.
Solve 2^2x + 3(2^x) - 4 = 0 2016-04-27
From Lloyd:
Solve the equation 2^2x + 3(2^x) - 4 = 0
Answered by Penny Nom.
sin 2x - sin x = 0 2016-04-24
From lilly:
sin 2x - sin x = 0 0
Answered by Penny Nom.
600(1+0.05)^7 2016-04-21
From chelsey:
I am unsure on how to solve this problem, 600(1+0.05) 7 ?
Answered by Penny Nom.
15.86 acres 2016-04-21
From Ronald:
If a rectangular piece of land is 1320 ft. on one side, how many feet would be required on the other side to equal 15.86 acres?
Answered by Penny Nom.
External and interior angles of a regular polygon 2016-04-19
From pearl:
a polygon has n sides.The exterior angle is 8 times the interior angle
find the value of the interior angle
find the value of n

Answered by Penny Nom.
Heights at various points along an arc 2016-04-15
From Isiah:
So I am working on a problem with a few friends; you have an arc with the center of its chord at 0,0. We also have a known sagitta and a known radius of curvature. How do we calculate the height extending in both the positive and negative directions?
Central sag: 2.48
Chord length: 9.6

Answered by Penny Nom.
Sloping my yard away from my house 2016-04-15
From Harold:
I need to slope a area of my yard away from my house and garage. The length of my house is 80 feet long and i need to slope it 22 feet away. I want to raise the dirt at the foundation by 6 inches and slope it down to nothing at the width of 22 feet. How much soil would i require?
Answered by Penny Nom.
Pizza delivery 2016-04-03
From Andrew:
Suppose you own a local pizza restaurant, Pizza with Pizzazz, and in order to compete with the big pizza chains in your area you are considering an advertising campaign offering customers a free pizza if their pizza is not delivered in 30 minutes or less. Even though your pizza restaurant is known for its fast and friendly delivery service, you are not sure if you can afford to give away too many pizzas for free. Looking over your past 12,421 pizza deliveries you find out 97% of the pizzas were delivered in 30 minutes or less.

Calculate the probability that all 100 randomly selected pizza deliveries will have been made in 30 minutes or less? Hint: Use the multiplication rule. (Round 4 decimals)

I'm really stumped on how exactly to do this problem. I don't need the answer just the steps broken down to show me how to get it! It would be gladly appreciated if you could help!

Answered by Penny Nom.
Maximizing the area of a two lot region 2016-04-03
From yousef:
A man wishes to enclose two separate lots with 300m of fencing. One lot is a square and the other a rectangle whose length is twice its width. Find the dimensions of each lot if the total area is to be a minimum.
Answered by Penny Nom.
A rotating schedule for a softball team 2016-03-25
From Caroline:
I couldn't find a similar question, hopefully there isn't one!

I have a softball team of 18 people (7 girls and 11 boys), but am limiting each game to 13 players (6 girls and 7 boys). The season is 10 games long. How do I create a rotating schedule which allows members to play evenly? I tried separating the boys and girls to create rotation for each but I got confused. Some are unable to attend all games but for the simplicity of a rotation schedule can you please help?

Answered by Robert Dawson and Victoria West.
A percentage problem 2016-03-02
From jehanzaib:
if x is a percentage: e.g. 40% than what does "x/(1+x)" = 29%. what is the explanation.
Answered by Penny Nom.
A rectangular prism 2016-03-02
From Paula:
Trying to help with a math problem. I don't know how to set up the equation for this.

A rectangular prism has a volume of 7.875m3rd and a height of 3.5 m. What is the area of the base of the prism?

Thanks for your help!

Answered by Penny Nom.
Solve for x and y 2016-02-27
From ntshidi:
Y=1/2x+4and1/4x-6
Answered by Penny Nom.
The sum of the angles of a triangle 2016-02-24
From Sophia:
Does every triangle add up to 180 degrees? (Such as a unique triangle)
Answered by Penny Nom.
The interior and external angles of a regular polygon 2016-02-17
From percy:
a regular polygon has n sides .The size of each interior angle is eight times the size of each exterior angle .
1.find the size of each exterior angle
2.calculate the value of n

Answered by Penny Nom.
Perpendicular lines 2016-02-14
From Brendon:
points A (-4; 6) , B (1;-2), C (5;-3) and D (4; 1) are given prove that AC and BD are perpendicular to each other
Answered by Penny Nom.
Calendar arithmetic 2016-02-14
From Jenalee:
January 1, 2001 is Julian Day 2 451 911 (the number of days that have passed since Day 0, January 1, 4713 BC).

If Julian Day 0 was a Monday, what day of the week was January 1, 2001?

Answered by Victoria West.
Two equations in two unknowns 2016-02-13
From Anumba:
4x + 2y = 4
7x - y = -11

Answered by Penny Nom.
I was paid 67% of the total owed 2016-01-25
From Julie:
I was paid $27000. This is 67% of the Total Owed. The Total Owed is unknown. How do I calculate the amount of the Total Owed?
Answered by Penny Nom.
A system of linear equations 2016-01-24
From kareem:
my name is kareem
and i am a student i have a math puzzle and i tried to solved it but it always have same mistake
x-y=9
x+z=12
z-n=14
y+n=2

Answered by Penny Nom.
A Max/Min problem with an unknown constant 2016-01-17
From Guido:
Question:

The deflection D of a particular beam of length L is

D = 2x^4 - 5Lx^3 + 3L^2x^2

where x is the distance from one end of the beam. Find the value of x that yields the maximum deflection.

Answered by Penny Nom.
A rectangular enclosure 2016-01-15
From Amber:
A rancher wants to use 300ft of fencing to enclose a rectangular area of 4400 square feet. What dimensions should the rectangle be?
Answered by Penny Nom.
A triangular shaped garden 2016-01-13
From Demetrie:
Dwayne's garden is triangle-shaped with two equal sides and a third side that is 4 ft more than the length of an equal side. If the perimeter is 49 ft, how long is the longest side?
Answered by Penny Nom.
The perimeter of a triangular plot of land 2016-01-11
From Janelle:
I need to fence off 6.5 acres. The plot is triangular shape. How many feet would I be fencing off?
Answered by Penny Nom.
Water flowing through a rectangular drain 2016-01-08
From Tiffany:
the cross section of drain is a rectangle 30 cm wide. If water 3.5 cm deep flows through the drain at a rate of 22 cm/s, how many litres of water will flow through in one minute?
Answered by Penny Nom.
Integration of dx/(x^2+1)^3 2016-01-07
From Ishank:
Integration of dx/(x^2+1)^3
Answered by Penny Nom.
A relative maximum and a relative minimum 2015-12-28
From kemelo:
show for the following function f(x)=x+1/x has its min value greater than its max value
Answered by Penny Nom.
Constructing simultaneous linear equations 2015-12-28
From Deborah:
Linda thinks of a two-digit number. The sum of the digits is 8. If she reverses the digits, the new number is 36 greater than her original number. What was Linda's original number?

Thank you!

Answered by Penny Nom.
Linear equations in two variables 2015-12-13
From priya:
I have problem in solving these equations please help me today itself very urgent:
I)2x+y=y
II)pie*x+y=9

Answered by Penny Nom.
Constructing a cross country district schedule 2015-12-13
From David:
Retired math teacher trying to help son-in-law schedule a cross country district schedule. The would like to have four tri-meets each week for five weeks and one week of dual meets. The score the tri-meets as three duals, i.e. 1v2, 2v3, 1v3 constitutes one tri-meet. After many hours, not sure its possible, but I have forgotten a great deal! Thanks
Answered by Victoria West.
A schedule for a league with 15 teams 2015-12-05
From Zac:
Hello,

I have a league schedule question. We have a league where we have say have 15 teams. Each team is to play each other twice during a 10 week session.
However each team tries only to play 3 matches(teams) per night(week).
How would we set up a random schedule for the 10 week session?

Answered by Victoria West.
A tangent line to a parabola 2015-12-02
From pei:
Given that the line y=mx-5 is a tangent to the curve y=2x^2+3 find the positive value of M.
Answered by Penny Nom.
Archimedes, Euclid and "Circular Reasoning" 2015-11-15
From Ron:
I have read about Archimedes and his work with sphere in cylinder and cone in cylinder and the volume relationships. Did he or any others also extend this to regular based polygon based regular like pillars, and columns? The ratio of 1/3 to 1 whole holds true with all regular based columns as example: a regular pyramid having a regular hexagon base inside a regular hexagon column of equal height.
Answered by Chris Fisher.
The area of a domed roof 2015-11-13
From Brandon:
I have a tank with a 13' radius that has a domed roof of 3.5' tall How do I figure out the area in SQFT?
Answered by Penny Nom.
Fencing around a rectangular field 2015-11-11
From Darlene:
Question from Darlene, a parent: A farmer has 10,000 meters of fencing to use to create a rectangular field. He plans on using some of the fencing to divide the rectangular field into two plots of land by constructing a fence inside the rectangle that is parallel to one of the sides. Let X be the width of the rectangular field. Write an equation to express the area of the field as a function of X. Find the value of X that maximizes the area of the field.
Answered by Penny Nom.
An 8 Team Basketball League Schedule 2015-10-28
From Janice:
We have an eight team league that play at four time slots each week. It's a seven week season. How do we schedule so that each teams plays each other at least once?
Answered by Victoria West.
A schedule for a pool league 2015-10-21
From Hazel:
I have to make a schedule for my pool league. I have twenty teams each of which must play all other teams. I have ten tables which must also be rotated to all teams play on all tables.
Answered by Victoria West.
Simplify -3(x-7) 2015-10-21
From geraldine:
simplify: -3(x-7)
Answered by Penny Nom.
Scheduling a social curling league 2015-10-20
From Tyler:
I'm scheduling a social curling league where all skips will play with all thirds, all seconds, all leads. And all thirds will do the same and so on. We have 6 teams of 4 and will be doing 6 rotations. Is it possible that all skips will play with all other players from other positions without anyone doubling up?
My initial thoughts were (1,1,1,1) (2,2,2,2) (3,3,3,3) (4,4,4,4)(5,5,5,5)(6,6,6,6)... then rotate the thirds up and seconds down but don't know what to do with the leads and even with just 3 positions there's doubling (1,2,6,x)(2,3,5,x)(3,4,4,x)...4s have doubled (4,5,3,x)(5,6,2,x)(6,1,6,x) as you can see I'm having problems
If you could let me know if this is even possible it would be greatly appreciated

Answered by Victoria West.
6 teams randomly arranged in groups of 3 2015-10-19
From Anthony:
im trying to make a game scheduled for 6 teams using a 1vs2vs3 ; 4vs5vs6 format. all 6 teams randomly arranged in groups of 3. each team will play all teams at least twice, im trying to see how to make the number of times each team play another the same. schedule should be arranged as such 1vs2vs3 4vs5vs6 so that (1vs2, 1vs3, 2vs3) and (4vs5, 4vs6, 5vs6) i am limited to having only 2 sets of 3 at a time with 6 teams.
Answered by Victoria West.
An 8 team schedule 2015-10-19
From Dean:
I need an 8 team schedule for 2 time slots where 3 teams are on the ice per slot. I understand that there will be 2 teams on a bye per day. How do make sure that the byes are fair? Can you help me out?
Answered by Victoria West.
A six team league to play a 20 game schedule 2015-10-19
From Kelly:
Hi there. Some of your posts are close, but my problem is evening out the home and away games. We have 6 teams in our league and we are going to play a 20 game schedule, playing everyone 4 times. We will play Fridays and Saturdays, each weekend. Of course the ideal would be to have each team have a home and an away game each weekend, but I realize that is impossible, but I would like it as close as possible. Any help would be much appreciated!! We also were considering opening with a home and away - Friday then Saturday with the same teams. Then carrying on with playing everyone else and then possibly finishing up with the same home and home
Answered by Victoria West.
Six teams playing five games 2015-10-18
From Aidan:
I have six teams that will be playing five games.
I want each team to play each game once and each team to play each other team once.
Is this possible or should I add an extra round and let some teams play each other twice?

Answered by Victoria West.
4 games in 4 time slots with 8 teams 2015-10-16
From Paul:
I'm trying to set up a game matrix for my kids that will have 4 games in 4 time slots with 8 teams. And every team is playing a different game in a different time slot. I provided the initial matrix and I am trying to ensure that no 2 teams play each other more than once. That's my problem.
       8 pm 9 pm 10 pm 11 pm
Crokinole 1 vs 2
Trivial Pursuit 3 vs 4
Darts 5 vs 6
Pictionary 7 vs 8
Please help, I've been at it for hours.

Answered by Robert Dawson and Victoria West.
Squash scheduling 2015-10-01
From Ed:
I have 5 teams and 2 courts. Every Thursday we play at four different times (6,7,8,9 o clock)

Each team will play each other 5 times over 25 weeks.

Everyone should get to play evenly at the best time (6:00) and the worst time (9:00)

Answered by Victoria West.
A 6-person team that has 9 players 2015-09-21
From Sheri:
I am organizing a 6-person team that has 9 players. How do I schedule them fairly over a 9 week league?
Answered by Victoria West.
A hockey roster of 19 kids 2015-09-21
From Brian:
We have a hockey roster of 19 kids. We only want to play 15 kids for each game. 4 players will not play each game. There are 16 games total. We want to rotate who doesn't play evenly. Can this be done? How many games will each player sit during the season?
Answered by Robert Dawson and Victoria West.
20 golfers for 6 days 2015-09-11
From Dave:
have 20 golfers for 6 days. Each player should pair with 18 golfers used a system on your website which is good for 5 days, but cannot get the 6th day. Thanks for your help Dave
Answered by Victoria West.
Scheduling for a bridge club 2015-09-09
From margot:
Can you help me with scheduling our bridge club?
8 rounds are played with four teams together.
There are 16 teams in total, so our schedule should look like eight 4x4 boxes.
(Each round the four teams play each other over the course of the evening)

Answered by Victoria West.
A schedule for eight teams and four stations 2015-09-04
From Joel:
We are having a youth activity where we have eight teams and four stations. At each station there will be two teams competing against each other. We need each team to go through all four stations, but without ever competing against the same team, and, of course, without ever doing the same station twice.

If this possible? Thank you!

Answered by Victoria West.
A schedule for an 8 person team 2015-08-27
From Julie:
We have 8 people on our team, but only 4 can play every week. We have 32 weeks, total. How can we divide this so everyone plays evenly ?
Answered by Robert Dawson.
Reinforced steel mesh in a circular foundation 2015-08-22
From Padmesh:
in a circular foundation we are laying a reinforced steel mesh . i.e., like chords in both ways. the circle diameter is 2.91m and rods are placed 0.1m spacing. so I want to find the number of rods present in that circle. here by I am attaching an auto cad drawing for your reference
Answered by Penny Nom.
Rotating speakers through a 10 week schedule 2015-08-03
From Timothy:
I want 15 students to speak 7 times each over the course of 10 weeks.
They each will have 5 minutes.
Thanks

Answered by Victoria West.
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 x 0 + 1 = ? 2015-06-18
From Sharon:
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 x 0 + 1 = ?

I got 1 as my answer despite BODMAS making it 12 because logic tells me I ought to place brackets around the first set of repeated addition. Could you please clarify this for me? Thank you 😊

Answered by Harley Weston.
The surface area of a round bar 2015-06-06
From chirag:
Please tell me the formula for finding round bar surface in square inches/ mm
Answered by Penny Nom.
Manipulating an equation 2015-06-05
From Leigh:
Hi, I'm having trouble trying to find out how the equation y=mx+b for b comes up with the answer b=y-mx. Could you please assist me with this
Answered by Penny Nom.
The surface area of a triangular prism 2015-06-03
From Alex:
Find the surface area of a triangular prism with Isoceles triangles and dimensions 4 feet by 6 feet
Answered by Penny Nom.
A tangent to y = x^3 2015-05-31
From Brayden:
Show that a tangent line drawn to the curve y=x^3 at the point (d,f (d)), where d>0, forms a right triangle with the x and y axes in quadrant 4 whose area is (2/3)d^4.
Answered by Penny Nom.
A pentagon inscribed in a circle 2015-05-30
From Victoria:
find the area of a regular pentagon inscribed in a circle with radius 3 units
Answered by Penny Nom.
A pile of mulch 2015-05-15
From Justin:
I have a pile of mulch that measures 19 feet wide at the bottom and has a height of 6 feet. I need to know how many yards of mulch I have.
Please help and help with the formula for further use. Thank you!

Answered by Penny Nom.
Two lorries approaching an intersection 2015-05-15
From Nuraini:
Two straight roads intersect at the right angles. Lorry A, moving on one of the roads, Approaches the intersection at 50mi/h and lorry B, moving on the other roads, approaches the intersection at 20mi/h. At what rate is the distance between the lorry changing when A is 0.4 mile from the intersection and B is 0.3 mile from the intersection?
Answered by Penny Nom.
A calculus optimization problem 2015-05-14
From Ali:
Given an elliptical piece of cardboard defined by (x^2)/4 + (y^2)/4 = 1. How much of the cardboard is wasted after the largest rectangle (that can be inscribed inside the ellipse) is cut out?
Answered by Robert Dawson.
The method of elimination 2015-05-01
From oreanna:

Question from oreanna, a student:

How do u solve 2x+9y=3

7x-4y=-25 in elimination


Answered by Penny Nom.
Constructing a box of maximum volume 2015-04-14
From Margot:
I need to do a PA for maths and I'm a bit stuck. The PA is about folding a box with a volume that is as big as possible. The first few questions where really easy but then this one came up.

8. Prove by differentiating that the formula at 7 does indeed give you the maximum volume for each value of z.

Answered by Penny Nom.
Team selection 2015-04-13
From Peter:
I manage a football team with a list of 28 players.
Only 24 can play each game.
The season is 16 games.
How do I fairly select 24 players each week.

Answered by Robert Dawson.
A word problem with fractions 2015-04-09
From Lorraine:
If the numerator of a certain fraction is doubled and the denominator is increased by 1, the fraction becomes 1/2.

If the numerator of the original faction is squared and the denominator is decreased by 2, the fraction becomes equal to 1.

Let x be the numerator and let y be the denominator of the original fraction. Write down two simultaneous equation in x and y.

Solve these equations to find two possible values for the given fraction.

Answered by Penny Nom.
The area of the ring between two concentric circles 2015-04-08
From Conner:
The area of the ring between two concentric circles is 25pi/2 square inches. The length of a chord of the larger circle tangent to the smaller circle is?
Answered by Robert Dawson.
n^2 is a multiple of 100 2015-03-30
From Rahul:
I have to prove that n^2 is a multiple of 100 is necessary or Sufficient condition (or both) for n being multiple of 10
Answered by Penny Nom.
A lot on a cul-de-sac 2015-03-06
From ana:
Julie lives on a cul-de-sac and wants to know if the city calculated the area of her plot of land correctly (see diagram below). We can assume the cul-de-sac is a circle and it has radius 40 feet.The boundary of the lot along the cul-de-sac (the arc from A to B) is 78.21 feet. The city found the area to be 7012.5 square feet–are they correct?
Answered by Penny Nom.
Two equations with fractions 2015-02-26
From Pulane:
Hi math centre I've been trying to solve these equations for days now please help (6/x)-(1/y)=4
(9/x)+1=(-2/y)

Please help me solve them simultaneously
Thank you

Answered by Penny Nom.
f(x)=(x^2-1)/(x-1) 2015-02-21
From Ahmed:
Is f(x)=[(x^2-1)/(x-1) and x=2 at x=1] differentiable at x=1 ? Why ?
Answered by Penny Nom.
Two equations 2015-02-16
From nigel:
2x+1/2y=1
6x-3/2y=21

Answered by Penny Nom.
Bearings and a rectangular plot 2015-02-14
From Mubashir:
A,B,C,D are the four corners of a rectangular plot marked on level ground. Given that the bearing of B from A is 040 degrees and that the bearing of C from A is 090 degrees. Calculate the bearing of
(a)B from C
(b)A from C
(c) D from C

Answered by Penny Nom.
A parallelogram inscribed in a circle 2015-02-04
From narendra:
how can we prove that a circular parallelogram is a rectangle?
Answered by Chris Fisher.
128/(-16)/(-2) 2015-01-28
From jackie:
128/(-16)/(-2) I was wondering if you can show me how to work this question out
Answered by Harley Weston.
A schedule for observing our peers 2015-01-23
From Jennifer:
I am a sales trainer. Each month we need to observe one of our peers and give feedback. What this means is every month, not only am I observing someone, but someone is also observing me. For example, in January, Amy observes Tracy, Tracy observes Rachel, Rachel observes Ryan, and so on. The last person would then observe Amy, bringing it full circle. There are 10 trainers on my team. How do I set it up to where each trainer observes another trainer only once over the course of the year (and in return, each trainer is only being observed once by each person)? I know they will eventually repeat but would that start in the 10th month?
Answered by Robert Dawson.
A schedule for 5 employees working 2 at a time 2015-01-23
From Cynthia:
We have 5 employees and need only 2 to work on Saturdays. what is the best way to fairly schedule everyone. PS. from time to time a sixth person will be thrown in to make things really interesting.
Answered by Victoria West.
Scheduling meetings with pairs of people 2015-01-22
From Jacey:
I am trying to figure out a formula/system to pair up a list of people so they meet with each other every month, but they rotate who they meet with. Right now I have 13 people and I would like to just type in their names and then have the system put each person with someone else every month and rotate so no one gets the same person twice. Can this be done?
Answered by Victoria West.
Scheduling 12 for lunch 2015-01-05
From Sabrina:
I have 12 staff members that need to have lunch together 1 time each week. I am trying to pair them in a way that we each have the same amount of lunches in the same amount of weeks. Please Help! Thanks!
Answered by Victoria West.
Revolutions per minute 2014-10-24
From Edward:
Hello; I have a 28.2 inch diameter tire; do not worry about engine RPM or gear ratios, please tell me what the RPM of that tire is at 8 MPH and 64 MPH. Thank you.

Sincerely; Edward

Answered by Penny Nom.
A linear system 2014-10-14
From pheter:
4/x - 1/y = 3 .... equation (1)
6/x - 2/y = 5 .... equation (2)

Answered by Penny Nom.
A fact family containing 4, 4 and 16 2014-10-14
From Leslie:
I am helping my son and the question is 4,4,16 in fact family what does that mean
Answered by Penny Nom.
A tennis ball in a triangular prism 2014-10-06
From Anna:
Hi, I need to find the the base and the height of a triangular prism, but I only know the diameter of a tennis ball that fits exactly in the triangular container.. The diameter for the ball is 8.50cm. Can you help me find the formula? Thank you!
Answered by Penny Nom.
Two equations in x and y 2014-09-25
From seyilogo:
solve y=2x - 3 and (4x - 2y) / x + y = 1 simultaneously
Answered by Harley Weston.
Continuity on a closed interval 2014-09-21
From Pragya:
The trouble I'm having is as follows :
a continuous function is most of the times defined on a closed interval, but how is it possible to define it on a closed interval ,because to be continuous at endpoints of the interval the function's limit must exist at that endpoint,for which it has to be defined in its neighborhood,but we don't know anything about whether the function is always defined in the neighborhood.
Please help...

Answered by Penny Nom.
Meetings for 77 students 2014-09-18
From Adam:
We have a new group of students starting, and would like to set up a series of small group meetings so each student meets each other, hopefully without meeting the same people twice.

We have 77 students. In theory I would like to have 11 meeting slots, with 10 groups in each slot, with up to 8 students in each group. Is there a way to do this?

I have wondered if it might be easier to do 9 meeting slots, with 9 groups per slot, with 9 students per group. Thanks!

Answered by Victoria West.
Two equations in two variables 2014-09-18
From Susan:
(28x + 36y) - [20000 - .75(28x + 36y) + 60000] = 5000
x + y = 10000
solving two equations involving variables

Answered by Penny Nom.
A tangent to a curve passing through a point not on the graph 2014-09-15
From Aquilah:
For the curve y = x2 + 3x, find the equations of all tangent lines for this graph that also go through the point (3, 14).
Answered by Penny Nom.
A six team track schedule 2014-09-15
From Paul:
I need to make a six (6) team track schedule. It needs to be five (5) triangular (3 team) meets with each team playing each team twice
Answered by Victoria West.
A barge of triangular cross section 2014-08-18
From tushar:
a barge of triangular cross section is 20m long 12 m wide and 6m deep.its floats in SW at a draft if 4m find its displacement
Answered by Penny Nom.
Multiplication in base five 2014-08-07
From Alise:
Hi Maths Central!

I was wondering if you could help me with multiplying in base 5. I have read a question previously answered by you in regards to this but got fairly confused by it and was hoping you could help me with my question.

My question is: Multiply 1422 base 5 by 21 base 5 keeping these numbers and answer in base 5.

Would you also be able to explain how to get to the answer?

Thanks!

Answered by Penny Nom.
A 6 team sports schedule 2014-08-02
From Daniela:
Hello,

My husband and I are volunteering at our church's Jrs camp and we were given the task of making the schedule for sports. There will be 6 teams and a total of 3 games for two days. We would like for every team to play each other but we cannot figure it out. Pls help!

Thanks.

Answered by Victoria West.
60% as much as $30. 2014-07-18
From Kenneth:
Question from Kenneth:

Hello:

Do you know why some "as...as" phrases indicate multiplication?

For example, ? is 60% as much as $30. This is equivalent to 60% X $30 = $18. How does this make sense?

I saw this example in an old textbook on business mathematics, but the author did not explain why it is equivalent to multiplication.

I thank you for your reply.

Answered by Robert Dawson.
A rotation schedule for 14 teams 2014-07-08
From Daniel:
I am organizing team activities for a summer camp. We have 14 teams and 7 rotations and 7 different games. every team will play a different game each rotation. Where I am having trouble is I would like each team to play a different team each rotation without a repeat. Is that possible? if so what is the formula?
Answered by Victoria West.
The method of elimination 2014-07-05
From leo:
please explain how can i solve this problem

3x-6y=-38
6x-9y=44

using elimination and simultaneous method thank you :)

Answered by Penny Nom.
Angular speed 2014-06-29
From andrea:
a wheel having a radius of 10cm rotates such that the linear speed at its rim is 30mls. what is the angular speed of the wheel in rpm?
Answered by Penny Nom.
Differentiate ln[x(2x-4)^1/2] 2014-06-28
From Igwe:
If y=In[x(2x-4)^1/2],find dy/dx at x=3
Answered by Penny Nom.
Simultaneous equations 2014-06-20
From rana:
solve the simultaneous equations
a)3x=7y
12y=5x-1

Answered by Penny Nom.
20 teams and 10 competition stations 2014-06-04
From Joel:
I have 20 teams. There are 10 competition stations. Each station will accommodate exactly 2 teams to compete with each other at a time.

Each of the 20 teams needs to compete at each of the 10 stations exactly one time.

Here's the catch I cannot solve: how to schedule it so that each team plays EVERY OTHER TEAM once and only once, while never repeating a station.

Answered by Victoria West.
10 golfers, playing 7 rounds in 2 x 3balls and 1 x 4ball 2014-06-04
From adrian:
Hi, We are off to Scotland on our yearly golfing trip soon. Question is we have 10 golfers, playing 7 rounds in 2 x 3balls and 1 x 4ball. I would like to ensure that each golfer plays with the other guys an equal amount of times, guess 3ish? and we share the amount of times each player plays in the 4ball. Hope you can help?
Answered by Victoria West.
A rotating schedule for 9 individuals 2014-05-29
From Josh:
I need to set up a rotating schedule for 9 individuals. The individuals will be pairing each week in groups of two. Thus, every week there will be 4 groups of two individuals and one individual not paired with anyone (i.e. a "bye week"). The rotating schedule should not repeat any pairing and it will continue until each individual has been paired with every other individual once.
Thank you

Answered by Victoria West.
A hexagon with different side lengths 2014-05-16
From Grace:
Sorry if this is a simple question, but I can't seem to understand how to solve it. I am Trying to find the area of a hexagon with measurements 6x7x6x6x7x6, or 2 sets of opposing sides with 6, and one set with 7. Thank you.
Answered by Penny Nom.
A 12 week poker tournament 2014-05-12
From Jamie:
Looking to schedule a 12 week poker tournament with 18 players ...playing 2 separate 9 person tables...I'm looking to have a balanced schedule where everyone player with each other an equal amount of time
Answered by Victoria West.
A schedule for 2 teams of 10 2014-05-07
From John:
How can I set up a schedule for 2 teams of 10 on a team to play each individually against each other over a 10 day span at 10 different course with 10 different start times each day. I was looking to not repeat any competition. As an example, Team A would consist of players 1-10, Team B would consist of players 11-20. I would want to have 10 start times a day for 10 days where a member of team A plays a member of team B each day without repeating any matches and any of the same courses and not repeating any of the same start times. Any help in this would be GREATLY appreciated!!!!
Answered by Victoria West.
The derivative of sin(x) 2014-04-26
From Lucky:
f(x)=Sin(x), by first principle its f'(x)...show me how to solve such problem.
Answered by Penny Nom.
A schedule for 9 teams on 3 fields for 18 days 2014-04-25
From Scott:
I need to schedule 9 teams on 3 fields for 18 days with no buys. Two teams play while other practices in field(little guys). Two fields have backstops and other is open field. Would like to have even time on each diamond if possible. Thank you
Answered by Victoria West.
Solve for theta 2014-04-25
From ALASTAIR:
Hi, The question asks Solve for 'theta' cos2theta=sintheta x costheta. Substituting for cos2th either 1-2sin^2th or 2cos^2th does not give an equation in either sine or cosine alone how do I solve this please?
Answered by Penny Nom.
Two 9 hole golf leagues 2014-04-23
From Sally:
I need help scheduling two 9 hole leagues. Here are the variables:
- Leagues alternate each week starting on the front and back
- League A starts at 4:30 with 7 groups and League B starts at 5:15 with 8 groups (all use carts and must be teed off by 5:30)
- Regular play must continue, customers who have started before league play begins have preference to continue their round whether they are playing 9 or 18 holes.
Thank you!!!

Answered by Victoria West.
Golf with 3 teams of 20 2014-04-21
From Joshua:
Thank in advance for this great service

Golf - new - 3 teams of 20 - to create 20 unique groups of 3

For example use 3 teams of 3

1a 2a 3a
1b 2b 3b
1c 2c 3c

So groups are
1a 1b 1c
2a 2b 2c
3a 3b 3c

Groups can only have one a, one and one c - and that combo should be unique

Answered by Victoria West.
Golf League Schedule for 15 weeks and three flights 2014-04-21
From bigdog:
I need help setting up a 12 team (3 flights with 3 teams in each flight) 15 week league play schedule. Each team must play teams in there perspective flight twice during the 15 week season.
Answered by Victoria West.
Simultaneous equations with fractions 2014-04-19
From Maryam:
I looked at your example of simultaneous equations with fractions and applied it to my question from an educate exam papers but I couldn't get it to work. The question is:

x/8 - y = -5/2
3x + y/3 = 13

Answered by Penny Nom.
The area bounded by the X-axis and y=x^(2)-4 from -5 to 0 2014-04-15
From Lexie:
Determine the area that is bounded by the following curve and the x-axis on the interval below. (Round your answer to three decimal places)

y=x^(2)-4, -5 ≤ x ≤ 0

The answer is 32.333 but I have no idea how to get there.

Answered by Penny Nom.
A tangent of the curve (x/a)^n+(y/b)^n =2 2014-04-15
From sudhir:
the equation of tangent of the curve (x/a)^n+(y/b)^n =2. at(a,b) is
Answered by Penny Nom.
The surface area of a circular dome 2014-04-10
From Shafiqah:
Is this a dome's surface area formula??
{{2 × π r × h square units}}
Is the surface area of the floor for the dome is calculate too in this formula?

Thanks for answering. =)

Answered by Robert Dawson and Penny Nom.
Two rectangular prisms 2014-04-10
From hannah:
two rectangular prisms have a combined volume of 432 cubic feet Prism A has half the volume prism b has what are the volumes of prism a and prism
Answered by Penny Nom.
The surface area of a rectangular prism 2014-04-08
From Manraj:
Find the surface area of a rectangular prism with dimensions 4, 5, and 7 units.
Answered by Penny Nom.
A schedule for 6 people 2014-03-29
From John:
How do I set up a schedule where six people are here for ten of twenty days. Arranged in rotating groups of three, so everyone works with everyone else. Everyone works with everyone else at least once and everyone works ten days.
Answered by Victoria West.
Percentage increase of the population of a town 2014-03-28
From hunter:
The population of a certain town in 1984 was 2900 people. The percent increase was 2.5% each year. What is the town's population in 2002?
Answered by Penny Nom.
14 teams divided into two equal divisions 2014-03-18
From C:
We have 14 teams divided into two equal divisions. We want each team to play each team in their division one time and four teams from the other division one time. What is the schedule
Answered by Victoria West.
A circle which is tangent to two perpendicular lines 2014-03-09
From MJ:
I'm a College Student taking up Bachelor of Secondary Education on Math Subject. And I'm struggling for my research about Circles. I done solving the said topic particularly on this question:

"What are the possible equations of a circle being tangent to a pair of perpendicular lines, having the origin as the Point of Intersection and the C (h, k), where h, k ∈ℤ"

But I can't get what would be the process that I must do in order to jive to my idea/goal for that problem.
Please check my idea that the numerical coefficients of the equation is equal to the radius of the circle. Thanks in advance! :)

Answered by Penny Nom.
A schedule for 6 teams over 12 weeks 2014-03-09
From Paul:
So I have a question. I noticed you came up with ways to create schedules and we are having a really hard time making our lineup correctly. Basically we have 6 teams that will play over a 12 week period every Monday night. The time slots are 1 hr each playing at 6, 7 and 8. We would like each team to play 3 games at each time slot over the 12 weeks. Is this something that can actually be accomplished?
Thanks so much for your help!

Answered by Eric Venables.
8 team schedule over 7 days 2014-02-21
From Andrea:
I need to organize 8 teams. Each team has to go through 8 games against another team, but not against the same as before.
Answered by Victoria West.
A 7 person golf schedule 2014-02-21
From Claude:
Golf Holiday: 7 guys, play a 4-some and a 3-some each day for 10 days. Want to have the best balance of each player playing with every other player the same number of times and each player playing in an equal number of 4-somes and 3-somes.
Answered by Victoria West.
Simultaneous fractional equations 2014-02-15
From benjamin:
hi math central. benjamin here. during class, i had problem with this topic. normally i wont have problems with math but this topic i just too hard for me. please help i am having exam and test next week on this topic

here is the question:
using substitution method, solve the simultaneous equation.
(x+1)/(y+2)=0.5

(x-2)/(y-1)=1/3

Answered by Penny Nom.
Can a cylinder be considered a circular prism? 2014-02-08
From Davina:
Can a cylinder be considered a circular prism?
Answered by Penny Nom.
Two nonlinear equations 2014-01-26
From Naryn:
(1÷x) + (1÷y) = (7÷12)
xy = 12

Answered by Penny Nom.
A rectangular shaped property 2014-01-17
From Donna:
If I I have property that is rectangle shaped. I I know the ends are 100 feet how many feet would the sides be to make 5.4 acres
Answered by Penny Nom.
When would one flip the inequality sign? 2014-01-09
From Natasha:
Would one flip the inequality symbol in this equation: (explain why) (-9a)/(-9) > 81
And please explain in what circumstances one would flip the inequality sign
THANKS!

Answered by Penny Nom.
Schedule for a 4 team basketball league 2013-12-08
From Sommer:
I need a schedule for my kids basketball league. There are 4 teams. We will play every Saturday for 4 weeks with 4 games per Saturday. Week 5 will be the playoffs where 1st will play 4th and 2nd will play 3rd. Week 6 will be winners of week 5. Please help!!
Answered by Victoria West.
Problem solving with fractions 2013-12-03
From Jennie:
Paul has 2/3 as many postcards as Shawn. Shawn has 3/5 as many postcards as Tim. If the 3 boys have 280 postcards, how many more postcards does Tim have than Paul?
Answered by Penny Nom.
Base 5 arithmetic 2013-11-27
From samuel:
Good day sir, please i don't understand when you say 4x4=13 in base five? In fact, am always having difficulties in addition, subtraction, division and multiplication of number in the same base other than base ten. Please can you give me one example each with details explainations?
Answered by Penny Nom.
A schedule for 32 golfers 2013-11-22
From Scott:
I would like a schedule for 32 guys playing in 8 foursomes for 13 week. I would like it so that no one plays in the same foursome more than once or twice. Is this possible to do??? Can you let me know at bogeysm@yahoo.com if you can do it and if you will do it.
Answered by Victoria West.
Admiring handblown glass ornaments 2013-11-21
From Ruby:
We are admiring hand blown glass ornaments 5% are unmarketable due to defects what is the probability the 3rd ornament is the first defective one
Answered by Penny Nom.
Scheduling 10 people for 5 rounds 2013-11-20
From Keith:
Using golf as an example, I would like to schedule 10 people for 5 rounds with 2 groups of 4 and 1 twosome each round. I would like to minimze the number of times any one player plays with another. Can you provide an optimal schedule? Thank you for your help.
Answered by Victoria West.
The area of an irregular octagon 2013-11-18
From zafar:
if i have a rectangular octagon then how i can find its area 1. The length of rectangle is 42 and the width is 21 and and the base length is 42-12 =30 i mean the length of base =30
Answered by Penny Nom.
A lever 2013-11-09
From Durgesh:
A farmer uses a 2 m long lever to lift large rocks from the ground of his field . He places a fulcrum 20cm from the rock end of the lever and then stands on the other end, levering out the rock. If the farmer weighs 100 kg , what is the heaviest mass of the ro ck that he can lift using this method? (how to solve)
Answered by Penny Nom.
The popcorn box problem 2013-11-07
From Dave:
We know that calculus can be used to maximise the volume of the tray created when cutting squares from 4-corners of a sheet of card and then folding up.

What I want is to find the sizes of card that lead to integer solutions for the size of the cut-out, the paper size must also be integer. EG 14,32 cutout 3 maximises volume as does 13,48 cutout 3.

I have done this in Excel but would like a general solution and one that does not involve multiples of the first occurence, as 16, 10 cutout 2 is a multiple of 8,5 cutout 1.

Answered by Walter Whiteley.
Substitution type simultaneous equations 2013-11-03
From Kayla:
I am having problems with substitution type simultaneous equations, when the variable you are substituting is a algebraic one:
y=x^2-3x+4 and 3x-2y=1
I have rearranged 3x-2y=1 to get x=(1+2y)/3 but when I substitute this x value into the other equation, I get the wrong answers!
Would appreciate any help! Thank you.

Answered by Penny Nom.
Water flowing out of a tank 2013-11-03
From Carolyn:
The flow of water out of a hole in a tank is known to be proportional to the square root of the height of water above the hole. That is,

dV/dt (proportional to) sq root (h)

The tank has a constant cross-sectional area A, show that the height of water in the tank is given by

h = ((-kt+C)/2)^2

If the tank is 9 metres high, and it takes 5 hours for it to drain from full to half full, how much longer will we have to wait until it is completely empty?

Answered by Penny Nom.
Is-5/-11 a positive rational number? 2013-10-30
From tazneem:
Is-5/-11 a positive rational number
Answered by Penny Nom.
A square inscribed in a circle 2013-10-14
From Jenn:
Hello! I am about to buy a 7'9" round rug, but I want to have it cut down into a square. What's the largest square I can obtain from this? Thank you!
Answered by Penny Nom.
Maximize the volume of a cone 2013-10-09
From Conlan:
Hi I am dong calculus at school and I'm stumped by this question:

A cone has a slant length of 30cm. Calculate the height, h, of the cone if the volume is to be a maximum.

If anyone can help me it would be greatly appreciated.

thanks.

Answered by Penny Nom.
A schedule for 2, 7 team divisions 2013-09-24
From Sampson:
I'm looking to set up a weekly schedule within a 22 week segment of 2 7 team divisions where every team plays every other team in their divison 3 times and have 4 cross over games with 4 of the other 7 teams in the other division. I've yet to figure this out. Thanks for your time.
Answered by Victoria West.
25 people are attending a 5 day meeting. 2013-09-20
From Lisa:
25 people are attending a 5 day meeting. There are 5 tables, with each table seating 5 (or 6). I want each person to sit at a different table every day with completely different people.
Is this possible. Can do I figure this out?
I have each of the people a letter designation from A to Y. Each table have a number from 1 to 5.
Thank you!

Answered by Victoria West.
A rectangular hyperbola 2013-09-19
From Soumya:
Is the graph of an inverse variation a RECTANGULAR HYPERBOLA? If it is, then how can be the equation of a rectangular hyperbola be xy=constant , whereas in the books it is written that the graph of a rectangular hyperbola is- x^2-y^2=a^2?
Answered by Chris Fisher.
The volume of an attic 2013-09-18
From David:
I have small equipment hut that has a small attic space that I want to blow insulation into it.
The attic size is shaped like a triangle that is about 8 feet by 10 feet by 7 inches at the highest point.
I need to estimate the volume in square feet or cubic feet to know how many bags of insulation to blow into the space.
Thanks

Answered by Penny Nom.
Intersection points and diagonals 2013-09-11
From Kenneth:
I was wondering, is there a relationship between the number of sides of a regular n-gon and the number of times its diagonals intersect?
Ie:
4 sides=1 intersect (center, diagonals form an 'X' )
5 sides=5 intersects (diagonals form a star)
6 sides=13 intersects
And so on.

Answered by Chris Fisher.
A schedule for 18 golfers 2013-08-29
From Brian:
After searching the data base which helped me solve at least 3 other issues I have one more un answered question. I have 18 golfers split into 6 threesomes for 4 days of golf. What is my best option for a schedule mixing them all up as much as possible over the course of the 4 days
Answered by Victoria West.
Euclid's Parallel Postulate 2013-08-20
From Justin:
Hello there,

I was wondering is Euclid's Fifth Parallel Postulate of parallel lines never intersecting, undecidable or essentially undecidable?

Thank you so much for any help you can provide!

Answered by Robert Dawson.
Equal ordinate and abscissa 2013-08-15
From sonit:
the slope of tangent to the curve y=(4-x^2)^1/2 at the point, where the ordinate and abscissa are equal, is
Answered by Penny Nom.
Two perpendicular lines 2013-08-15
From Hanna:
The problem says, "Write the equation in standard form for the line that is perpendicular to the graph of y=5x+1 with a y-intercept of 4." I have no clue how to do this. Please help me!
Answered by Penny Nom.
Differentiate x^x - 2^sinx 2013-08-09
From tarun:
derivative of x^x - 2^sinx
Answered by Penny Nom.
16 golfers 2013-07-31
From Pat:
16 golfers...3 nine hole rounds a day...for 4 days. what are the best pairings for the fewest repeats of partners?
Answered by Victoria West.
What is the value of |2((i)^(1/2))|? 2013-07-22
From Delilah:
What is the value of |2((i)^(1/2))| ?
i.e. absolute value of 2 multiplied by square root of i.

Answered by Penny Nom.
10 guys playing 8-9 hole rounds 2013-07-19
From Jason:
I have 10 guys playing 8 9 hole match-play rounds. I need to have everybody play the other 9 men, but need to limit them to only a 9 hole match between them. If we need to go 3-3-4 or 2-4-4 for a better solution, that may be possible.
Answered by Victoria West.
Simultaneous equations 2013-07-10
From Warren:
solve this simultaneous equation:
xy=4
2x+3y=14

Answered by Penny Nom.
Scheduling a 12 person fishing 2013-07-09
From Don:
Greetings Math Central!
I searched the index, but could not find a similar quandary.
Here's my predicament:
I am seeking help in scheduling a 12 person fishing outing.
We have four boats.
I would like to schedule three fishermen to a boat.
We fish 2 1/2 days, split into morning and afternoon sessions.
Thursday afternoon, Friday morning, Friday afternoon, Saturday morning, and Saturday afternoon
We switch boats after lunch, with each fisherman moving to a different boat, with different partners.
I would like to have each fisherman fish with as many others in the group as possible, with a minimum of partner duplication.
I would like to have each fisherman fish in all of the four different boats over the course of the trip at least once.

Would you please suggest a boat / fishing partner schedule that fits my parameters as closely as possible.

Thank you!

Don

Answered by Victoria West.
4 couples golfing 2013-07-06
From Brian:
We have 4 couples going on a 4 day golf vacation playing 4 rounds of golf. I have spent hours trying to set up a schedule that allows the 4 spouse to play together, and then each spouse to play with one of the other spouses (men with women) for the] other 3 rounds.
I would like the foursomes to be different as possible. Also, no-one should RIDE in a cart with the same person more than once.
I am not a math guy so I try to do this by working it out on paper, over and over again. It ain't working!!
If you can help, I am very thankful.
Brian

Answered by Victoria West.
8 golfers playing 8 games 2013-07-03
From Johan:
We have 8 golfers playing 8 games, and we want to schedule them so that they play together equal amount of times, or as close as you can get to that. They will be playing in two four balls each day. Anyone sorted this one out yet, I will really appreciate a solution? Thanks Johan
Answered by Victoria West.
13 golfers playing 5 rounds 2013-07-03
From Alan:
i have 13 golfers playing 5 rounds. want everyone to play together at least once.
Answered by Victoria West.
A league schedule for 6 hockey team 2013-07-02
From Giovanni:
Hello, I try to make a league schedule for 6 hockey team. Each team will play 36 games during the regular season.
I cannot find a proper schedule generator. Can you help me please?
Thank you

Answered by Victoria West.
Fantasy football league 2013-06-18
From Chris:
Hello, I am the commissioner of a fantasy football league. In this week, we play all 17 weeks of the season. It's a 12 team league, and we play each team twice. To do that, we have 5 "double header" weeks, which means you play 2 different teams. I am struggling to come up with a schedule to make this work. Does anyone have a solution?
Answered by Victoria West.
Compound interest 2013-05-10
From Kyla:
I am doing correspondents and cannot figure out how to explain the solution to this question, I do not understand how they came to this answer and need it explained step by step so I can complete the following questions in this unit, please help!!! Calculating compound Interest

Johnny invest $800 that pays 8% compounded quarterly for 5 years. How much is the investment worth at the end of the 5th year?

Answered by Penny Nom.
The rings of a bull's eye 2013-04-28
From Math:
The bull’s eye of a target is a circle 20 cm in diameter. It is surrounded by four rings, each 15 cm wide. Find the area of each ring.
Answered by Penny Nom.
How do i reverse this formula? 2013-04-20
From MK:
I have 22,000,000 worth of gold and wants to want to resell the gold back with a profit. Each transaction of gold will have a transaction fee of 15%, so if i resell the gold back at 22,000,000, I will only get back 18,700,000 after 15% transaction cut. The current formula is X-15%X = Y where X = 22,000,000 and Y = 18,700,000 Will u be able to come up with a new formula if we don't know the value of X but we know the value of Y
Something like this X-15%X = 22,000,000. How do i reverse this formula to find the value of X
Thanks

Answered by Penny Nom.
4 linear equations with 3 unknowns 2013-04-12
From Marian:
how to solve for 3 unknowns in 4 simultaneous equations
Answered by Penny Nom.
A gravel pile in the shape of a triangular pyramid 2013-04-04
From Casey:
Hello
Right now I am stuck and I feel embarrassed because I feel like the answer is so easy I should know it.

I am working on a project and need to find a volume of gravel it will take to occupy this triangular prism like area. I am not sure what formulas I should use whether it be that for the volume of a pyramid or something more complex? Basically it forms a right triangle at one side then from there all points slope to one singular point about 10412mm away.
I am attaching a picture drawn up in paint with the actual dimensions to clear up any confusion.

Thank you for any help. Casey

Answered by Penny Nom.
Question 2013-04-04
From Casey:
Hello
Right now I am stuck and I feel embarrassed because I feel like the answer is so easy I should know it.

I am working on a project and need to find a volume of gravel it will take to occupy this triangular prism like area. I am not sure what formulas I should use whether it be that for the volume of a pyramid or something more complex? Basically it forms a right triangle at one side then from there all points slope to one singular point about 10412mm away.
I am attaching a picture drawn up in paint with the actual dimensions to clear up any confusion.

Thank you for any help. Casey

Answered by Penny Nom.
Simultaneous equations with fractions 2013-03-31
From Terence:
5/x-6/y=1 17/x+30/y=16 I been spending whole day to solve this question. Would be very grateful if you can help I try The denominator value is a equations term which make is simultaneous equations so hard.
Answered by Penny Nom.
Tangents to the curve y = x^3 2013-03-24
From Ethan:
How many tangent lines to the curve y = x^33 pass through the point (2, 4)? For each such line, and the exact coordinates of the point of tangency on the curve.
Answered by Penny Nom.
Cumulative Frequency Math Question 2013-03-20
From Primadonna:

Hi,

Please help me solve this question.

Thank you so much.

The cumulative frequency table below shows the length of time that 30 students spent text messaging on a weekend.

Minutes Used Cumulative Frequency
31-40 2
31-50 5
31-60 10
31-70 19
31-80 30

Which 10-minute interval contains the first quartile?

(1) 31–40

(2) 41–50

(3) 51–60

(4) 61–70


Answered by Penny Nom.
Five players in a 4-player partnership game 2013-03-19
From Dee:
I have 5 players who are playing in a 4-player partnership game & want to rotate the 5th person in in such a way that each person is each other person's partner for a game. How can such a rotation be done?
Answered by Penny Nom.
Six-digit passwords 2013-03-19
From Judy:
Hello:
Can you please explain why the answer to the following question is 10^6? What is the number of possible six-digit passwords when using the digits 0 through 9, with repetition allowed.
Thank you.

Answered by Penny Nom.
Related rates 2013-02-17
From Ishaak:
A hemispherical bowl is filled with water at a uniform rate. When the height of water is h cm the volume is π(rh^2-1/3 h^3 )cm^3, where r s the radius. Find the rate at which the water level is rising when it is half way to the top, given that r = 6 and the bowl fills in 1 minute.
Answered by Penny Nom.
A word problem involving toys 2013-02-14
From sandy:
Each boy gets 5 toys.Each girl gets 3 toys.There are 150 pupils.
The boys had 74 more toys than girls.
How many boys?
How many girls?

Answered by Penny Nom.
Simultaneous equations 2013-02-10
From Michael:
2P + 1/3V =8
3P - 2/V=5

Answered by Penny Nom.
We have 10 golfers and four rounds of golf in two days 2013-02-05
From Steve:
We are having a golf tournament. We have 10 golfers and four rounds of golf in two days. We are going to break the group of 10 into two flights. Flight A and Flight B. We would like all members in Flight A to play one nine hole match against each other. All players in Flight B to play one nine hole match against each other. Could we play in groups of 4,3 and 3? What is the best way to make the pairings work?
Answered by Robert Dawson.
Integration from 0 to 2pi of 1/(3cos x + 2) dx 2013-02-04
From ankit:
Integration from 0 to 2pi of 1/(3cos x + 2) dx
Answered by Harley Weston.
Multiplication in base two 2013-02-01
From Michael:
multiply in the indicated base

110two*11two

Answered by Penny Nom.
The fourth side of an irregular polygon 2013-02-01
From Emran:
I have a irregular polygon. I know 3 of the 4 sides, and 2 of the angles. A-B is 285, B-C is 149, and C-D is 310. Angle B is 135 degrees. and Angle C is 45 degrees. Is there a formula to solve for the final side? Thanks.
Answered by Penny Nom.
The multiplication table for the different bases 2013-02-01
From sylvia:
I am having a difficult time trying to figure out how to fill in the multiplication table for the different bases. i don't know how to get the numbers.
Answered by Penny Nom.
We have 2 teams of 6 couples each that play 6 games 2013-01-25
From Denise:
We put together a game night where we have 2 teams of 6 couples each that play 6 games. We haven't been able to figure out an arrangement that allows each couple to play each game with a different couple from the opposite team (i.e. Team A couples play every game with a different couple from Team B). Is this possible? It works with 2 teams of 5 couples each.
Answered by Chris Fisher.
A railroad embankment 2013-01-22
From clint:
the pennsylvania railroad found it necessary,owing to land slides upon the roadbed,to reduce the angle of inclination of one bank of certain railway cut near pittsburgh,pa.,from an original angle of 45 degrees to a new angle of 30 degrees. the bank as it originally stood was 200 ft.long and had a slant length of 60 ft.. find the amount of the earth removed, if the top level of the bank remained unchanged.
Answered by Penny Nom.
Maximize profit 2013-01-19
From Chris:
A firm has the following total revenue and total cost function.
TR=100x-2x^2
TC=1/3x^3-5x^2+30x
Where x=output
Find the output level to minimize profit and the level of profit achieved at this output.

Answered by Penny Nom.
The weight of a pipe full of water 2013-01-16
From joe:
how do you figure out the weight of a pipe full of water
Answered by Harley Weston.
A large ditch 2013-01-11
From steve:
hi
i have a large ditch to make a road entrance accross, the ditch is a green field on one side and a highway on the other side the ditch depth is 1.8m on the field side and 3.2 on the highway side the culvert pipe is 1,2m in diameter are you with me so far? the entrance from the highway will be 26m wide tapering in to 6m - ,20 m in from the highway there will be a concrete slab of 150mm over the top

the fall from highway to field must not exceed 1/8

any ideas how much stone it will need

Answered by Harley Weston.
A trig identity 2013-01-04
From Tehmas:
Prove sinC+sinD=2sin(C+D/2)cos(C-D/2)
Answered by Harley Weston.
The quadratic formula 2013-01-03
From itsel:
Find the discriminant ans use it to determine the use the quadratic formula to solve the equasion -2x^2+3x+2=0
Answered by Penny Nom.
Mod versus Rem in Turing 2013-01-01
From Eric:
I am a teacher teaching computer science using Turing. I am having difficulty understanding why one would use the mod operator versus the rem remainder operator.

Mod seems to make the resulting sign depend on the sign of the divisor, whereas rem makes the resulting sign depend on the dividend.

Examples:

11 mod 5 = 1 and 11 rem 5 =1
-11 mod 5 = 4 and -11 rem 5 = -1
11 mod -5 = -4 and 11 rem -5 =1
-11 mod -5 = -1 and -11 rem -5 = -1

What I can't understand is why this would matter. For example, -11 / 5 = -2.2 and 11 / -5 = -2.2 get the same result.
So how is a remainder dependent on the sign of one of the parts? What benefit would using one over the other have?

Any insight would be most helpful!

Eric

Answered by Harley Weston.
An integral 2012-12-16
From Slavena:
integration of (lnx)^2 / x dx
Answered by Penny Nom.
An area bounded by lines 2012-12-16
From sidra:
find area bounded by functions:
y=x
y=2x
and y=5-x

Answered by Penny Nom.
A max/min problem 2012-12-14
From bailey:
A right angled triangle OPQ is drawn as shown where O is at (0,0). P is a point on the parabola y = ax – x^2 and Q is on the x-axis.

Show that the maximum possible area for the triangle OPQ is (2a^3)/(27)

Answered by Penny Nom.
The derivative of y = sin (30º + x) 2012-11-07
From Saskia:
derivative of y = sin (30º + x)
Answered by Harley Weston.
birdhouse in the shape of a rectangular prism 2012-10-29
From Tiffany:
Hello, I am Tiff M. from NYC.
I was solving a math problem about adding,subtracting,multiplying or dividing fractions and mixed numbers. I am not getting this question below.
* Laura is building a birdhouse in the shape of a rectangular prism. The base of the birdhouse has an area of 5 square inches. The height of the birdhouse is 2 7/12 inches. Laura calculated the volume of the bird house to be 10 7/12in. Is she correct?
If not, what did she do wrong?

Answered by Robert Dawson.
An implicit differentiation problem 2012-10-26
From Katie:
find y' of x^2y-2y^3=3x+2y
Answered by Harley Weston.
How fast is the distance between the aircraft and the car increasing? 2012-10-24
From Steven:
At a certain instant an aircraft flying due east at 240 miles per hour passes directly over a car traveling due southeast at 60 miles per hour on a straight, level road. If the aircraft is flying at an altitude of .5mile, how fast is the distance between the aircraft and the car increasing 36 seconds after the aircraft passes directly over the car?
Answered by Penny Nom.
Differentiation rules 2012-10-23
From Morgan:
Use the derivative rules to differentiate each of the following:
1. f(x)=1/x-1
2. f(x)= sqrt(x)

Answered by Penny Nom.
Revolutions per second 2012-10-18
From Crystal:
Suppose a car wheel is 26 inches in diameter.
a) If the tire completes one rotation, how far would the car travel?
b) If the car is traveling at 60 miles per hour, how fast is the car wheel spinning in revolutions per second?

Answered by Penny Nom.
A word problem involving a fraction 2012-10-12
From Derrick:
If the numerator and denominator of a fraction are both decreased by 1 the fraction becomes 2/3. If the numerator and denominator are both increased by 1 the fraction will be 3/4. Find the original fraction. How to do?
Answered by Penny Nom.
Changing the sign of an inequality 2012-09-19
From Bryauna:
Why do you change the signs in inequalities?!
Answered by Penny Nom.
An equilateral triangle and a regular hexagon in a circle 2012-09-11
From Heidemarie:
The vertices of an equilateral triangle with side length of 10 sqrt 3 cm lie on a circle. Find the side length of the regular hexagon whose vertices lie on the same circle.
Answered by Penny Nom.
Angular velocity 2012-09-05
From Kyra:
A belt connects a pulley of radius 8cm to a pulley of radius 6cm. Each point on the belt is travelling at 24 cm/sec. Find the angular velocity of each pulley.
Answered by Penny Nom.
A tangent to f(x) = 1/x 2012-09-04
From Steven:
Consider the graph of the function f(x) = 1/x in the first quadrant, and a line tangent to f at a point P where x = k. Find the slop of the line tangent to f at x = k in terms of k and write an equation for the tangent line l in terms of k.
Answered by Penny Nom.
12 golfers, 4 rounds 2012-08-29
From Paul:
We have 12 golfers who will play four rounds of golf - how can we organize the foursomes so that each player has the most exposure to the other 11 players?
Answered by Victoria West.
A schedule for 6 teams and 37 games 2012-08-29
From Giovanni:
Hello, i try to prepare a schedules for 6 teams, and every teams will play 37 games before the playoff. How to make a schedules? thanks
Answered by Victoria West.
A rotating schedule 2012-08-16
From Dusty:
Ok, Im trying to create a rotating schedule. There are four jobs and four people but, one of four people cant preform one job. How can I figure out a rotating schedule for this issue?
Answered by Victoria West.
A volume of revolution 2012-07-15
From Tewodros:
Let f(x) = e^x and g(x) = x^1/2 both be defined on [0,1]. Consider the region bounded by f(x), g(x), x = 0, x = 1. Rotate this region about the y-axis and determine the volume using the shell method.
Answered by Harley Weston.
Scheduling an academic competition 2012-06-12
From Mike:
I need to schedule 18 high school teams to play each other in a "Jeopardy!"-like academic competition. Teams compete against each other 6 at a time (simultaneously) in 3 different rooms. What will the minimum amount of matches (I believe 6 ?) we would have to play to ensure that each team plays every other team exactly twice?

And more importantly: what would that schedule look like?

The best I've come up with is having most teams playing twice, but with 2 pairs of teams having to play either only once or sometimes 3 times.

Thanks in advance for any help you can give! :-)

Mike

Answered by Chris Fisher.
A multinomial theorem 2012-06-08
From Anuj:
if (1+x+xsquare) whole raise to 20 is a0 + a1x + ........ + a20xraise to 40, then find a0 + a2 + a4 + .......... + a38.
How do you solve this???????

Answered by Robert Dawson.
The volume of a wedge 2012-05-28
From olwethu:
volume of wedge that have side 3,3 cm and 6,2 cm and 20 cm long?
Answered by Penny Nom.
Multiples 2012-05-28
From Kenneth:
If I understand correctly , a multiple is a product of two numbers. For example some of the multiples of 6 are 6, 12, 18, 24, 30, etc. I just multiplied 6 by 1, 2, 3, 4, 5, etc.

Are the multiples of a fraction, for example, 2/3, determined in the same way? Are they 2/3, 4/3, 6/3, 8/3, 10/3, etc., or are they instead, 2/3, 4/6, 6/9, 8/12, 10/15, etc.?

Or do fractions have no multiples?

Answered by Penny Nom.
Multiplying binomials 2012-05-14
From Jordan:
How do I solve the equation:
3(x+4)(x-6)

Answered by Penny Nom.
A 25% sulfuric acid solution 2012-05-03
From Scott:
In order to make a 25% solution with 96% Sulfuric Acid, how much of the Sulfuric do I add to DI water to make up 2000ml??
Answered by Penny Nom.
The area of a quadrilateral 2012-04-21
From Rajat:
calculate the area ABCD in which AB is 48'1'',BC is 98'4'',CD is 61'4'',DA is 102'10'',AC is 110'3'',BD is 116'9''.
Answered by Penny Nom.
16 golfers 2012-04-20
From steve:
i have 16 golfers, 4 in "A" flight , 4 in "B" flight , 4 in "C" and 4 in "D"

We are playing 4 rounds (4 teams of 4) and every group must have a player from the A B C an D flight, and in no round may 2 people have already played together!

Answered by Victoria West.
Golf for 12 2012-04-18
From Brent:
I have a golf group that is set up as follows: 12 players, broken into 2 teams of 6. I am looking for a formula to have one player from team A play against one player for team B each round, not repeat the match, and ride with as little duplication as possible. I know that it is not statistically possible with these numbers and will have at least one round that has duplication.
Answered by Robert Dawson.
Two cars approach a right-angled intersection 2012-04-10
From Michael:
Two cars approach a right-angled intersection, one traveling south a 40km/h and the other west at 70km/h. When the faster car is 4km from the intersection and the other case if 3km from the intersection, how fast is the distance between the car cars changing?
Answered by Penny Nom.
Golf for 28 2012-04-10
From EARL:
HI, I HAVE 28 GOLFERS AND I NEED A SCHEDULE FOR 5 DIFFERENT DAYS THERE WILL BE 7 GROUPS OF 4 PLAYERS EACH DAY. ALL PLAYERS WOULD LIKE TO PLAY WITH ONE ANOTHER ONCE AND NOT PLAY WITH EACH MORE THAN ONCE IF POSSIBLE OR LIMIT THE TIMES A GOLFER PLAYS WITH ANOTHER TO A MINIMUM IF POSSIBLE. (PLEASE SEND AN EXAMPLE OF THE SCHEDULING OF THE GROUPS FOR THE TEE OFF ORDER)
THANKS FOR ANY SOLUTIONS YOU CAN PROVIDE.
EARL

Answered by Robert Dawson.
A semi-circular roof gutter 2012-04-09
From Kyle:
A semi-circular roof guttering contains some water.
The cross-section of the guttering has a diameter of 10 centimetres. The surface of the water collected in the guttering is 8cm. What is the depth of water in the gutter?

Answered by Penny Nom.
A maximization problem 2012-04-09
From Nancy:
After an injection, the concentration of drug in a muscle varies according to a function of time, f(t). Suppose that t is measured in hours and f(t)=e^-0.02t - e^-0.42t. Determine the time when the maximum concentration of drug occurs.
Answered by Penny Nom.
The spread of a rumor 2012-04-09
From Roohi:
The function f(t) = a/(1+3e^(-bt)) has also been used to model the spread of a rumor. Suppose that a= 70 and b=3 0.2. Compute f(2), the percentage of the population that has heard the rumor after 2 hours. Compute f'(2) and describe what it represents. Compute lim t approaches infinity and describe what it represents.
Answered by Penny Nom.
A rectangular prism 2012-04-05
From Tori:
How do you find the base height if the base width is 10ft. The height is 7ft. And the volume is105ft.
Answered by Penny Nom.
Golf for 17 2012-03-29
From Richard:
Hi Guys,
I have a scheduling problem which I don't think you have covered before.
Apologies if you have!
I have 17 golfers due to play 4 rounds of golf.
Each round will consist of 3 threeballs and 2 fourballs (ie. 17 golfers in 5 groups)!
Is it possible to come up with a schedule where each golfer plays
with different partners in each round?

Answered by Robert Dawson.
The period T of a pendulum 2012-03-27
From Ashley:
The period T of a pendulum is given in terms of its length, l, by T=2pi sqrt(l/g) where g is the acceleration due to gravity(a constant)
a. find dT/dl
b. what is the sign of dT/dl
c. what does the sign of dT/dl tell you about the period of the pendulums?

Answered by Penny Nom.
The area of an irregular hexagon 2012-03-20
From Jacob:
I am having trouble finding the area of an irregular hexagon with 5 right angles. It has 5 given sides, with the lengths as follows:

8.2 ft.
6 ft.
4.5 ft.
2.2 ft.
6 and one third ft.

Answered by Chris Fisher.
The volume of an irregular tetrahedron 2012-02-22
From Brittany:
If I am given an irregular tetrahedron with the coordinates of the 4 points how do I find the volume? For example I am asked to find the volume and only given the points A(-4,-3,5), B(2,-1,2), C(0,-5,0), and D(-2,0,0) can you shown me the working and formular to find the volume?
Answered by Robert Dawson.
Dt[sin t tan (t^2+1)] 2012-02-21
From Ayu:
Ayu
Dt[sin t tan (t^2+1)]
derivatives

Answered by Harley Weston.
36 golfers 2012-02-15
From Steve:
We will have 36 golfers playing 4 rounds of golf and would like to have different foursomes each round. In other words, no player will play with another more than once.
Answered by Harley Weston.
The derivative of x^-(1/2) 2012-01-14
From Eric:
I have an problem figuring out the derivative of the negative square root of x i.e. x^-(1/2) using the first principle.
Could someone please show me?
Thanks in advance!

Answered by Harley Weston.
Lost in the woods 2012-01-12
From Liz:
I am lost in the woods. I believe that I am in the woods 3 miles from a straight road. My car is located 6 miles down the road. I can walk 2miles/hour in the woods and 4 miles/hour along the road. To minimize the time needed to walk to my car, what point on the road should i walk to?
Answered by Harley Weston.
A volume of revolution 2012-01-11
From john:
find volume of solid generated by revolving the region in the first quadrant bounded by the curve y squared=x cubed, the line x=4 and the x-axis about the line y=8. The answer in the back of the book is 704 pi divided by5
Answered by Penny Nom.
Triangular numbers that are square 2011-12-27
From Luke:
The “TnS” is a positive integer which is both Triangular number and Square number. For example, 36 is a “TnS” number since 36=1+2+3+4+5+6+7+8 (Triangular number) and 36=6x6 (Square number). What is the next “TnS” which is greater than 36?
Answered by Penny Nom.
Three sides of a triangle 2011-12-24
From saba:
the three sides of a triangular lot have lengths 10,11and 13cm,respectively. find the measure of its largest angle and the area of the lot?
Answered by Penny Nom.
Water is flowing into a cup 2011-12-19
From Tim:
A cup has a radius of 2" at the bottom and 6" on the top. It is 10" high. 4 Minutes ago, water started pouring at 10 cubic " per minute. How fast was the water level rising 4 minutes ago? How fast is the water level rising now? What will the rate be when the glass is full?
Answered by Penny Nom.
A cube of ice is melting 2011-12-05
From Emily:
a cube of ice (i.e.) each side is of the same length) is melting at a rate such that the length of each side is decreasing at a rate of 5cm per hour. how fast is the volume of the cube decreasing (in cubic cm per hour) at the instant the length of each side is 25cm?
Answered by Penny Nom.
The average age of 300 cars 2011-11-22
From Jason:
I have 300 used cars built from 1970 to 1980, I would like to know the average age by total volume. If I provide the qty built per year, can I determine the average age of the lot (300) by total volume?
Total built 50 56 30 10 30 25 64 9 12 14
Year built 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980

Thanks

Answered by Penny Nom.
Water pouring into a conical tank 2011-11-21
From Patience:
Hi my name is patience and I'm having a problem with this question.
Water pours into a conical tank of semi vertical angle 30 degrees at the rate of 4 cm^3/s, where h is the depth of the water at time t. At what rate is the water rising in the tank when h = 10 cm?
Thank you

Answered by Penny Nom.
I started with Euler's identity and manipulated it 2011-11-14
From anonymous:
I started with Euler's identity and manipulated it
e^i*pi=-1
e^-i*pi=(-1)^-1
e^-i*pi=-1
e^-i*i*pi=(-1)^i
e^--pi=(-1)^i
e^pi=(-1)^i
type it in in a calculator and you get e^pi=23.1406926... and (-1)^i=0.0432139183... What did I do wrong?

Answered by Robert Dawson.
Lines tangent to y^2=4x 2011-11-11
From Reuchen:
Find equations of the lines tangent to y^2=4x and containing (-2,1).
Answered by Penny Nom.
Modular arithmetic 2011-10-30
From Kim:
Hello,
I am editing a resource for students, and I think some of the answers may be incorrect. The text I was given and my questions are in the attachment. Any help you could give would be appreciated.
Thanks,

Kim

Answered by Harley Weston.
A mythical soccer ball 2011-10-27
From Joel:
We've been working on this problem diligently and can't seem to come up with the answer book's answer. We think it may be wrong, yet want to check it with an expert. Here goes. The school's new soccer balls are covered with 64 regular hexagonal panels. Each hexagon measures 2 inches between opposite corners and 1.5 inches between opposite sides. What is the total surface area of the soccer ball?
Answered by Robert Dawson and Lorraine Dame.
A spherical ball in a conical wine glass 2011-10-26
From Jules:
A heavy spherical ball is lowered carefully into a full conical wine glass whose depth is h and whose generating angle (between the axis and a generator) is w. Show that the greatest overflow occurs when the radius of the ball is (h*sin(w))/(sin(w)+cos(2w)).
Answered by Claude Tardif.
Implicit differentiation 2011-10-20
From Monica:
Find dy/dx in terms of x and y, if sin(xy)=(x^2)-y.
Answered by Penny Nom.
A hemispherical bowl with a lead ball inside 2011-09-27
From Jean:
"(a) Water is being poured into a hemispherical bowl of radius 3 inch at the rate of 1 inch^3/s. How fast is the water level rising when the water is 1 inch deep ?

(b) In (a), suppose that the bowl contains a lead ball 2 inch in diameter, and find how fast the water level is rising when the ball is half submerged."

Answered by Penny Nom.
The derivative of f(x) = (x+1)^1/2 2011-09-05
From Carla:
Find the derivative using the limit process of
f(x) = (x+1)^1/2

Answered by Harley Weston.
4 x 2 2011-08-30
From Lucjan:
how to sketch a diagram that shows 4x2 expression?
Answered by Penny Nom.
Romeo throws a pebble at Juliet's wondow 2011-08-22
From Natalie:
There is a picture of Romeo trying to attract Juliet's attention without her nurse who is in a downstairs room, noticing. he stands 10m from the house and lobs a small pebble at her bedroom window (3.5m high). Romeo throws the pebble from a height of 1m with a speed of 11.5m/s at an angle of 60degrees to the horizontal. I have already found that it take 1.74seconds to reach the window and that it does in fact hit Juliet's window however i cannot work out the speed of the pebble when it hits the window! The answer is 9.12m/s but I cannot reach this answer. Hope you can help me :)
Answered by Robert Dawson.
3.8 x 2.2 2011-08-18
From Isaac:
Question from isaac, a student: I am struggling in math & I need help on multiplying 3.8 x 2.2. Can you helpme
Answered by Melanie Tyrer and Harley Weston.
The height of a fluid in a horizontal tank 2011-07-24
From jason:
Same set up as many others, cylindrical tank on its side, but I am interested in defining the change in volume and/or fluid level as a function of time at a constant volumetric outflow. I plan on hooking a pump to the tank so "gpms' will be constant. I have a couple different sized tanks and pumps so I want a general equation. Thanks for your help.
Answered by Harley Weston.
A regular hexagon inscribed in a circle 2011-07-18
From Courtney:
If ABCDEF is a regular hexagon inscribed in a circle of radius r, prove that the length of each side of the hexagon equals r.
Answered by Penny Nom.
Golf for 14 2011-07-11
From Doug:
We have 14 players playing over 4 days. can we play with different players every day and keep the 3 x foursomes and 1 x pair format
Answered by Victoria West.
Golf for 12 2011-07-07
From Jim:
I have a golf trip scheduled with a total of 12 guys. We are playing three rounds of golf. For round 1 Players A B C D must play together. Is there a formula that would allow me to set up the other 8 foursomes with no repeats or minimal repeats? Thanks.
Answered by Victoria West.
A line tangent to f(x)=1/x 2011-06-05
From Michael:
A line tangent to f(x)=1/x in the first quadrant creates a right triangle with legs the x-axis and the y-axis. Prove that this triangle is always 2 square units regardless of where the point of tangency is.
Answered by Penny Nom.
16 golfers and 8 rounds 2011-05-26
From Gerry:
16 golfers and 8 rounds. To have each player play with as many others as possible.
Answered by Victoria West.
The length of a belt around three pulleys 2011-05-18
From Grant:
I need to calculate the belt length around these pulleys, please can you help or refer me?

Known variables
D - Large Pulley Diameter
d - Small Pulley Diameter
c - Center Distance between D and d
T - Tension Pulley Diameter
x - Horizontal Distance between T and d' Centers
y - Vertical Distance between T and d's Centers
I need to calculate the belt length around these pulleys.


Kind Regards,
Grant

Answered by Harley Weston.
The volume of a triangular shaped aquarium 2011-05-07
From Jeff:
HI, I searched the site but really couldn't find my answer, at least that I could understand! I have a triangular shaped aquarium ( think of a cube, except its an equal triangle shape). all 3 sides are 48 inches, and it is 34" tall. Can you please tell me what the volume is in gallons? Thanks!
Answered by Penny Nom.
Solve x(x-3) = 5 (x+4) 2011-04-19
From Ashley:
I have to solve using the quadratic formula. And my answer should be in simplest exact form. And I can't approximate.
I really need help to prepare for a test ....
x(x-3) = 5 (x+4)

Answered by Penny Nom.
An antiderivative of the square root of (8t + 3) 2011-04-19
From Caitlyn:
I know how to take an antiderivative. But this one's stumping me. I need it to finish a problem. What's the antiderivative of the square root of (8t + 3)

~Caitlyn=

Answered by Penny Nom.
The volume of a triangular pyramid 2011-04-15
From Chelsea:
There is a triangular pyramid which is an equilateral on the base with all sides 16.5 and the height is 25. I have to find the volume. Please help!
Answered by Penny Nom.
2 cubic foot bags of mulch 2011-04-11
From Ron:
if I buy 2 cubic foot bags of mulch, how bags would I need to equal 1 yard? (13 bags?)
Answered by Penny Nom.
Eliminate y 2011-04-07
From Lynn:
2x + y = 8
y + 3z =5
z + 2w =1
5w + 3x = 9

Form three equations with y eliminated

Answered by Penny Nom.
Tennis schedule 2011-04-04
From Toni:
I need to create a doubles tennis schedule for 6 players playing over a 32 week schedule where no player repeats with a partner.
Answered by Victoria West.
Designing a tin can 2011-03-31
From Tina:
A tin can is to have a given capacity. Find the ratio of the height to diameter if the amount of tin ( total surface area) is a minimum.
Answered by Penny Nom.
[(90+36-4) ÷ 2] x 15 = 2011-03-30
From ken:
[(90+36-4) ÷ 2] x 15 =
Answered by Penny Nom.
A stone is dropped into a lake 2011-03-24
From AnneMarie:
A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 25 cm/s. Find the rate at which the area within the circle is increasing after 4s.
Answered by Penny Nom.
If 25 items are evenly spread over 7 days 2011-03-23
From michael:
What is the formula to calculate:
If 25 items are evenly spread over 7 days, but one day has 3 items less than the other days, what is the number if items for each of the remaining 6 days?

Answered by Penny Nom.
What is x to the power of 0? 2011-03-23
From Jason:
What is x to the power of 0?
Answered by Robert Dawson.
Regular and irregular polygons 2011-03-10
From thaera:
the difference between regular shape and irregular shapes.
Answered by Penny Nom.
Vertices and sides of a polygon 2011-03-04
From RINA:
My questions is : would a vertices and sides of a polygon be the same number.  For example, a octagon it has 8 points and 8 sides. Am i correct?
Answered by Robert Dawson.
At what rate is the grain pouring from the chute? 2011-02-26
From MJ:
Suppose that grain pouring from a chute forms a conical heap in such a way that the height is always 2/3 the radius of the base. At the moment when the conical heap is 3 m high, its height is rising at the rate of 1/2 m/min. At what rate (in m^3/min) is the grain pouring from the chute?
Answered by Penny Nom.
Slicing a rectangular parallelepiped 2011-02-23
From tom:
a) Pass a plane containing a vertex of a rectangular parallelepiped and a diagonal of a face not containing that vertex to cut a pyramid from the parallelepiped. What fraction of the volume of the parallelepiped is the volume of the pyramid thus cut off?

b)Pass a plane through a cube of edge 8 in so that the section formed will be a regular hexagon. Through each side of the hexagon pass two planes, one plane containing one of the two vertices of the cube which are farthest away from the plane of the hexagon, the other plane containing the diagonally opposite vertex of the cube. Find the volume of the solid bounded by these planes.

c)three of the edges of a rectangular parallelepiped that meet in a point are also the lateral edges of a pyramid. What fraction of the parallelepiped is this pyramid...?

you know the my only problem is how to illustrate this one...if only i could ...can you help me....all I need is the drawing and I can do the rest ..it's fine if you'll only answer any of these but I'll be thankful if you will do the three :)....

Answered by Penny Nom.
Prove sin x = sin (pi - x) 2011-02-15
From Janet:
Prove sin x = sin (pi - x)
Answered by Penny Nom.
An irregular hexagon 2011-02-09
From Emma:
Hello, I have math question about how to find the area of an irregular hexagon.
It is shaped like a backwards L and the side lengths are as follows
11cm
8cm
5cm
5cm
6 cm
3cm
Can you please help me find the area of this?
Emma

Answered by Penny Nom.
Multiplication and order 2011-01-21
From Janet:
IN A MULTIPLICATION SENTENCE BASED ON A DRAWING..IS THERE ANY ORDER FOR THE MULTIPLICAND ANG MULTIPLIER FOR THE ANSWER TO RIGHT?
Answered by Robert Dawson.
Integrating ln^3x/x 2011-01-14
From ken:
y=ln^3x/x from x=1 to x=11
Answered by Penny Nom.
Angular speed 2010-12-12
From Jason:
7 in. pulley traveling @ 175ft/sec. What is the rpm?
Answered by Stephen La Rocque and Penny Nom.
The length is twice its breadth 2010-12-09
From jenu:
The length of the rectangular field is twice its breadth. A man jogged around it 5 times and covered a distance of 3 km. what is the length of the field?
Answered by Penny Nom.
A rectangular solid 2010-12-08
From ryan:
Good day! Have a question on rectangular solids. We were asked to find the dimensions of a rectangular solid, we were only given the volume of the rectangular solid, the total area, and the altitude. I tried using the volume of the rectangular solid and was able to get the area of the base, but I don't know how to get its length and its width. Hope you could help me again. Thanks!
Answered by Penny Nom.
Simultaneous equations 2010-12-05
From ryan:

Question from ryan, a student:

3         4
--   -    --      =     1      (1)
x         y

7       2             11
--   -  --        =   --       (2)
x       y              12


Answered by Chris Fisher and Stephen La Rocque.
Angular speed 2010-12-03
From Julie:
If the angular speed of a circle is 360 degrees divided by the time it took to rotate, how do I calculate ones that have greater rotations than the amount of time? I mean, you calculate the angular speed of a merry-go-around that spins once every 5 seconds by doing 360degrees/5 sec, but how do you calculate a merry-go-around that has 16 rotations every 4 seconds?
Answered by Penny Nom.
Can determine if it is scalene, isosceles, or equilateral 2010-12-01
From Jessie:
find the measures of the sides of triangle KPL and classify each triangle by its sides. my first problem would be K(-3,2) P(2,1) L(-2,-3) ...The three points they give you are the vertices of the triangle and you need to match them up. Draw the triangle and write in the vertices and the related point with the vertex. You will then do the distance formula three times to find the distance of all three sides. Once you have the three sides you can determine if it is scalene, isosceles, or equilateral...using the distance formula how do i solve this?
Answered by Penny Nom.
A man made circular lake 2010-11-25
From ailish:
A man made circular lake has a diameter of 338 m. A bridge is to be constructed across the lake in such a way that it is 119 m away from the center of the lake. How long is the bridge?
Answered by Penny Nom.
Two girls agree to mow a lawn 2010-11-23
From Milorad:
Two girls agree to mow a lawn 60m by 80m so that the first girl cuts one half by cutting a uniform strip around the lawn. How wide a strip should the first girl cut?

I've been struggling with the question above, mainly with the equation and I have set it up as 2400=(60-2x)(80-2x), if this is incorrect I would like to know where I've gone wrong and also would like a full answer to see it properly done. I need an algebraic answer and not one with a diagram.

Answered by Penny Nom.
i^i 2010-11-21
From trale:
Can we use e^ix=cosx+isinx for finding i^i like that: x= pi/2 => e^(ipi/2)=0+i then [e^(ipi/2)]^i=i^i.then we find i^i= 0,207879576.... is it true? can we give value for x for free?thank you.
Answered by Harley Weston.
Convert to multiplication 2010-10-23
From angelina:
how to covert 5+5+5=15 to multiplication
Answered by Penny Nom.
An exponential equation 2010-10-19
From Sandi:

Question from sandi, a student:

I have several questions similar to this one and was wondering if you could walk me through this one. I'm totally lost on how to do it.
Paramecia reproduce by splitting in two. In a laboratory flask, a colony of paramecia had an initial population of 500. Each day, the population of the paramecia was counted. The results are as listed.
Time (in days)------Population
0-----------------------500
1-----------------------600
2-----------------------720
3-----------------------864
4----------------------1037
5---------------------1244
6---------------------1493
7----------------------1792
8---------------------2150
1.)Using graphing calculator make a scatter plot of the data in table.
I think I did this part right I set my window at Xmin=0 Xmax=10 Xscl=1 Ymin=0 Ymax=2500 Yscl=100 Xres=1
2.) Determine an exponential equation to represent the population as a function of time without using a graphing calculator.I have no clue how to do this.
3.)Suppose the flask and food supply is large enough to support the trend of the population growth. Estimate the population of the colony when the time is 10 days.


Answered by Penny Nom.
Geocaching 2010-10-15
From Clint:
I am stuck on a puzzle for Geocaching which is a GPS game. I know it is a number matrix but don't know how to start.

[1 -7 16 -3 -9; 1 -3 18 -20 -33] x [1 8 -9 3 5; 0 1 0 4 2; 0 0 1 2 1; 0 0 0 1 -1; 0 0 0 0 1] = ?

Answered by Stephen La Rocque.
What is the maximum weekly profit? 2010-10-10
From Joe:
A local artist sells her portraits at the Eaton Mall. Each portrait sells for $20 and she sells an average of 30 per week. In order to increase her revenue, she wants to raise her price. But she will lose one sale for every dollar increase in price. If expenses are $10 per portrait, what price should be set to maximize the weekly profits? What is the maximum weekly profit?
Answered by Stephen La Rocque and Penny Nom.
x/200+x/400+x/600+x/800 2010-10-08
From Ashishthombre:
step by step LCM of x/200+x/400+x/600+x/800
Answered by Penny Nom.
Rectangular arrays 2010-09-29
From Kim:
My 4th grader has started working on rectangular array that shows 2 factors of a number.

The problem reads on centimeter grid paper draw as many arrays as you can for each of the #'s 2,3,4, 5,6,7,,11,12,15 and 16. That would be great except I have no idea what they are talking about and I cannot offer any help to my daughter.

Answered by Penny Nom.
A Taylor polynomial for (lnx)/x 2010-09-29
From Dave:
I have a series problem that I cannot solve. The problem asks for you to compute a Taylor polynomial Tn(x) for f(x) = (lnx)/x. I calculated this poly out to T5(x) and attempted to use this to identify a pattern and create a series in order to calculate Tn(x). However, the coefficients on the numerator out to F5prime(x) are as follows: 1, -3, 11, -50, 274... Ok, so the negative is an easy fix -> (-1)^n-1. But the other coefficients are stumping me. I can't see any sort of pattern there and I've tried every trick I know. Is there another way to go about this? Thanks!
Answered by Chris Fisher.
limit as x approaches a of ((x^(1/2))-(a^(1/2)))/(x-a)? 2010-09-29
From emily:
limit as x approaches a of ((x^(1/2))-(a^(1/2)))/(x-a)?
Answered by Penny Nom.
May Lee's cake 2010-09-18
From Wafa:
May Lee bought a cake which is circular in shape. Her sister ate a quarter of the cake. Given that the area of the top surface of the remaining portion is 520 square cm, find the diameter of the cake.
Answered by Penny Nom.
Continuity 2010-09-18
From Carina:
Hi. My name's Carina and I'm currently a sophomore in high school. I'm having a lot of difficulties in AP Calculus with continuity, one-sided limits, and removable discontinuities. Basically, I have no idea how to do them or even what they are. I read the lesson but I still don't get it. Can someone put it in simpler terms so I can understand how to complete my questions? Thank you!
Answered by Robert Dawson.
Two perpendicular chords 2010-09-11
From edwin:
two perpendicular chords AB and CD intersect at P. if X,Y are their midpoints and M the centre of the circle, prove that MP=XY. I do not a have clue on how to do it so can you please help me with it
Answered by Robert Dawson.
Maximizing the volume of a cylinder 2010-08-31
From Haris:
question: the cylinder below is to be made with 3000cm^2 of sheet metal. the aim of this assignment is to determine the dimensions (r and h) that would give the maximum volume. how do i do this? i have no idea. can you please send me a step-to-step guide on how t do this? thank you very much.
Answered by Penny Nom.
Three cars 2010-08-30
From Anil:
3 cars are moving at speed of 4 kmph,5.5 kmph and 8 kmph in a circular track.The circular track has a distance of 11 km. What is the time taken for all the 3 cars to meet at the starting point ?
Answered by Stephen La Rocque.
A max min problem 2010-08-19
From Mark:
a rectangular field is to be enclosed and divided into four equal lots by fences parallel to one of the side. A total of 10000 meters of fence are available .Find the area of the largest field that can be enclosed.
Answered by Penny Nom.
Two cars on a circular track 2010-08-12
From david:
If two cars starts to drive at point 1 and go in a circle when will they meet? (one cars speed is faster the other ) all I need is a formula
Answered by Tyler Wood.
70 cubic meters of mulch 2010-07-30
From zsuzsi:
i have 70 cubic meters of mulch to move and an 8 tonne truck to use how much tonnage is to 1 square meter so that i can work out how many trips i need to make
Answered by Penny Nom.
The area of a hexagon 2010-07-28
From Katie:
Hi i have to find the area of a hexagon with only the side length 2cm given would you be able t help?
Answered by Walter Whiteley.
An 18ft round pool 2010-07-19
From christine:
will an 18ft round pool fit on a 12x16 ft rectangular cement slab?
Answered by Tyler Wood.
777777 times 111111 2010-07-07
From Chew:
What is 777777 times 111111 without using a calculator?
Answered by Chris Fisher.
Maximize the floor area 2010-07-07
From shirlyn:
A rectangular building will be constructed on a lot in the form of a right triangle with legs of 60 ft. and 80 ft. If the building has one side along the hypotenuse, find its dimensions for maximum floor area.
Answered by Penny Nom.
(x^3 + 11x) is divisible by 6 2010-06-24
From PT:
Given that x is a non-zero integer, how do you show that for all values of x, (x3 + 11x) is divisible by 6?

I know it works but how do I answer the "all values of x" part?

Thanks in advance!

Answered by Robert Dawson.
A max/min problem 2010-06-12
From valentin:
What is the maximum area of an isosceles triangle with two side lengths equal to 5 and one side length equal to 2x, where 0 ≤ x ≤ 5?
Answered by Harley Weston.
Compound interest 2010-06-01
From Kenneth:
Hello: I have a question regarding the following compound interest and future value calculation.

Year 1 P + rP equals balance after the first year.
Year 2 (P + rP) + r(P + rP) equals balance after the second year.
Year 3 ? equals balance after the third year.

This question is in two parts.

1. What would follow for year three?

2. I know that a pattern will develop. What will it be so that I can determine the extended pattern for following years ?

Answered by Penny Nom.
Integration of sin^3 (2x) 2010-05-29
From ascher:
how do you integrate this equation ∫ sin^3 (2x) dx
Answered by Robert Dawson and Penny Nom.
Weighing a 1000 lb cylinder on a 500 lb scale 2010-05-28
From Jerry:
I am trying to weigh a large possibly 1000 lb cylinder on a 500 lb scale, is this possible? If so what is the actual formula to figure out the correct weight? I am told it is possible with the fulcrum method but have not been able to find a formula. Thanks Jerry
Answered by Robert Dawson.
Two problems 2010-05-27
From debbie:

Question from debbie, a parent:

hi, i have a daughter and she asked me a maths question I cannot solve. I was just wondering if you can give me the answers plus the working out so I could explain to my daughter,

1. The leftmost digit of a six-digit number N is 1. If this digit is removed and then written as a rightmost digit, the number thus obtained is three times N .Find N.

2. Four friends are racing together down a flight of stairs. A goes 2 steps at a time, B 3 steps at a time. C 4 steps at a time and D 5 steps at a time. The only steps which all four tread on are the top one and the bottom one. How many stairs in the flight were stepped on exactly once?


Answered by Penny Nom.
An optimization problem 2010-05-23
From Marina:
Hello, I have an optimization homework assignment and this question has me stumped..I don't even know

A hiker finds herself in a forest 2 km from a long straight road. She wants to walk to her cabin 10 km away and also 2 km from the road. She can walk 8km/hr on the road but only 3km/hr in the forest. She decides to walk thru the forest to the road, along the road, and again thru the forest to her cabin. What angle theta would minimize the total time required for her to reach her cabin?
I'll do my best to copy the diagram here:

                             10km
Hiker_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _Cabin
      \                           |                              /
       \                          |                             /
     f  \                      2km                          /
         \                        |                           /
theta   \___________________________ /
                            Road


Answered by Penny Nom.
The rejection region 2010-05-01
From Mong:
In Tests of Hypothesis, what is the decision when the test statistic we compute from the sample information is exactly equal to the critical value? that is, we reject null hypothesis or do not reject it? Thanks!
Answered by Chris Fisher.
The rate of change of y with respect to x 2010-04-29
From Tom:
I just had a quick calc question about wording that wasn't ever addressed in class. When the book says "the rate of change of y with respect to x", should it be considered how fast y is changing in comparison to x?

I ask because the textbook says that "y is changing 3 times faster than x, so the rate of change of y with respect to x is 3." I'm use to rate being like velocity, as in units of distance per units of time. All we're told in class is that it's the slope of the tangent line, I was hoping you could clarify for me what exactly is meant by the wording of a "rate of change of something with respect to something else". More specifically, what "rate" and "with respect to" mean within this context?

Thanks for your time

Answered by Harley Weston.
A trig equation 2010-04-28
From Steve:
2cos^2(X)-2sin^2(x)+1=0
Answered by Harley Weston.
cos(x) = sin(x - 1) 2010-04-28
From alex:
In the equation cos x = sin x-1 for -pi/2 A: solve for x graphically
B: solve algebraically and prove the solution is correct.

Alex

Answered by Penny Nom.
y = - log(x) 2010-04-28
From Alex:
y= - log(x), where y = 4.3
solve for x.

Answered by Harley Weston.
A rectangular prism 2010-04-27
From Savannah:
A rectangular prism is made of exactly 8 cubes. Find the length, width, and height.
Answered by Penny Nom.
A rectangular garden 2010-04-25
From Billy:
Tanisha wants to make a rectangular garden with a perimeter of 38 feet. What is the greatest area possible that tanisha can make the garden?
Answered by Penny Nom.
If (x, 4) is equidistant from (5, -2) and (3, 4), find x. 2010-04-21
From abeth:
If (x, 4) is equidistant from (5, -2) and (3, 4), find x.
Find the point on the y - axis that is equidistant from (-4, -2) and (3, 1).

Answered by Penny Nom.
What are the dimensions of the box? 2010-04-13
From Steven:
The longest rod that will just fit inside a rectangular box, if placed diagonally top to bottom, is 17 inches. The box is 1 inch shorter and 3 inches longer than it is wide. How much must you cut off the rod so that it will lie flat in the bottom of the container? What are the dimensions of the box?
Answered by Robert Dawson.
Integrate the ((4th root of x^3)+1) dx 2010-04-12
From Bridget:
integrate the ((4th root of x^3)+1) dx
Answered by Tyler Wood.
The derivative of y=x^x 2010-04-09
From David:
So, its David, and I was wondering about the derivative of y=x^x. I have often seen it be shown as x^x(ln(x)+1), but when I did it through limits it turned out differently. Here's what I did:
It is commonly know that df(x)/dx of a function is also the limit as h->0 of f(x+h)-f(x)/h. To do this for x^x you have to start with lim h->0 ((x+h)^(x+h)-x^x)/h. The binomial theorem then shows us that this is equal to lim h->0 (x^(x+h)+(x+h)x^(x+h-1)h+...-x^x)/h
This is also equal to lim a->0 lim h->0 (x^(x+a)+(x+h)x^(x+h-1)h...-x^x)/h.
Evaluating for a=0 you get lim h->0 (x^x+(x+h)x^(x+h-1)h...x^x)/h
Seeing as the last 2 terms on the numerator cancel out you can simplify to a numerator with h's is each of the terms, which you can then divide by h to get:
lim h->0 (x+h)x^(x+h-1)... which when evaluated for h=0 gives us: x(x^(x-1)). This statement is also equal to x^x.
This contradicts the definition of the derivative of x^x that is commonly shown. So, my question is: can you find any flaws in the logic of that procedure? I do not want to be shown how to differentiate x^x implicitly because I already know how to do that.

Answered by Robert Dawson.
A model for the population of a Canadian city 2010-04-07
From jess:
Let t^2 represent t-squared. The population of a Canadian City is modelled by: f(t) = 12t^2 + 800t + 40,000, where t is the time in years. When t= 0, the year is 2007.
a) According to the model, what will the population be in 2010?
B) In what year is the population predicted to be 300,000?

Answered by Penny Nom.
A max min problem 2010-04-06
From Terry:
The vertex of a right circular cone and the circular edge of its base lie on the surface of a sphere with a radius of 2m. Find the dimensions of the cone of maximum volume that can be inscribed in the sphere.
Answered by Harley Weston.
The derivative of cos^3x 2010-04-06
From Erson:
Find y' of the given function: y = cos^3x.
Answered by Harley Weston.
Sand falling off a conveyer 2010-04-02
From Katherine:
sand is falling off a conveyer onto a pile at the rate of 1.5 cubic feet per minute. The diameter of the base is approximately twice the altitude. At what rate is the height of the pile changing when it is 10 feet high?
Answered by Penny Nom.
Pyramids and parallelograms 2010-04-01
From Vivi:
Hi, my name is Vivi, and math teacher is giving a geometry test. I tend to forget how to find the surface area and volume of triangular pyramids and parallelograms. Do you have a way of remembering how to find the surface area?
Answered by Harley Weston.
A champagne pyramid 2010-03-22
From Kathy:
I have 680 champagne glasses and my pyramid can only be 15 levels high. How many glasses need to be on each level? Is there a formula I can use?
Answered by Robert Dawson.
Water in a culvert 2010-03-18
From Chip:
Hello, I have a problem to which I know there must be an analytical solution - but as it has been 50 years since I studied math I can't remember quite how to do it!! I have a 12" round culvert in my yard that runs water all year. I would like to be able to calculate the flow through the culvert by measuring the depth of water flowing through and measuring the speed of the current. I can measure the depth and the speed, but I forget how to calculate the cross section of the flow. If you could help I would greatly appreciate it. Thank you
Answered by Penny Nom.
Angular velocity 2010-03-17
From Lindsay:
Determine the angular velocity, in radians per second, of a 14-inch car wheel, if the car is traveling at 60 miles per hour
Answered by Harley Weston.
An irregular octagon 2010-03-09
From Gayle:
Question from Gayle:

I am building an irregular shaped octagon wooden box.
The measurements are 291/2 inches by 211/2 inches.
Sides are 12 inches.
It will be 36 inches high.

What would the cutting angles degrees be?

Answered by Harley Weston.
0.999 ^ (500) 2010-03-07
From debra:
I just need to know how to solve the following problem without using a calculator: .999 ^ (500). I know the answer is .606, I just want to do it by hand since I can't use a calculator on my test.
Answered by Penny Nom and Claude Tardif.
The integral of X^3/the square root of 1-x^2 dx 2010-03-07
From William:
The integral of X^3/the square root of 1-x^2 dx.
Answered by Harley Weston.
The base area of rectangular prism 2010-03-05
From Desiree:
How do you find the base area of rectangular prism that has 4 cm by 4cm by 6cm ?
Answered by Penny Nom.
1/6 x 5 x 12 = what 2010-02-19
From dana:
1/6 x 5 x 12 = what
Answered by Lorraine Dame.
The center of a rectangular room 2010-02-16
From Diana:
Consider a rectangular room, 15 feet wide, 30 feet long and 12 feet high. What is the exact distance from any of the 8 corners of the room and its geometric center? Can you write a generic formula for such a distance? And if we keep the same proportions on all dimensions, can you write an expression for the same distance as a function of the floor perimeter?
Answered by Penny Nom.
Two bus routes 2010-02-03
From kiyah:
from 4:30 pm to 6:30 pm the route 1 bus stops every 12 min at the gym's bus stop. the route 2 bus stops there every 15 min. if both buses are now at the stop and schedule is kept, how long will it be before both buses will be at the stop again?
Answered by Penny Nom.
Everything in a cube 2 miles long? 2010-01-31
From Naresh:
in a book, i got to read this :

Is it possible to pack the entire population of earth and everything that was created by humankind in a cube whose edges are 2 miles long ?

Is it possible? Thanks.

Answered by Stephen La Rocque.
The inradius of an icosahedron 2010-01-21
From fnavroth:
Suppose you have an equilateral triangle. The area of the triangle is exactly 1200 square centimetres. Now suppose you have twenty of those triangles. It's possible to assemble those twenty triangles into a closed three-dimensional shape, a regular polyhedron. What would be the volume, in cubic centimetres, of the largest sphere that could fit inside the shape?
Answered by Chris Fisher.
Loading a headboard in a uhaul 2010-01-20
From gina:
I have a uhaul 9'10" long 4"9"wide 4'7"height I have a headboard 74 inches in height would it fit the box diagonally
Answered by Penny Nom.
A cone circumscribed about a given hemisphere 2010-01-19
From Neven:
The cone of smallest possible volume is circumscribed about a given hemisphere. What is the ratio of its height to the diameter of its base?
(G.F.Simmons, Calculus with Analytic Geometry, CH4 Applications of Derivatives)

Answered by Chris Fisher.
A schedule for a pool tournament 2010-01-14
From john:
I need to know how to set up a pool tournament 12-14 players playing once a week, either 10-12 weeks whichever works out the best, what players would play what players week one through week ten or twelve? I hope you can help, I cant figure out the formula.

thanks

John

Answered by Victoria West.
A triangular prism 2010-01-13
From Breon:
what is the formula for a triangular prism?
Answered by Robert Dawson.
Trigonometry and picture hanging 2010-01-13
From george:
The top of a picture 1m high 0.8m from the ceiling. At a point on the ceiling directly in front of the picture, we wish to install a light so that the angle subtended by the picture equals to the angle of depression of the top of the picture. How far out from the wall should the light be installed?
Answered by Penny Nom.
Related Rates Problem 2010-01-12
From Neven:
A woman raises a bucket of cement to a platform 40 ft above her head by means of a rope 80 ft long that passes over a pulley on the platform. If she holds her end of the rope firmly at head level and walks away at 5ft/s, how fast is the bucket rising when she is 30 ft away from the spot directly below the pulley? (G. F. Simmons, Calculus with Analytic Geometry, pg.142)
Answered by Penny Nom.
A pair of simultaneous equations 2010-01-09
From Yumiko:
Solve the following pair of simultaneous equations.

x^2 -4x = y^2-4
3y=2x - 3

Answered by Penny Nom.
A sports schedule for the ymca 2010-01-08
From Erich:
i have to make a sports schedule for the ymca. i have 7 teams. they need to play each other 2 times. we have 3 time slots per night. i would like them to have an even number of time slots thru the season. one team must have abye each week. can you chow mw the schedul. example time 1 team 1 vs. team 2. time 2 team 3 vs. team 4 time 3 team 5 vs. team 6. team 7 bye week 1.
Answered by Victoria West.
A networking event 2010-01-07
From Tricia:
I have 70 people to go around to 10 tables with 7 at each table. only 6 from each table will rotate each time. There is 1 table monitor that always stays at same table. How do I make the rotation so everyone moves and gets to see all 70 people at the networking event?
Answered by Robert Dawson.
Dividing seashells among girls 2010-01-06
From Eileen:
A group of girls collected some seashells from the beach. They tried to divided these seashells equally among them. If each girl received 8 seashells, they would need 5 more seashells. If each girl received 7 seashells, they would have 3 seashells extra. How many seashells did they collect from the beach altogether?
Answered by Robert Dawson and Penny Nom.
A triangular pyramid 2010-01-05
From ally:
how many vertices, edges, faces in a triangular pyramid?
Answered by Robert Dawson.
Figure out the square root of something 2009-12-20
From eric:
is there an ez equation to figure out the square root of something?
Answered by Harley Weston.
A pile of sand 2009-12-16
From Malik:
Sand is leaking out of a hole at the bottom of a container at a rate of 90cm3/min. As it leaks out, it forms a pile in the shape of a right circular cone whose base is 30cm below the bottom of the container. The base radius is increasing at a rate of 6mm/min. If, at the instant that 600cm3 have leaked out, the radius is 12cm, find the amount of leakage when the pile touches the bottom of the container.
Answered by Harley Weston.
Energy in calories 2009-12-15
From Josephine:
A soft drink manufacturer claims that a new diet soft drink is now "low Joule". The label indicates that the available energy per serving is 6300 J. What is the equivalent of this energy in calories? (1 Calorie=1000 cal)
Answered by Robert Dawson.
f(x)=x+2sinx 2009-12-12
From amroziz:
for which values of x does the graph of f(x)=x+2sinx have horizontal tangent
Answered by Harley Weston.
How fast is the distance between the two cars decreasing? 2009-12-08
From Jenny:
Two cares are on a collision course toward point P. The paths of the two cars make a 30 degree angle with each other. The first car is 40 km from P, and traveling toward P at 16 km/hour. The second car is 50 km from P, traveling at 20 km/hour. How fast is the (straight line) distance between the two cars decreasing. (Hint: Law of Cosines)
Answered by Harley Weston.
Solving two equations, one with a square root 2009-11-23
From kacie:
y = square root of x+3
x-4y = -7

im having trouble with this problem...i have to find where they intersect.

Answered by Harley Weston.
The triangle formed by the tangent and the coordinates axes 2009-11-23
From Nirmala:
Given that y=1/x, x is not equal to zero. Prove that the area of the triangle formed by the tangent and the coordinates axes is 2.
Answered by Harley Weston.
Angular speed 2009-11-19
From Atalie:
The engine of a sports car rotates at 5000 revolution per minute. Calculate the angular speed of the engine in radians per second, given that 2pi radians = 1 revolution
Answered by Robert Dawson.
A triangular shaped ditch 2009-11-12
From Tim:
I am planning on constructing a triangular shaped ditch the measures 550 meters in length, 6 meters wide at the surface, .3048 meters at the invert of the ditch and 2 meters deep.

How many cubic meters of material will have to be excavated to construct this ditch

Answered by Robert Dawson.
f(x)= (e^x) / [(e^x)+(ex^2)] 2009-11-10
From natalie:
I'm trying to graph the function, f(x)= (e^x) / (e^x)+(ex^2) [e to the x divided by e to the x plus e times x squared] I know that there aren't any vertical asymptotes, but is there a horizontal asymptote? and also, I'm stuck on finding the concavity for this graph. I tried to find f "(x), but it came out to be really long and I am not sure how to find the x values for f "(x) without using a graphic calculator. thanks, natalie
Answered by Chris Fisher and Harley Weston.
At what rate are the people moving apart? 2009-11-01
From saira:
A man starts walking north at 4 ft/s from a point P. 5 minutes later a woman starts walking south at 5 ft/s from a point 500 ft due east of P. At what rate are the people moving apart 15 minute after the woman starts walking ?
Answered by Harley Weston.
A path around a pond 2009-10-31
From adeniji:
find the area of a concrete path 2m wide surrounding a circular pond 12m in diameter
Answered by Penny Nom.
Painting a dome 2009-10-30
From Jessica:
A hemispherical dome with a radius of 50 ft will be given a coat of paint .01 inch thick. The Contractor for the job wants to estimate the number of gallons of paint needed. Use a differential to obtain an estimate (231 cubic inches/gallon) HINT: Approximate the change in volume of hemisphere corresponding to increase of .01 inch in the radius.
Answered by Robert Dawson.
Acreage calculation 2009-10-29
From Angela:
I am appraising a small portion of property for a right of way for a new sewer line. I have appraised many similar projects in the past; however the engineer always calculated the exact acreage and/or dimensions of the parcel being taken. My survey states the following: "141 linear ft. of 25' permanent R/W. I divided the linear feet x 12 and mult. by 25 to get the square footage, but it just doesn't seem right. Any suggestions? Am I missing something?
Answered by Robert Dawson.
An irregular quadrilateral 2009-10-29
From riya:
what is irregular quadrilateral?
Answered by Penny Nom.
Is it a rectangle? 2009-10-29
From sefora:
The coordinates of the vertices of quadrilaterals are given. Draw each quadrilateral on a grid. Determine whether it is a rectangle (show your work)

P(5,1), Q(-4,4), R(-6,-2), S(3,-5)

Answered by Penny Nom.
Graphing y=(4-x^2)^5 2009-10-25
From natalie:
I want to graph the curve of y=(4-x^2)^5 without using a graphing calculator. To do this, I'm suppose to find: domain, y and x intercepts, asymptotes, intervals of increase/decrease, local max/min, concavity and points of inflection. I got all the way to the step where I'm solving the concavity and I'm stuck. I found the f"(x) and it came out to be really large polynomial. I want to know how I can solve for the x of f"(x) without the use of a graphing calculator, when the polynomial has x^6 and x^8. Thank you so much, natalie
Answered by Harley Weston.
A max/min problem 2009-10-12
From avien:
a rectangle has a line of fixed length Lreaching from the vertex to the midpoint of one of the far sides. what is the maximum possible area of such a rectangle? SHOW SOLUTION USING CALCULUS
Answered by Penny Nom.
Golf for 8 2009-10-10
From Chris:
I have a group of 8 golfers who will be playing three rounds, What is the best formula so we can all try to play with different people during the 3 rounds .
Answered by Victoria West.
24 golfers, 6 days 2009-10-03
From patrick:
i need a pairing schedule for 24 golfers for six days playing in foursomes. Please
Answered by Victoria West.
A line tangent to a parabola 2009-10-01
From kanchan:
for what value of c a line y=mx+c touches a parabola y^2=4a(x-a)
Answered by Penny Nom.
24 golfers 2009-10-01
From Peter:
I am working on a 19 week golf schedule with 24 golfers, and I would like to know how to make up six foursomes each week without having a player paired with the same golfers.
Answered by Victoria West.
5 x 8 + 6 divided 6 - 12 x 2 2009-09-24
From Susan:
5 x 8 + 6 divided 6 - 12 x 2. I am not sure of the rules of operation for this type of question
Answered by Penny Nom.
24 golfers: 4 days 2009-09-21
From Steven:
We have 24 golfers (6 A's, 6 B's, 6 C's & 6 D's) playing 4 days. Each day a foursome consist of an A, a B, a C & a D player. Can you give me a pairing list so that no two golfers will play on the same foursome for the 4 days?
Answered by Chris Fisher and Victoria West.
Dart teams 2009-09-18
From Sally:
I have 14 dart teams. Each team has a home bar.Usually it is one week home, the next week away. I have 3 locations that have one board only, yet have 2 teams at each location. I have one location that has 2 dart boards, and 3 teams. The last location have 3 dart boards and 4 teams.Can you make me a schedule that will be home and away, and every teams plays each other twice. In case you are wondering, the bars sponsor the teams.Thank you. Sally
Answered by Robert Dawson.
solve integral of ( x^2+x+1)^5 2009-09-18
From jaka:
solve integral of ( x^2+x+1)^5
Answered by Robert Dawson.
Common multiples of 36 and 48 2009-09-15
From Kamaldeep:
Find the first 2 common multiples of 36 and 48.
Answered by Penny Nom.
Jogging and swimming 2009-09-11
From Brandon:
Trevor swims jogs 3 days and swims every 4 days. How often does he jog and swim on the same day
Answered by Leeanne Boehm.
A circular border around a pool 2009-09-08
From Calvin:
A pool in the shape of a circle measures 10 feet across. One cubic yard of concrete is to be used to create a circular border of uniform width around the pool. If the border is to have a depth of 3 inches, how wide will the border be? ( 1 cubic yard=27 cubic feet )
Answered by Stephen La Rocque.
4 couples seating themselves at a round table 2009-09-04
From Hui:
Q: 4 couples seating themselves at a round table. Men must seat together and women seat together. How many ways are there? Answer in the printed text is 576. I got 144. Pls advice.
Answered by Claude Tardif.
An area problem 2009-08-30
From Amber:
Area of hexagon ABCDEF with the vertices (3,0) (7,0) (9,2) (7,4) (3,4) (1,0)
Answered by Harley Weston.
Simultaneous equations 2009-08-28
From onias:
solve 3/a - 2/b = 1/2 , 5/a + 3/b = 29/12
Answered by Robert Dawson.
A football schedule 2009-08-14
From Bill:
I am having trouble with a football schedule that has two divisions of five teams each, 1-5 and 6-10. 1-5 will play against each other in the first 4 weeks and also the the last 4 weeks with teams 6-10 completing the middle of the schedule. The schedule is 13 weeks. Thank you for your time
Answered by Chris Fisher and Victoria West.
An antiderivative problem 2009-08-13
From Indrajit:
∫4e^x + 6e^-x/(9e^x + 4e^-x)dx = Ax + Bloge(9e2x - 4) + C

then A=?......B=?.....C=?

plz solve it...."^" stands for "to the power of"....

Answered by Harley Weston.
A rectangular pen 2009-08-13
From Kari:
A rectangular pen is to be built using a total of 800 ft of fencing. Part of this fencing will be used to build a fence across the middle of the rectangle (the rectangle is 2 squares fused together so if you can please picture it). Find the length and width that will give a rectangle with maximum total area.
Answered by Stephen La Rocque.
Angular speed 2009-08-04
From Mary:
The engine of a sports car rotates at 5000 revolutions per minute (rpm). Calculate the angular speed of the engine in radians per second. Use 2 radians = 1 revolution.
Answered by Penny Nom.
Torricelli's trumpet 2009-07-29
From Gary:
I was reading about torricelli's trumpet which is described by the equation1/x which is then rotated around the x axis which results in a figure which looks like a trumpet. Now in order to find the volume the integral 1/x^2 dx is used which diverges when integrated so the volume is finite.However if you integrate 1/x dx which is the formula on the plane the answer diverges. Now if you took an infinite area then rotated it around the x axis shouldn't you get an infinite volume? Notice the area I am talking about is under the line 1/x not the surface area of the trumpet which is what the painters paradox is about What am I missing? Thanks
Answered by Robert Dawson.
Golfing with an unpopular golfer 2009-07-23
From Ian:
"We are a group of 8 golfers, one of whom is unpopular. How can we construct a schedule, of two foursomes, so that each person is scheduled to play with him the same number of times. What does the week by week schedule look like?"
Answered by Robert Dawson and Victoria West.
Annular sector 2009-07-20
From Ed:
What is the name for the section of a flat ring (annulus)? Similar to a section on a radar screen, a quadrilateral but the top and bottom are curved.
Answered by Robert Dawson.
A golf league with 12 players 2009-07-17
From Jane:
My weekly golf league has 12 players in 4 threesomes. How many weeks would it take to play everyone once and not have too many duplications? What would be the schedule each week? Thanks
Answered by Victoria West.
Finding the Line Joining Perpendicular Feet 2009-07-16
From mukulu:
Please help I've been tryng to search in your data but i failed to get the solution Find the equation of a straight line joining the feet of the perpendiculars drawn from the point A(1,1) to the line 3x-3y-4= 0 and 3x+y-6=0.
Answered by Janice Cotcher.
The surface area of a rectangular pyramid 2009-07-13
From Shivani:
What is the surface area of a rectangular pyramid with a length of 6 inches, a width of 7 inches and a SLANT height of 4 inches.
Answered by Penny Nom.
Multiplying Large Numbers 2009-07-09
From Jessica:
What is 12 billion X 6 trillion?
Answered by Janice Cotcher.
Multiplying Large Numbers 2009-07-09
From Jessica:
What is 12 billion X 6 trillion?
Answered by Janice Cotcher.
Simultaneous Equations 2009-07-06
From Mukulu:
Solve the equation simultaneously X/5=(Y+2)/2= (Z-1)/4 ……………….eqt 1 3X+4Y+2Z-25=0 ………………eqt 2
Answered by Janice Cotcher.
Investing in multiple accounts 2009-06-26
From Kenneth:
Hello:

If an investor has $1000.00 to invest in multiple accounts, and he wants a total return of 4%, is there one calculation that can be used to determine what these amounts could be even though there may be numerous amounts used as answers for most of the following examples?

For example,
Invest $1000.00 @ 2% and 5% for total return of 4%.
Invest $1000.00 @ 2%, 3% and 5% for total return of 4%.
Invest $1000.00 @ 2%, 3%, and 5% for total return of 4%.
Invest $1000.00 @ 2%, 3%, 4% and 5% for total return of 4%.
etc.

Answered by Robert Dawson.
The surface area of a tank 2009-06-25
From Charles:
I need to calculate the external wall and top sqft surface area of a tank 54ft od x 15ft high with a dome top 54ft od x 8ft high.
Answered by Penny Nom.
(570 divided by 15) multiplied by (5 plus 26) 2009-06-24
From Sherrie:
What is the answer to this math question:
(570 divided by 15) multiplied by (5 plus 26)..........
Thank you,
Sherrie:-)

Answered by Penny Nom.
The Pythagorean theorem 2009-06-24
From supreet:
What are some real-world applications of the Pythagorean theorem?
and
How are the Pythagorean theorem and the distance formula related?

Answered by Harley Weston.
Two questions from math class 2009-06-18
From Con:
Hello,

My name is Con and my son is required to answer the following questions for his maths class.

He has attempted Q1 through trial and error and has found the answer to 72453. Is this correct?

He has attempted to draw the triangles described in Q2 in a number of ways and has found that BE can not equal ED and is dependent of angle BAC. Therefore, he claims that the triangle can not be drawn/practical. Is this correct or is there a slolution?

Q1.
Digits 2, 3, 4, 5 and 7 are each used once to compose a 5-digit number abcde such that 4 divides a 3-digit number abc, 5 divides a 3-digit number bcd and 3 divides a 3-digit number cde. Find the 5-digit number abcde.

Q2.
Let ABC be a triangle with AB=AC. D is a point on AC such that BC=BD. E is a point on AB such that BE = ED = AD. Find the size of the angle EAD. Con

Answered by Chris Fisher.
The integral of x^x 2009-06-18
From ANGIKAR:
what would be the integration of (X^Xdx)?

give answer in details.

Answered by Robert Dawson and Harley Weston.
Triangular Numbers 2009-06-16
From Chinonyerem:
Question from Chinonyerem, a student:

Each of the numbers
1 = 1, 3 = 1+2, 6 = 1+2+3, 10 = 1+2+3+4 ,...
represents the number of dots that can be arranged evenly in an equilateral
triangle:
                            .
                  .        . .
        .         .       . . .             ...
.      . .      . . .    . . . .
This led the ancient Greeks to call a number TRIANGULAR if it is the
sum of consecutive integers, beginning with 1. Prove the following facts
concerning triangular numbers:
(a) A number is triangular if and only if it is of the form n(n+1)/2 for some n >= 1
(b) The integer n is a triangular number if and only if 8n+1 is a perfect square
(c) The sum of any two consecutive triangular numbers is a perfect square
(d) If n is a triangular number, then so are 9n+1, 25n+3, and 49n+6
Answered by Penny Nom.

11 golfers playing 4 rounds 2009-06-14
From Brian:
I have 11 golfers playing 4 rounds of golf. It would be great if we could play at least once with everybody. I realize we will have 2 foursomes and 1 threesome each round...can you help?
Answered by Victoria West.
The product of gradients between 2 perpendiculars lines 2009-06-11
From Alister:
how do i prove that the product of gradients between 2 perpendiculars lines equal to -1....
Answered by Penny Nom.
A rotating schedule 2009-06-10
From Doreen:
We have seven people - we want to create a rotating schedule for two people at a time to attend one day a week with each person working the same amount of days in the year.
Answered by Victoria West.
Cubic yards in an Irregular Shape 2009-06-08
From ron:
hi i have a berm 100'w x200'L at the base and 9'tall the top is 85'L x 20'w i would to find out how many cubic yards are in the pile and the formula
Answered by Janice Cotcher.
An aeroplane flying in a wind 2009-06-02
From Maria:
The aeroplane flies in a wind of speed 50 kph from the direction S80◦W. However, the direction in which it is pointed, and its speed in still air, are such that its resultant speed and direction are 800 kph, and direction N71.6◦E

I need to find the size of the angle between v and vw, in degrees to one decimal place, and find the speed at which the aeroplane would fly if the air were still, to the nearest kph.

It would help me greatly if I could see a diagram illustrating the velocity va that the aeroplane would have if the air were still, the velocity vw of the wind, and the resultant velocity v of the aeroplane (diagram should be in the form of a triangle illustrating how one velocity vector is the sum of the other two)

Thanks

Answered by Harley Weston.
The position of the fulcrum 2009-05-23
From jim:
I think I need a formula. I need to know how far an object will be lifted. A beam is 246 inches long on one side of the fulcrum, and 41 inches on the other side, if I push down 36 inches on the long side of the beam, how much will the short side move up?
Answered by Stephen La Rocque.
28 teams 14 lanes , 9 weeks no repeats 2009-05-19
From paul:
28 teams 14 lanes , 9 weeks no repeats
Answered by Karen Meagher.
Fraction Word Problem 2009-05-13
From Sonya:
Debbie wants to eat 1/6 of her 12 pieces of candy. How many pieces did she eat ?
Answered by Janice Cotcher.
16 teams, 15 weeks, would like to pair up with no repeats. 2009-05-12
From Kimberly:
16 teams, 15 weeks, would like to pair up with no repeats. Thank you so very much.
Answered by Robert Dawson.
differentiate y sin[x^2]=x sin[y^2] 2009-05-11
From mamiriri:
derivate y sin[x^2]=x sin[y^2]
Answered by Harley Weston.
Six teams, two sites, and four days 2009-05-08
From John:
I have six teams, two sites, and four days. We have decided that we want to have tri-meets, where there would be three teams competing against each other at the same site each day. Here is the problem, I need to make sure that each team sees each other team at least once and each team goes to each site at least once.
Answered by Victoria West.
The dimensions of a toy chest 2009-05-07
From charlotta:
My son needs to find the 3 dimensions of a toy chest that has to have a volume of 24 cubic feet can you show how to get the answer
Answered by Penny Nom.
Perpendicular lines 2009-05-07
From shabnam:
the line presented by y= 3x-2 and a line perpendicular to it intersect at R(1,1). Determine the equation of the perpendicular line
Answered by Stephen La Rocque.
A 6 team social softball league 2009-05-02
From Don:
Hi We have a 6 team social softball league with only two fields. Each team plays two games each Saturday. We have three time slots 10:00, 12:00 and 2:00 We play for 11 Saturdays and than have a 2 weekend playoff. All teams prefer double headers vs the split at 10:00and 2:00. How do we schedule as balanced a schedule as possible and minmize the splits ? Thanks Don
Answered by Laura Morrison and Victoria West.
Rectangular prisms 2009-05-01
From deborah:
Could you please tell me some examples of different objects in the real world of rectangular prisms?
Answered by Harley Weston.
The integral of a to power x squared 2009-04-28
From JIM:
WHEN I ATTENDED U.OF T. (TORONTO ) MANY YEARS AGO WE WERE TOLD THE FOLLOWING INTEGRAL COULD NOT BE SOLVED : a to power x squared . is this still true ?

CURIOUS , JIM

Answered by Robert Dawson.
Completing the square 2009-04-27
From Daniel:
I tried following an example of yours but I still couldn't figure it out. Here is my question,

2x^2 - 6x + 1 = 0.

Any help would be greatly appreciated.

Answered by Stephen La Rocque.
Common multiples of 2 and 5 2009-04-23
From pat:
what are the common multiples of 2 and 5, through 30, because i been working on it for hours
Answered by Robert Dawson and Stephen La Rocque.
Two regular hexagons 2009-04-21
From niko:
Two regular hexagons are ____________ similar.
Answered by Stephen La Rocque.
Volume of a prism 2009-04-21
From David:
The base of a rectangular prism has an area of 15.3 square inches and a volume of 185.13 cubic inches. Write an equation that can be used to find the height "h" of the prism
Answered by Robert Dawson and Stephen La Rocque.
A perpendicular line in standard form 2009-04-21
From Kristy:
Can you help me with this equation? Find the equation, in standard form of the line perpendicular to 2x-3y=-5 and passing through (3,-2) With the equation in standard form with all integer coefficient.
Answered by Stephen La Rocque.
A max-min problem 2009-04-20
From Charlene:
A fixed circle lies in the plane. A triangle is drawn inside the circle with all three vertices on the circle and two of the vertices at the ends of a diameter. Where should the third vertex lie to maximize the perimeter of the triangle?
Answered by Penny Nom.
28 golfers 2009-04-18
From DON:
HI, I HAVE 28 GOLFERS AND I NEED A SCHEDULE FOR 24 DIFFERENT DAYS THERE WILL BE 7 GROUPS OF 4 PLAYERS EACH DAY. ALL PLAYERS WOULD LIKE TO PLAY WITH ONE ANOTHER AS EVEN AS POSSIBLE (SAY 2 TO 4 TIMES EACH OVER THE 24 DAYS)...THANKS DON
Answered by Victoria West.
Exponential form 2009-04-16
From Pete:
Hi, How do you express ³√h^-4 in exponential form. I am having a lot of trouble with this one.
thanks
Pete

Answered by Stephen La Rocque.
10 yards of rubber mulch 2009-04-15
From Donna:
If I want to buy 10 yards of rubber mulch (bulk), but it only comes in 20 pound bags, how many bags do I need to buy?
Answered by Harley Weston.
Infinity and Aleph-Null 2009-04-14
From Justin:
Yes, I am reading the Paul Halmos book on Set theory, thanks for telling me how to get it! I was just wondering from your last answer though if the positive real infinity of calculus then corresponds to Aleph-null? I am sorry if this is a similar question to the one I asked before but I was just wondering about this!

All the Best,

Justin

Answered by Robert Dawson.
Choices at a restaurant 2009-04-13
From Rob:
There is a restaurant you get:

Rice/Noodles (1) Main Ingredient (any) Sauce (1)
1 1 1
2 2 2
3 3 3
4 4 4
5 5 5
6 6 6
7 7  
  8  
  9  
  10  
  11  
  12  

So the question is how many different combinations are there. You can only have 1 rice/noodles in a selection and only 1 sauce in a selection but you can have between 1 and all twelve mains in a selection. there are 7 rice/noodles , 12 mains and 6 sauces. How many possibilies. I did it mentally in the restuarant, no pen, paper or calculater and i got 3276..i think thats wrong. please help

Rob
Answered by Robert Dawson, Stephen La Rocque and Claude Tardif.

2sinB=3tanA 2009-04-10
From Xanathax:
ABC is a right-angled triangle. 2sinB=3tanA. Calculate the measure of angle A.
Answered by Penny Nom.
Winding paper after a break 2009-04-10
From Olen:
Question from Olen:

I work in a paper mill and have been handed the task to search for a formula to determine how much paper needs to be added to a parent roll to make up the difference at the winder. (Ex. The spool diameter at the reel is 18.25" we measure roughly 33.5" to make two 58" rolls in the winder. If the is a paper break and the roll diameter in the winder is 30" how much do I add to a single parent roll (22" roughly) to make one 58 " and the 28" needed at the winder. I would appreciate any help to complete this task. I would like to be able to build a chart that operators can refer to based on what is needed. Thank you.

Answered by Harley Weston.
Positive real infinity and Aleph-null 2009-04-09
From Justin:
Hello, I was just wondering why does the positive real infinity correspond to Aleph-null? Thanks a lot for answering my question!

Justin

Answered by Ami and Robert Dawson.
Parallel and perpendicular lines 2009-04-08
From Blake:
I need to know what the formula for working a problem. I need to know how to find if i line is parallel or perpendicular by only looking at the equation. i know you must know the slope but how do i find slope?
Answered by Stephen La Rocque.
Multiplication of polynomials 2009-04-07
From Carla:
I am struggling to understand Multiplication of Polynomials. No matter how hard I try to understand Multiplication of Polynomials, I just can't get it!

The problem that I am trying to solve is this :

-3x^3y(-y + 2 -x^2 + x)

Answered by Robert Dawson.
Sand falls from a conveyor belt 2009-04-01
From Tracy:
Sand falls from a conveyor belt at the rate of 10 cubic feet per minute onto a conical pile. The radius of the base is always equal to half the pile's height. How fast is the height growing when the pile is 5ft high?
Answered by Stephen La Rocque.
A spherical Tootsie Roll Pop 2009-04-01
From Tracy:
A spherical Tootsie Roll Pop you are sucking on is giving up volume at a steady rate of .8 ml/min. How fast will the radius be decreasing when the Tootsie Roll Pop is 20 mm across?
Answered by Harley Weston.
An isosceles triangle 2009-03-26
From sela:
An isosceles triangle has two equal sides of length 10 cm. Theta is the angle between two equal sides.
a) Express area of a triangle as a function of theta
b) If theta is increasing at a rate of 10 degrees/minute, how fast is area changing at the instant theta=pi/3?
c) at what value of theta will the triangle have the maximum area?

Answered by Penny Nom.
A max-min problem 2009-03-24
From Jay:
Determine the area of the largest rectangle that can be inscribed between the x-axis and the curve defined by y = 26 - x^2.
Answered by Harley Weston.
The diameter of a roll of plastic 2009-03-24
From truong:
hi. i have trouble to calculate the diameter of the plastic roll. the sheet is 765 m long and 0.8 mm to wrap around the core 400 mm in dia. please help me with the formula to calculate the dia of plastic roll, thanks in advance
Answered by Harley Weston.
A rectangular open box 2009-03-21
From tina:
An open box is to be made from a rectangular piece of tin by cutting two inches squares out of the corners and folding up the sides. The volume of the box will be 100 cubic inches. Find the dimensions of the rectangular piece of tin.
Answered by Stephen La Rocque.
A dead fly is stuck to a belt that passes over two pulleys 2009-03-21
From Jules:
A dead fly is stuck to a belt that passes over two pulleys 6 inches and 8 inches in radius. Assuming no slippage,how fast is the fly moving when the large pulley (8 inches) makes 21 revolutions per second ? How many revolutions per second does the small pulley make ? How long will it take the dead fly to travel 1 mile ?
Answered by Penny Nom.
16 golfers 2009-03-18
From Bill:
We have 16 golfers. We golf for 5 days, in foursomes. It should work out that each player plays with each other player 1 time exactly.
I just can't figure it out.

Thank you in advance!

Bill

Answered by Claude Tardif and Victoria West.
A 14 team league that is divided into 2 divisions 2009-03-07
From Ronnie:
I have a 14 team league that is divided into 2 divisions. We have a total of 18 weeks to play. I would like for each team to play the team in their division twice. The remaining 6 weeks would be played with the other division. Any help would be appreciated.
Answered by Chris Fisher and Victoria West.
A common tangent to two curves 2009-03-02
From Jay:
For what values of a and b will the parabola y = x^2 + ax + b be tangent to the curve y = x^3 at (1,1)?
Answered by Penny Nom.
Implicit differentiation 2009-03-01
From Emily:
determine the derivative y' at the point (1,0)
y= ln(x^2+y^2)

y'(1)= ??

Answered by Stephen La Rocque.
36cm to the second power divide 10cm 2009-02-26
From val:
36cm to the second power divide 10cn
Answered by Penny Nom.
A triangular pyramid 2009-02-26
From Craig:
Can you help with this question:
Write the names of the faces and the number of each kind of face on a triangular pyramid?

Answered by Penny Nom.
Multiplying in different bases 2009-02-25
From Susan:
11 base 2 X 22 base 3 + 33 base 4 = _________ base 5
Answered by Robert Dawson.
A rectangular prism 2009-02-25
From Christina:
I am trying to find the area of the base of a rectangular prism where one cube=_1 cu in. The Answer is given in square inches. I also need the volume of the prism in cu in. For example length=3, w=2, h=5
Answered by Penny Nom.
mutiplying decimals 2009-02-24
From telly:
how to do this sum0.24*0.398
Answered by Robert Dawson and Penny Nom.
Time in a Swing 2009-02-22
From Barb:
I looked at the questions concerning a pendulum as I know I need to use this formula but I am stiil not able to figure this problem out. Can you help? If a child is on a swing with a 10 foot chain, then how long des it take to complete one cycle of the swing? I know I am suppose to use the formula 8T^2 = pi^2 L but I do not understand how to do this. Thanks
Answered by Janice Cotcher.
16 golfers playing one round of golf on each of four days 2009-02-22
From Jim:
I have seen solutions for other combinations of setting up a golf trip but I haven't seen one for my group. We have 16 golfers playing one round of golf on each of four days. Is there a way for all of them to play in foursomes so that everyone gets to play with everyone else? Thanks for your consideration.
Answered by Chris Fisher.
6 golfers playing 8 rounds 2009-02-21
From evan:
I have a group of 6 golfers playing 8 rounds. we would like to rotate the 3 somes so each person golfs with different people as many times as possible
Answered by Chris Fisher.
A ten player schedule 2009-02-19
From john:
I HAVE 10 PLAYERS ONE GAME PER NITE FOR 10 WEEKS WHO PLAYS WHO FOR WEEK 1 THRU 10 THANK YOU
Answered by Victoria West.
Implicit differentiation 2009-02-18
From Sunny:
Find slope of the tangent line to the curve 2(x^2+y^2)2=25(x^2–y^2) at (3,-1)
Answered by Robert Dawson and Harley Weston.
The area between the x-axis and a curve 2009-02-18
From Lauren:
This is from a homework question I can't figure out.

Let R be the region in the fourth quadrant enclosed by the x-axis and the curve y= x^2 - 2kx, where k > 0. If the area of the region R is 36 then what is the value of k?

Answered by Robert Dawson.
The second derivative of h(x)=f(g(x)) 2009-02-16
From Kristina:
If h(x)=f(g(x)), and is differentiable, then find h"(x).
Answered by Robert Dawson.
The surface area of a cube and rectangular prism 2009-02-16
From Mhiko:
how to derived the total surface area of a cube and rectangular prism using geoboard??
Answered by Robert Dawson.
Nullity 2009-02-16
From Justin:
What exactly does the term nullity mean in the context of transreal numbers invented by Dr. James Anderson?

Thanks for your help in answering this question!

All the Best,

Justin

Answered by Robert Dawson.
0/0 2009-02-15
From Justin:
Hello, I was just wondering, what is the difference between 0/0 being represented as nullity or as an indeterminate form?

Justin

Answered by Harley Weston.
The height of a triangle 2009-02-14
From GARIMA:
IF THE SIDES OF TRIANGLE ARE GIVEN . HOW WE WILL CALCULATE THE HEIGHT OF TRIANGLE.
Answered by Penny Nom.
8 golfers, 5 rounds 2009-02-12
From John:
8 of us are going on a golf trip next month. We are golfing 5 rounds. Is there any way that everyone can play with each other at least twice? I have been trying to figure it out but it always seems that someone plays with another golfer only once.
Answered by Chris Fisher.
9 golfers 2009-02-12
From Beth:
I am organizing a golf trip for 9 women. We are playing in threesomes and are playing four days. I would love to mix it up so that everyone gets to play with each other at least once. Any mathematical suggestions as to how I can make this happen??
Answered by Robert Dawson.
A semi circular room 2009-02-11
From Taylor:
being 450pi (the area of a semi circle)

how much money would it cost to lay carpet at $2.57 per foot???

if the area of a semi circular room is 450 pi ft then what is the volume being that the diameter is 60 feet and the ceiling is 16 feet tall

Answered by Robert Dawson and Penny Nom.
Solid figures 2009-02-10
From Rebecca:
I need to know the names of solid figures. I have several pictures that I need to answer what type they are. Thanks, Rebecca 3rd grade
Answered by Penny Nom.
A definite integral 2009-02-09
From Mathata:
Evaluate: integral from 0 to 1, x^2 e^x^3dx
Answered by Harley Weston.
Seating around a circular table 2009-02-09
From Jenny:
A committee of 15 -- 9 women and 6 men -- is to be seated at a circular table (with 15 seats). In how many ways can the seats be assigned so that no two men are seated next to each other?
Answered by Victoria West.
A triangular pyramid 2009-02-06
From kamran:
what would be an example of a triangular pyramid
Answered by Stephen La Rocque.
A trig limit 2009-02-05
From Samantha:
lim x-> 0 ( ( r*cos(wt +h) + r*cos(wt) )/ h )

Where r & w are constants.

Answered by Harley Weston.
Faces, edges and vertices 2009-02-04
From sheila:
what is the relationship between the number of faces and the number of edges of a triangular pyramid ?
Answered by Penny Nom.
A point on -8x^2+5xy+y^3=-149 2009-02-04
From Vivian:
Consider the curve defined by -8x2+5xy+y3=-149
a) find dy/dx
b) Write an equation for the line tangent to the curve at the point (4,-1)
c) There is a number k so that the point (4.2,k) is on the curve. Using the tangent line found in part b), approximate the value of k.
d) write an equation that can be solved to find the actual value of k so that the point (4.2,k) is on the curve
e) Solve the equation found in part d) for the value of k

Answered by Harley Weston.
12 golfers 2009-02-04
From david:
12 golfers playing in 3 four balls over five rounds. can everyone play with everyone else at least once.
Answered by Victoria West.
Simultaneous equations with an xy term 2009-02-01
From angelee:
xy+5x-2y-10=0 2x+y=1
Answered by Penny Nom.
7 golfers playing 4 days of golf 2009-01-30
From Trish:
I have 7 golfers and we are playing 4 days of golf. I would like to do pairings so that everyone gets to play with each other at least one time. Can you help with this? Not a math whiz here and looking for help. Thank you.
Answered by Victoria West.
limit sinx/x 2009-01-30
From Jackie:
how to evaluate limit sinx/x as x tends to zero if x is in degrees
Answered by Stephen La Rocque and Harley Weston.
A tennis schedule 2009-01-26
From Lorraine:
I need to create a tennis schedule. We have 8 players, but only 4 play at one time. I need to create a schedule for 34 matches, but of the 34 each player plays 17 times. Each player must also play with each of the other 7 the same number of times. For instance player 1 will play 17 times, and will play with the other players the same number of times as player 2 does. Is this even possible?
Answered by Robert Dawson.
An integral from 1 to infinity 2009-01-24
From Ray:
Determine the area bounded by the x-axis and the curve y=1/(x^2) from x=1 to x=infinity.
A. 1.00
B. infinity
C. indeterminate
D. 2.00

Answered by Harley Weston.
20 of us golf together in groups of 4 2009-01-24
From D.:
Every Sunday, 20 of us golf together in groups of 4. I am looking for a way that each of us play with 3 other people each week and ultimately get to play in groups that are unique. For instance if week 1, I play with 2, 3, 4 and then the next week I play with 5, 6, 7, and the 3rd week I play with 8, 9, 10 and so forth until I have played with everyone. Everbody else should be doing the same thing. Can you give me a schedule for this and how many weeks would it take for all of us to accomplish this where we all play with different combinations of people. (We should not play with the same person very often or even the same pairs of people but everyone should play with everybody else) I hope this makes sense........whew and thanks!
Answered by Victoria West.
Archimedes' formula for parabolic arches 2009-01-23
From La:
Use calculus to verify Archimedes' formula for y=9-x^2. Prove Archimedes' formula for a general parabolic arch.
Answered by Harley Weston.
In the shadow of a flagpole 2009-01-22
From La:
How fast is the length of the shadow of an 18 foot flagpole growing when the angle of elevation of the sun is 45 degrees and is decreasing at a rate of 10 degrees per hour?
Answered by Harley Weston.
The volume of a prism 2009-01-19
From Mady:
What is the general equation used to find the volume of a triangular prism?
Answered by Robert Dawson and Harley Weston.
Partial derivatives 2009-01-17
From Meghan:
I have a question I've been working at for a while with maxima/minima of partial derivatives.

"Postal rules require that the length + girth of a package (dimensions x, y, l) cannot exceed 84 inches in order to be mailed. Find the dimensions of the rectangular package of greatest volume that can be mailed. (84 = length + girth = l + 2x + 2y)"

Answered by Harley Weston.
A 28 week golf schedule 2009-01-17
From Don:
You have a 12 man golf schedule playing 8 weeks. Can you go further and make it a 28 week schedule. 3 foursomes. any help would be greatly appreciated.
Answered by Victoria West.
A golf trip with 12 golfers 2009-01-16
From Brad:
I am organizing a golf trip with 12 golfers. We will play 5 rounds (3 foursomes each round) total and play two 9 holes matches per round (18holes). So two matches are created within each foursome. What are the possible combinations of foursomes so that everyone plays each other at least once with the least number of repeat matches? For example: Here are the foursomes for round 1:(1,2,3,4) (5,6,7,8) (9,10,11,12) match 1 round 1: 1vs2, 3vs4, 5vs6, 7vs8, 9vs10,11vs12 we can not split foursomes up for the second match (9 hole matches): So match 2 round 1: 1vs3, 2vs4,5vs7,6vs8,9vs11,10vs12
Answered by Victoria West.
A line is perpendicular to another line 2009-01-16
From Greg:
A line is perpendicular to the line y=2x+3 and has the same x-intercept as x+3y+10. Find the equation of this line. Express your answer in the form of y=mx+b. Justify your answer.
Answered by Robert Dawson.
Multiplying negative numbers 2009-01-15
From stephanie:
hi, I'm currently working in a grade 8 class where the students are learning about integers. the students were asked to find examples of how integers are applied in real life. they were able to find aplications for: adding and subtracting both positive and negative integers. however, we could not find an example of where two negative integers would be either divided or multiplied together in real life. For example: (-2)(-4)= +8. please help.
Answered by Harley Weston.
A rectangular prism 2009-01-13
From nika:
How many bases does a rectangular prism have? What are they?
Answered by Harley Weston.
Negative rate of change 2009-01-12
From hemanshu:
when i have to find rate of change of decrease in any value my ans comes in negative why??????????
Answered by Penny Nom.
16 golfers 2009-01-11
From Bill:
I have read many of your answers to similar questions but still need your assistance. We have 16 golfers that will be playing in 4 groups of 4 each day on an upcoming golf vacation. Can you suggest the best way to scheudle the individuals assigned to each daily foursome so that we have the most diversity in foursomes throughout the vacation. I am trying to have evryone play with as many members of the group over the week with the least amount of repetition. If you would please provide it for both 6 and 7 days, since we are not sure yet how many days we will be playing.
16 golfers-playing in groups of 4 each day-6 days
16 golfers-playing in groups of 4 each day-7 days

Answered by Victoria West.
Triangular prisms and pyramids 2009-01-10
From KJ:
What are some items found in a home or school that could be considered a triangular prism or triangular pyramid?
Answered by Robert Dawson and Penny Nom.
18 golfers and 5 rounds 2009-01-10
From steve:
We have 18 golfers 5 rounds . Would like 3 foursomes and 2threesomes each day Different groups each day.
Answered by Victoria West.
What is the maximum revenue? 2009-01-09
From Kristy:
A skating rink manager finds that revenue R based on an hourly fee x for skating is represented by the function R(x) = -200x^2 + 1500x

What is the maximum revenue and what hourly fee will produce maximum revenues?

Answered by Harley Weston.
A max/min problem 2009-01-09
From Angelica:
have 400 feet of fence. Want to make a rectangular play area. What dimensions should I use to enclose the maximum possible area?
Answered by Robert Dawson.
The area of a region bounded by two curves 2009-01-07
From Rogerson:
Find the area, S, enclosed by the given curve(s) and the given line.
y = x^2 - x - 1, y = x+2

Answered by Harley Weston.
A kennel with 3 individual pens 2009-01-06
From Jean:
An animal clinic wants to construct a kennel with 3 individual pens, each with a gate 4 feet wide and an area of 90 square feet. The fencing does not include the gates. Write a function to express the fencing as a function of x. Find the dimensions for each pen, to the nearest tenth of a foot that would produce the required area of 90 square feet but would use the least fencing. What is the minimum fencing to the nearest tenth?
Answered by Harley Weston.
The area enclosed by a curve and the x-axis 2009-01-04
From Rogerson:
Find the area, S, enclosed by the curve y = -x^2 + 6x - 5 and the x-axis in the interval 0≤x≤4.
Answered by Harley Weston.
Determine y'' by implicitly differentiating twice 2009-01-04
From Walter:
Given x^3 - 3xy + y^3 = 1 , determine y'' by implicitly differentiating twice. I cannot solve this. Would you be kind enough to perform the mathematics and show the steps involved in obtaining the solution?
Answered by Harley Weston.
The area of a region in the plane 2009-01-03
From Rogerson:
Find the area, S, of the shaded region enclosed by the given cureve, the given line and the x-axis.

y = -x^2 + 1
line x = 2

Answered by Harley Weston.
24 golfers playing golf for 9 rounds 2008-12-23
From Duane:
Got 24 golfers playing golf for 9 rounds. Any formula where everyone can play with everyone else at least once. We are playing 4somes only. Thanks, Duane
Answered by Victoria West.
Pouring angles for a crucible 2008-12-20
From Richard:
I am trying to work at pouring angles and volume left in during pouring a crucible, The crucible is cylindrical and flat bottomed.

I know the diameter, radius and volume of the crucibles. and the volume of liquid going into it.

So lets say the crucible is only half full firstly I need to work out the angle just before its going to pour. ( I can work this out as long as there is a certain volume of liquid if its not enough I cant do it)

Now the problem I also need to work out how much I should tilt the crucible to allow a certain amount out and be able to do this untill the volume reaches 0 at 90' turn. This is where I am stuck.

The reason for needing to be able to work this out is so i can develop a constant flow for example 10Kg of metal per second. Thank you very much for you time

Answered by Harley Weston.
Three circular rings 2008-12-18
From seema:
three circular rings of equal radii of 1cm each are touching each other. a string runs all around the set of rings very tightly. what is the minimum length of string required to bind all the three rings ?
Answered by Robert Dawson.
Integral of cos^2 X between pi/2 and 0 2008-12-18
From Wanda:
Integral or Area of cos^2 X between pi/2 and 0.

The answer that I got is -pi/4. Is this correct? If not, how did you come up with your answer?

Answered by Robert Dawson.
The 2 rightmost digits 2008-12-18
From Peter:
Is there a pattern for the 2 rightmost digits of a power? For example, one problem for a math competition was what are the 2 rightmost digits of 3^1993?
Answered by Robert Dawson and Victoria West.
Surface area of an irregular shape 2008-12-15
From Patrick:
An irregular shaped object (lets say a gold nugget, not smooth with pockets) can have its volume determined by comparing its mass in water.

Is there any method or means or anything that could be used to determine the surface area of this shape? Whether that be theoretical mathematical formula to using a special infrared technique,etc...

The problem I foresee is that the component parts cannot be divided into smaller geometric shapes. I would propose an answer although I don't know if it is a good one: A liquid material that dries super-thin, but has a very specific and easily determined volume/mass is coated over the object. Measure the mass difference between the beginning sample of fluid and the mass after the object has been coated. Then determine the surface area of the same mass of fluid in a geometric shape. Is this feasible?

Answered by Robert Dawson.
A sphere in a can of water 2008-12-12
From Meghan:
A cylindrical can open at the top has (inside) base radius equal to 1. The height of the can is greater than 2. Imagine placing a steel sphere of radius less than 1 into the can, then pouring water into the can until the top of the sphere is just covered.

What should be the radius of the sphere so the volume of water used is as large as possible?

Answered by Harley Weston.
Golf - 24 guys 4-somes 6 rounds 2008-12-07
From Duane:
Thank you. What about 24 guys 4-somes 6 rounds everyone playing with each other at least once.

Thanks again.
Duane

Answered by Victoria West.
Gravity's Effect at a Distance 2008-12-06
From ROHAN:
AT WHAT HEIGHT FROM THE SURFACE OF EARTH,THE WEIGHT OF THE BODY BECOMES HALF? (RADIUS OF THE EARTH = 6400)
Answered by Stephen La Rocque.
6 golfers play threeball 2008-12-04
From Ian:
I have a group of 6 golfers wanting to play 3 rounds as 2x threeballs, but with different players each day. Is this possible? Can you provide some threeball combinations for this please?
Answered by Victoria West.
Six golfers 2008-11-25
From Joe:
I have a group of 6 golfers wanting to play 3 or 4 rounds but with different players each day if possible. We know we cannot make it happen without some playing with the same person. Can you provide some pairings for this?
Answered by Victoria West.
Jogging around a circular track 2008-11-19
From kim:
Joan wants to jog 10 miles on a circular track 1/4 miles in diameter. How many times must she circle the track?
Answered by Penny Nom.
Insulation in an attic 2008-11-18
From Scott:
A homeowner wishes to insulate her attic with fiberglass insulation to conserve energy. The insulation comes in 40-cm-wide rolls that are cut to fit between the rafters in the attic. If the roof is 6 m from peak to eave and the attic space is 2 m high at the peak, how long does each of the pieces of insulation need to be? Round to the nearest tenth.
Answered by Harley Weston.
A word problem about a regular pentagon 2008-11-16
From Sandra:
If the area of a regular pentagon is A=1.720a^2, in which a is one of the sides. Find the area of a regular pentagon with a side that measures 50cm.
Answered by Chris Fisher and Penny Nom.
Multiplication 2008-11-14
From natalie:
what is 8 times 30
Answered by Penny Nom.
Confusion in a multiple choice question 2008-11-14
From BJ:
My son got this math problem which he could mostly solve. Here it is:

The highest location in a certain country is 4525 m above sea level. The lowest point in the same country is 192 m below sea level.

a) Find the difference of the two elevations. His answer: a-(-b)= a+b or 4525-(-192)= 4525+192=4717 m. No problem.

b) A city is 2221 m above sea level. Is this elevation closer to the highest point or the lowest point? His answer: highest point because: 4525-2221= 2304 m (closest to the highest point) and 2221-(-192)=2221+192= 2413 m. (farthest to the lowest point). OK so far.

But then he was given 4 choices for this question with no other information:

a) 4717 m; lowest b) 4333 m; lowest c) 4333 m; highest d) 4717 m; highest

What does it mean? What's the connection with the rest of the problem?

Answered by Harley Weston.
How fast is the distance between the airplanes decreasing? 2008-11-10
From Crystal:
At a certain instant, airplane A is flying a level course at 500 mph. At the same time, airplane B is straight above airplane A and flying at the rate of 700 mph. On a course that intercepts A's course at a point C that is 4 miles from B and 2 miles from A. At the instant in question, how fast is the distance between the airplanes decreasing?
Answered by Harley Weston.
The height of an equilateral triangle 2008-11-06
From touqeer:
My question is that how can we find the height of an equilateral triangle without using pythagoras theorem?
Answered by Penny Nom.
A trig limit 2008-11-04
From Teri:
Although I have this problem completely worked out in front of me I still cannot understand how it was done. The problem is:
Find the limit.
lim x->0 sin2x/tan7x.

Answered by Harley Weston.
Separating variables 2008-11-04
From Terry:
by separating variables solve the initial value problem

(x+1)y' + y = 0 y(0) = 1

Answered by Harley Weston.
A belt drives a pulley 2008-11-03
From Rebecca:
A point on a belt is moving at the rate of 30 ft/sec and the belt drives a pulley at the rate of 200 rpm. What is the radius of the pulley?
Answered by Penny Nom.
An irregular, truncated pyramid 2008-10-24
From phillip:
Hi, I have a rectangular base to square top, pyramid shape to fabricate out of steel plate (4 sections). The base is 3000mm by 800mm, the height is 1100mm and the top is 350mm square. What I need to know is the lengths of the sides of the plate(were they meet vertically). Hope ive made it clear enough. Thanks Phil.
Answered by Stephen La Rocque.
Taxes in Taxylvania 2008-10-22
From April:
Taxylvania has a tax code that rewards charitable giving. If a person gives p% of his income to charity, that person pays (35-1.8p)% tax on the remaining money. For example, if a person gives 10% of his income to charity, he pays 17 % tax on the remaining money. If a person gives 19.44% of his income to charity, he pays no tax on the remaining money. A person does not receive a tax refund if he gives more than 19.44% of his income to charity. Count Taxula earns $27,000. What percentage of his income should he give to charity to maximize the money he has after taxes and charitable giving?
Answered by Harley Weston.
Antiderivative of 1/(x(1 - x)) 2008-10-22
From Matt:
derivative of dx/(x(1-x))

From what I've seen I should break apart the equation as such derivative of dx/x - dx/(1-x) and then get the 2 corresponding log functions.

If that is correct why does this factoring work, if that is incorrect what is the proper way to find the derivative.

Answered by Harley Weston.
I have 6 vertices and 10 edges 2008-10-20
From Jacquelin:
I have 6 vertices and 10 edges. One of my faces is a regular polygon.
Answered by Chris Fisher.
The slope of a tangent line 2008-10-18
From Amanda:
If f(x)=square root of (x+4), and the slope of the tangent line at x=21 was 1/n for some integer n, then what would you expect n to be?
Answered by Stephen La Rocque.
Two equations in two unknowns 2008-10-17
From Dushayne:
Please help me in solving this problem:
a. 3x-4y=32
5x+2y=10

b. 2x+3y=11
4x+3y=10

Answered by Penny Nom.
Perpendicular lines 2008-10-16
From Hailey:
In the xy-plane, the line with equation 2x + y = 3 is perpendicular to the line with equation y = mx + b, where m and b are constants. What is the value of m?
Answered by Penny Nom.
Concavity and the second derivative 2008-10-15
From Christina:
I'm having trouble solving for a second derivative for the following graphing question.

f(x) = (X^2+2x+4)/2x

using the quotient rule, I found:
f'(x) = (x^2-4)/(2x^2)

however, using the quotient rule again I can't seem to solve it (concavity):
f'''(x)=[(2x)(2x^2)-(x^2-4)(4x)]/[(2x^2)^2]
f''(x)=[(4x^3-(4x^3 -16x)]/4x^4
f''(x)=16x/4x^4
f''(x)=4/x^3

and making the equation equal to zero result in 0=4 which doesn't seem to make sense...

Answered by Penny Nom.
The volume of fluid in a semi circular trough 2008-10-10
From Kerry:
How do I find the volume of fluid in a semi circular trough?
Answered by Penny Nom.
Linear and Angular Velocity 2008-10-10
From Matthew:
The pedal and gear relationship of a bicycle is shown. The radii of the gears are r(sub1) = 5 cm and r(sub2)= 12 cm. The radius of the wheel is r(sub3) = 30 cm. How many rotations per minute of the pedal gear will produce a racing cyclist's speed of 60 km per hr. For a diagram: http://bikepedalsgears.weebly.com/
Answered by Stephen La Rocque.
Two modular equations 2008-10-08
From Mhiko:
please solve this Chinese remainder problem..and give me a solution or rule in order to solve this problem/

x=2mod15
x=1mod25

Answered by Stephen La Rocque.
3,6,10,15,and 21 2008-09-28
From jarred:
i am currently stumped on a math project that requires me to find out the recursive formula for a sequence of numbers. the numbers in the sequence are 3,6,10,15,and 21. Thank you for your time.
Answered by Walter Whiteley.
The region between two circles 2008-09-24
From Carol:
Good day! Here is a picture of the problem that we need to solve. (I send the picture through e-mail.) A small circle is inside a larger circle, the only given in the problem is the chord of the larger circle tangent to the smaller circle which measures 16cm. The question is, what is the area of the shaded region? Can you answer this question? Thanks! :)
Answered by Harley Weston.
An Euler diagram and a logic argument 2008-09-18
From Regina:
Use a Euler diagram to determine whether the following argument is valid or invalid.

No wizard can yodel
All lizards can yodel

No wizard is a lizard

Answered by Penny Nom.
A multiple choice exam 2008-09-13
From Phalange:
A multiple choice exam consists of 12 questions, each having 5 possible answers. To pass, you must answer at least 9 out of 12 questions correctly. What is the probability of passing if:
a. You go into the exam without knowing a thing, and have to resort to pure guessing?
b. You have studied enough so that on each question, 3 choices can be eliminated. But then you have to make a pure guess between the remaining 2 choices.
c. You have studied enough so that you know for sure the correct answer on 2 questions. For the remaining 10 questions you have to resort to pure guessing.

Answered by Harley Weston.
Perpendicular 2008-09-08
From amanda:
hi my name is amanda medjuck i am in grade 7. we are learning basic geometry terms and have to define words BUT I DONT KNOW WHAT A PERPENDICULAR LINE IS PLEASE HELP ME!!!
Answered by Penny Nom.
The biggest right circular cone that can be inscribed in a sphere 2008-09-08
From astrogirl:
find the volume of the biggest right circular cone that can be inscribed in a sphere of radius a=3
Answered by Harley Weston.
An array of tulip bulbs 2008-09-06
From Mary:
My daughter had this problem on one of her tests. She forgot to ask her teacher what she did wrong. I understand she did not answer the question in full, but what she did answer I feel is right.

Please explain to me the correct answer. Thank you. Mary

Answered by Harley Weston.
Parallel and perpendicular lines 2008-09-06
From C:
Can you help me determine whether these lines are parallel, perpendicular or neither and why?

Problem 1: y=3x+2
y=1/3x - 4

Problem 2: y=1/3x + 1/2
y=1/3 x -2

Answered by Penny Nom.
How accurate is the following calculation? 2008-09-03
From Craig:
Given that these numbers are only accurate to 2 decimal places, how accurate is the following calculation?

1.73 - 2.16 + 0.08 + 1.00 - 2.23 - 0.97 + 3.02 = 0.47

How do I work out the accuracy?

Answered by Penny Nom.
Irregular polygon and Circle that Intersects All Sides 2008-08-20
From Xetro:
Hi, Suppose you have an irregular polygon(convex or concave) with n > 3 sides. The question is - Find some circle that will cut(in limiting case - touch) all the sides of that polygon. It doesnt matter how many times it cuts the side(1 or 2), it just have to cut or touch it. How to find such a circle? or how to decide if such circle even exists? What if those segments do not form a polygon but are some arbitrary segments ? Really want to know how to do it................ Thanks a lot.. Regards, Xetro
Answered by Janice Cotcher.
Angular & Linear Speed from a Sine Graph 2008-08-19
From Kim:
Kim, a student: I am given a graph with a wave. The amplitude is 5cm and the period is 4cm. I am suppose to find the angular speed. What I need to know is the formula for angular speed and how do I use these numbers to get the correct answer.
Answered by Janice Cotcher.
A triangular field 2008-08-15
From joneka:
Barb walked five times aroun a triangle field all together she walked 435 feet the first side of the triangle fiel is 23 feet the length of the other two sides are of the same measure. What are the dimensions of the triangle field?
Answered by Penny Nom.
[f(x)-f(1)]/(x-1) 2008-08-14
From katie:
Evaluate (if possible) the function of the given value of the independent variable:

f(x)=(x^3)-x:

[f(x)-f(1)]/(x-1)

Answered by Penny Nom.
Angles in a regular tetrahedron 2008-08-07
From Carla:
Hi guys, A regular tetrahedron has all its edges 8cm in length. Find the angles which an edge makes with the base. Thanks. Carla
Answered by Penny Nom.
Find the product of 2^35 and 5^38 in sci. notation. 2008-08-03
From Peter:
I am preparing for a competition and a lot of the non-calculator problems are like find the product of 2^35 and 5^38 in sci. notation. How would you do that?
Answered by Penny Nom.
Right Sided Limit of an Exponential Function 2008-07-29
From joseph:
I am trying to find the limit as X approaches 0 from the positive side of x to the sin of x which look like this lim x^sinx x->0+
Answered by Harley Weston.
Integral of X^2 2008-07-28
From Hemanshu:
Integral of X^2
Answered by Janice Cotcher.
Simultaneous equations 2008-07-23
From Franco:
Solve

3 D + E - F = -10
-2 D - F = -4
-3 D - 4 E - F = -25

Franco

Answered by Penny Nom.
The maximum range of a projectile 2008-07-22
From kwame:
the range R of projectile fired with an initial velocity Vo ,at an angle of elevation (@ )theta from the horizontal is given by the equation R = (Vo(squared) sin2theta)/g. where g is the accelation due to gravity . Find the angle theta such that the projectile has maximum range .
Answered by Harley Weston.
A square and a circle 2008-07-20
From kobina:
4 ft of a wire is to be used to form a square and a circle. how much of the wire is to be used for the square and how much should be used for the square in order to enclose the maximum total area
Answered by Harley Weston.
multiply = 3a - 3b by a+b 2008-07-15
From chaleen:
multiply = 3a - 3b by a+b
Answered by Penny Nom.
A Falling Rock 2008-07-11
From Rita:
This question has 3 parts. If a rock falls from a height of 20 meters on the planet Jupiter, its height H (in meters) after x seconds is about H(x) = 20 - 13x^2 (a) What is the height of the rock when x = 1.2 seconds? (b) When is the height of the rock 15 meters? (c) When does the rock strike the ground? Thank you
Answered by Janice Cotcher.
A difference quotient 2008-07-10
From Rita:
Find the difference quotient of f, that is, find [f (x + h) - f (x)]/h, where h does not = 0 for the given function. Be sure to simplify.

f(x) = 1/(x + 3)

Answered by Janice Cotcher.
A dog tied to a round building 2008-07-08
From maitham:
i have this question which i don't know how to solve it :

One dog was linked to the outer wall of a building round of 20 meters in diameter. If the length of chain linking the dog sufficient turnover of half the distance around the building, What area can guard dog?

they said that we can solve it by integral .. can you solve it for me?

Answered by Harley Weston.
A rectangular room 2008-06-30
From Peter:
A rectangular room has a perimeter of 42 feet and an area of 108 square feet. What is the length, in feet, of the shorter side?
Answered by Penny Nom.
Remainders 2008-06-30
From vivek:
what is the remainder when 2050*2071*2095 is divided by 23 ? this question needs to be done in as less time as possible.
Answered by Penny Nom.
A golf tournament 2008-06-24
From Roland:
We have a golf tournament, 12 players, three rounds. We want to pair so that we have pairings with as few duplications as possible.
Answered by Janice Cotcher.
Two forces acting on a body 2008-06-21
From Rita:
Before answering the question below, what exactly is, in basic words, resultant force? QUESTION: Two forces of 50 and 68 pounds act on a body to produce a resultant force of 70 pounds. Find, to the nearest 10 minutes or nearest tenth of a degree, the angle formed between the resultant force and the smaller force.
Answered by Harley Weston.
sin(2x)/sin(3x) 2008-06-19
From matt:
how does sin2x break down (not with identities) and how would sin3x be created. My prob. is sin 2x/ sin 3x and I want to know how the double(or triple angle) would break down. I want to be able to cancel out sins. Thanks!
Answered by Harley Weston.
A line which is perpendicular to another line 2008-06-18
From Emily:
How do you solve perpendicular bisectors with a slope and a point?
Answered by Penny Nom.
Escort cards on a rectangular table 2008-06-13
From Susan:
What size rectangular table will we need to put 230- 2" X 3.5" escort cards on for my daughter's wedding reception with a spacing of .5 inch between them on all sides? Thanks so much for your help
Answered by Penny Nom.
The current in a river 2008-06-12
From Joi:
To approximate the speed of the current of a river, a circular paddle wheel with radius 4 feet is lowered into the water. If the current causes the wheel to rotate at a speed of 10 revolutions per minute, what is the speed of the current? Express your answer in miles per hour.
Answered by Harley Weston.
The rate of change in the depth of the water 2008-06-12
From Liz:
A rectangular pool 50ft long and 30ft. wide has a depth of 8 ft. for the first 20 ft. for its length and a depth of 3 ft. on the last 20ft. of its length and tapers linearly for the 10 ft in the middle of its length. the pool is being filled with water at the rate of 3ftcubed/ min at what rate is the depth of the water in the pool increasing after 15 hours?
Answered by Harley Weston.
Two circles 2008-06-10
From cey:
the diameter of the larger circle is 20cm, and the smaller 10cm. what is the shaded area??
Answered by Janice Cotcher.
How do i find the area of an irregular figure? 2008-06-10
From DAVE:
How do i find the area of an irregular figure?
Answered by Penny Nom.
A recursive formula for 9, -18, 36, -27, ... 2008-06-05
From Rita:
I am having trouble understanding how to write formulas (I should say create formulas) from a given sequence. It does not matter what sort of sequence it is. The confusion remains. I have not found a textbook or easy math book that explains this process for the average Joe to grasp. Here are the two questions:

(1) Write a recursive formula for the sequence
9, -18, 36, -72, ...

(2) Write a recursive formula for the sequence
3, 3(sqrt{3}), 9, 9(sqrt{3})

Answered by Penny Nom.
The area of a regular pentagon 2008-06-02
From Jenna:
I would like to know if there is a formula to find the area of a regular Pentagon that is not inscribed in a circle only apothem and side length are given.
Answered by Penny Nom.
The length of a shadow 2008-05-27
From Simon:
A figure skater is directly beneath a spotlight 10 m above the ice. IF she skates away from the light at a rate of 6m/s and the spot follows her, how fast is her shadow's head moving when she is 8m from her starting point? The skater is (almost) 1.6m tall with her skates on.
Answered by Stephen La Rocque and Harley Weston.
A season schedule for 9 teams 2008-05-22
From James:
would like to put together a season schedule for 9 teams with each team playing three or 4 games leading to a 1 to 9 ranking.
Answered by Victoria West.
The angles of an irregular pentagon 2008-05-20
From victoria:
The sum of the measure of two angles is 240. If the remaining angles are congruent, what is the measure of each angle?
Answered by Penny Nom.
The weight of a concrete column 2008-05-11
From russell:
a cylindrical form is filled with a slow curing concrete. The base of the form is 10 ft in radius, and height is 25 ft. while the concrete hardens, gravity causes the density to vary from a density of 90 lbs/ft^3 at the bottom to a density of 50 lb/ft^3 at the top. Assume that the density varies linearly from the top to the bottom, and compute the total weight of the resulting concrete column
Answered by Harley Weston.
A linear model 2008-05-09
From Shelby:
How would you write a linear model to represent the population of a city that has a population of 547,725 and a growth rate of -25,195 per year with t represents the number of years since 1994?
Answered by Penny Nom.
How do you reduce an equation with multiple variables? 2008-04-30
From Jonathon:
How do you reduce an equation with multiple variables?

For example, if 3x + y = k(x-3), what would x be equal to?

Answered by Penny Nom.
A bowl is the shape of a hemisphere 2008-04-28
From josh:
a bowl is the shape of a hemisphere with diameter 30 cm and water is poured into the bowl to a height h cm. how do i find the volume of the water in the bowl
Answered by Harley Weston.
A lidless box with square ends 2008-04-28
From Chris:
A lidless box with square ends is to be made from a thin sheet of metal. Determine the least area of the metal for which the volume of the box is 3.5m^3. I did this question and my answer is 11.08m^2 is this correct? If no can you show how you got the correct answer.
Answered by Stephen La Rocque and Harley Weston.
An octagonal prism 2008-04-27
From Melanie:
My son is identifying geometric shapes in the real world? We are stuck on octagonal prism, rectangular prism and square prism. Can you help me out with some examples. Thanks
Answered by Penny Nom.
At what value of t is the maximum acceleration? 2008-04-25
From Mary:
Velocity of a function (which is the first derivative of its position) is defined over the interval 0 to 12 using the following piecewise function: v(t)=-1 from 0 to 4, v(t)=x-5 from (4 to 8 and v(t)=-x+11 from (8 to 12. At what value of t is the maximum acceleration?
Answered by Stephen La Rocque.
An irregular tetrahedron 2008-04-24
From RAUL:
I am looking an expression for an edge length as function of the other five edge lengths of irregular tetrahedron.
Answered by Walter Whiteley.
A volume of revolution 2008-04-24
From Sabahat:
Hi, i have a region enclosed by both axes, the line x=2 and the curve y=1/8 x2 + 2 is rotated about the y-axis to form a solid . How can i find the volume of this solid?. (Please note that y equation is read as y =1 over 8 times x square plus 2.) I will be really grateful if you answer this question. :)
Answered by Harley Weston.
An open box 2008-04-23
From Le:
Metal Fabrication; If an open box is made from a tin sheet 8 in square by cutting out identical squares from each corner and bending up the resulting flaps, determine the dimensions of the largest box that can be made.
Answered by Harley Weston.
What is the integral of 13sin^3(x)*cos^7(x)dx? 2008-04-22
From Cathrine:
I am having trouble integrating this problem. It says to evaluate the integral but I don't know what to do or how to do it.

It is the integral of
13sin^3(x)*cos^7(x)d

Answered by Harley Weston.
f(x)=sin^3(3x^2) find f ' (x) 2008-04-21
From Michael:
f(x)=sin^3(3x^2) find f ' (x)
Answered by Harley Weston.
A solid figure with 3 rectangular faces and 2 triangular faces 2008-04-17
From Emily:
I am in the 3rd grade and my teacher gave us a question. What is a solid figure with 3 rectangular faces and 2 triangular faces?
Answered by Penny Nom.
The area bounded by 3 curves 2008-04-13
From Sabahat:
Hi, I have enclosed a diagram.
The diagram shows the curve y=(2x-5)4. The point P has co-ordinates (4,81) and the tangent to the curve at P meets the x-axis at Q.

Find the area of the region (shaded in the diagram) enclosed between the curve, PQ and the x-axis . (Please note that the equation y is read as y=2x -5 whole raise to power 4.)

Answered by Stephen La Rocque.
f(x) =ax^blnx 2008-04-13
From charles:
supposef(x) =ax^blnx is a real- valued function. Determine exact values(not decimal approximations) fro nonzero constants a and b so that the function f has a critical point at x=e^3 and a maximum value of 1/2e
Answered by Harley Weston.
The chain rule 2008-04-10
From joey:
pls help me to Differentiate
y=(3x^2-4x)^8

Answered by Harley Weston.
A regular polygon 2008-04-09
From chase:
name the regular polygon if the sum of the measures of the polygon is 1,440 and the measure of one angle is 144
Answered by Stephen La Rocque.
Side lengths and angles in a regular octagon 2008-04-09
From Lori:
I am a builder and need to find the length of the sides of an octagon. I know the length between the parallel sides (26 feet). What is the length of each side? What is the angle measurement?
Answered by Harley Weston.
Matrix multiplication 2008-04-08
From manashi:
i. why matrix division is not possible?
ii.when we add or subtract two matrix , getting the result by addind or subtracting correspondind elements....but in case of multiplication it is not but why?

Answered by Harley Weston.
How many bags of mulch? 2008-04-07
From MJ:
I have an area that is 35' X 50' and I want to cover it with 2" of mulch.

Do I take length X Width X depth? Bags of mulch are sold in 2 or 3 cubic feet per bag.....I just want to know how to do the math. can you please send me the equation?

Answered by Penny Nom.
What fraction of 45 is 10? 2008-04-06
From Scott:
45 x fraction? = 10
Answered by Penny Nom.
1-(1-P)^75=0.05 2008-04-05
From Amy:
1-(1-P)^75=0.05
Answered by Stephen La Rocque and Penny Nom.
A volume of revolution 2008-04-04
From ted:
Consider the region bounded by y=x^2 + 1, y=5-3x and y=5. Sketch and shade the given region; then set up but dont evaluate teh integrals to find the following:

a) The volume of the solid generated by rotating the region about the line y=5

b) the volume of the solid generated by rotating the region about the y-axis

Answered by Penny Nom.
lim as x approaches infinite of 5x + 2/x-1 2008-04-04
From Jordan:
how to solve this.

lim as x approaches infinite of 5x + 2/x-1

Answered by Stephen La Rocque and Harley Weston.
A shape 2008-04-03
From Joshua:
what shape has 4 faces, 4 corners and 9 edges.
Answered by Penny Nom.
The integral of dx / (4x^2 - 25)^3/2 2008-04-01
From Meghan:
I have a question from the trigonometric substitution of my calculus course.

integral of dx / (4x^2 - 25)^3/2

Answered by Harley Weston.
A rectangular prism 2008-03-31
From Chanlie:
i need need to find a rectangular prism with a total surface area of 210 units.
Answered by Penny Nom.
2 times 0 times 0 times 4 2008-03-30
From ben:
what is 2 times 0 times 0 times 4?
Answered by Penny Nom.
A fish tank in the shape of an irregular pentagon 2008-03-29
From richie:
i am building a fish tank. it is going to be an irregular pentagon. the sides are going to be
24"
24"
8"
8"
32"(approximately)

there will 3 right angles A, B, E

my question is how to figure out the degree of the angles that are not right angles (C,D)?

Answered by Chris Fisher.
A max-min problem 2008-03-27
From LSL:
show that of all rectangle with a given area, the square has the smallest perimeter.
Answered by Penny Nom.
A hydraulic cylinder 2008-03-24
From james:
I am trying to adjust the placement of a hydraulic cylinder that raises a dump bed up from the frame of a truck. How long would the cylinder (height of a triangle) have to be to raise the bed to a 70 degree angle? The base from pivot to cylinder is 132.5 inches.
Answered by Stephen La Rocque.
A train and a boat 2008-03-15
From Sabrina:
A railroad bridge is 20m above, and at right angles to, a river. A person in a train travelling at 60 km/h passes over the centre of the bridge at the same instant that a person in a motorboat travelling at 20km/h passes under the centre of the bridge. How fast are the two people separating 10s later?
Answered by Harley Weston.
Repeating decimals 2008-03-10
From Blaine:
Is it possible to put a repeating decimal number into a calculator to solve a problem?

EX: Write 39.3939... as a fraction.

Answered by Penny Nom.
The volume of a countertop 2008-03-08
From Matthew:
I need to calculate volume down to cubic feet. I pour concrete countertops and cant figure out the formula to convert inches and feet. If I have a 2.5 inch by 2 foot by 16 foot concrete countertop how do I convert it to cubic feet and hence know how many bags of concrete at .6 cubic feet per bag I will need. I am trying to input the formula into a spreadsheet. thank you so much Matt
Answered by Penny Nom.
Two perpendicular lines 2008-03-07
From Daphne:
Does anyone know how to find a line perpendicular to -3x=4y=20 and passes through the point (-12,0)?
Answered by Stephen La Rocque and Penny Nom.
A 6 pointed star 2008-03-04
From Siddharth:
When 2 congruent equilateral triangles share a common center, their union can be a star If their overlap is a regular hexagon with an area of 60, what is the area of one of the original equilateral triangles?

a) 60 b) 70 c) 80 d)90 e)100

Answered by Stephen La Rocque.
Triangular prisms and pyramids 2008-03-03
From LORENA:
hi i am in yr 6 and i need to know how many faces,vertices and edges these shapes have..
. TRIANGULAR PYRAMID
. TRIANGULAR PRISM

Answered by Penny Nom.
What point on the graph y = e^x is closest to the origin? 2008-03-03
From elvina:
What point on the graph y = e^x is closest to the origin? Justify your answer.
Answered by Stephen La Rocque.
Simultaneous equations 2008-02-29
From CONOR:
I was wondering if you could help me with this problem

7x - 5y = -1
3y = 4x

Answered by Penny Nom.
A Norman window 2008-02-25
From Jason:
If the perimeter of a Norman window is 20 feet, what is the maximum area of the window?
Answered by Stephen La Rocque.
A ball bearing is placed on an inclined plane 2008-02-15
From Leah:
A ball bearing is placed on an inclined plane and begins to roll. The angle of elevation of the plane is x. The distance (in meters) that the ball bearing rolls in t seconds is s(t) = 4.9(sin x)t^2. What is the speed of the ball bearing, and what value of x will produce the maximum speed at a particular time?
Answered by Penny Nom.
Two regions with equal area 2008-02-13
From James:
There is a line through the origin that divides the region bounded by the parabola y=3x-5x^2 and the x-axis into two regions with equal area. What is the slope of that line?
Answered by Harley Weston.
A square and an equilateral triangle 2008-02-10
From Emily:
A square pen and a pen shaped like an equilateral triangle have equal perimeters. Find the length of the sides of each pen if the sides of the triangular pen are fifteen less than twice a side of the square pen.
Answered by Stephen La Rocque.
Radians 2008-02-08
From Brian:
I'm teaching Precalculus right now and will be covering the formula to convert angular speed into linear speed. My question is about the units involved. Using v=rw, if r is mearsured in feet and w is measured in radians/second then v is measured in ft/sec. What happened to the units of radians? I can't find a good way to explain why they are not part of units for velocity. Do you have a good explanation? Thanks,
Answered by Stephen La Rocque.
Multiplying decimal numbers 2008-02-05
From alwyn:
Why should when you Multiplying Decimal numbers is value becoming less and less? don't you think even decimal number is a quantity and in no chance when it multiplies its should become less or nil !!!

In fact all Multiplying and or adding the value will go up and only when you subtract and divide it should become less !!

Answered by Stephen La Rocque and Penny Nom.
The radius of a circular arc 2008-02-04
From Bill:
Hi,the Central Angle of a sector of a circle is 40 degrees. The circular arc of the curve has a chord length of 3000 ft. Find the radius(r) of the circular arc.
Answered by Penny Nom.
Numbers and Operations 2008-02-02
From Charlotte:
On the TABE (Test for Adult Basic Education) test, one of the categories is number operation. I would like to know what consist of number operation.
Answered by Penny Nom.
Integration by parts 2008-01-30
From seth:
hi i really dont understand integr ation by parts. for example, the integral(t^2sintdt. i have u=t^2 and v'=sint also u'=t^/3 v=-cost for the formula i have uv-integralvu' dx this is all well and good but i cant get it right.
Answered by Harley Weston.
Angle of Elevation 2008-01-29
From Rita:
Uluru or Ayers Rock is a sacred place for Aborigines of the western desert of Australia. Chun-Wei uses a surveying device to measure the angle of elevation to the top of the rock to be 11.5 degrees. He walks half a mile closer and measures the angle of elevation to be 23.9 degrees. How high is Ayers Rock in feet?
Answered by Stephen La Rocque.
Inflection points 2008-01-25
From Armando:
Hi, Im trying to write a program that takes an equation ( f(x) = 0 ) and returns a list of the inflexion points in a given interval. there must be (I think) a mathematical method or algorithm to do this, probably involving the (second) derivate of the function. However I have not found such a method yet. Any help on this will be much appreciated.
Answered by Stephen La Rocque and Harley Weston.
Maximize income 2008-01-18
From Chris:
Lemon Motors have been selling an average of 60 new cars per month at $800 over the factory price. They are considering an increase in this markup. A marketing survey indicates that for every $20 increase, they will sell 1 less car per month. What should their new markup be in order to maximize income?
Answered by Stephen La Rocque and Harley Weston.
A large concrete shape 2008-01-16
From Keith:
what is the cubic yards of an area that is not a perfect 1/4 circle? The dimensions are 100ft. x 60ft. x 125ft. curcumferal arch x 3ft. depth?
Answered by Stephen La Rocque.
Fact families with multiplication and division 2008-01-16
From Donna:
I am trying to help my granddaughter with some math homework. I looked at what you have on fact families. Am I correct to assume that the same process applies to multiplication and division as well? Her question asks for fact families for 2, 8, & 16.
Answered by Penny Nom.
Balancing on a fulcrum (net torque and equilbrium) 2008-01-15
From Eric:
If I have a 4" bar that has no weight value with a 275lb. weight on one side and a 125lb. weight on the other side what would be the folcrum point? Please keep the answer very simple. Also is there a fixed equation to figure folcrum points? Is there an equation for if the 4" bar had a weight value?
Answered by Stephen La Rocque.
Multiplying numbers in bases other than 10 2008-01-08
From Imaiya:
In class we've been learning about numbers with a base other than ten. For example, base 7, base 5, and base 6. What's really stumping me is how to multiply these numbers, when they aren't a base of 10. I've had it explained to me once, but don't seem to understand it. Here are the equations, and I've listed the first few numbers for that particular base.

Base 5: 0,1,2,3,4,10,11,12,13,14,20 etc... The Equation: 34 x 42 Base 9: 1,2,3,4,5,6,7,8,10,11,12,13,14, etc... The Equation: 56 x 78

If you could explain to me how to multiply numbers with any type of base, I'd really appreaciate it. Also if you could show me how to do one of the questions that I listed, that would really help me =) Thanks so much, and once again, thank you for your great site!

Answered by Stephen La Rocque.
The area of a piece of property 2008-01-05
From Greg:
I need to know the area of a six sided piece of property. I sent a map by regular mail.
Answered by Harley Weston.
The surface area of the rectangular solid 2007-12-30
From Sara:
For my math homework i found the volume of a rectangular solid whose deminsions were in feet and the numbers were 10 by 20 by 30
10 = hight
20 = short side base
30 = long side base
and now i have to find the surface area of the rectangular solid....
i know how to do this but i can't get the right answer it should be 2,200 ft squared but i keep getting 13,00 feet squared

Answered by Penny Nom.
The integral of 1/ (x(x+1)^0.5) 2007-12-29
From Nooruddin:
Integral of
dx / x(x+1)^0.5
(boundaries are 5 and 3)

Answered by Harley Weston.
The standard normal distribution 2007-12-29
From GEORGE:
Statistics texts state that in a normal distribution, 1 standard deviation covers 68%, 2SD 95% 3SD 99.7%. However, on looking at the tables for normal curve areas, the percentage for a z value of 1 is 84.13. 68 % of values are covered at a z value of 0.47. The discrepancies exist even for other values but are smaller. So why is the rule of thumb so different from the Table for Normal Curve areas?
Answered by Harley Weston.
The centroid of a polygon 2007-12-29
From David:
I am playing around with an idea. I've read previous answers to questions (using surveyor calculation methods) related to finding the area of an irregular shape parcel of land (or irregular polygon). Is there a formula or method for calculating the centroid (mid-point) for this type of polygon. I've seen plenty of methods for calculating the mid-point for a triangle or regular shape poloygon but few for an irregular shape polygon such as a parcel of land. Thanks...
Answered by Harley Weston.
Differentiate 2007-12-28
From taiwo:
i am finding it difficult to use first principle to differentiate this question: y=xcos2x. can u help me.
Answered by Penny Nom.
An irregular octagon 2007-12-23
From Sheldon:
I am attempting to construct an irregular octagon picture frame out of bamboo. The bamboo is 1" in diameter and the opening should be 20" H X 16"W.
What measurements should be used?

Answered by Penny Nom.
lim sinx/(x +tanx) 2007-12-16
From shimelis:
i have problem how do you solve this equation lim sinx/(x +tanx)
Answered by Harley Weston.
Shooting an arrow over a wall 2007-12-11
From Amy:
The path of a large arrow fired from a non torsion catapult can be modeled by y=-0.0044x^2 + 1.68x, where x is the distance the arrow travelled (in yards) and y is the height of the arrow (in yards). Given the height of a castle wall, find the safest distance from the wall to launch an arrow over a 120 yard-high wall.
Answered by Victoria West and Stephen La Rocque.
Polygons 2007-12-09
From Nicholle:
a polygon with all sides the same length and all angles the same measure is called a ---- polygon.

What word goes in the blank.

Answered by Penny Nom.
LCM over 100 2007-12-09
From Aris:
A teacher has more than 100 sweets. She thinks that if she give 6, 8 or 9 sweets to her students she will have no remaining in the case. What is the smallest number of sweets in the bag?
Answered by Stephen La Rocque.
System of equations 2007-12-06
From Jenn:
change the equation,x-y=4 to form y=mx+b the solution to the system of equations y=2x and y=-x+3 is
Answered by Stephen La Rocque.
Chicken and goat feet 2007-12-05
From Kim:
Old McDonald raises goats and chickens. The animals have a total of 100 heads adn 360 feet. How many goats and how many chickens does Mr. McDonald have?
Answered by Stephen La Rocque and Penny Nom.
Proving a quadrilateral is a rhombus 2007-12-03
From Jeanie:
How do you prove that a quadrilateral is a rhombus because the diagonals of the quadrilateral are perpendicular and bisect each other using the 2-column proof method?
Answered by Stephen La Rocque.
An arched entry 2007-11-28
From amber:
i am working with an arched entry. i know that the radius is 25' and the height is 20'-11". i need to know the length of the arch and degree of bend of the arch. how do i find these?
Answered by Stephen La Rocque.
Maximize the product 2007-11-25
From David:
Hi i have this site call calcchat.com, but i dont understand how they explained this can you take a look? The question is: Direction: Find two positive numbers that satisfy the given requirements. The sum is S and the product is a maximum this is what they did 1) Let x and y be two positive numbers such that x + y = S 2)P = xy 3) = x (S - x) 4) =Sx - x^2 5)...etc. the thing i dont get is how did they go from step 2 to step 3 and also i know this sound dumb but how did they get step 2? =)
Answered by Harley Weston.
A rectangular plot of farmland 2007-11-25
From Christy:
A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a single-strand electric fence. With 800m of wire at your disposal, what is the largest area you can enclose, and what are its dimensions?
Answered by Harley Weston.
A curve sketch 2007-11-22
From Ahson:
Find critical points, determine the monotonicity and concavity and sketch a graph of f(x) with any local maximum, local minimum and inflection points labeled:

1. f(x) = x^4 - x^3 - 3x^2 + 1

Answered by Harley Weston.
Area of a 17-sided lot 2007-11-21
From Lynda:
My uncle is wanting to buy this piece of land [a 17-sided polygon] but we are questioning the acerage total. the measurements are [on the attached diagram].
Answered by Stephen La Rocque.
The derivative 2007-11-19
From ralf:
Find the derivative of the function
1-. y=1+2x8
2-. y=(1+2x )8

Answered by Harley Weston.
A rectangle in an ellipse 2007-11-18
From David:
I need to find the max area of a rectangle inscribed in an ellipse with the equation x^2+4y^2=4.. What I have so far is f(x,y)=4xy g(x,y)=x^2+4y^2-4=0,

y=sqrtx^2-4/4 f'(x)=2x^2/sqrt-4x^2+2(sqrt-4+x^2).

What I need to know is how to finish the problem and find the actual mas area of the rectangle. David

Answered by Penny Nom.
lim [x + squareroot(x^2 + 3)] as x->-inf 2007-11-16
From David:
Find the limit. (Hint: treat the expression as a fraction whose denominator is 1, and rationalize the numerator.)

lim [x + squareroot(x^2 + 3)] as x->-inf

i got to

lim -3/(x - squareroot(x^2 + 3)) as x->-inf

but i'm having trouble understanding why the answer is 0 plz explain thx

Answered by Harley Weston.
A rectangular prism 2007-11-16
From nicholas:
What is the height the surface area to a rectangular prism with a volume of 350 milliliters?
Answered by Stephen La Rocque.
A limit of the form 0 times infinity 2007-11-13
From Russell:
find the following limit

lim x((e^1/x) -1) as x --> infinity

Answered by Penny Nom.
Radial motion 2007-11-13
From abdulai:
a circular saw with diameter 18.4cm rotates at 2400rpm. What is the angular speed of a point on the edge of the saw blade in radians per second?
Answered by Penny Nom.
Local maxima, minima and inflection points 2007-11-13
From Russell:
let f(x) = x^3 - 3a^2^ x +2a^4 with a parameter a > 1.

Find the coordinates of local minimum and local maximum

Find the coordinates of the inflection points

Answered by Harley Weston.
Maximize his profit 2007-11-12
From apoorva:
During the summer months Terry makes and sells necklaces on the beach. Last summer he sold the necklaces for $10 each and his sales averaged 20 per day. When he increased the price by $1, he found that he lost two sales per day.

a. Find the demand function, assuming it is linear.
b. If the material for each necklace costs Terry $6, what should the selling price be to maximize his profit?

Answered by Penny Nom.
Family of functions 2007-11-12
From Russell:
Consider the family of functions
f(t)= Asin3t + Acos3t +Bsin8t + Bcos8t

find exact values of parameters A and B so that f(0) = 2 and f ' (0) = 1

Answered by Stephen La Rocque.
6 consecutive multiples of 6 2007-11-11
From jeff:
find 6 consecutive multiples of 6 whose sum is the least common multiple of 13 and 18
Answered by Penny Nom.
Two integrals 2007-11-09
From Akilan:
how to integrate these (tan x)^6(sec x)^4 and sinh(x)(cosh(x))^2.

Please send me how to do this question. Having exams on Monday. Please help.

Answered by Harley Weston.
Increasing and decreasing for functions 2007-11-09
From David:
Direction: Identify the open intervals on which the function is increasing or decreasing.

f(x)=1/(x^2)
f'(x)= -2/(x^3)

i understand how to get up until there, and the undf. is x=0, but now i'm having problem setting up the number table chart. i cant remember how, and where to place the increase and decrease + - the chart, for example <---------0----------> where would the increase and the decrease be place?

Answered by Harley Weston.
The height of a triangle 2007-11-03
From William:
I need to find the height of a triangle if the base is 15, one side is 14 and the other side is 13.
Answered by Stephen La Rocque and Penny Nom.
f(x+y) = f(x) + f(y) + 2xy 2007-11-01
From Marcia:
For all real numbers x and y, let f be a function such that f(x+y) = f(x) + f(y) + 2xy and such that the limit as h -> 0 of f(h) / h = 7, find: f(0), use the definition of the derivative to find f'(x), and find f(x).
Answered by Penny Nom.
A circular table is pushed into the corner 2007-10-31
From Will:
A circular table is pushed into the corner of a square room so that one point is 8 inches from one wall and 9 inches from the other. What is the radius of the table?
Answered by Penny Nom.
How to solve related rates problems 2007-10-27
From David:
Can you plz explain how and where you come up with an equation to solve this?
Find the rate of change of the distance between the origin and a moving point on the graph of y = sin x if dx/dt = 2 centimeters per second.

Answered by Stephen La Rocque.
Area of a triangle formed by three points on a graph 2007-10-26
From Betty:
My question is 'find the are of a triangle whose vertices have coordinates (3,5),(6,-5), and (-4,10)
Answered by Stephen La Rocque.
The volume of a regular octagonal prism 2007-10-20
From Chris:
I am trying to figure out the volume of a regular octagonal prism, with side lengths of 4 inches. How do I do this?
Answered by Penny Nom.
A triangular lot 2007-10-17
From Brian:
Seeking the square footage of a triangular property lot, dimensions are: 620 X 620X 720.
Answered by Penny Nom and Melanie Tyrer.
5x + 9 = 3x + 7 2007-10-16
From kristina:
hi im kristina and i cannot figure out how 2 do these multi-step equations

5x + 9 = 3x + 7 i can on getting the wrong answer according 2 the book

Answered by Penny Nom.
lim x->1 (root x - x^2)/{1 - root x) 2007-10-16
From Meghan:
Hi! I have a question from my Calculus textbook that I've been picking at for a while and I'm stuck.

lim x->1 (root x - x^2)/{1 - root x).

Answered by Stephen La Rocque and Penny Nom.
Four triangles in a square 2007-10-15
From Kristina:
A square with side lengths of 6 cm is divided into 3 right triangles and a larger isosceles triangle. If the three right triangles have equal area, find the exact area of the isosceles triangle.
Answered by Stephen La Rocque.
lim (1- 2 cosx) / (sin(x- pi/3)) 2007-10-15
From hanan:
lim (1- 2 cosx) / (sin(x- л/3))
Answered by Harley Weston.
Working with x 2007-10-12
From Robert:
The question: The measure of an exterior angle of a regular polygon is given. Find the measure of an interior angle, and find the sides.
41. 36
42. 18
44. 'X'

The attachment has what she has done for 41 and 42. Need help with 44 (lots of help) Thank you in advance for your site and your help. Robert

Answered by Penny Nom.
13 year and 17 year locusts 2007-10-12
From stefan:
how many years pass between the years when both 13 year and 17 year locusts are out at the same time?
Answered by Penny Nom.
A dinner club schedule 2007-10-12
From irv:
The problem is that I have 12 couples, 1 through 12, in a dinner club, and each couple is host once with 3 of the other couples. he dinners will take place over 4 months. I am trying to not repeat any of the couples. We had the formula for 16 and 20 couples but not for 12. Are you able to help with the groupings for 12. Thanks very much. Irv
Answered by Victoria West.
A 9 team league 2007-10-11
From Dary:
I have a 9 team pool league. Each team must play each other once only. But 2 teams cannot play at the same place location each week. I can't seem to match this up and I get stuck.
Answered by Victoria West.
The average rate of change of a function 2007-10-11
From vern:
Find the average rate of change of the function over the given interval. Compare this average rate of change with the instantaneous rates of change at the endpoints of the interval. f(X)=sinX for the inverval [0,pi/6]?
Answered by Harley Weston.
Substitution method 2007-10-11
From Kevin:
3xx+2y=-36-y=11
Answered by Stephen La Rocque.
Coin jar 2007-10-07
From a student:
Sally empties his jar of coins. It contains $3.75 in nickels, dimes, and quarters. The number of dimes is twice the number of nickels and the number of quarters is three less than the number of nickels. Determine how many nickels, dimes, and quarters were in the in the jar.
Answered by Stephen La Rocque.
Solving four simultaneous equations (system of four linear equations) 2007-10-07
From Johan:
I need some help in solving this question
x + 2y - 3z + 4w = 12
2x + 2y - 2z + 3w = 10
0 + y + z + 0 = -1
x - y + z - 2w = -4

Answered by Stephen La Rocque.
Triangle perimeter and area 2007-10-05
From divakar:
The sides of the triangle are integers. The perimeter is 8. What is the area?
Answered by Stephen La Rocque.
Golf pairings 2007-10-02
From Mike:
Regarding arranging golf players so no person plays with anyone more than once. You have given examples for 16 and 24 players. If it can be done, i need a solution for 20 players, 4 players per team one round per day for 5 days
Answered by Victoria West.
Equation of a circle circumscribing a triangle with given vertices 2007-10-01
From Randy:
How do I determine the equation of a circle when it is circumscribed by a triangle whose vertices are (-1, 6), (3, -2), and (2, 5)?
Answered by Stephen La Rocque.
y squared over 3 times 8 over y 2007-09-30
From John:
y squared over 3 times 8 over y
Answered by Stephen La Rocque.
Sample variance and population variance 2007-09-22
From Willy:
I have a question in sample variance and population
my name is Willy
the question in the attached file...

Answered by Harley Weston.
Finding equations, intersection point of two lines at right angles 2007-09-22
From Yaz:
Find the equation of the line joining A(-1,-9) to B(6,120). Another line passes through C(7,-5) and meets AB at rigth angle of D. Find the euation of CD and calculate the co-ordinates of D.
Answered by Stephen La Rocque.
Least Common Multiples 2007-09-20
From Aiyanna:
What is The Lcm Of 3,7,and 8 Because my Teacher gave me That and he didnt even know the answer.... I Worked and worked but I Couldnt Find It.....
Answered by Penny Nom and Victoria West.
The perimeter of a regular polygon 2007-09-18
From Ashwynn:
why does the area of regular polygons with a perimeter of 1000m increase as the number of sides increase?
Answered by Stephen La Rocque.
An irregular lot 2007-09-12
From Jay:
How do I calculate the area of the following Lot?
N 15 degrees 1 minute 22 seconds E for 182.2 feet
S 89 degrees 46 minutes 26 seconds E for 218.4 feet
N 51 degrees 16 minutes 21 seconds E for for 307.1 feet
L= 31.63 feet with a radius of 50 feet

There is a discrepancy between county records and what the landowner is telling me

Answered by Stephen la rocque and Harley Weston.
Perpendicular lines 2007-09-06
From dinesh:
we know that for two perpendicular lines m1*m2=-1perpendicular but this is not true for x-axis and y-axis?
Answered by Harley Weston.
The area of a circle knowing only the length of a chord 2007-09-05
From James:
I need some help in the right directions with a problem. I was presented with a problem where I need to find the area of a circle knowing only the length of a chord.

the is a circle in the center of a larger circle (which the size of either could change) the only thing that matter is that the chord is 100 ft long and rests on top of the smaller circle.

Answered by Stephen la Rocque and Brennan Yaremko.
The tangent to y = x^3 at x = 0 2007-09-04
From Amit:
consider the equation = x^3. The equation of tangent to this curve (which is smmetrical in Ist and IVth quadrant) at (0,0) is y=0, which is x-axis. but graphically one can visulize that x-axis intersects the curve, so how can it be the tangent to the curve. Please help.
Answered by Harley Weston.
Is there a way I can calculate correct square footage for odd shapes? 2007-08-31
From Tom:
I manage a golf course, and we are about to over seed the course for the upcoming winter months. We will be over seeding all greens, fairways, and tee boxes. Noone of the area that we will be placing seed on is a regular shape. The closest shapes they would be is a circle, rectangle or square, but most of them are all odd CURVED shapes. I know what the equation is for Square ft., and I know how many Square ft. are in an acre, but I need to be precise with the amount of seed I order. Is there a way I can calculate correct square footage for odd shapes.
Answered by Harley Weston.
Can you solve this by factoring? 10r^2 - 35r = 10 2007-08-12
From Aranxa:
how do u solve this equation by factoring:
10r^2 - 35r = 10

Answered by Stephen La Rocque.
Angular speed 2007-08-05
From Virginia:
the engine of a sports car rotates at 5,000 revolutions per minute (rpm). calculate the angular speed of the engine in radians per second. use 2n radians = 1 revolution
Answered by Stephen La Rocque.
All five angles of a pentagon ABCDE are equal 2007-08-04
From Jerry:
All five angles of a pentagon ABCDE are equal. The diagonals AC, AD and BD have the same length. Prove that all five sides of the pentagon are equal in length.
Answered by Penny Nom.
Using the chain rule to solve a derivative 2007-07-29
From Charles:
I need to find the derivative fo the following function.   _______________________
\/ ______________
  \/ (x - 1) / (x + 2) + 1

Answered by Stephen La Rocque.
Equation of a perpendicular line 2007-07-28
From Marina:
Find the equation, is standard form, with all integers coefficients, of the line perpendicular to x+3y=6 and passing through (-3,5)
Answered by Stephen La Rocque.
Multiplcation of two negative numbers 2007-07-26
From Brett:
Someone asked a question about multiplication and division of two negative numbers yielding a positive result here: http://mathcentral.uregina.ca/qq/database/QQ.09.99/butler1.html I was not fully happy with the explanation b/c I want to give me daughter a real-world example and I can't seem to find one.

The following illustrates why multiplying negative numbers has become difficult to explain:

2 X 2 = 4

----(-4)---(-2)---0---2---4
In this example we start with 2 and then want 2 more of them. When we move across the number line from 2 to our answer, which is four, we have moved only 2 units to the right.

-2 X -2 = 4

----(-4)---(-2)---0---2---4
In this example we start with -2 and then want -2 more of them. When we move across the number line from -2 to our answer, which is four, we have moved 6 units to the right.

How can the phenomenon of multiplying two negative numbers being more powerful than multiplying two positive numbers be explained? -Brett

Answered by Stephen La Rocque and Harley Weston.
Guessing multiple choice answers 2007-07-24
From carla:
You are taking a multiple choice quiz that consist in 3 questions, each question has 3 possible answers only one is correct. To complete the quiz you randomly guess the answer to each question . Find the probability of guessing exactly 2 answer correctly. b) at least to answer correctly . c)less than two answer correctly
Answered by Stephen La Rocque.
A complex number in polar form 2007-07-23
From roland:
write the given complex number z in polar form lzl(p+qi) where lp + qil=1 for 3 - 4i.
Answered by Harley Weston.
f(x) = (x^4) - 4x^3 2007-07-22
From Michael:
I'm a student who needs your help. I hope you'll be able to answer my question. Here it is: Given the function f(x)=(x^4)-4x^3, determine the intervals over which the function is increasing, decreasing or constant. Find all zeros of f(x) and indicate any relative minimum and maximum values of the function.
Any help would be appreciated. Thank you for your time.

Answered by Harley Weston.
A triangular trough 2007-07-19
From janine:
A trough is formed by nailing together, edge to edge, two boards 11 ft. in length, so that the right section is a right triangle. If a 15 gallon of water are poured into the trough and if the trough is held level so that a right section of water is an isosceles right triangle, how deep is the water? (231cu.in=1 gal.)
Answered by Penny Nom.
Fractions of fractions 2007-07-18
From Bridget:
Sam and Mary each owned one-half stock in a printing company. Sam sold 2/3 of his stock to Mary. What fractional part of the printing business does Mary now own?
Answered by Penny Nom.
Calculating the area (acreage) of a four sided lot 2007-07-18
From A property owner:
I have a real estate property and the lot size is something I need to find out. I know the lengths of the four sides, but it isn't a rectangle, it is an odd shape. How do I find the acreage?
Answered by Stephen La Rocque.
The area of a triangular pyramid 2007-07-18
From Jhezelle:
What is the formula of finding the surface area of a triangular pyramid?
Answered by Penny Nom.
A normal to a curve 2007-07-16
From Samantha:
The function f is defined by f:x --> -0.5x^2 + 2x + 2.5
Let N be the normal to the curve at the point where the graph intercepts the y-axis. Show that the equation of N may be written as y = -0.5x + 2.5.
Let g:x--> -0.5x + 2.5
(i) find the solutions of f(x) = g(x)
(ii) hence find the coordinates of the other point of intersection of the normal and the curve

Answered by Penny Nom.
The isosceles triangle of largest area with perimeter 12cm 2007-07-16
From sharul:
find the dimension of isosceles triangle of largest area with perimeter 12cm
Answered by Harley Weston.
Implicit Derivatives 2007-07-13
From Charles:
I need help computing y' by implicit differentiation the question is: y^2 + x/y + 4x^2 - 3
Answered by Stephen La Rocque.
Derivative of a Function 2007-07-09
From Bob:
What is the derivative of the function a sub n = [n/(n+1)]^n ?
Answered by Stephen La Rocque.
Finding the radius of an inscribed circle 2007-07-05
From Maria:
I need to find the radius of a circle which is inscribed inside an obtuse triangle ABC. I know all the angles and all the lengths of the triangle.
Answered by Stephen La Rocque and Chris Fisher.
Using calculus to prove the formula for the area of a triangle 2007-07-04
From Apratim:
Using calculus how can one show that the area of any triangle is 1/2 times its base times its height?
Answered by Stephen La Rocque.
An irregular hexagon 2007-07-03
From Rebecca:
I need to find the shape of an irregular hexagon, but only have the lengths four of the sides.

It actually looks like a rectangle with a trapezoid on top of it.

The bottom of the rectangle is 150'. The sides are 75'. The length of the top is 130'. I do not have the lengths of the two smaller sides.

Is there any way to find the area of this shape?

Answered by Penny Nom.
A cylindrical slab of concrete 2007-06-30
From Kenn:
I have a tank that needs a base of cement put in it. I dont know how to do this. The tank is 8 feet across and I want the cement to be 5 or 6 inches deep. Can you please tell me how much cement I need to do this.
Answered by Harley Weston.
The number of blocks on the face of a pyramid 2007-06-27
From Heather:
I was wondering if there was an equation in order to calculate the number of blocks on the face of a pyramid. For example:

X
X X
X X X

Is there a specific formula in order to calculate that there are 6 blocks here? Thank You, Heather

Answered by Harley Weston.
Log base 2 of log base 2 of x 2007-06-27
From alex:
y = log base 2 of lag base 2 of x The slope of the tangent to the given curve at its x-intercept is..?
Answered by Harley Weston.
Using Heron's Formula to help maximize the area of a triangle 2007-06-27
From Claire:
Given one side of a triangle is 4 cm and the ratio 1:3 for the other 2 sides. What is the largest area of the triangle?
Answered by Stephen La Rocque and Harley Weston.
The area of an irregular polygon 2007-06-27
From chris:
finding square footage of a polygon with unequal measurements
Answered by Stephen La Rocque and Harley Weston.
sin|x| and cos|x| 2007-06-25
From Mac:
Can anyone tell me whether sin|x| and cos|x| is differentiable at x=0 ? As far as i know, cos(x) and sin(x) is differentiable at all x.
Answered by Penny Nom and Stephen La Rocque.
Limits as x approaches a constant 2007-06-25
From Mac:
can you please tell me what is the reason they say "denominator is a negative quantity" in the solution 11 and "denominator is a positive quantity" solution 10 ??
If i guess correctly, for solution 10, its because of x^2 in the denominator.

Answered by Penny Nom.
Exponential form: x^y 2007-06-22
From Kishor:
whats the easy way to calculate X raised to Y where y is much greater than x.
Answered by Stephen La Rocque.
Simultaneous equations : the Elimination method 2007-06-21
From Patricia:
I need to find the value of X and Y using the Elimination method.

5/x + 3/y=4
25/x-2/y=3

Answered by Stephen La Rocque.
Simultaneous inequalities 2007-06-18
From Freddy:
Watson Electric has production facilities in Valley Mills, Marlin,and Hillsboro. Each one produces radios,stereos,and TV sets. There production capacities are

Valley Mills: 10 radios, 12 stereos, and 6 TV sets per hour Marlin: 7 radios, 10 stereos, and 8 TV sets per hour Hillsboro: 5 Radios, 4 Stereos, amid 13 TV sets per hour

QUESTION

How many hours should each plant be scheduled to fill an order of 1095 radios, 1230 stereos, and 1490 TV sets?

Answered by Stephen La Rocque.
What is the name of the shape that is 3D and irregular? 2007-06-14
From alan:
What is the name of the shape that is 3D and irregular?
Answered by Stephen La Rocque and Penny Nom.
Circumscribing a golden cuboid with a sphere: surface areas 2007-06-14
From Ainslie:
A golden cuboid is defined as a rectangular prism whose length, width and height are in the ratio of phi : 1 : 1/phi.
Prove that the ratio of the Surface Areas of the golden cuboid to that of the sphere that circumscribes it is Phi : Pi.

Answered by Stephen La Rocque.
Angles of depression 2007-06-13
From Phonda:
The pilot of a small private plane can look forward and see the control tower for a small airstrip. Beyond that is a large factory that is 3 milies from the airstrip. The angles of depression are 12.5 degrees and 4.8 degrees respectively. Find the airplane's altitude, to the nearest ten feet.
Answered by Stephen La Rocque.
Two tangent lines to y=x^3 2007-06-07
From stephanie:
find the equations of two tangent lines to the y=x^3 function through the point (2,8)
Answered by Penny Nom.
Solving a quadratic equation using the Quadratic Formula 2007-06-05
From Stuart:
Solve the following quadratic equation: 3xsquared-5x-4=0
Answered by Stephen La Rocque.
Finding the area of a lot without knowing the angles 2007-06-05
From Cristin:
I have a land-locked piece of land. I need to know the square footage in order to determine the acreage. My deed only gives the lengths of its five sides.
Answered by Stephen La Rocque.
What angle does the tire turn in 60s? 2007-06-04
From San:
An automobile, travelling at 80km/h, is towing a trailer. The wheels of the trailer are 40cm in diameter. Through what angle does the tire turn in 60second?
Answered by Stephen La Rocque.
The volume of a triangular prism 2007-06-01
From Hannah:
How do I find the area of the base of a triangular prism, so that I can find the volume by using the equation on the attachment. The formula is that volume equals one half times (base times height) times triangle height. Thank you for your help. Hannah
Answered by Penny Nom.
The lcm of polynomials 2007-05-31
From devin:
x^3-8 , x^3-4, x^2+4x+4
Answered by Penny Nom.
The number of grams of sulfuric acid 2007-05-31
From cookie:
Hi,
Can you please let me know if I've done this correctly?

Calculate the number of grams of sulfuric acid in 0.500L of battery acid if the solution has a density of 1.28 g/mL and is 38.1% sulfuric acid by mass.

Answered by Stephen La Rocque.
Water tank volume 2007-05-29
From Cecelia:
I HAVE A SEMI CIRCULAR TANK AGAINST A WALL MEASURING 6'10" ACROSS THE WIDEST PART AND 3' FROM THE WALL TO THE FRONT OF THE TANK. THE DEPTH IS 14". PLEASE HELP ME TO CALCULATE THE VOLUME OF WATER IN THE TANK.
Answered by Stephen La Rocque.
The limit of a rational function 2007-05-28
From Imad:
     3 _______ 3 _______
lim \/ 1 + x -    \/ 1 - x
x->0 ---- ----------------------------
              x

Answered by Penny Nom.
A circular blob of molasses 2007-05-28
From Julie:
A circular blob of molasses of uniform thickness has a volume of 1 m^3. The thickness of the molasses is decreasing at a rate of 0.1 cm/hour. At what rate is the radius of the molasses increasing when the radius is 8 m?

Thanks,
Julia

Answered by Penny Nom.
Discovering the incircle of an irregular polygon 2007-05-25
From Joaquim:
I've been searching in some books and many websites, but I couldn't find a formula or algorithm for discovering the incircle of an irregular polygon, could you please help me?
Answered by Walter Whiteley.
System of equations 2007-05-24
From Chris:
Find all real solutions (x,y,z,w) of the system of equations:
2y= x + x/17, 2z= y + y/17, 2w = z + z/17, 2x= w + w/17

Answered by Penny Nom.
Mulch price comparison (price per cubic yard versus price per cubic foot) 2007-05-23
From Dianna:
This is a 2-fold question. I am getting some mulch that is measured in 1 cubic yard for $25.00. Walmart has a 2 cubic bag for $3.00. I need to cover a 376 sq ft area. I need to know which is the best deal and how much I need to buy to cover the 376 sq ft.
Answered by Stephen La Rocque.
Set up two simultaneous equations 2007-05-21
From Admire:
The cost of producing windscreen wipers blades at a factory ais partly fixed (due to operating overheads) and partly dependent on the number of blades produced. It costs $300 to produce 1000, and $600 to produce 5000 blades. How much would it cost to produce 24000 blades?
Answered by Penny Nom.
Weight per area conversions 2007-05-13
From Dermot:
A lawn weedkiller to be spread at the rate of 35g per Sq meter. My new spreader is calibrated in lbs per 1000 sq ft !!!!
Answered by Penny Nom and Stephen La Rocque.
Null hypothesis 2007-05-13
From Dani:
A poll of 1068 American voters indicated that 48% supported te Democratic candidate for presidency. At the 0.05 level of significance, test the claim that less than 50% of American voters preferred the Democratic candidate.
Answered by Penny Nom.
Pattern for a truncated cone 2007-05-11
From Mike:
I have been trying to get this cone flat so I can build this column. Can you please help me so I can figure this out? Thanks for your help.
Answered by Stephen La Rocque.
Probability 2007-05-07
From Danielle:
A box contains 3 defective lights and 5 non-defective lights. The lights are tested one at a time without replacement. What is the probability that the 3 defective bulbs will be found in the first 3 tests? is it 1/56 by chance?
Answered by Stephen La Rocque.
Optimization - carrying a pipe 2007-05-05
From A student:
A steel pipe is taken to a 9ft wide corridor. At the end of the corridor there is a 90° turn, to a 6ft wide corridor. How long is the longest pipe than can be turned in this corner?
Answered by Stephen La Rocque.
Edging surrounding a round pool 2007-05-03
From Carol:
Hello, I am new at this and very rusty on my math. I am getting a 24 Ft. round pool and would like to put 2ft width stone (small) edging around it. How much would I need to buy. I have to buy it by the yard (cubic yard) I am not looking for an exact, just an approx. even would be great. Thanks Carol
Answered by Stephen La Rocque.
Two concentric circles form an annulus 2007-05-02
From A student:
In the diagram below, two concentric circles form an annulus. The vertical line is tangent to the inner circle, and forms the diameter of a third circle.

Explain why the areas of the annulus and third circle are the same.

Answered by Penny Nom.
Angular velocity 2007-05-01
From Bruce:
a tachometer of a Ford Explorer reads 2,100 rpm at 60 mph. Find the equivalent angular velocity in degrees per minute and radians per minute
Answered by Stephen La Rocque.
A tugboat's speed 2007-04-30
From Amanda:
a tugboat must travel 24 miles against a 4 mile per hour current on the Potomac River and return. At what constant speed must the tugboat travel to make the trip in 12 hours. Round answer to the nearest tenth mph.
Answered by Stephen La Rocque.
Finding out if two line equations are parallel or perpendicular 2007-04-28
From Vincent:
Can you determine if the two lines are parallel, perpendicular, or neither 1/2x+4y=3/5 y/1 + 10/5= 8x I think there perpendicular but how would you solve the equations
Answered by Stephen La Rocque.
Maximize the volume of a cone 2007-04-27
From ashley:
hello, I've been stumped for hours on this problem and can't quite figure it out. The question is: A tepee is a cone-shaped shelter with no bottom. Suppose you have 200 square feet of canvas (shaped however you like) to make a tepee. Use calculus to find the height and radius of such a tepee that encloses the biggest volume. Can you help??
Answered by Stephen La Rocque and Penny Nom.
A cylinder inside a sphere 2007-04-25
From Louise:
i need to find the maximum volume of a cylinder that can fit inside a sphere of diamter 16cm
Answered by Penny Nom.
Constructing an octagonal deck around a circular pool 2007-04-20
From Cliff:
[I am building an] octagonal desk encompassing 17 foot diameter circle for pool. I have seen other octagonal calculations but none of these tell me how much allowance for a circle to fit within the octagon without losing the circle edge can anyone help thanks cliff
Answered by Stephen La Rocque.
Liquid is being poured into the top of a funnel 2007-04-19
From neroshan:
Liquid is being poured into the top of a funnel at a steady rate of 200cm^3/s. The funnel is in the shape of an inverted right circular cone with a radius equal to its height. It has a small hole at the bottom where the liquid is flowing out at a rate of 20 cm^3/s. How fast is the height of the liquid changing when the liquid in the funnel is 15 cm deep? At the instant when the height of the liquid is 25cm, the funnel becomes clogged at the bottom and no more liquid flows out. How fast does the height of the liquid change just after this occurs?
Answered by Penny Nom.
Minimum cost for a fixed volume 2007-04-18
From James:
My question goes: A silo is to be constructed and surmounted by a hemisphere. The material of the hemisphere cost twice as much as the walls of the silo. Determine the dimensions to be used of cost is to be kept to a minimum and the volume is fixed.
Answered by Penny Nom.
The area of a regular octagon 2007-04-17
From Adam:
I need to find the area of a regular octagon with side length of 12.5m
Answered by Penny Nom.
Simultaneous equations 2007-04-16
From kyrie:
simultaneous equation 4x + 3y = 21 2x * y = 8
Answered by Penny Nom.
The second derivative 2007-04-14
From Gerry:
In mathematical context,what do you understand by the term "Second Derivative"
Answered by Penny Nom.
The area of a regular hexagon 2007-04-14
From Chantel:
Could you please explain to me why the formula for a regular hexagon is 3√3/2 multiplied by side²? Thank you very much.
Answered by Stephen La Rocque.
The area of an irregular pentagon 2007-04-14
From Steven:
I have been given a coursework in which i have to investigate various shapes to find the one that would give the largest area with 1000m perimeter. I'm stuck in a part where i have to calculate the area of a irregular pentagon. i don't know where to start from. I can make up the length of all the sides (5 sides), so long they add up to 1000, but i'm not quite sure what to do after that.
Answered by Penny Nom.
What is the limit of 3.x^(3/x) as x approaches +infinity? 2007-04-11
From Teodora:
What is the limit of 3.x^3/x as x approaches +infinity ?
Answered by Haley Ess.
I am filling a hole in the shape of a cube 2007-04-11
From Bethany:
If I am filling a hole in the shape of a cube with 64 cubic yards of dirt, how many feet deep will my hole be.
Answered by Stephen La Rocque.
Find the volume of the solid 2007-04-07
From tricia:
a solid is constructed so that it has a circular base of radius r centimeters and every plane section perpendicular to a certain diameter of the base is a square, with a side of the square being a chord of the circle. find the volume of the solid at first i thought the length of a side of the square would be r, but that isn't awlays be true- only when the chord is in the center. so how can i solve this without any values? i dont understand the relationship between the chord and radius, except that the radius intercepts the chord at the midpoint. i know i hav to take the integral to get the volume, but how do i even find the area of one of the squares? please help, thanks, tricia
Answered by Penny Nom.
3 divided by 3 to it's fifth root 2007-04-06
From Annie:
How do I transform the equation 3 divided by 3 to it's fifth root to simple radical form (getting the radical out of the denominator)?
Answered by Penny Nom.
The area of a parcel of land 2007-04-03
From Ricky:
I need the attached land parcel (#0436) converted to acreage. This would be of great help to me. Thanks, Ricky
Answered by Penny Nom.
Interior and exterior angles 2007-04-02
From Anuj:
If in a regular polygon, each exterior angle is twice the interior angle,find the number of sides?
Answered by Leeanne Boehm.
Golf schedule 2007-03-30
From Jim:
I am organising a golf break for 12 golfers playing in 3 fourballs over 5 days. I would like to maximise the number of different golfers each player can play with. Any help would br greatly appreciated.
Answered by Penny Nom.
6- team schedule for softball 2007-03-29
From Angie:
I have 6-teams that can only play 3 days a week. Each team must get 18 games in for the season. I have to split them being the home team and the away team sometimes.
Answered by Penny Nom.
A beam on a lighthouse 2007-03-28
From Lisa:
A beam on a lighthouse 2000 metres away from the nearest point P on a straight shoreline revolves at the rate of 10 pi radians per minute. How fast is the beam of the light moving along the shoreline when it is 500 metres from P?
Answered by Stephen La Rocque.
Slopes of perpendicular lines 2007-03-27
From Mykolyn:
How do you find the slope of a line that is perpendicular to the graph of: y= -1/2x+4?
Answered by Leeanne Boehm and Sara Ulmer.
Schedule for a 10 team league 2007-03-27
From Pete:
I don't know if this question involves a math solution, but I am running out of ideas. I have a 10 team league. Each team must play each other once only. I can't seem to match this up and get stuck at the end. Please help. Thanks, Pete
Answered by Penny Nom.
A triangular prism 2007-03-26
From Tom:
Hi, I need to find a container in the shape of a triangular prism that will fit four table tennis balls (this is for a math project!). These balls have a diameter of 4cm, so a radius of 2. I know that the formula for finding an incircle from a triangle is:
radius of incircle = 2area of triangle / perimeter of triangle
But I need to know the length of one side of the triangle from the incircle (the triangle needs to be equalateral). Can you help me find a formula for this? Thanks so much! Tom

Answered by Penny Nom.
The area of an irregular pentagon 2007-03-26
From grace:
hi I am doing graphics and need to find the area of the section given to us (it is just drawn). the sides measure 15m, 35.4m, 5m, 17.8m, 35.7m. the angle between the 15m side and the 35.4m side is 17degrees, the angle between the 35.4m side and the 5m side is 73degrees. the angle between the 5m side and the 17.8m side is 151degrees, the angle between the 17.8m side and the 35.7m side is 90degrees and the angle between the 35.7m side and the 15m side is 95degrees. if you could tell me the area i would be extremely grateful. thanks very much.
Answered by Penny Nom.
y = sin(2x) 2007-03-22
From bader:
sin(2x) find dx/dy
Answered by Penny Nom.
Which solid figure has 4 more edges than vertices? 2007-03-22
From dawn:
which solid figure has 4 more edges than vertices?
Answered by Penny Nom.
The Reuleaux Triangle 2007-03-22
From Dani:
Hi! My question is: Determine how the area of the Reuleaux Triangle of width h compares to the area of a circle of width h? Thanks! Dani
Answered by Penny Nom.
28 golfers playing golf over 7 days 2007-03-20
From ian:
I have 28 golfers playing golf over 7 days I would like everybody to play with each other at least once Is there a schedule? Thank you Ian
Answered by Penny Nom.
A one pass calculation of standard deviation 2007-03-19
From Murtaza:
Hi I searched the listings but couldn't find what i am looking for. I have a dataset and i am allowed only 1 pass through it. At the end of this pass i must have the mean and standard deviation. Calculating the mean is easy as also demonstrated in your listings. I think the same can be done for standard deviation as well. But the doubt that i have is this :- Will the calculated standard deviation be sequence dependent ? i.e. if i change the order in which the data items enter the system, will the std deviation also change ?? Thanks in advance Murtaza
Answered by Penny Nom.
A line that is perpendicular to another line 2007-03-16
From Jesse:
How do you write an equation of a line that is perpendicular to y+2x+3 and passes through (3,4); I don't understand the steps of how to do this????
Answered by Stephen La Rocque and Penny Nom.
Triple angle tangent formula 2007-03-15
From sam:
Hi I am trying to derive a triple angle formulae for tan. I know i need to use compound and double angle formulae but am finding it difficult to "clean" up my fraction to get the triple angle formulae can you show me a worked derivation?! thanks
Answered by Penny Nom.
The area of a property 2007-03-14
From Greg:
Hi my name is Greg. I have a piece of property I am trying to buy, but need to find out the square feet of it first. The four sides are unequal lengths and none at a right angle or parallel. Here are the measurement in feet. The base of the square is 29.12 feet in width.
The right side of the square is 44.33 feet high.
The top of the square is 28.80 feet in width.
The left side of the square is 46.20 feet high.
I have not done this math in ages and really need your help.

Answered by Harley Weston.
A regular quadrilateral 2007-03-13
From Jackie:
How can the measure of each angle of a regular quadrilateral be determined?
Answered by Haley Ess.
The period of a simple pendulum 2007-03-10
From Melissa:
The period of a simple pendulum of length L feet is given by: T=2pi(sqrt(L/g))seconds. It is assumed that g, the acceleration due to gravity on the surface of the earth, is 32 feet per second per second. If the pendulum is a clock that keeps good time when L=4 feet, how much time will the clock gain in 24 hours if the length of the pendulum is decreased to 3.97 feet? (Use differentials and evaluate the necessary derivative at L=4 feet.) Answer is in seconds. Melissa
Answered by Penny Nom.
An irregular pentagon 2007-03-08
From kelly:
If I have a pentagon with 2 sides of length 5 and one with a length of 2, what are the lengths of other 2 sides?
Answered by Stephen La Rocque.
Find the length of the belt 2007-03-08
From Helen:
Find the length of the belt
Answered by Penny Nom.
An irregular polygon 2007-03-06
From Dike:
How do i construct an irregular polygon
Answered by Penny Nom.
Finding the x-intercept 2007-03-02
From Ash:
Y = -1/100X^2 =27/10X +0 = 0 THE Y INTERCEPT IS 50 HOW DO I FIND THE X INTERCEPT
Answered by Gabriel Potter.
Simultaneous equations with fractions 2007-02-28
From Alyca:
Hello Math Central, I am a grade 10 student taking Academic math. Our unit right now is method of substitution and elimination. I'm stuck on this one question that I've been doing forever. Please help =)

*For this equation I have to do method of elimination, but it's so much harder with fractions...could some one please explain to me how to do it step by step?*
x y 2
-- - -- = - --
3 6 3

x y 1
-- - -- = 1---
12 4 2

Answered by Steve La Rocque and Ashley Mang.
sin(3a), cos(3a) and tan(3a) 2007-02-28
From mailene:
hi, i...indeed,to..need..your..help
how..cn..i..prove..this,formula???
sin3a=3sina-4sin^3a
cos3a=4cos^3-3cosa
tan3a=3tan-tan^3a /1-3tan^2a

the..symbol...^is..the..expOnent

Answered by Haley Ess and Penny Nom.
The grade 6 math curriculum 2007-02-24
From Ajay:
Do you have a list of topics a 6th grade students should learn in the 6th grade? I am "rusty" in math and would like to assist my son... Example: if an icetray has X cc of water and is split into 8 parts...what is the volume of each part...is this truly 6th grade level math?
Answered by Pam Fowler and Penny Nom.
At what rate is the area of the triangle changing? 2007-02-24
From mac:
two sticks 3.5 feet long are hinged together and are stood up to form an isosceles triangle with the floor. The sticks slide apart, and at the moment when the triangle is equilateral, the angle is increasing at the rate of 1/3 radian/sec. At what rate is the area of the triangle increasing or decreasing at that moment?
Mac

Answered by Penny Nom.
Surface area of a triangular prism 2007-02-21
From Katrina:
What is the formula to finding the surface area of a triangular prism?
Answered by Gabriel Potter.
Find the area of the triangle 2007-02-20
From Christina:
Graph the function f(X)= x+1/x-1 and graph the tangent line to the function at the points A:(2,3) and B:(-1,0). The point of intersection of the two tangent lines is C. Find the area of the triangle ABC.
Answered by Stephen La Rocque.
What constitutes a face for a geometric solid? 2007-02-14
From Erica:
What constitutes a face for a geometric solid? We have been getting conflicting answers from different textbooks. Some teachers are saying that cylinders and cones do not have faces. I'm thinking that cylinders have 2 and cones have 1. Please enlighten me. Thanks!
Answered by Walter Whiteley.
a specific 3-d shape 2007-02-12
From Robby:
What three dimensional shape has 6 vertices, 5 faces, and two congruent triangular bases? I can't find the answer to this question anywhere. Your help will be appreciated. Thanks, Robby Craig
Answered by Pam Fowler, Gabe Potter and Walter Whiteley.
Exponential form of complex numbers 2007-02-12
From Austin:
When dealing with imaginary numbers in engineering, I am having trouble getting things into the exponential form. The equation is -1+i now I do know that re^(theta)i = r*cos(theta) + r*i*sin(theta). Just not quite understanding the order of operations. Thanks
Answered by Penny Nom.
Simultaneous equations with envelopes 2007-02-08
From Mick:
There were 17 envelopes bought, some were brown, some were white. The brown envelopes cost one cent more per envelope than the white ones. The total cost was 80 cents. How much of each type of envelope was bought? --Many thanks!
Answered by Stephen La Rocque.
Multiplying and dividing by zero 2007-02-05
From colin:
i would like to if u multiply 1,000,000 by 0 does it equal o or 1.

if you have a number eg 15689 and you divide by o what would the answer be is it 1

Answered by Penny Nom.
The substitution method 2007-01-31
From Victoria:
how do i solve this problem using the substitution method?
2x-5= -14
-7x+14y= -5

Answered by Stephen La Rocque.
The elimination method 2007-01-31
From Addrianna:
x-2y=2
3x-5y=7

Answered by Stephen La Rocque.
Water in a triangular trough 2007-01-30
From Trina:
the trough is 5 feet long and its vertical cross sections are inverted isosceles triangles with base 2 feet and height 3 feet. water is draining out of the trough at a rate of 2 cubic feet per minute. at any time t, let h be the depth and v be the volume of water in the trough.
a. find the volume of water in the trough when it is full
b. what is the rate of change in h at the instant when the trough is .25 full by volume?
c. what is the rate of change in the area of the surface of the water at the instant when the trough is .25 full by volume?

Answered by Penny Nom.
The altitude of regular n-side pyramid 2007-01-26
From Wendimu:
The altitude of regular n-side pyramid is half of it's base side.What is the angle between the lateral face and it's base?
Answered by Penny Nom.
A regular pentagonal pyramid 2007-01-25
From Vickifazio:
a regular pentagonal pyramid has a base perimeter of 1,085 ft. How long is one side of the base?
Answered by Stephen La Rocque.
Which lets you put equal groups together? 2007-01-20
From Kathy:
Which lets you put equal groups together? division, multiplication, subtraction, estimation
Answered by Stephen La Rocque.
Irregular multi sided polygon 2007-01-20
From Graham:
I have an irregular polygon. I know the length of all the sides and know approximately all the internal angles. Is there a formula or table that can calculate the area for me?
Answered by Steve La Rocque, Chris Fisher and Penny Nom.
The area of an irregular pentagon 2007-01-18
From Ranjit:
I would like to find the area of an irregular pentagon where the total perimeter is 1000m. Is there a Heron's formula for this?
Answered by Stephen La Rocque.
Angular speed 2007-01-18
From Cristina:
A car is moving at a rate of 50 miles per hour, and the diameter of its wheels is 2.5 feet.
a) Find the number of revolutions per minute the wheels are rotating.
b) Find the angular speed of the wheels in radians per minute.

Answered by Stephen La Rocque.
Comparing two fractions 2007-01-18
From Kayla:
Why does eight over twelve compared to one half work when you use cross multiplication.
Answered by Penny Nom.
The volume of a frustum of a pyramid 2007-01-17
From Sam:
Find the volume of a frustum of a pyramid with square base of side b, square top of side a, and height h.
Answered by Penny Nom.
A line perpendicular to another line 2007-01-13
From Dusty:
Find an equation for the line perpendicular to: 3x - 4y + 1 = 0 passing through (4,7)
Answered by Leeanne Boehm and Penny Nom.
Products with symbols 2007-01-09
From Jennifer:
Find the product of each
(8x)(-4)
(3x)(5y)(7z)
(8x^3y)-5X^2)
(6a)(3a)(-b^2)

Answered by Penny Nom.
Integrate x^8 (x^8 + 2)^2 ((x^8 + 2)^3 + 1)^4 2007-01-09
From James:
How do you integrate x^8 (x^8 + 2)^2 ((x^8 + 2)^3 + 1)^4
Answered by Penny Nom.
Angular speed 2007-01-06
From Robert:
A rear wheel and tire on a John Deere 8520 farm tractor has a 39-in. radius. Find the angle (in radians) through which a wheel rotates in 12 sec if the tractor is traveling at a speed of 22 mph.
Answered by Penny Nom.
What are the dimensions of the most economical container? 2007-01-04
From Ashely:
A cylindrical container costs $2.00 per square foot for the sides and $3.00 a square foot for the top and bottom. The container must hold 100 cubic feet of material. What are the dimensions of the most economical container.
Answered by Stephen La Rocque.
What size pulley would I need? 2006-12-29
From Chris:
If I have a motor that's spinning at 950 RPM's with a pulley that's 6in diameter with a belt running to a generator, What size pulley would I need on the generator to make it spin at 3600 RPM
Answered by Penny Nom.
A regular polygon inscribed in a circle 2006-12-19
From Katy:
If a regular hexagon is inscribed in a circle of radius 6.72 centimeters, find the length of one side of the pentagon. How would I got about explaining this?
Answered by Penny Nom.
1, 3, 6, 10... 2006-12-15
From Lisa:
What is the nth term for the sequence, '1, 3, 6, 10...' and could you say how you got the anwser.
Answered by Stephen La Rocque and Penny Nom.
Parallel and perpendicular lines 2006-12-07
From Valeria:
I m having trouble with parallel and perpendicular lines a problem i need help with is y=6 find the slope if al line parallel to the graph of each equation
Answered by Stephen La Rocque.
Rolle's Theorem 2006-12-07
From Erika:
If f(x) = (x^2)(square root of [3-x]) on the interval [0,3] is given, Does Rolle's Theorem apply? If yes, find any values of c such that f '(c)=0
Answered by Penny Nom.
A 15% tip 2006-12-06
From Danielle:
When she eats at a restaurant,Viviana like to leave a 15% tip,multiplying the price of the meal by 0.15. Franklin usually leaves a 20% tip,multiplying the price by 0.20.They both round up to the nearest $0.05. How much tip would Viviana leave for a $24.85 meal?
Answered by Penny Nom.
The length of each side of a regular n-gon 2006-12-06
From Shannen:
The problem is: Find the length of each side of a regular n-gon when a=80ft, n=20ft, and A is approx. 20,000 square feet.
What do "a" and "n" stand for and how do I find the side length of an n-gon?

Answered by Penny Nom.
A Norman window 2006-11-30
From Joe:
a norman window is a rectangle with a semicircle on top. If a norman window has a perimeter of 28, what must the dimensions be to find the maximum possible area the window can have?
Answered by Stephen La Rocque.
Sally plays roulette 2006-11-21
From Sherry:
Sally plans to bet 100 bets of $1.00 each on red roulette. the probability of the ball landing on red is 18/38 what is the probability that Sally will win at least half the time
Answered by Penny Nom.
Calculating volume of concrete, dirt, sand, anything. 2006-11-17
From Debbie:
[This article contains a special calculator to help you find the volume (for example, the cubic yards) of material required to fill (or empty) a space if you know the length, width and depth.]
We are wanting to pour a 24'x30' slab that is 5" deep. How many cubic yards of cement do we need?

Answered by Penny Nom.
Tangent lines 2006-11-09
From Melissa:
let f be a function with f(1)=4 such that for all points (x,y) on the graph of f the slope is given by (3x^(2)+1)/(2y)

a.)Find the slope of the graph of f at the point where x=1.
b.)Write an equation for the line tangent to the graph of f at x=1 and use it to approximate f(1.2)
c.) Find whether f is concave up or concave down when x=1. Is your answer in part b an overestimate or an underestimate?

Answered by Stephen La Rocque.
Least common multiple 2006-11-08
From Melenie:
I have a daughter in 5th grade she can't seem to grasp the concept of finding LCM's does anyone have a quick easy way for her to learn?????
Answered by Stephen La Rocque.
Simultaneous equations 2006-11-06
From An other:
e^2y-x+2=0
ln(x+3)-2y-1=0

Answered by Penny Nom.
ESL and math-speak 2006-11-03
From Matt:
My name is Matt and I am an ESL teacher in Korea. Recently I have begun tutoring a student who will be going to Canada soon as a 9th grade student. She is a very capable student and is concerned that her mathematical abilities outstrip her ability to communicate in English. I am writing mainly to inquire what level of math-speak I should teach to this student. For instance: should I be explaining geometric terms, or simply algebra? And if algebra, should I include complex numbers and the quadratic formula? If there are things that she will be taught in Canada, I'd prefer her to learn them firsthand from a math teacher. However, knowledge that she will be presumed to have I would like to teach.
Answered by Karen McIver.
Pulleys and belts 2006-10-31
From Lynn:

A belt has a linear speed of 32 mph. It is spinning three pulleys.
Pulley A has diameter 14 in. radius = 7 inches
Pulley B has diameter 26 in. radius = 13 inches
Pulley C has radius 3 ft. radius = 36 inches

Angular speed in Radians per min for
I got
Pulley A= .08 rads/min Pulley B= .04 rads/min Pulley C=.01 rads/min

How many cm would pulley C travel in 14 seconds?


Answered by Penny Nom.
Induction 2006-10-31
From Ross:
Suppose that A and B are square matrices with the property AB= BA. Show that AB^n = B^n A for every positive integer n.
Answered by Stephen La Rocque and Penny Nom.
The area of an irregular hexagon 2006-10-30
From Ashish:
I want to find out area of an irregular HEXAGON in square feet, whose sides are as follows,
Answered by Stephen La Rocque.
The surface area of a triangular prism? 2006-10-29
From Amanda:
What is the formula for the surface area of a triangular prism?
Answered by Haley Ess.
Water is being pumped into the pool 2006-10-24
From Jon:
A swimming pool is 12 meters long, 6 meters wide, 1 meter deep at the shallow end, and 3 meters deeps at the deep end. Water is being pumped into the pool at 1/4 cubic meters per minute, an there is 1 meter of water at the deep end.

a) what percent of the pool is filled?

b) at what rate is the water level rising?

Answered by Stephen La Rocque.
The area of a regular octagon 2006-10-22
From Farhana:
I have a regular octagon with sides of 0.8m and I need to find the area,
Answered by Karen McIver and Penny Nom.
An approximation 2006-10-22
From Ellen:
consider the curve -8x^2 +5xy+y^3 +149 =0 Write an equation for the line tangent to the curve at (4, -1) use this equation to approximate the value of K at the point (4.2, K)
Answered by Penny Nom.
How fast is the water level rising when the water is 1 meter deep? 2006-10-19
From Don:
The cross section of a 5-meter trough is an isosceles trapezoid with a 2-meter lower base, a 3-meter upper base and an altitude of 2 meters. Water is running into the trough at a rate of 1 cubic meter per minute. How fast is the water level rising when the water is 1 meter deep?
Answered by Stephen La Rocque.
Lattice multiplication 2006-10-16
From Patti:
I am a parent of a 5 th grader, and am a bit loss in the "new" math. I know how to multiply using the "old fashion" method. But, could you please explain lattice multiplication.
Answered by Diane Hanson.
How many feet tall is the tunnel 2006-10-14
From Charles:
A tunnel in the Smoky Mountains is semicircular. At a distance of 12 feet from the center of the tunnel, the tunnel has a height of 16 feet. How many feet tall is the tunnel at its center?
Answered by Penny Nom.
Is a circle a regular shape? 2006-10-10
From David:
Is a circle a regular shape or an irregular shape?
Answered by Stephen La Rocque.
Angular speed 2006-10-04
From Jack:
A horse on a merry-go-round is 7m from the center and travels at a speed of 10km/h. What is its angular speed?
Answered by Stephen La Rocque.
Family of lines 2006-09-29
From Sasha:
could a "Family of Lines" have both parallel and intersecting equations that aren't related directly but otherwise related by each other to create a curve
Answered by Chris Fisher.
Least common multiple 2006-09-25
From A student:
What is the LCM of 10,45 and 38?
Answered by Stephen La Rocque.
A rectangular tank 2006-09-19
From Milton:
What size rectangular tank will I need to hold 841.5 gallons of water. The water level is 3'-0" from the bottom of tank.
Answered by Penny Nom.
The volume of a triangular box 2006-09-12
From Irene:
How do I find the volume of a triangular box?
Answered by Penny Nom.
The velocity of a pendulum, part II 2006-09-07
From Erin:
We saw the question in your database about the velocity of a pendulum swinging.....It is the same exact question....but there is another question......it says....

"estimate the instantaneous rate of change of d with respect to t when t = 1.5. At this time, is the pendulum moving toward or away from the wall? Explain."

Answered by Harley Weston.
How many microliters (ul) are there in 0.5 ml? 2006-08-29
From Monica:
How many microliters (ul) are there in 0.5 ml?
Answered by Stephen La Rocque.
The area of an irregular octagon 2006-08-23
From Billy:
How do you figure the area of an irregular octagon? Measurements are 4 equal sides of =BD", and 4 equal sides of =BE". It measures 1 1/2" = from flat to flat.
Answered by Penny Nom.
Differentiate Y= sin3x + cos7x 2006-08-22
From james:
Differentiate the function of x using the basic rules.

Y= sin3x + cos7x

Answered by Stephen La Rocque.
A golf schedule for three days 2006-08-18
From Jon:

I was wondering if I could trouble you to assist me with the following: I am working on a playing schedule for 28 golfers. 7 groups of 4. I have 3 golf days to schedule.

Ideally, I would like to schedule all 28 golfers in 7 different groups of 4 on each day. Here is the catch.....no golfer in any group can be grouped togther more than once. Every group of 4 each day will have 4 new golfers that have never played together before. Is this possible?


Answered by Penny Nom.
How fast is the water level rising 2006-08-12
From Erin:
Water runs into a conical tank at the rate of 9ft3/min. The tank stands point down and has a height of 10 ft. and a base radius of 5 ft. How fast is the water level rising when the water is 6 ft. deep? (V=1/3 pi r2 h).
Answered by Penny Nom.
A problem with exponents 2006-08-09
From A student:
(8a to the negative 2 b cube c to the negative 4/4a squared b to the negative 3 c squared) to the negative 2
Answered by Stephen La Rocque.
The area of a lot 2006-08-05
From Lyn:
I have no idea how to find the square feet of an uneven polygon. I am in the process of making a land agreement and need to know.
Please tell me how to figure out the footage and acreage of land as follows.
road-front 360'
back 360'
left side 220'
right side 180'

Answered by Penny Nom.
Gallons of water in a well 2006-07-31
From Martha:
I have a shallow water well that is 30 feet in depth.

I have 8 feet of water in the well.

The water well is a 30 inch in diameter.

My question : How many gallons of water is in my tank?

Answered by Penny Nom.