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Maximizing the volume of a cone 2020-05-18
From Ella:
Hello, this is question - 'If you take a circle with a radius of 42cm and cut a sector from it, the remaining shape can be curled around to form a cone. Find the sector angle that produces the maximum volume for the cone made from your circle.'
Form a square and a triangle from a wire 2020-04-08
From Raahim:
2. A 2 meter piece of wire is cut into two pieces and once piece is bent into a square and the other is bent into an equilateral triangle. Where should the wire cut so that the total area enclosed by both is minimum and maximum?
Degrees, minutes and seconds 2020-02-21
From Jonathan:
If a cone has an angle of 22 degrees, when i place it flat on a surface, the new resulting central angle is now at 68.69123834, but how come when i saw it on my friend it say 68 degree and 40 minutes, what is this minute?
Investigating y = (-2)^x 2020-01-13
From Gonzalo:
This is not precisely a maths question, but it is formulated based on my maths curiosity. Fidgetting with my new graphic calculator, I started graphing things and had the idea to graph \$y=(-2)^x.\$ The result surprised me, and I thought a little bit about it, stored it on the back of my brain, and promised myself to look deeper into it someday.
What is -5 squared? 2019-09-10
From Pori:
What is -5 squared?
A negative minus a negative 2019-09-03
From Maggie:
Why is a negative minus a negative a negative?
A cone of maximum volume 2019-08-14
From Refilwe:
The slant height of a cone is 10cm. Determine the radius of the base so that the volume of the cone is a maximum
The maximum volume of a cone 2019-07-14
From A student:
find the maximum volume of a cone if the sum of it height and volume is 10 cm.
Why Mean? 2019-05-08
From Jill:
A group of teachers were trying to figure out why the”mean” is called mean - do you know??
More on dominoes 2019-04-09
From B:
A previous answer (http://mathcentral.uregina.ca/QQ/database/QQ.09.00/mark2.html) considered a method to make a line of all 28 dominoes.

Since there are an even number of each value, such a solution can be put into a circle.

Aside from the choice of starting tile, is the solution unique?

Form a cone from a circle sector 2018-08-12
From Tinashe:
A 216 sector of a circle of radius 5cm is bent to form a cone. Find the radius of the base of the cone and its vertical angle.
A fraction 2018-05-02
The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 the number obtained is 3 by 2. Find the number.
The intersection of a curve and a line 2018-03-08
From lola:
find the set of values of constant C for which the line y=x+c intersects the curve y=2 square root x at, at two distinct points
The maximum area of a rectangle with a given perimeter 2017-06-02
From Bob:
How would I go about finding the maximum area of a rectangle given its perimeter (20m, for example)?
Spraying an acre 2016-08-07
From Sara:
I have a spray rig that is 80' wide. How many feet must I go to have sprayed an acre?
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.
An equation with fractions 2016-03-09
From Ed:
7/10-___ +3/2=6/5
The evaluation of a 3 by 3 determinant 2016-02-19
From Kristen:
What is the step-by-step process on how to evaluate the determinant of a 3*3 matrix, using the expansion method (not the diagonal method)
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.

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
Dealing with surds 2015-11-14
From Agnes:
simplify (1-√3)(1÷3+√3)
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?
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

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.

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.

A cone of maximum volume 2015-03-16
From Mary:
I have to use a 8 1/2 inch by 11 inch piece of paper to make a cone that will hold the maximum amount of ice cream possible by only filling it to the top of the cone. I am then supposed to write a function for the volume of my cone and use my graphing calculator to determine the radius and height of the circle. I am so confused, and other than being able to cut the paper into the circle, I do not know where to start. Thank you for your help! -Mary
Largest cone in a sphere 2015-01-15
From Alfredo:
What is the altitude of the largest circular cone that may be cut out from a sphere of radius 6 cm?
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

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 :)

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?
1÷[1-√2(order of surd is 4)] 2014-05-02
From Anoushka:
if t=1÷[1-√2(order of surd is 4)] , then t=?
An inequality 2014-01-25
From LANELL:
this is a problem to solve: 1/3 + 2/7 >=x/21 -- part of the answer is (-oo) not exactly that similar--it is on a calculator as a symbol- sure you know what it is I am talking about- the x will be a number
From Kathy:
1 3/4 + 1 2/3= ?

5 1/2 - 2 5/6= ?

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.

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.

Miles per minute to miles per hour 2013-09-08
Convert 250 miles per min to miles per hour
Four equations 2013-08-08
From may:
HI how to solve this 4 equations?
A+C = 0
-4A+B-8C+D=1
3A+16C-8D=-29
-12A+3B+16D=5

{(1+x)^1/3-1/3X(1+x)^-2/3}/(1+x)^2/3 2013-06-17
From STEPHEN:
{(1+x)^1/3-1/3X(1+x)^-2/3}/(1+x)^2/3
4 linear equations with 3 unknowns 2013-04-12
From Marian:
how to solve for 3 unknowns in 4 simultaneous equations
A linear programming problem 2013-02-27
From Kelley:
A manufacturer of skis produces two types: downhill and cross-country. Use the following table to determine how many of each kind of ski should be produced to achieve a maximum profit. What is the maximum profit? What would the maximum profit be if the time available for manufacturing is increased to 48 hours.
Downhill Cross-country time available
manufacturing time per ski 2 hrs 1 hr 40 hr
finishing time per ski 1 hr 1 hr 32 hr
profit per ski \$70 \$50

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.

From itsel:
Find the discriminant ans use it to determine the use the quadratic formula to solve the equasion -2x^2+3x+2=0
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)

A project on reclaiming water 2012-12-11
From shannon:
I'm doing a report to reclaim water off of our campus facility to store in a cistern to use to flush toilets.

In Southeast Wisconsin and average of 82 inches of rain and snow fall annually. I want to collect that off of the roof of our school building. The roof is 37128 square feet. how many gallons annually could I collect?

Minutes and seconds 2012-08-29
From Casey:
I have to write a variable equation. The questions says there are 60 seconds. but we need to write and equation to solve for minutes. Is it 1/60 or 1/s
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.
A max min problem 2012-02-26
From Christy:
Hello, I have no idea where to start with this question. Bob is at point B, 35 miles from A. Alice is in a boat in the sea at point C, 3 miles from the beach. Alice rows at 2 miles per hour and walks at 4.25 miles per hour, where along the beach should she land so that she may get to Bob in the least amount of time?
Four apples and two oranges cost Rs. 30... 2012-01-13
From nasr:
Four apples and two oranges cost Rs. 30, and one apple and 3 oranges costs Rs.15.How much does each apple and each oranges cost?
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?
How many rpm does a 3.5 in. diameter wheel turn at 7 miles per hour? 2011-12-06
From Al:
how many rpm does a 3.5 in. diameter wheel turn at 7 miles per hour
Maximum area of a rectangle 2011-10-04
From Lyndsay:
A rectangle is to be constructed having the greatest possible area and a perimeter of 50 cm.

(a) If one of the sides of the rectangle measures 'x' cm, find a formula for calculating the area of the rectangle as a function of 'x'.

(b) Determine the dimensions of the rectangle for which it has the greatest area possible. What is the maximum area?

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

From brian:
Hi , If I have direct job costs of \$100. and my administration is 20 % and I want to make a 15 % profit , how would I calculate the administration and profit and what would be the total of each be and also the final total?

Thanks,
Brian

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.
8 3/8 - 6 1/4 2011-03-21
From lenora:
explain an error pattern in each of the following. 8 3/8 - 6 1/4 = 2 2/4
1/a^2 + 1/b^2 2011-01-19
From robert:
If (a + b)^2 = 81 and ab = 18, find the value of 1/a^2 + 1/b^2 ?
Tiling a swimming pool 2011-01-09
From rustom:
(a) Find the volume of water in swimming pool with vertical ends and sides . The length measured at the water line is 50 ft. and the breadth is 20 ft. The bottom of the swimming pool is a plane sloping gradually downward so that the depth of the water at one end is 4 ft. and 8ft. at the other end. (b) If the sides, ends, and bottom of the swimming pool are constructed of tile blocks whose glaze surface dimensions are 3in by 6in. , and if the ends and sides of the pool extend 2ft.above the water level, find the number of blocks used if 1/20 of the surface area is covered by sealing material.

I got the (a) question but I don't know the (b) question which have the answer of 16,136 blocks. I hope I can get the procedure for this, THANK YOU!

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.
Hours minutes and seconds 2010-11-26
From beket:
I need to turn 1.486588292 into real time hours minutes and seconds. I keep getting multiple answers. Online conversions give me 1 hour 29 minutes and either 11 or 12 seconds. On the calculator I get 1 hour 29 minutes and 20 seconds. Can you explain how to turn this decimal into time?
Answered by Robert Dawson and Penny Nom.
Terminal zeros 2010-11-04
From morgan:
if I have to multiply 1*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16*17*18*19*20 how many terminal zeros do i get?
30,000 US gallons of water 2010-10-12
From mike:
If a swimming pool can hold 30,000 US gallons of water - is it possible to calculate the number of yards of dirt it would take to fill the hole?
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
Elimination and substitution 2010-09-18
From Lauren:
Solve one using the method of substitution and the other with the method of elimination.

v a. y=5x+4
x=2y+1

b. 4x+3y=7
6x-3y=13

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.
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.
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.
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?
x/a +y /b =a+b : x/a^2+ y/b^2 =2 2010-05-30
From smithu:
x/a +y /b =a+b : x/a2+ y/b2 =2 solve by using elimination method , cross multiplication, substitution method
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   \___________________________ /

Algebraic fractions 2010-04-22
From rory:
3x/(x²-64)+4/(x²-6x-16)=
Answered by Robert Dawson and Harley Weston.
Two max/min problems 2010-04-11
From Amanda:
1) Find the area of the largest isosceles triangle that canbe inscribed in a circle of radius 4 inches.

2)a solid is formed by adjoining two hemispheres to the end of a right circular cylinder. The total volume of the solid is 12 cubic centimeters. Find the radius of the cylinder that produces the minimum surface area.

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.
A negative times a negative 2010-03-25
From priya:
why is minus into minus plus?
The distance travelled by a minute hand 2010-03-06
From Patric:
How much distance will the minutes hand of length 14mm of a clock cover in moving from 5 to 10?
Least common denominator 2010-02-13
From Priscila:
3/8 + 4/5 + 7/3 + 9/10 = ?

Priscila

Combining fractions 2010-02-10
From Nick:
Combine the fractions

2m/t + 5/mt

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)

The discriminant 2010-01-17
From Sonjonnia:
What is the value of the discriminant?
16x^=16x-4

The adjacency matrix of an undirected graph 2010-01-15
From Bhavya:
Let Cn be the undirected graph with vertex set V = {1,2,3,...,n} and edge set E = {(1,2), (2,3), (3,4),.... , (n-1,n), (n,1)}. Let An be the adjacency matrix of Cn.
a. Find the determinant of An.
b. Find (An)^2

The minimum point of a quadratic 2009-12-31
From rachel:
y=0.0008x^2-0.384x
What is the minimum point of this equation?

Linear programming using the Simplex Method 2009-12-28
From William:
A gold processor has two sources of gold ore, source A and source B. In order to keep his plant running, at least three tons of ore must be processed each day. Ore from source A costs \$20 per ton to process, and ore from source B costs \$10 per ton to process. Costs must be kept to less than \$80 per day. Moreover, Federal Regulations require that the amount of ore from source B cannot exceed twice the amount of ore from source A. If ore from source A yields 2 oz. of gold per ton, and ore from source B yields 3 oz. of gold per ton, how many tons of ore from both sources must be processed each day to maximize the amount of gold extracted subject to the above constraints? I need a linear programming solution or algorithm of the simplex method solution. Not a graphical solution. Thanks.
A Lagoon, free form, inground swimming pool 2009-12-22
From donna:
What is the linear footage of a 14 x 23, Lagoon, free form, inground swimming pool?
A minute hand 2009-11-05
From Pardha:
A minute hand of table clock is 3cms long. How far its tip move in 20 minutes
A linear system 2009-10-20
From marissa:
Solve this linear system
2x-y=5
3x+y=-9

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
Elimination method 2009-10-08
From Kenty:
How do I solve this problem using the elimination method?
3x-7y=0
6x+4y=0
I am not sure how so if someone can show me a similar problem (instead of solving this one for me) that would be fantastic.

Ordering pizza for 162 people 2009-10-01
From Jean:
Need to know how to feed about 162 people 70 square inches of pizza at the lowest price.

22" Pizza is \$9.95
16" Pizza is \$5.25
12" Pizza is \$2.99

Two equations in two unknowns 2009-09-18
From Citizen:
x+-3y=7
-x+4y=7

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.
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?
The optimal retail price for a cake 2009-03-25
From Shawn:
Your neighbours operate a successful bake shop. One of their specialties is a cream covered cake. They buy them from a supplier for \$6 a cake. Their store sells 200 a week for \$10 each. They can raise the price, but for every 50cent increase, 7 less cakes are sold. The supplier is unhappy with the sales, so if less than 165 cakes are sold, the cost of the cakes increases to \$7.50. What is the optimal retail price per cake, and what is the bakeshop's total weekly profit?
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.
The weight of water in a swimming pool 2009-03-10
From ely:
How much does the water in a swimming pool 20 ft long, 10 ft wide, and 6 ft deep weigh?
Linear systems 2009-02-20
From Rose:
I have been having trouble trying to figure out these three math problems , I need help breaking them down so I could understand them better please help.
1. x = 7 - x
2 x - y + 8

2. 8 x + 5 y = 1 8 4
x - y = 3

3. y + 2 x = 3
y + 2 x = 4

I can't figure out how to break them down in the right order.

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

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)"

A maximum area problem 2009-01-13
From Kylie:
Help me please! I don't know how or where to start and how to finish. The problem is: A window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 15 ft., find the dimensions that will allow the maximum amount of light to enter.
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?

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?
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?
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?
Maximize revenue 2008-10-08
From Donna:
A university is trying to determine what price to charge for football tickets. At a price of 6.oo/ticket it averages 70000 people per game. For every 1.oo increase in price, it loses 10000 people from the average attendance. Each person on average spends 1.5o on concessions. What ticket price should be charged in order to maximize revenue. price = 6+x, x is the number of increases.
ticket sales = 70000- 10000x
concession revenue 1.5(70000 - 10000x)
I just do not know what to do with the concession part of this equation (6+x) x (70000 - 10000x) I can understand but not the concession part please help. thx.

The minimum value of f(x)=maximum{x,x+1,2-x} 2008-09-21
From Saurabh:
The minimum value of the function defined by f(x)=maximum{x,x+1,2-x} ?
The volume of a swimming pool 2008-08-10
From Ron:
What is the volume of a swimming pool when its length is 40 ft, width 20ft, the deep end is 10 ft and the shallow end is 3 ft.?
Non-terminating, non-repeating decimals 2008-08-03
From Peter:
How do you take a random, non-terminating, non-repeating decimal into a fraction?
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
4 by 4 determinants 2008-06-27
From rav:
How to solve problems of determinants which has four rows and four columns& please give me easy tips to solve permutations and combinations problems.
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.
Lowest common denominator 2008-05-31
From marlene:
cant get the common lowest denominator of 10,46,64
x/4 = 3 1/2 2008-05-30
From Kelsey:
How do you solve for "X" in the problem below?

X
--- = 3 1/2
4

--Kelsey

How many presses should be used? 2008-05-04
From Sarah:
Hi! I am in Calculus and this problem is on my study guide and i just cant figure it out!? A printing company had eight presses, each of which can print 300 copies per hour. It costs \$5.00 to set up each press for a run and 12.5+6n dollars to run n presses for an hour. How many presses should be used to print 6000 copies most profitably? Let h equal the number of hours used to print the 6000 copies.
Determinants 2008-05-02
From Henry:
I have a question about solving 3x3 matrices.

The traditional way, or at least the way I've been taught, is that if one has a 3x3 matrix such as:

[ a b c ]
[ d e f ]
[ g h i ]

one solves it according to this formula:

[ei - hf) - (bi - hc) + (bf - ec) = determinant.

According to a book I'm now studying to prepare for the California CSET exam, there is another, easier, way to solve it:

[ a b c ] [ a b ]
[ d e f ] [ d e ]
[ g h i ] [ g h ]

In other words, one repeats the first two rows of the matrix and adds them to the right.

At this point, the determinant is calculated thus:

(aei) +(bfg) + (cdh) - (gec) - (hfa) - (idb).

Is this, in fact, correct?

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.
Minimize the cost 2008-04-26
From A:
A power line is to be constructed from the shore of a lake to an island that is 500 m away. The closest powerline ends 4km along the shore from the point on the shore closest to the island. If it costs 5 times as much to lay the powerline underwater as along the shore, how should the line be installed to minimize the cost?
1 mile per minute 2008-04-01
From jennifer:
If you are traveling at 1 mile per minute how fast would you need to be going
How long will it take to pump the water out of the basement? 2008-04-01
From Shiva:
I need to pump water out of a flooded basement, using two 50 (gpm) pumps. The basement has the dimensions shown and is flooded to a depth of 16 inches. How long will it take to pump the water out of the basement?
The amount of water in a pool 2008-03-30
From anurag:
what will the weight of water in a swimming pool having dimensions of 18ft *10ft*5 ft? how much water will be needed for filling it up?
A max-min problem 2008-03-27
From LSL:
show that of all rectangle with a given area, the square has the smallest perimeter.
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.
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?
The smallest possible perimeter 2008-01-23
From RS:
If two points of a triangle are fixed, then how can the third point be placed in order to get the smallest possible perimeter of the triangle.
Answered by Chris Fisher and Penny Nom.
Maximum volume of a box 2008-01-15
From Rajesh:
A square piece of a cardboard of sides ten inches has four equal peices are removed at the corners, then the sides are turned up to form an open box. What is the maximum volume such a box can have?
Protecting a carrot patch 2008-01-03
From Kate:
A farmer has a problem with rabbits and skunks in his rectangular carrot patch that is 21m^2 in area. Determine the dimensions that will require the least amount of fencing if a barn can be used to protect one side of the garden.
Smallest cone containing a 4cm radius inscribed sphere 2007-12-19
From Eva:
A sphere with a radius of 4cm is inscribed into a cone. Find the minimum volume of the cone.
ln(x)/x 2007-12-07
From Nooruddin:
How can I calculate the absolute minimum of (ln x)/x?
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.
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].
Ordering fractions 2007-11-15
From DEL:
Hi. I feel really stupid ! I'm a mature student and i have completely forgotten How to find out the order of fractions from largest to smallest. I Have been put this poser; 7/4...1/6....7/2 Can you please tell me what is the largest and lowest? Will be very grateful....thank you
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

For which values of k will k/240 be a terminating decimal? 2007-10-28
From Clara:
For which values of k will k/240 be a terminating decimal?
Is there a practical use for radian measure? 2007-10-26
From Paula:
Is there a practical use for radian measure in any profession? Which professions might us radian as opposed to degree measure?
I need to order 3/11, 1/8, 2/9 from least to greatest 2007-10-19
From Andrew:
I need to order 3/11, 1/8, 2/9 in least to greatest.
Metres per minute to miles per hour 2007-09-20
From Angela:
If a person is traveling 150 meters per minute, what is their speed in miles per hour?
Answered by Stephen La Rocque and Harley Weston.
The range of a projectile 2007-09-18
From Claudette:
This is a maximum minimum problem that my textbook didn't even try to give an example of how to do it in the text itself. It just suddenly appears in the exercises. Problem: The range of a projectile is R = v^2 Sin 2x/g, where v is its initial velocity, g is the acceleration due to gravity and is a constant, and x is the firing angle. Find the angle that maximizes the projectile's range. The author gives no information other than the formula. I thought to find the derivative of the formula setting that to zero, but once I had done that, I still had nothing that addressed the author's question. Any help would be sincerely appreciated. Claudette
How many gallons per minute? 2007-09-12
From Diane:
HI I have a natural water spring and I am trying to determine how many gallons per minute will flow in an 8" pipe? I know one gallon is 231 cubic inches and V=nr2h - so if i had one foot of 8" pipe it would hold 2.6 gallons but I'm looking for the flow rate of how many gallons per minute? Thanks for your help.
The number of minutes in n hours 2007-08-28
From sharquea:
the number of minutes in n hours
Answered by Leeanne Boehm and Stephen La Rocque.
Filling an old swimming pool 2007-08-27
From Russ:
I would like to know how much fill material I would need to fill an old swimming pool. The pool is 18' wide x 36' long and is 4' to 10' deep.
From John:
Ive completely forgot anything to do with the subject mentioned, so my question is straight to the point..

I need to know how to do the following problem (Preferably do not give me an answer though) (k/3k-8) - (4/k+2)

Simplifying an algebraic fraction expression 2007-07-25
From Jessica:
How do I simplify b/(b2-25) + 5/(b+5) - 6/b?
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.

A matrix of polynomials 2007-07-18
From Mac:

Let A be a n*n matrix, the elements of which are real (or complex) polynomial in x. If r rows of the determinant becomes identical when x=a, then the determinant
A) has a factor of order r
B) has a factor or order > r
C) has no factor
D) has a factor of order < r

Values of k for which k(x^2+2x+3) - 4x - 2 is never negative 2007-06-29
From claire:
Find the range of values of k for which k(x^2+2x+3) - 4x - 2 is never negative.
The roots of (x - k)(1-3x) + 1 = 0 2007-06-28
From Claire:
Show that the roots of (x - k)(1-3x) + 1=0 are real and distinct for all real values of k. Hence, or otherwise, find the range of 9sin^2 r - 6sin r + 13
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

Simplifying complex denominators 2007-06-21
From Krys:
How do I simplify completely? ((4+i ) / (3+i )) - ((2-i ) / (5-i ))
What happens when you have zero's on both sides? 2007-06-05
From Lily:
On the substitution method what happens when you have zero's on both sides of the equation? Is that considered no solution or infinitely many?
Answered by Stephen La Rocque and Penny Nom.
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?
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
Linear programming 2007-04-24
From Sylvia:
What is graphing linear programming?
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.
Swimming pool water 2007-04-12
From tina:
How much water does a 24' round, 4' deep swimming pool hold?
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.
Evaluating a determinant 2007-02-25
From Suud:
Please send me the detailed steps of calculating the determinant of the following 4by4 matrix -1 -3 1 2 -2 0 -1 1 3 2 0 4 0 -3 1 -2
The elimination method 2007-01-31
x-2y=2
3x-5y=7

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.

Common denominator 2007-01-10
From A parent:
what is the common denominator of 3/5, 2/7 and 4/8?
Order the fractions from least to greatest 2007-01-04
From Justin:
I am a sixth grader, and I am having trouble with the last question in my homework assisgnment. 1/6, 2/5, 3/7, 3/5!
Answered by Stephen La Rocque and Penny Nom.
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
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?
How much labor should the firm employ? 2006-10-28
From Christy:
A dressmaking firm has a production function of Q=L-L(squared)/800. Q is the number of dresses per week and L is the number of labor hours per week. Additional cost of hiring an extra hour of labor is \$20. The fixed selling price is P=\$40. How much labor should the firm employ? What is the resulting output and profit? I am having a difficult time with this, HELP!
How do you solve for variables in the denominator? 2006-10-15
From Donna:
How do you solve for variables in the denominator?

178 = 17/R

Least common denominator 2006-10-04
From Paulette:
Why is the LCD of 3/4 and 4/8 not the product of 4 and 8?
Mini Golf 2006-08-17
From Sarah:
I am a sixth grade teacher in Minnesota. I want to have my students explore mini golf and calculate the reflections and angles so that they can figure out how to hit a hole in one. I know that my daughter had various problems like this in eighth grade geometry, but I can't seem to find any internet activities of the appropriate level.
Litres of water in my swimming pool 2006-08-16
From A student:
I need to calculate how many litres in my swiming pool, it is a circle shape, 5.5 m in diametre by 1.07 m deep.
1/x + 1/y 2006-08-11
From Sonya:
what is 1/x+1/y = ? is it equal to 1/x+y or what?
How old would i be in minutes 2006-08-09
From Mariah:
i would like to know how old would i be in minutes if i was thirteen years old including leap years
Minimizing a cost 2006-07-25
From Edward:
The cost of running a car at an average speed of V km/h is given by c= 100 + (V2 / 75) cents per hour. Find the average speed (to the nearest km/h) at which the cost of a 1000 km trip is a minimum.
Mini Golf geometry 2006-07-18
From Sarah:
I want to have my students explore mini golf and calculate the reflections and angles so that they can figure out how to hit a hole in one. I know that my daughter had various problems like this in eighth grade geometry, but I can't seem to find any internet activities of the appropriate level. If you can steer me towards any resources, I'd be most grateful.
The lowest denominator 2006-07-02
From Lisa:

What is the lowest denominator for the following numbers:

a) 26
b) 21
c) 47

How many gallons of water are in a 24' X 4' round swimming pool? 2006-06-15
From Nicole:
How many gallons of water are in a 24' X 4' round swimming pool?
A fence around a pen 2006-03-30
From Daryl:
I hope you can help me out with the attached problem, It has been driving me crazy.
Answered by Stephen La Rocque and Penny Nom.
From Barbara:
I know that to subtract 1/4 from 2/3 I must find a common denom. Now the 2/3 becomes 8/12.....i understand the 12, but where does the 8 come from?
What names are known for the quarter circle shape? 2006-03-06
From Christina:
What names are known for the quarter circle shape?
Answered by Stephen La Rocque and Penny Nom.
From Grace:
Daddy Warbucks always carries a specific number of \$100 and \$500 bills for impulse purchases and \$1 bills for tips. If he has 500 bills in his briefcase and they total \$50,000, how many bills of each denomination does he carry?
The box of maximum volume 2006-02-01
From Elizabeth:
A box factory has a large stack of unused rectangular cardboard sheets with the dimensions of 26 cm length and 20 cm width.
The question was to figure what size squares to remove from each corner to create the box with the largest volume.
I began by using a piece of graph paper and taking squares out. I knew that the formula L X W X H would give me volume. After trial and error of trying different sizes I found that a 4cm X 4cm square was the largest amount you can take out to get the largest volume. My question for you is two parts

First: Why does L X H X W work? And second, is their a formula that one could use, knowing the length and width of a piece of any material to find out what the largest possible volume it can hold is without just trying a bunch of different numbers until you get it. If there is, can you explain how and why it works.

A max-min problem 2005-12-16
From Julie:
A car travels west at 24 km/h. at the instant it passes a tree, a horse and buggy heading north at 7 km/h is 25 km south of the tree. Calculate the positions of the vessels when there is a minimum distance between them.
Mrs. Faria lives on an island 2005-12-15
From Julie:
Mrs. Faria lives on an island 1 km from the mainland. She paddles her canoe at 3 km/h and jogs at 5 km/h. the nearest drug store is 3 km along the shore from the point on the shore closest to the island. Where should she land to reach the drug store in minimum time?
A 24 sided polygon 2005-12-14
From Matt:
I would like to know if there is a name for a 24 sided shape
Inclusive definitions 2005-12-14
From Layla:

recently the solvable quandary of 5+5+5=550 came up (the question says that you have to put 1 straight line somewhere in the equation to make it true with out turning the "=" into a "not=" sign).

So two answers were put forward:
545+5=550 (the use of a line converting a + into a 4)
AND
5+5+5(less than or equal to)550

There is currently an argument about the second solution. The disagreement is about whether this sign can be used. One person is arguing that the "less than or equal to" sign defines that the number on the left is in the range 550 and below. The other is saying that since the number (which is clearly defined with no variables) can never equal 550, then the "less than or equal to" sign cannot be used in this case.

Which one is the correct definition?

From Paula:
I would like a simple step by step explanation on how to add improper fractions.
Rational expressions 2005-11-15
From Zach:
I can solve easy problems such as (x/2)+3=2+(3x/4). That is easy because the Lowest Common Denominator is 4. But what really gets me stuck is a problem like this one. (6/x-2) = ( 21/(x-2)(x+2) )+ 1.
A variable rectangle 2005-11-08
From Mussawar:
find the lengths of the sides of a variable rectangle having area 36 cm2 when its perimeter is minimum i do not want solution of this question. i would like to know what is mean by variable rectangle.and what is difference between rectangle and variable rectangle.also what is mean by when its perimeter is minimum.
Percent or percentage 2005-11-03
From Kenneth:

Which word should be used in the following?

Change a (percent or percentage) to a decimal.

Should the word percent be used only when a number precedes it as in 45 percent?

Answered by Harley Weston and Chris Fisher.
The language of subtraction 2005-09-26
From Chris:
When you have an addition problem you have two addends that equal a sum. Therefore . . .

I know the answer to a subtraction problem is the difference - what is the name of the numbers that make up a subtraction problem?

Answered by Diane Hanson and Harley Weston.
Framing an arched wall 2005-08-12
From Mike:
I'm framing a building wall with a curved (arcing) top section. The radius of the section is 74'6" with a height above finish floor of 16'0". The horizontal run of the arced section is 23' 1 1/2" with a low height above finish floor of 12'4". If I start with a 16' stud at the high end how long are the subsequent studs if they are on 16" centers? Short of laying this out on a tennis court how can I work out the lengths of the studs?
Discriminant 2005-06-20
From A student:
If a quadratic has real root, its discriminant b2-4ac>=0 Is there any similar condition or method by which you can find whether roots of a cubic equation are real or not?
A matrix problem 2005-04-04
From Alan:
 Let A = 1 -1 0 2 -1 2 a b c

where a, b, c are constant real numbers. For what values of a, b, c is A invertible? [Hint: Your answer should be an equation in a, b, c which satisfied if and only if A is invertible.]

Gasoline in a cylindrical tank 2005-03-23
From Jennifer:

Gasoline is stored in a tank which is a cylinder on its side. Height of fuel is "h" meters and the diameter is "d". The length is "l".

I need to find the amount of gas in the tank when the height is h and also to calculate the fraction of how full it is.

Also, the part I am really confused on is this one,
E(h/d) is the error of the function of h/d, when h/d is used to measure how full the tank is. For what value of h/d is the error maximal?

Discrimination based on gender? 2005-03-10
From A student:
After being rejected for employment, Kim learns that the Bellevue office has hired only two women among the last 20 new employees. She also learns that the pool of applicants is very large, with an approximately equal number of qualified men and women. Help her address the charge of gender discrimination by finding he probability of getting two or few women when 20 people are hired, assuming that there is no discrimination based on gender. Does the resulting probability really support such a charge?
The least common denominator 2004-11-03
From A student:
Write the LCD for each pair of fractions.

13. 1/3,1/5

14. 2/7,1/4

15. 3/4,3/5

Rational expressions 2004-09-24
From A student:
In general, I understand rational expressions except when it comes to solving problems such as:

x+y/2x-y - 2x/y-2x or m-4/3m-4 + 3m+2/4-3m

I am confounded by the issue of having to find a common denominator. For example, if I tried to solve these problems by multiplying both denominators they would still be uncommon.

Nine minutes 2004-09-02
From A student:
You have two hour glasses-one measures 7 minutes and one measures 4 minutes.How can you time 9 minutes?
A trig problem 2004-08-02
From A student:
Given that the maximum value of [sin(3y-2)]^2 -[cos(3y-2)]^2 is k. If y>7, Find the minimum value of y for which [Sin(3y-2)]^2 - [cos(3y-2)]^2 =k.
Maximizing the angle to the goal mouth 2004-05-15
From Yogendra:
You are running down the boundary line dribbling the ball in soccer or hockey. Investigate where in your run the angle the goal mouth makes with your position is at a maximum.
Subtracting fractions 2004-05-11
From Filipe:

Question:
_5_ - __7__
6ab 8a

A/30 + B/105 = (7A + 2B)/x 2004-02-05
From Jim:
If A/30 + B/105 = (7A + 2B)/x and A, B, and x are integers greater than 1, what must x equal?
From Carl:
A walkway of uniform has 72m2 and surrounds a swimming pool that is 8m wide and 10m long. Find the width of the walkway.
Dividing zero by infinity 2004-01-08
From Jason:
What do you get when dividing zero by infinity? Our Calculus teacher was pretty sure that the expression was indeterminate from. However, if this is so...Why? Zero divded by any number (except zero) is zero, true. Any number (except infinite) over infinite is zero. So, why isn't Zero divided by infinite zero. A simpler way if I had 4 potatoes and was to split them among 2 friends, each friend would get 2 potatoes. However, if I had 0 potatoes and split them a infinite number of ways, each person would still have 0. Explain please!
The hour hand and the minute hand 2003-12-17
From Minnie:
When you are looking at the clock at 12:00 the hour hand and minute hand are exactly together. (one on top of the other). Between 1:00pm and 1:15pm there is another time when the hour and minute hands are exactly together again.
Systems of equations 2003-11-19
From Scott:

I hope that u can help me....I am a college student taking a class in Pre Calculus.....I have homework due this Friday and it counts a BIG Percentage on my FINAL grade.....I am getting mixed up and can not figure out a few problems.....Please help me.....

Method Of Subsitution

Problem 1. y- 8x = -5
x(squared) + y(squared) = 25

Problem 2. y = x(squared) - 2x - 6
Y = x(squared) - 4

From Ken:
My name is Ken and I am taking my GED course for my High School and have not been in a class for 35 years. I am doing this for re-training. I am at the part about fractions. Here is an example that I am having trouble with.

1 3/7 + 4 2/3 + 11/21

They have no common denominators. Could you PLEASE help me. If you could send me a step by step explanation it would be greatly appreciated.

A rock on a string 2003-10-26
From A student:
a rock on a 4' string is rotated at 80 rpm. what is the linear speed in feet per second? in miles per hour?
Indeterminate forms 2003-10-06
From A teacher:
Is it possible for me to find any geometrical interpretation without using calculus to explain indeterminate forms?
Grooming the king's horses 2003-09-04
From Janelle:
the stable boy had 90% of the kings horses groomed.the next day the king acquired 25% more horses. Now there was 105 horses not prepared for the kings men. How many horses did the king originally have?
Terminology 2003-08-31
From Maria:
My daughter Veronica is a rising 6th grader and has to complete some Summer Math
assignments and would like to ask you three questions:
1. ___________ are number pairs that have a product of 1.

2. You can name any point on a plane with two numbers. These two numbers are called _____________.

3. A _______________ is the size of a cube that is exactly 1 inch on each edge.
Thanks,

Subtracting rational expressions 2003-05-10
From Simone:
hi, i'm totally lost. i understand that you need to find a lowest common denominator to subtract two fractions (rational expressions) with different denominators. but what if the denominators are "x-1" and "x". is x the common denominator? if so what happens to the "-1"? do you know of any live online help i can get with the following:

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

The volume of air flowing in windpipes 2003-05-02
From James:
The volume of air flowing in windpipes is given by V=kpR4, where k is a constant, p is the pressure difference at each end, R is the radius. The radius will decrease with increased pressure, according to the formula: Ro - R = cp, where Ro is the windpipe radius when p=0 & c is a positive constant. R is restricted such that:
0 < 0.5*Ro < R < Ro,
find the factor by which the radius of the windpipe contracts to give maximum flow?

Division names 2003-03-10
From A parent:
what is the answer to a division problem called
A determinant 2003-02-13
From A student:

I have to find the determinant of the following matrix

 -2 3 1 2 4 -3 0 -2 5 1 4 2 1 -3 5 2 3 4 -1 2 6 0 3 2 -4

The least common denominator 2003-01-21
From Brittan:
Hi there I need help! My name is Brittany and i am in the 6th grade.

I need help finding the least common denominator(LCD), and the book says Find the LCM of the denominators and i've done that and then it says write equivalent fractions,using the LCM as the least commonn denominator.The directions say Use the LCD to write each pair as like fractions. and the problem is 1/8 and 5/40. Could u explain how in the word u do this? Thanks a lot

Brittany

From Erikson:
I am a student in the 10th grade and attending advanced math at my high school. I was assign to do a report about the unit circle and the radian. But there seems to be no information available about the history of the radian; who first found out about them, which civilizations used it if any. Well, hopefully you'll assist me in this troubling question. Thank you for your kind consideration.
Filling A swimming pool 2002-11-21
From Sarah:
A swimming pool is being filled by three pumps. Alone pump A would take 6 hours, pump B would take 3 hours, and pump C would take 3 hours. If all three pumps are used to fill the pool, what fraction of the process is pump A.
Rational expressions 2002-10-03
From Ashley:
1/x(squared) + 5/xy
A max/min problem 2002-09-21
From Evelina:
A window is the shape of a rectangle with an equilateral triangle on top. The perimeter of the window is 300 cm. Find the width that will let the maximum light to enter.
How many dominoes? 2002-09-13
From A student:
Dominoes are split into two halves. If you were allowed up to 6 dots on each half, how many options of dominoes could you get?
Common Denominator 2002-08-26
From Slobodanka:
What is a Common Denominator?
Linear programming 2002-05-27
From Jes:
A machine shop makes two parts, I and II, each requiring the use of three machines, A, B, C. Each Part I requires 4 minutes on Machine A, four minutes on Machine B and five minutes on machine C. Each Part II requires five minutes on Machine A, one minutes on Machine B and six minutes on Machine C. The shop makes a profit of \$8 on each Part I and \$5 on each Part II. However, the number of units of Part II produced must not be less than half the number of Part I. Also each day the shop has only 120 minutes of machine A, 72 minutes of Machine B, and 180 minutes of Machine C available for the production of the two parts. What should be the daily production of each part to maximize the shop's profit?
A rectangular marquee 2002-05-07
From Alyaa:
a marquee with rectangular sides on a square base with a flat roof is to be constructed from 250 meters square of canvas. find the maximum volume of the marquee. i find this topic so hard
350 students took the math A exam 2002-02-22
From Jim:
at a high school 350 students took the math A exam. 82% passed the test. 40 students that failed the exam in june, took the exam in August. 70% of this group passed the August test. How many of the original 350 students have passed the exam before september?
Answered by Paul Betts and Penny Nom.
Getting to B in the shortest time 2001-12-19
From Nancy:
A motorist in a desert 5 mi. from point A, which is the nearest point on a long, straight road, wishes to get to point B on the road. If the car can travel 15 mi/hr on the desert and 39 mi/hr on the road to get to B, in the shortest possible time if......

A.) B is 5 mi. from A

B.) B is 10 mi. from A

C.) B is 1 mi. from A

Normal lines 2001-12-11
From Kristie:
Why are perpendicular lines called normal lines?
Undetermined coefficients 2001-11-22
From Hoda:
The equation is:

y" - 2y' + y = t et + 4

We need to use The method of Undetermined coefficients. I have tried assuming that the solution is Atet+Bet+C, but all I get is C=4 and I tried (At2+Bt+C)et+D, but again I get 0=0 when I calculate the first and second derivatives, so i get no information on the constants. Any suggestions?

A lighthouse problem 2001-11-02
From A student:
A lighthouse at apoint P is 3 miles offshore from the nearest point O of a straight beach. A store is located 5 miles down the beach from O. The lighthouse keeper can row at 4 mph and walk at 3.25 mph.

a)How far doen the beach from O should the lighthouse keeper land in order to minimize the time from the lighthouse to the store?

b)What is the minimum rowing speed the makes it faster to row all the way?

60 seconds in a minute 2001-10-11
From Andy:
I am a fourth grade teacher. Yesterday my students asked "Why are there 60 seconds in a minute?" Which also led to 60 minutes in an hour? I have had trouble determining why the number 60? Any help would be appreciated.
A phone bill 2001-06-18
From Janet:
What is the formuala to calculate cost per minute?

Here is the data below

# of calls - 238
# of minutes - 443
cost - \$70.06

Adding and subtracting rational expressions 2001-05-03
From Donna:
Adding and subtracting Rational expressions. I am in grade 10 and I am a student here is an example of the questions:

1/(x+1) - 1/(x-1) = ?

Dominos 2001-04-28
From Mark:
A standard dominoe set consists of 28 pieces, from double-zero to double-six

1. Is it possible to arrange all those pieces in a straight line in such a way that the dots of any pair of adjacent pieces match? Please include picture

2. Is it possible to arrange them in a circle and still meet the conditions in 1?

Hexominos 2001-04-05
From Tom:
What is a hexomino and how many different shapes are possible?
An emergency response station 2001-03-29
From Tara:
Three cities lying on a straight line want to jointly build an emergency response station. The distance between each town and the station should be as short as possible, so it cannot be built on the line itself, but somewhere east or west. Also, the larger the population of a city, the greater the need to place the station closer to that city. You are to minimize the overall sum of the products of the populations of each city and the square of the distance between that city and the facility. City A is 6 miles from the road's origin, City B is 19 miles away from the origin, and City C is 47 miles from the origin. The populations are 18,000 for City A, 13,000 for City B, and 11,000 for City C. Where should the station be located?
Answered by Claude Tardif and Penny Nom.
Airflow in windpipes 2001-03-25
From Ena:
The volume of air flowing in windpipes is given by V=kpR4, where k is a constant, p is the pressure difference at each end, R is the radius. The radius will decrease with increased pressure, according to the formula: Ro - R = cp, where Ro is the windpipe radius when p=0 & c is a positive constant. R is restricted such that:
0 < 0.5*Ro < R < Ro,
find the factor by which the radius of the windpipe contracts to give maximum flow?

Timing with hour glasses 2001-03-20
From Nathan:
How can a chef use an 11 minute hour glass and a seven minute hour glass to time a vegtable that needs to be steamed for 15 minutes.
Expanding determinants using minors 2001-02-20
From A student:
Question:
1) Determinants by expansion by minors.

i)
| 1 2 1 2 1 |
| 1 0 0 1 0 |
| 0 1 1 0 1 |
| 1 1 2 2 1 |
| 0 1 1 0 2 |

Law of cosines 2001-02-20
From Emily:
I missed a few days of class and I can't figure out how to solve Law of Cosines problems. I have the notes and formulas but I can't figure out how to do the math involved to answer the problems. I am also getting confused about how to use degrees and seconds in the Law of Sine and Cosine. I can't seem to get the correct answers and I don't really know how to solve them and enter them into my TI 86.
Vitamins A and B 2001-01-14
From Sara:
A diet is to include at least 140 mg of Vitamin A and at least 145 mg of vitamin B. these requirements are to be obtained from two types of food. type X contains 10 mg of vitamin A and 20 mg of vitamin B per pound. Type Y contains 30 mg of vitamin A and 15 mg of vitamin B per pound. if type X food costs \$12 and Type Y \$8 per pound, how many pounds of each type of food should be purchased to satisfy the requirements at the minimum cost?
Answered by Claude Tardif and Harley Weston.
Domain of a function 2000-11-15
From Mickey:
state any restrictions on the domain of the function.

y = 5x - 12 over 27x + 6 x does not equal what________?

Pillows and Cushions 2000-09-27
From Fiona:

The following problem was given to grade eleven algebra students as a homework assignment. To manufacture cushions and pillows, a firm uses two machines A and B. The time required on each machine is shown. Machine A is available for one full shift of 9.6 hours. Machine B is available for parts of two shifts for a total of 10.5 hours each day.

The smaller of a and b 2000-09-14
From Jenna:
For any two real numbers, a and b, give a mathematical expression in terms of a and b that will yield the smaller of the two numbers. Your expression should work regardless of whether a>b, a
A problem with a quadratic 2000-08-09
From David Xiao:
Find the value of a such that 4x2 + 4(a-2)x - 8a2 + 14a + 31 = 0 has real roots whose sum of squares is minimum.
PreCalculus 2000-08-09
From Angela:
Use absolute values to define the interval or pair of intervals on the real line.

```
<--|--- |--- ]--- |--- |--- |--- [---| ---|-->
18  19  20  21  22  23  24  25  26
```

A car is moving at the rate of 50 miles per hour, and the diameter of its wheels is 2.5 feet.
a) Find the number of revolutions per minute that the wheels are rotating.
b) Find the angular speed of the wheels in radians per minute.

Numerator and denominator 2000-06-18
From Maureen Beard:
What is the origin of the terms numerator and denominater?
Divisors of 2000 2000-06-06
From Amanda Semi :
1. find the product of all the divisors of 2000
2. dog trainer time has 100m of fencing to enclose a rectangular exercise yard. One side of the yard can include all or part of one side of his building. iff the side of his building is 30 m, determine the maximum area he can enclose

Thearcius Functionius 2000-05-03
From Kevin Palmer:
With the Olympics fast approaching the networks are focusing in ona new and exciting runner from Greece. Thearcius Functionius has astounded the world with his speed. He has already established new world records in the 100 meter dash and looks to improve on those times at the 2000 Summer Olympics.

Thearcius Functionius stands a full 2 meters tall and the networks plan on placing a camera on the ground at some location after the finish line(in his lane) to film the history making run. The camera is set to film him from his knees(0.5 meters up from the ground) to 0.5 meters above his head at the instant he finishes the race. This is a total distance of two meters(the distance shown by the camera's lens).

Minimizing the metal in a can 2000-05-02
From May Thin Zar Han:
A can is to be made to hold 1 L of oil. Find the dimensions that will minimize the cost of the metal to manufacture the can.
An integer max-min problem 2000-03-13
From Paul Servic:
Maximize Q = xy 2 where x and y are positive integers such that x + y 2 = 4
Maximize 2000-03-12
From Tara Doucet:
My question is Maximize Q=xy^2 (y is to the exponent 2) where x and y are positive integers such that x + y^2 ( y is to the exponent 2)=4
Two calculus problems 2000-03-03
From Tara Doucet:
1. The height of a cylinder with a radius of 4 cm is increasing at rate of 2 cm per minute. Find the rate of change of the volume of the cylinder with respect to time when the height is 10 cm.

2. A 24 cm piece of string is cut in two pieces. One piece is used to form a circle and the other to form a square. How should the string be cut so the sum of the areas is a maximum?

Slant height of a cone 2000-02-24
From Jocelyn Wozney :
I need help with this problem for my high school calculus class. Any help you can give me will be greatly appreciated-I am pretty stumped. "Express the volume of a cone in terms of the slant height 'e' and the semi-vertical angle 'x' and find the value of 'x' for which the volume is a maximum if 'e' is constant.
order 4+ determinants 1999-12-06
From Joe Kron:
Why is it never shown how to calculate the value of 4x4 (or larger size) deteminants by the diagonal multiply methods that are generally shown for 2x2 and 3x3 determinants? The method I'm talking about is called Cramer's Rule??? Is this method not extensible to order 4+ and if not why not? Anyway the method always shown for order 4+ is called "reduction by minors" which is not the answer to this question.
The elimination method 1999-12-02
From Jennifer:
Could I get an answer to this one:

2x+5y=36
3x+2y=32

I have to use the Elimination method, as I already know how to do Substitution. How do I begin and show my work? I'm attempting to eliminate the values for y.

Area of a circle and an inequality 1999-10-30
I have two problems.

The first: prove that the area of a cirlce is pi times radius squared without using calculus.

The second: show that ln(x) < x - 1 for all x > 0.

-log(a) 1999-10-22
From Brenda Miskimmin:
I need to know the mercury concentration in mg/L or ng/L for the following:

-log M (Hg) = 8.5

where mw of Hg=200.59

A double negative 1999-09-01
From Dennis:
If b = -2 what does -b = ? As in (a + 8.5) - [(-b) + |c|] a = 1.5, c = -1.7
From Nicholas:
A vertical wall, 2.7m high, runs parallel to the wall of a house and is at a horizontal distance of 6.4m from the house. An extending ladder is placed to rest on the top B of the wall with one end C against the house and the other end, A, resting on horizontal ground. The points A, B, and C are in a vertical plane at right angles to the wall and the ladder makes an angle@, where 0<@
Area of a triangle from vertex coordinates 1999-04-21
From Mark Tyler:
I'm no schoolkid, but I liked your answers about triangles. You might enjoy a quick look at this, the kids may too.

I was working on a Voronoi dual where I had to calculate the areas of very many triangles expressed as vertex coordinates, so I derived the following very direct formula:

A = abs((x1-x2)*(y1-y3)-(y1-y2)*(x1-x3)) for triangle (x1,y1)(x2,y2)(x3,y3)

I've never seen this in a textbook. Is it original? I doubt it, the proof is only a few lines long.

Regardless, it may be fun for the kids, even if it's not on the curriculum.

Linear programming and optimization 1999-04-09
From Shams:
What is Linear programming and optimization?
Answered by Jack LeSage and Penny Nom.
From Mary:
I would like to know how to simplify this question:
```
4 __________________ squareroot7 + squareroot3 ```
I know the answer is (sqrt7 - sqrt3) but i would really love to know how to get that answer!! Thanks.

Answered by Jack LeSage and Penny Nom.
Indeterminate forms 1998-12-11
From R. Dixon:
What is the correct evaluation of infinity/0 ? I've checked three different math sites. One says definitively, that infinity/0 is "not" possible. Another states that infinity/0 is one of the indeterminate forms having a large range of different values. The last reasons that infinity/0 "is" equal to infinity.
Answered by Walter Whiteley and Harley Weston.
Intersection of Planes 1998-12-03
From Lindsay Fear:
My name is Lindsay Fear. I am an OAC student (which is the Ontario equivalent to Grade 12 in most other states and provinces). I am in an Algebra and Geometry course and am currently studying a unit on equations of planes. Our teacher has given us this question that my friend and I have attempted several times, but we are still unable to solve it. My teacher has also suggested using the internet as a resource. The question is:

Prove that a necessary condition that the three planes

` -x + ay + bz = 0 ax -  y + cz = 0 bx + cy -  z = 0 `
have a line in common is that
a^2 + b^2 + c^2 + 2abc = 1

Terminating decimals 1998-11-16
From Debra Karr:
A college student studying elementary education asked me a question that I could not think of the correct answer. How can you look at a fraction and tell if is a terminating or non terminating decimal?
Answered by Jack LeSage and Penny Nom.
Operations Research 1998-10-08
From Lisa Barrett:
What is the history of operations research and the study of linear programming?
From Pam Bailey:
Can you help me simplfy this?

(1/2a + 1/3b) - (1/4a - 1/5b) + (1/6a - 1/7)

thanx

Triminoes 1998-09-09
From Roxanne Hale:
I am doing an investigation about a game called triminoes (like dominoes). The game is played using triangular pieces of card. Each card has 3 numbers on it. I have to investigate the relationship between the number of trimino cards in a set and the largest number on the cards. I found;

largest no. used 0 1 2 3 4
no. of trimino cards 1 4 10 20 35

I was ginen the formula for this which is:
UN= UN - 1 + 1/2 (n + 1 ) (n+2)

UN=no. of trimino cards n= largest no.

I don't know how to get to this equation I think it has something to do with triangle numbers!

Some Calculus Problems. 1997-10-30
From Roger Hung:
1. What real number exceeds its square by the greatest possible amount?

2. The sum of two numbers is k. show that the sum of their squares is at least 1/2 k^2.

3. .
.
.

Fractions 1997-10-20
From Rebecca Henry:
When we add fractions, we find a common denominator and add the numerators When we multiply fractions, we simply multiply both numerators and denominators with no regard to commonality.
1. Why do we not have to find a common denominator when multiplying?

2. Why do we multiply both numerators and denominators?

Billions and more! 1997-09-15
From Mahabir B. Gupta:
I would like to know how you americans write the number 1 billion.

Do you say "One thousand million"..can you answer by giving me examples?

1,000,000----> 1 million
1,000,000,000---->1 billion

Why is it that in spanish it is different?

Pentominoes 1996-11-14
From Sam Maraldo:
What is a pentominoe? I need to understand the concept and how/why it is used?
(-3)x(-2) 1995-10-25
From Azmat:
Why is (-3)x(-2) = 6?
Answered by Herley Weston and Ed Giesbrecht.
Terminologie mathematique 2010-10-31
Bonjour ,

Pourriez-vous m'indiquer les titre et auteur d'un bon dictionnaire francais anglais de terminologie mathematique ? Auriez-vous egalement l'adresse d'un site web traduisant du francais a l'anglais les termes ert expressions mathematiques ?

Merci par avance,

Calculs de minutes en heures 2009-02-23
From Denis:
Je suis en train de suivre un cours en navigation maritime et je dois changer souvent des minutes en heures. ex: 495 minutes = ?h??

Je désire avoir le cheminement le plus simple a faire pour ce type de calcul. Je ne travail pas avec excell. Je veux une formule a faire seulement avec une calculatrice élémentaire. Merci pour votre aide, j'apprécie beaucoup votre coup de main. Denis.

calcul heures et minutes 2008-06-08
je n'arrive pas à comprendre et resoudre mes problèmes d'heures et de minutes,ex parti à 22h30, j'arrive à 7h15 quelle est la durée du trajet
Combien d'heures et de minutes 2007-05-30
From masson:
pouvez vous m'aider pour resoudre ce probleme car je suis perdue combien d'heures et de minutes dormez vous si vous vous couchez a 22h15 et si vous vous levez a 6h57? car en suivant le raisonnement de la soustraction d'heure je trouve 15h12 et je trouve cela pas logique merci d'avance de votre aide
addition et soustraction des heures, minutes, secondes 2006-11-22
From Halnais:
13 h. 25 mn + 18 h. 06 mn
23 h. 31 mn + 19 h. 33 mn

je ne me souviens plus très bien de ces opérations, faut-il additioner les heures à part puis les minutes, etc. pour les heures je crois qu'il ne faut pas dépasser 24 h. Pourriez-vous m'aider, et me donner le résultat, merci infiniment.

Taux à déterminer 2006-11-01
From Barrault:
Une certaine année,un article augmente d' un certain taux "t" au premier semestre puis d' un taux triple du premier au second semestre, sachant que l' augmenation globale sur l' année est 66.75%; uels sont les taux pour chacun des deux semestres de l' année?
Matrice 2006-02-01
mon probleme est le suivant soit deux matrices carrees A et B d'ordre n qui sont anticommutatives AB= -BA , demontrer que au moins une des deux matrices n'est pas inversible si n est impair. je n'arrive pas a utiliser le fait que n soit impair, trouver le rapport entre n impair et inverse des matrices, je pars sur la base de DETAB=DETA*DETB
convertir une duree en heure et minute 2005-01-12
From Sébastien:
pouvez vous me donner la formule permettant de convertir une duree en heure et minute precise pour exemple : 589 minutes donne 10h35min. Quelle serait donc la formule pour passer directement de 589 min a 10h35 (sans avoir 9h81)?