







A pattern for a truncated cone 
20131220 

From Josh: I need to know how to layout a truncated cone with a base diameter of 18" a top
Diameter 15.25 and a height of 20". Your help will be greatly appreciated. Answered by Penny Nom with a spreadsheet by Don. 





Solving a cone 
20080129 

From Marija: [Note: this problem shows how to solve anything about a cone if you are given two measurements.]
Is there a formula for finding the diameter of the base of the cone? Answered by Stephen La Rocque. 





Pattern for a truncated cone 
20070511 

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. 





The graph of graph y= 2x1 
20171111 

From Natividad: How do you graph y= 2x1? Answered by Penny Nom. 





The volume of a cone without calculus 
20171002 

From Akash: How to find the volume of a cone without the knowledge of calculus? Answered by Penny Nom. 





An alphabetic sequence 
20170917 

From malik: find the letter of the following series....?
ZOTTFFSSE Answered by Penny Nom. 





The angle between two planes 
20170912 

From Arthi: Hello. hope you are having a good day.
I am stuck on a maths question in which it is asking, how to find the angle between two given planes. These planes are in a 3D shape such as a prism.
How can I do this?
Please reply as soon as possible
Thank You Answered by Penny Nom. 





Simultaneous equations with fractions 
20170909 

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. 





Simultaneous equations 
20170902 

From keto: xy=2,x^2+xy=12 Answered by Penny Nom. 





A pair of linear inequalities 
20170808 

From Hempstone: Solve the inequalities 3x5<2x+5>4x+9 Answered by Penny Nom. 





Catherine, Molly and Tom 
20170719 

From liezel: what is the answer of this problem, If Catherine and molly has 320pesos altogether, Molly and tom have 360 in all. Tom and Catherine have 240pesos altogether.How much does each of them have? Answered by Penny Nom. 





Parallel and Perpendicular lines 
20170717 

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. 





Exponential form 
20170706 

From estela: what is exponential form of 9×1000 Answered by Penny Nom. 





Solve the equation completely cos 2x = 1 
20170608 

From Lava: Solve the equation completely cos 2x = 1 Answered by Penny Nom. 





Simultaneous equations with fractions 
20170602 

From Jamal: 1/x + 1/y =5 and 1/y  1/x =1 Answered by Penny Nom. 





Two wires between two buildings 
20170511 

From Bill: I need to find the height of the intersection point of two building wires< br />
Building A is 860 feet high and building B is 480 feet high. The wires existent from the top of one building to
The bottom of the other < br />
The distance between is 32 feet Answered by Penny Nom. 





A lost iPhone pass code 
20170417 

From Sam: I have a locked iPhone and it has all my of my holiday photos on it. I changed the password and then I think I did a incorrect number pattern but anyway I know it ends with 99 and the first 4 digits are 235 and 6 could you please send all of the combinations for this password (without the 99) Thx and plz get back ASAP I need it for school Answered by Penny Nom. 





A function which is onto but not onetoone 
20170416 

From Avinash: Define a function f(x):N>N which is onto but not oneone.Where N is set of natural numbers. Answered by Penny Nom. 





Forming a cone from a circle 
20170415 

From Tasha: A sector of a circle subtends an angle of 216 degrees at the centre, If this sector is used to form a cone of vertical height ,8cm, calculate the base radius of the cone Answered by Penny Nom. 





A rectangular box filled with oil 
20170411 

From morpal: we want to calculate volume of rectangular box height 1275mm and lengths 2400mm and breadth 1270mm and oil s. gravity is .950 how much kg. of oil i can store Answered by Penny Nom. 





Successive Differences 
20170406 

From Twaha: Please find the equation of the sequence 1 2 4 7 11 16 22 Answered by Penny Nom. 





How to find last two or three digits of a large exponent like 17^256? 
20170330 

From Raginee: How to find last two or three digits of a large exponent like 17^256? Answered by Penny Nom. 





2^a, 2^b, 1^1 and 1^0 
20170317 

From Émile: If you had 2^a = 4 and 2^b = 4 you could assume that a = b right? Yet we can observe that 1^1 and 1^0 both equal 1, yet 1 = 0 isn't true. So if given a log base 1 number 1 the would the answer be 1 AND 0? Answered by Penny Nom. 





What is the grade of the incline? 
20170312 

From Jon: If I am climbing 16 feet in elevation over 80 feet horizontal. What is the grade of the incline Answered by Penny Nom. 





Exponential form 
20170304 

From michael: I was teaching my student about exponent when we stumbled across this problem.
"write (125)^3 in exponent form"
The problem is with the number "125". I think 125 = (5)^3. But one of my student thought that it is 125= 5^3.
Both of them is equal to 125 but they totally different in structure. I wonder which one is correct and why it is. I am worried if they get this wrong, it might spell problem in the future when we start substituting the numbers with variable.
Thank you very much for reading my question and answering it. Answered by Penny Nom. 





Five equations 
20170116 

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. 





One millionth of one percent of 90,000,000,000 
20170116 

From Gene: What absolute number is one millionth of one percent of 90,000,000,000 Answered by Penny Nom. 





Plans for dog kennels 
20170104 

From Pat: So... I'm trying to draw up a plan for my new kennel buildings. They are going to built
out of grain bins. I know, cool,... right. Anyway the kennels will be along the outside
of the circle and be shaped like wedges. the center will be a play area. All of the kennel
sides are 6 ft in length so the size of the gate will determine how many kennels I can
fit in each bin. If I want to put an odd number of kennels in and I cant draw
a straight line across to make all of the wedges the same size... how do I figure out the
angles...degrees ? maybe i'm making it too hard but i'd like to give the dogs as much space
as i can. I did up some ... attached. Answered by Harley Weston. 





Simultaneous equations with fractions 
20161221 

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. 





Joining a fitness center 
20161218 

From Salem: A fitness center offers a special price for groupclass students. The cost of registration is 30 dollars and then you have to pay 25 dollars per month. What is the rule of the equation in the light of c=m+? Answered by Penny Nom. 





How far apart are the boats? 
20161213 

From Halley: Two boats leave port at the same time. Boat A travels east at a speed of 12 km/hr. Boat B travels southwest at a speed of 14 km/hr. After two hours, how far apart are the boats? North is 0 degrees. How do I figure this out.
Thanks Answered by Penny Nom. 





Acres and miles 
20161130 

From Carolyn: If I am running a pipeline of 1,100 miles, how many one acre plots will it take to cover this distance?
Carolyn Answered by Penny Nom. 





2^x= 2x  11 
20161127 

From Kathy: I don't know how to start this problem:
2^x= 2x  11 Answered by Penny Nom. 





Simultaneous equations 
20161125 

From Rohan: x2/3 + y  1/4 = 13/12
2x/2 + 3 + y/3 = 11/6 Answered by Penny Nom. 





Parallel lines 
20161026 

From Jordan: (7,5) 3x 4y=5 Answered by Penny Nom. 





y = mx + c and Ax + By + C = 0 
20161018 

From Erick: please explain to me how to convert an equation from the form y=mx+c to Ax+By+C=o form. Answered by Penny Nom. 





A linear relationship 
20161016 

From Bianca: x represents the number of hours since 8am. y represents the number of children the school nurse has seen during the school day. The nurse has seen 3 children by 8am and 27 children by noon.
How many children has the nurse seen at 2pm?
If the nurse has seen 18 children, what time is it? Answered by Penny Nom. 





An airplane schedule 
20161014 

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. 





The equation of a line 
20161001 

From Miriam: write the equation of the line that passes through (6,7) and is perpendicular to 3x+5y=0 Answered by Penny Nom. 





The length of stock on a roll 
20160923 

From Ken: I have a roll that is 13.5 inches wide ( OD) , and is wound on a 3 inch core. the thickness of the material is 3.5 thick.
Do you know of a formula that can calculate the linear feet on that roll?? Answered by Harley Weston. 





The equation of a ski slope 
20160831 

From Hannah: The information provided is
A ski slope has a slope of 0.2. You start at an altitude of 10,000ft.
Then the question is "Write the equation giving altitude (a) as a function of horizontal distance moved (d).
I know this is probably a very simple question but I didn't take a math class my senior year and now I'm a freshman in college, so some of it is very frustrating to me.
Any help is much appreciated, thank you! Answered by Penny Nom. 





Exponential form 
20160831 

From Lily: Hi! I was wondering, I was having a little issue understanding this one problem. It was "write 81 in exponential 2 different ways" and I already got 9(2) but I was wondering what the second one could be! Thanks! Lily Answered by Penny Nom. 





Two sequences 
20160820 

From Ting: The first four terms of a sequence are 4, 20, 56 and 120. By comparing with the nth term of sequence 1,5,14 and 30 which is 1/6n(n+1)(2n+1), find a formula for nth term. Can you precisely show out how you do this questions ( with the steps please) Answered by Penny Nom. 





A cone inscribed in a hemisphere 
20160807 

From anonymous: A cone is inscribed in a hemisphere. the slant height of the cone is 20cm. When cut along its slant height, the cone forms a sector of a circle.
find the angle of the sector, to the nearest 1 decimal place. Answered by Penny Nom. 





The dimensions of a rectangle 
20160725 

From Krunox: A rectangle is twice as long as it is wide. Its perimeter (the sum of the lengths of its sides) is 60 cm. Find its length and width. Answered by Penny Nom. 





The temperature inside and outside a greenhouse 
20160722 

From Mehzad: Every day, the temperature in a greenhouse is at its low temperature, 70 degrees Fahrenheit, at 2 a.m. and at its high temperature, 84 degrees Fahrenheit, at 2pm. Its temperature increases linearly between 2 am and 2pm , and decreases linearly from 2 pm and to 2am. The outside temperature follows the same linear patterns, but has a low temperature of 60 degrees Fahrenheit at 2 am and a high temperature of 78 degrees Fahrenheit at 2 pm. At which of the following times will the temperature inside and outside the greenhouse be the same?
a) 8:00 am
b) 12:00 noon
c) 4:00 pm
d) The two temperatures will never be the same Answered by Penny Nom. 





Two equations with fractions 
20160722 

From kanesh: p/2+q/3=3
p/4+2q/3=3 Answered by Penny Nom. 





Simultaneous equations 
20160625 

From sena: 2x/3+3y/2=1
4x5y=22
simultaneous equation Answered by Penny Nom. 





The lateral side length of a cone 
20160605 

From Diane: Question is find the lateral side length of a right cone with area of 372 sq. cm and base circle radius of 9 cm. Answered by Penny Nom. 





A pair of equations with fractions 
20160511 

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. 





Solve 2^2x + 3(2^x)  4 = 0 
20160427 

From Lloyd: Solve the equation 2^2x + 3(2^x)  4 = 0 Answered by Penny Nom. 





600(1+0.05)^7 
20160421 

From chelsey: I am unsure on how to solve this problem, 600(1+0.05) 7 ? Answered by Penny Nom. 





A stained glass cone lamp 
20160409 

From Edwin: In making a 16" dia. cone lamp (stained glass), how many square feet of glass do I need. Answered by Penny Nom. 





The last two digits of a phone number 
20160403 

From Joshua: I want to find the last two digits of a phone number whose first eight numbers of a ten digit phone numbers are known. Answered by Penny Nom. 





The volume of a cone 
20160331 

From Odum: Find the volume of a cone with radius 6.5cm and height 12.6cm Answered by Penny Nom. 





Angles 
20160312 

From Laurynn: What are angles in general (please include the 'angle of incline')
Thank you
Laurynn Answered by Penny Nom. 





Corrosion inhibitor in a pipeline 
20160302 

From Edu: I have a 12 in pipeline and 5 miles long. I need to coat it with corrosion inhibitor how much chemical will I need Answered by Penny Nom. 





Solve for x and y 
20160227 

From ntshidi: Y=1/2x+4and1/4x6 Answered by Penny Nom. 





Perpendicular lines 
20160214 

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. 





Two equations in two unknowns 
20160213 

From Anumba: 4x + 2y = 4
7x  y = 11 Answered by Penny Nom. 





The equation of a vertical line 
20160207 

From Kagiso: The equation for a vertical line that goes through the point (7; 3) is? Answered by Penny Nom. 





Exponential form 
20160126 

From Jufe: What is the exponential form of ł√11x˛ Answered by Penny Nom. 





Exponential growth 
20160126 

From Paul: The value of a stamp was 0.03 in 1851. The value in 2011 is $50,000. If the value increased exponentially, what is the annual growth rate? Answered by Penny Nom. 





A system of linear equations 
20160124 

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
xy=9
x+z=12
zn=14
y+n=2 Answered by Penny Nom. 





The diameter of the top of a truncated cone 
20160124 

From Peter: I am trying to calculate the diameter of a truncated cone given
one diameter the height of the cone and a 10% taper from one end
to the other. For example a butter churn is 18" tall and 9" in
diameter at the base. the sides need to slope inward at 10%
What is the diameter at 9" and 18" Answered by Penny Nom. 





The perimeter of a one quarter acre square 
20160115 

From Kerry: If you have a perfect square that is one quarter of an acre what are the length of the sides and how do you arrive at the solution? thank you, Kerry. Answered by Penny Nom. 





The range of a function defined piecewise 
20160113 

From sarah:
f(x)={x2, x<2
{x^24, 2_<x_<2
{x+2, x>2
find the range Answered by Penny Nom. 





Two transport companies 
20160106 

From Brynleigh: The Sugar Sweet Company will choose from two companies to transport its sugar
to market. The first company charges $5096 to rent trucks plus an additional fee of
$200.75 for each ton of sugar. The second company charges $5500
to rent trucks plus an additional fee of $175.50 for each ton of sugar.
For what amount of sugar do the two companies charge the same?
What is the cost when the two companies charge the same? Answered by Penny Nom. 





A sequence 
20160105 

From Mia: the next three terms in each sequence. 0.4, 0.54, 0.68, 0.82, Answered by Penny Nom. 





A graph of the water level of a river 
20160105 

From emoni: Suppose that the water level of a river is 34 feet and that it is receding at a rate of 0.5 foot per day. Answered by Penny Nom. 





The height of a parabolic arc 
20151230 

From Tom: Is there an algebraic means to determine the highest point of a parabolic arc if the base and perimeter are known? Answered by Penny Nom. 





Constructing simultaneous linear equations 
20151228 

From Deborah: Linda thinks of a twodigit 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. 





Sierpinski Pyramid 
20151214 

From victor: Is a tetrix (a Sirpienski Pyramid/Tetrahedron) its own hyperplane?...alternatively, is it a hyperplane? Answered by Robert Dawson. 





The positive root of sin(x) = x^2 
20151213 

From Kemboi: Find the positive root of the equation sin(x) = x^2 Answered by Penny Nom. 





Linear equations in two variables 
20151213 

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. 





The line of intersection of two planes 
20151209 

From Rabz: Determine the vector equation for the intersection between the two given planes
2x+7y equal to 14,x+z equal to 7 Answered by Penny Nom. 





The height of a truncated cone 
20151204 

From Jack: I need to build a truncated cone that has a top of30 inches and a base of 64 inches . The sides need to be at a 64.5 degree angle. This will determine the height. Can this be calculated? Answered by Penny Nom. 





A tangent line to a parabola 
20151202 

From pei: Given that the line y=mx5 is a tangent to the curve y=2x^2+3 find the positive value of M. Answered by Penny Nom. 





Pouring a foundation 
20151127 

From Lisa: Hi im building a house 30ft long 18 ft wide I would like to pour a foundation of 6 inches
deep. How much sand, cement , 1/2" gravel do i need. Answered by Penny Nom. 





A concrete container 
20151112 

From Karstin: The exterior of a concrete container will be 10 feet by 8 feet by 4 feet tall. The walls and the bottom are 6 inches thick. What will it cost to construct it if concrete is $98.95/cubic yard? Answered by Penny Nom. 





The uniqueness of the lub 
20151025 

From Aishwarya: Prove that if the lub and glb of a set exist then they are unique Answered by Penny Nom. 





Exponential form 
20151017 

From Will: What is exponential form of 8? Answered by Penny Nom. 





The sequence 1,2,4,7,11,16... 
20151015 

From HEMANT: what is the next term in the sequence : 1,2,4,7,11,16,? Answered by Penny Nom. 





How can the probability be zero? 
20151013 

From anagha: Hi,
thank you for answering (beforehand)
The other day I was just thinking of circles and I came across this peculiar thing.
Most of'em say that there are infinite number of points on the circumference.
and, if it is true, if we spin the radius, the probability that it will point a a particular point is 1/infinity, right?
It didn't make any sense to me and so, I thought there might be an explanation or something of the kind...? Answered by Harley Weston. 





Mathematics 
20151013 

From anagha: Hi,
thank you for answering (beforehand)
The other day I was just thinking of circles and I came across this peculiar thing.
Most of'em say that there are infinite number of points on the circumference.
and, if it is true, if we spin the radius, the probability that it will point a a particular point is 1/infinity, right?
It didn't make any sense to me and so, I thought there might be an explanation or something of the kind...? Answered by Harley Weston. 





A tangent line to a circle 
20150903 

From Jamie: Use the Greek method to find an equation of the tangent line to the circle
x^2+y^24x+6y+4=0 at the points (3,2square root 23. Answered by Penny Nom. 





A two digit number 
20150821 

From Cameron: Write the 2 digit number that matches the clues.
My number has a tens digit that is 8 more than the ones digit. Zero is not one of my digits.
My number is ________. Answered by Penny Nom. 





The nth term 
20150704 

From ujjal: What is the nth term in the order 6,8,10.... Answered by Penny Nom. 





A tangent to y = x^3 
20150531 

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 stone walkway around a pool 
20150529 

From Jerri: I have a rectangular pool 15x30 and it will require stone placed around it 4 feet out and 4 inches deep how much will I need? Thanks, jerri Answered by Penny Nom. 





The intersection of a plane and a cone 
20150516 

From Tom: Is there a way to derive an equation that describes the perimeter of the intersection of a plane and a cone regardless of the angle of the plane to the cone. Assume that the plane does not cut through the base of the cone, the x, y, z location of the vertex is known, the distance from the vertex to the plane through the axis is know., and that the angle of the cone is known. Answered by Chris Fisher. 





The method of elimination 
20150501 

From oreanna:
Question from oreanna, a student:
How do u solve 2x+9y=3
7x4y=25 in elimination Answered by Penny Nom. 





A fraction with a negative exponent in the denominator 
20150430 

From ellen: 7/ab to the 4 power Answered by Penny Nom. 





An inequality 
20150419 

From mr.: Simplify the inequality √x>x and represent on a number line Answered by Penny Nom. 





A wireless fence 
20150418 

From Dave: I'm buying a wireless fence to keep my pet in my yard. It has a half acre range. In a straight line how far would that be? Answered by Penny Nom. 





Two airplanes 
20150414 

From john: two planes leave an airport at the same time, one going northwest (N35*W)at 400 mph and the other going east at 332 mph. How far apart are the planes after 4 hours to the nearest mile? Answered by Penny Nom. 





A word problem with fractions 
20150409 

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. 





A tangent to y=x^3 passes through (0,2) 
20150405 

From Kevin: Given that the curve y=x^3 has a tangent line that passes through point (0,2). Find the equation of the tangent line Answered by Penny Nom. 





n^2 is a multiple of 100 
20150330 

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 region defined by three lines 
20150316 

From Lucinda: find the area of the figure formed by the line y=5x+9 and the xaxis and yaxis. Answered by Penny Nom. 





A cone of maximum volume 
20150316 

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 Answered by Robert Dawson. 





Constructing a cone 
20150312 

From Levi: While the mathematics at the welding shop page was very helpful there is one vital part missing. If I have never built a cone how do I figure out how much bigger the diameter of my
circle has to be when laying flat on the floor verses the diameter when it has been pulled into a cone. Answered by Harley Weston. 





Extraneous solutions 
20150307 

From Emily: I have a question about Extraneous Solutions, Because I was recently researching to figure out
on how to determine that a solution is extraneous and many of the answers talked about how if a answer is negative
that it should always be extraneous but now I found out that positive solutions can also be considered as extraneous solutions
so that is why I am really confused Extraneous Solution's.
I would really appreciate it if you could clearly explain to me how to determine an extraneous solution from a normal solution.
Thanks,
Emily Answered by Chris Fisher. 





Two equations with fractions 
20150226 

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. 





A region described by inequalities in cylindrical coordinates 
20150221 

From Rahul: I am not able to visualize a solid given by inequalities as under (in cylindrical coordinate system)
0=
I know that (can visualize) first 2 inequalities say it is a cylinder of infinite length.
It seems that third inequality poses the restriction to the height as well as it makes us to remove a cone.
But I just can not understand it clearly.
Thanks in advance!
Regards,
Rahul Answered by Penny Nom. 





Two equations 
20150216 

From nigel: 2x+1/2y=1
6x3/2y=21 Answered by Penny Nom. 





The volume of a cone 
20150205 

From Linda: How do you calculate the volume of a cone that is 25cm high and has an angle of 20 degrees? Answered by Penny Nom. 





1,4,9,61,52,___ 
20150121 

From Mubashir: 1,4,9,61,,52,___,84,___,18,1,121,___
please tell me its formula and also that rule that is being applied here like adding 3 or subtracting 5 etc. Answered by Walter Whiteley. 





Largest cone in a sphere 
20150115 

From Alfredo: What is the altitude of the largest circular cone that may be cut out from a sphere of radius 6 cm? Answered by Penny Nom. 





A sequence 
20150113 

From cyaz: write a rule for each sequence then find next 3 terms for 7/8, 3 1/8, 5 3/8 Answered by Penny Nom. 





Missing digits in a phone number 
20150107 

From Janelle: I had a friend try and play a game on me, regarding phone numbers, so I only know the area code , and the last four digits of the phone number. Which means, there are 3 digits that I need to figure out all the possibilities to. Answered by Penny Nom. 





A line segment of length root 5 
20141215 

From angela: On the dot grid below, draw and label a line segment with length square root 5
the dot grid is 8 by 10 Answered by Penny Nom. 





A cone is 2/3 full of sand 
20141214 

From Janice: A cone with a radius of 3.5 cm and a height of 12 cm is 2/3 full of sand.
What is the volume of the sand inside? Answered by Penny Nom. 





Planar curves 
20141213 

From ann: what does planar curve mean in your definition of a cone? Answered by Penny Nom. 





1999 equations in 1999 unknowns 
20141128 

From Subrahmanya: Solve the following system of 1999 equations in 1999 unknowns :
x1+x2+x3=0, x2+x3+x4=0……., x1997+x1998+x1999=0,
x1998+x1999+x1=0, x1999+x1+x2=0.
(in x1,x2,...................,x1999 the numbers 1,2,.............,1999 are subscripts) Answered by Penny Nom. 





Exponential notation 
20141127 

From Jaqui: May sound super easy, but how would you SHOW that you simplified
3x3 to the power of 2 (the little 2)?
thank you!
Jaqui Answered by Penny Nom. 





Doubling the dimensions of a cone 
20141121 

From Hannah: If the volume of a cone of height 10 cm is 261.8 cm3, show that this
volume is increased by a factor of 8 if the dimensions of the cone are doubled. Answered by Penny Nom. 





Two quadratic equations 
20141120 

From rajesh: Sir,
I would like to discuss on question
Find the value of variable X and Y, equations are
X2+Y2+2XY=25
X2+Y22XY=1
Sir, my point is equation looks not so easy.My opinion is there many
(more than 4)value possible for both X and Y.
Kindly help me.
Waiting for your response.
regards,
rajesh Answered by Penny Nom. 





The cube root of 729 
20141112 

From Alexis: What would be the square root of 729 to the third power and could you
explain how to get the answer? Answered by Penny Nom. 





What is 3 squared? 
20141112 

From Christine: On a math test, it said "What is 3 squared?" It did NOT say "What's is (3)squared"
The teacher's explanation is that if there are no brackets or parenthesis, you ALWAYS square the number first then do the negative, so the answer should be 9, but I can't find anywhere that confirms this.
Help please. Answered by Robert Dawson. 





Prime factorization in exponent form 
20141031 

From Emma: I need to find out how to make a prime factorization of 120 in exponential form. Answered by Penny Nom. 





Water in a spherical container 
20141017 

From Natalie: A spherical container with radius 10cm being filled with water such that the water level, h cm, in the container increase at a rate of 0.5 cm s^(1). Show that the area of the horizontal surface of water, A cm^(2), in the container is given by A = π(20h  h^(2) ). Answered by Penny Nom. 





A linear system 
20141014 

From pheter: 4/x  1/y = 3 .... equation (1)
6/x  2/y = 5 .... equation (2) Answered by Penny Nom. 





One zero to a quadratic expression 
20141006 

From Kevin: Find a value of n such that f(x) = 3^x2 + nx + 6 only has one zero, is this the only solution to the question? Answered by Penny Nom. 





Sieve of Eratosthenes 
20141003 

From Hope: using Sieve of Eratosthenes to determine for in instance prime numbers between 1 to 200, to what nth number should i stop?, 4th, which is 11 or what? Answered by Robert Dawson. 





Trig functions and the unit circle 
20141002 

From Jake: I was wondering what conclusions can be drawn about the trigonometric functions and how they work about the circle. Can you also please give me an explanation for it? Thank you. Answered by Penny Nom. 





Two equations in x and y 
20140925 

From seyilogo: solve y=2x  3 and (4x  2y) / x + y = 1 simultaneously Answered by Harley Weston. 





Meetings for 77 students 
20140918 

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 
20140918 

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 
20140915 

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. 





Three collinear points 
20140828 

From jhanavi: p,q,r are three collinear points.p and q are(3,4) and (7,7) respectively and PR is equal to 10 units.find coordinates of R Answered by Penny Nom. 





Filling three holes with stones 
20140820 

From mark: how many tonnes of hardcore/crushed stone would it take to fill
1 hole 9ft diameter 5ft deep
and 2 holes both 3ft diameter and 5ft deep Answered by Penny Nom. 





1/3 of $320 
20140813 

From Student: Grade:5
Please help I got tutor for selective and this question is really
bugging me a lot what is 1/3 of $320?
plez answer quick before I fail :( Answered by Tyler Wood. 





The method of elimination 
20140705 

From leo: please explain how can i solve this problem
3x6y=38
6x9y=44
using elimination and simultaneous method thank you :) Answered by Penny Nom. 





An oval pool 
20140621 

From steve: I have a 16' x 28' oval pool that is buried 24" deep inground. The dig site is dug
2' wider all the way around the pool. I need to back fill this area with stone. I want to fill this area with 6 to 8"
of stone. How many tons of stone will this take?
Thanks you
Steve Answered by Penny Nom. 





Simultaneous equations 
20140620 

From rana: solve the simultaneous equations
a)3x=7y
12y=5x1 Answered by Penny Nom. 





Two regression lines 
20140614 

From catherine: Given a set of data values ,we can get two regression lines .Explain. Answered by Robert Dawson and Penny Nom. 





The equation of a line 
20140516 

From Michael: Find the equation of a line that passes through (2,1); the sum of the x and yintercepts is 2. (There are two answers) Answered by Penny Nom. 





A piecewise graph 
20140510 

From Zoe: Lightning Energy charges residential users for each unit of electrical energy bought from them each quarter, according to the scale below:
0500 units cost 17 cents per unit
5001500 units cost $85 plus 10 cents for each unit in the excess of 500
1500 or more units cost $185 plus 9 cents for each unit in excess of 1500
Sketch a graph showing the charge C as a function of U for up to 2000 electricity units Answered by Penny Nom. 





A question concerning two lines 
20140509 

From Hela: The equation of the line L is 6x+5y=3, and the equation of line Q is 5x6y=0, which statement below about the line is true?
A) same y intercept
B)parallel
C) Same x intercept
D)perpendicular Answered by Penny Nom. 





x  2 Sin[x] = 0 
20140508 

From chanmy: please help me to sole this equation x  2 Sin[x] = 0,thank you Answered by Penny Nom. 





If x+y+z=1 then x^2 + y^2 + z^2 = ? 
20140430 

From Nitin: If x+y+z=1
then
x^2 +y^2+z^2 = ? ? Answered by Robert Dawson. 





A cone of vision 
20140429 

From David: It is known that a fish in water looking up has a 97 degree "cone" of vision that sees "through" the surface of the water. If a fish lies 4 inches below the surface, the cone forms a window (circle) smaller than if a fish lies 8 inches below the surface. What is the ratio of inches of depth to the radius of the circle on the surface that is its visual window? Answered by Penny Nom. 





A triangular chicken pen 
20140427 

From Cierra: Margaret has two lengths of fence, 20 meters and 24 meters, for two sides of a triangular chicken pen. The third side will be on the north side of the barn. One fence length makes a 75° angle with the barn. How many different pens can she build if one fence is attached at the corner of the barn? What are all the possible lengths for the barn side of the pen?
Not sure what they are asking here... please show step by step what to do! Thank you so much! Answered by Penny Nom. 





A trig problem 
20140425 

From srishti: Consider the points P= (sin(ab),cosa), Q=(cos(ab),sina), R=(cos(ab+c),sin(ac), where 0 Answered by Chris Fisher. 





Simultaneous equations with fractions 
20140419 

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. 





A tangent of the curve (x/a)^n+(y/b)^n =2 
20140415 

From sudhir: the equation of tangent of the curve (x/a)^n+(y/b)^n =2. at(a,b) is Answered by Penny Nom. 





Two cones 
20140409 

From c.j: what is the length of the radius of the LARGER cone(the LARGER cone has a slant height of 15) when the SMALLER cone has a radius of 8 and a slant height of 12ft ,please help. Answered by Penny Nom. 





The sides of a triangle 
20140406 

From Michael: I am supposed to sove for the length of side "b" of an irregular triangle. I am given the following:
Side a: 65'
Side b: Find this length
Side c: 50'
Angle A: unknown
Angle B: unknown
Angle C: 52 degrees
I am supposed to use the law of cosines to solve for side "b" and my teacher
says there is no mistake in the "givens" for the problem. I do not see how
this can be done using the law of cosines and i have not figured out how to sove for
angle B to use the law of cosines. Answered by Penny Nom. 





An inequality 
20140327 

From James: a step on a stairway is at least 8 inches high. write and solve an inequality to represent the maximum number of steps between floors that are 10 feet apart Answered by Penny Nom. 





Ms. Werenich's nickels, dimes and quarters 
20140319 

From London: Ms. Werenich has twice as many dimes as nickels and 4 more quarters than nickels. If she has $4.50, how many of each coin does she have? What would the let statements be of this problem and can you solve it? Answered by Penny Nom. 





A circle which is tangent to two perpendicular lines 
20140309 

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. 





Determine the selling price 
20140308 

From augustine: knowing an auctioneer charges a 7% fee and I know I want $74,400 what is the formula to determine selling price. Answered by Penny Nom. 





A cone inscribed in a sphere 
20140228 

From joel: how can I find the radius and the height of a cone INSCRIBED in a sphere, given the sphere having a radius of 6? ( note: the diameter of the cone is equal to its slanted height). Answered by Penny Nom. 





Four digit phone numbers 
20140225 

From Tom: Hi, I'm an online math teacher, working on lessons for my students.
This question is in their book and I can't do it...! Help!
It has to do with phone numbers, and in this problem,
we are only dealing with
the last 4 digits of the number.
It asks how many possible numbers we have
if at least one digit repeats in the last 4 digits of the number. Answered by Penny Nom. 





The diameter of the base of a cone 
20140223 

From elwin: i have a sector of a circle that has 120 degree and 6 cm length. What will be the diameter of the base of the cone.
and what is the diameter of the angle is changed to 180. Answered by Harley Weston. 





Paycheck after deductions 
20140223 

From Louise: So I got a paycheck for 89.02 they took out in deductions 15.69.
I want to know the percentage they are taking out so that I can figure my take home pay each week before I get it. So I know what to expect for pay each week so I can budget my bills from now on a weekly basis. If I know the percentage than I can just figure out the percentage through how many hours in the week I worked and multiply my gross pay and know what my take home will be Answered by Penny Nom. 





Three investment partners sharing the profit 
20140222 

From Ayatullah: Hello;
We are three partners and bought a property at 2050000 and sold at 2300000.
Details of investment of the partners
X= 1500000
Y= 400000
Z = 150000
My questions are
1) How could i calculate percentage of investment of each partner?
2) How could i deduct 30% commission from each partner in profit?
3) How could i distribute the profit amongst the partners?
Thanks in advance Answered by Penny Nom. 





What is the exponential form of 1/square root of 6v? 
20140216 

From Prince: What is the exponential form of 1/square root of 6v Answered by Penny Nom. 





Simultaneous fractional equations 
20140215 

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
(x2)/(y1)=1/3 Answered by Penny Nom. 





Water in a conical funnel 
20140211 

From Marcus: Water is running out of a conical funnel at the rate of 1 inch^3/sec. If the radius of the base of the funnel is 4 in. and the altitude is 8 in., find the rate at which the water level is dropping when it is 2 in. from the top. Answered by Penny Nom. 





A sequence 
20140210 

From Joshua: hello..the question I have today is... A sequence... 1,5,14,30,55,91 find the general terms. Answered by Penny Nom. 





The volume of a cone 
20140208 

From hibba: why is the volume of right circular cone divided by 3? Answered by Penny Nom. 





Prime factorization 
20140206 

From Kadeejah: Write the prime factorization of 37 in exponential form Answered by Penny Nom. 





A sequence 
20140130 

From joshua: hi...really struggle with one question that the teacher gave us...
The sequence is 1,2,1,5,8,1,11,___,___ Answered by Penny Nom. 





Two nonlinear equations 
20140126 

From Naryn: (1÷x) + (1÷y) = (7÷12)
xy = 12 Answered by Penny Nom. 





An inequality 
20140125 

From LANELL: this is a problem to solve: 1/3 + 2/7 >=x/21  part of the answer is (oo)
not exactly that similarit is on a calculator as a symbol sure you know what it is I am talking about the x will be a number Answered by Penny Nom. 





Mixing water and wine 
20140119 

From manish: a man mixes three part of water to one part of wine.When he consumes
one part of mixture he realise that the drink is too dilute and hence adds one part of
wine to the remaining quantity what is the ratio of water to wine in the new mixture. Answered by Penny Nom. 





An inequality 
20140117 

From Rosie: 4x/x2<3
four x divided by x2 is less than or equal to 3 Answered by Penny Nom. 





Fractions and exponents 
20140111 

From john: what is the exponent form of 9^4/7^2 and 6^3/10^5 Answered by Penny Nom. 





A boxandwhisker plot with one whisker 
20140109 

From Susan:
Question from Susan, a teacher:
I read your answer to the question about could a box & whisker have NO whiskers.
It made sense to me. However I am preparing for my advanced class and I have a sample graph comparing box plots of data.
Several of the box have only 1 whisker. There is no explanation for this. Can you help me out. I cannot think of a data set that would produce this. Thanks! Answered by Penny Nom. 





When would one flip the inequality sign? 
20140109 

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. 





A scalene triangle 
20140107 

From cherry: Hi
I have been given a scalene triangle of sides 
8m, 6m, and 10m ..
Please help me to find out the area and help me to find out the height .. Answered by Penny Nom. 





25% profit 
20140102 

From Finn: Hello,
The question is all about buyandsell business.
Problem:
Pencil  $6 for whole sale price
$8 if I sell the item
How do I get the 25% profit? (you can change the whole sale price and the retail price[if i sell the item])
if I buy the pencil at 24 pieces and sell it at 24 pieces. Answered by Penny Nom. 





The slope of the line y=2x+5 
20131229 

From victoria: what is the slope of the line with the equation y=2x+5 Answered by Penny Nom. 





Distance from a point to a line 
20131228 

From Sue: I need to find the distances from the west line on 1st Take Point and 2nd
Take Point.
Thanks,
Sue Answered by Penny Nom. 





A linear equation 
20131226 

From khushboo: A farmer sowed wheat and paddy in two fields of total area 5000 sq.m. Write a linear equation and draw a graph to represent the same? Answered by Penny Nom. 





Find the next 3 terms of the sequence 
20131219 

From Lanelyn: Find the next 3 terms of the sequence 2,3,9,23,48,87,__,__,__ Answered by Robert Dawson. 





7 digit phone numbers 
20131208 

From Sean: Hi I was wondering how you would calculate how may 7 digit phone numbers there are with only odd digits? Answered by Penny Nom. 





How do I graph y=2x1? 
20131207 

From cindy: How do I graph y=2x1? Answered by Penny Nom. 





Exponential form 
20131201 

From Alina: My question says to express each number in exponent form in as many different ways as I can; 16, 81 and 64. How do I do this? Answered by Penny Nom. 





What is the slope of this line? 
20131201 

From Charlene: What is the slope of this line? Answered by Penny Nom. 





n log n = 36 * 10 ^ 12 
20131112 

From shihab: How to find value of n in this equation :
n log n = 36 * 10 ^ 12 Answered by Penny Nom. 





Substitution type simultaneous equations 
20131103 

From Kayla: I am having problems with substitution type simultaneous equations, when the variable you are substituting is a algebraic one:
y=x^23x+4 and 3x2y=1
I have rearranged 3x2y=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. 





A plane 
20131027 

From Thomas: Why is this 3d plane flat?
if m ≠ n
arcsin(sin(m*arctan(x/y))), arcsin(cos(n*arctan(x/y))),
Piarcsin(sin(m*arctan(x/y)))arcsin(cos(n*arctan(x/y)))
This is using radians.
These are angles of a triangle, when m and n are the same it is a right triangle. All three inputs are not equal to each other. The last input is pi minus the first two inputs, which makes a complete triangle.
I was kind of hoping to find more lissajous curves. It doesn't make sense to me that this is a flat plane, a diagonal one at that.
I'm not a student or anything. I'm just wasting time. Answered by Chris Fisher. 





Extraneous solutions 
20131022 

From tom: i need an equation where x=2 is the correct answer and x=3 is an extraneous solution. can you provide me with such an equation?? Answered by Harley Weston. 





A frustum 
20131012 

From Lily: A cone of height 6in. and radius of base 4in. has its top cut off by a plane parallel to its base and 4in from it.
Find the volume of the remaining frustum.
I have worked out the volume of the entire cone but I don't know how to work out the radius of the top of the frustum.
Thanks Answered by Penny Nom. 





Proportional rates 
20131010 

From Varsha: A province's Ministry of Social services has found that both the number of people needing social assistance and the province's total expenditures on social assistance are proportional to the rate of unemployment. Last August when the provincial unemployment rate was 8.4 %, the province provided assistance to 89,300 individuals at a total cost of 4107.4 million. The forecast unemployment rate for next August is 7.9%. How many people can the province expect to need social assistance next August? What amount should the province budget for social assistance in August? Answered by Penny Nom. 





Maximize the volume of a cone 
20131009 

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 line through (5, 1) 
20131008 

From allison: find an equation in standard form for line passing through point (5,1) and perpendicular to line x=4 Answered by Penny Nom. 





A triangle problem 
20131002 

From raneem: ABC is a triangle in which : BC=20cm. M(<B) =29 and m(<C)=73 . D is the midpoint of BC
Find the length Of AB and AD approximated to 2 decimal places Answered by Penny Nom. 





A Holeinone on all four par 3's 
20130904 

From Robert: There are four (4) par 3's at a specific 18 hole course.
One member has the honor of making a Holeinone on all four par 3's.
It has taken him 8 years to do it!
How does one go about computing the odds of this TREMENDOUS accomplishment?
Respectfully,
Robert laffal Answered by Victoria West. 





Ordering crushed stone 
20130903 

From Prakash: Dear Sirs,
I am working in a Soft Landscaping contracting company. If I need to purchase crushed stone with the size 5070mm for $53,429 m^2$ area, how many 20feet containers should I need to order to my suppliers? The 20foot container has internal dimensions 5,897 mm by 2,348 mm by 2,285 mm and the $53,429 m^2$ area is to be covered by 10 cm of stone. Answered by Harley Weston. 





Two perpendicular lines 
20130815 

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 yintercept of 4." I have no clue how to do this. Please help me! Answered by Penny Nom. 





A system of equations 
20130813 

From Nina: 3x2y=8
x+3y=5
What is the solution of the system of equations Answered by Penny Nom. 





An equation in slopeintercept form 
20130812 

From Brittney: write an equation in slopeintercept form of the line that is parallel to the grapg of y=3/4x+6 passes through 8,5 Answered by Penny Nom. 





Differentiate x^x  2^sinx 
20130809 

From tarun: derivative of x^x  2^sinx Answered by Penny Nom. 





Slicing through a cone to form an ellipse 
20130806 

From Pulkit: we get an ellipse on slicing through a cone. Is there a relation between central axis of the cone and this ellipse?
Does it pass through the any of the foci of the ellipse? Answered by Chris Fisher. 





Simultaneous equations 
20130710 

From Warren: solve this simultaneous equation: xy=4
2x+3y=14 Answered by Penny Nom. 





A one acre plot of land 
20130619 

From Carol: If I have a one acre plot of land, what is the measurement in feet on each of the four sides? Answered by Penny Nom. 





An isosceles tiangle 
20130616 

From Izzy: what's the height of an isosceles triangle which has a base of 50 m, and both of the other sides are 25 m? Answered by Penny Nom. 





A kennel for a beagle 
20130603 

From david: Hi, I'm building some beagle kennels and I am in need of help with an angle problem. I need to place a roof on my kennel with a drop of 2inches across 3ft 10inches. the posts on the right side will be 5ft and the post on the left will be 4ft 10in. the posts are 4x4 and the space to be covered is 3ft 10in from the outside of the 4x4. Please help, thanks. Answered by Penny Nom. 





Simson line 
20130523 

From Nazrul: From any point p lying on the circumcircle of the triangle perpendiculars
PD , PE are drawn on BC,CA respectively. The line segment ED intersects at
the point 0 ; prove that PO ⊥ AB ( PO is perpendicular to AB ). Answered by Chris Fisher. 





siin (A) and sin (A/2) 
20130509 

From shanaia: given that sin A=4/5 and A is obtuse.find sin (A/2) Answered by Penny Nom. 





650*(1+0.005)^96 
20130417 

From joAnn: i am trying to figure out how to solve a question like this for example:
650(1+.005)96
I have been doing it this way but takes forever and wanted to know a shorter way
650 x 1.005 x 1.005 x 1.005 x 1.005 96 times
HELP Answered by Penny Nom. 





A cone problem 
20130414 

From Courtney: Hello,
I am having difficulty solving this cone problem. The biggest challenge I have is figuring out what angle they are talking about:
The angle at the base of a cone is 34.5 degrees. Find the diameter of the cone at point on the edge of the cone 26cm from the tip. Answered by Penny Nom. 





How do i write log_8(P) =7 in exponential form? 
20130414 

From nancy: How do i write this in exponential form log8P =7 Answered by Penny Nom. 





4 linear equations with 3 unknowns 
20130412 

From Marian: how to solve for 3 unknowns in 4 simultaneous equations Answered by Penny Nom. 





The equation of a line 
20130404 

From Miranda: My coordinates provided are (6, 6) and (8, 9) and i need to put this into ax=bx=c format. I remember the equation to find the slope of y2y1/x2x1 to get the slope. However when i put that back into the y=mx+b format it still leaves me with a lot of variables. Please help :) Answered by Penny Nom. 





The distance between 2 lines in 4D 
20130401 

From samane: how can i measure the distance between 2 lines in 4D?? Answered by Chris Fisher. 





We can't write sinx and cosx as a finite polynomial. 
20130331 

From rimoshika: prove that we can't write sinx and cosx as a finite polynomial. Answered by Walter Whiteley. 





Simultaneous equations with fractions 
20130331 

From Terence: 5/x6/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 
20130324 

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. 





A linear programming problem 
20130227 

From Kelley: A manufacturer of skis produces two types: downhill and crosscountry. 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 
Crosscountry 
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 

Answered by Penny Nom. 





An equation with exponents 
20130224 

From Chelsea: (81 to the power of 3n+2 over 243 to the power of n) is equal to 3 to the power of 4
Find the value of n.
The answer I got was n is equal to negative (4 over 7).
The answer in my text was n is equal to negative (4 over 17) Answered by Penny. 





Write a rule for the sequence 
20130220 

From Angelia: Write a rule for the sequence. Then, find the unknown term. 1 3/8, 1 ľ, 2 1/8, _______, 2 7/8 Think: The pattern is increasing. Add 1/6 to find the next term. Rule: _______________ Answered by Penny Nom. 





Extraneous solutions 
20130218 

From Eileen: (5x+4)^1/23x=0 Answered by Penny Nom. 





A word problem involving toys 
20130214 

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. 





Dropping supplies from an airplane 
20130214 

From Claire: An airplane flying at an altitude of 3500 feet is dropping supplies to researchers on an island. The path of the plane is parallel to the ground at the time the supplies are released and the plane is traveling at a speed of 300 mph.
a) write the parametric equations that represent the path of the supplies
c)How long will it take for the supplies to reach the ground?
d) how far will the supplies travel horizontally before they land? Answered by Penny Nom. 





Is a line lying in a plane an open or a closed region? 
20130213 

From pardeep: please help with this question on the open and closed intervals ::
Is a line lying in a plane an open or a closed region? my teacher says it is a closed region reasoning out that it contains all it boundary points. please help how is it so? Answered by Harley Weston. 





Simultaneous equations 
20130210 

From Michael: 2P + 1/3V =8
3P  2/V=5 Answered by Penny Nom. 





The height of a sheet metal cone 
20130209 

From Charles: Sheet metal cone.
I need a cone with a finished base of 38.19719 diameter
The cone is to be from a 48 diameter round with the wedge cut out.
The best calculation I have is the arc is 286.479. (correct?)
Could you verify this arc angle but more so what is the cone height? Answered by Harley Weston. 





Exponential form 
20130205 

From Sandra: What is 37,008 in exponential form? Help me please!!! Answered by Penny Nom. 





The fourth side of an irregular polygon 
20130201 

From Emran: I have a irregular polygon. I know 3 of the 4 sides, and 2 of the angles. AB is 285, BC is 149, and CD 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. 





How many edges does cone have? 
20130128 

From Meriem: how many edges does cone have pls? Answered by Lorraine Dame, Chris Fisher and Walter Whiteley. 





A geometry word problem 
20130124 

From Matthew: "G", "A" and "B" are collinear. "A" is between "G" and "B". "GA" Is 14 less than 3 times "AB". "GB"=46 Find "GA"
How would you solve this? Answered by Penny Nom. 





A triangular island 
20121229 

From Udit: A long time ago Mr Gibson found an island shaped as a triangle with three straight shores of length 3 km,4 km and 5 km. He declared an 'exclusion zone' around his island and forbade anyone to come within 1 km of his shore. What was the area of his exclusion zone? Answered by Penny Nom. 





Solve 2x^4+x^337x>26x^2+12 using a graphical approach. 
20121229 

From Tehmas: Solve 2x^4+x^337x>26x^2+12 using a graphical approach.
I don't know how to find the xintercepts or yintercepts in this form. Answered by Penny Nom. 





A 4 digit phone lock using the digits 4, 2, 3 and 0 
20121224 

From Ragu: I would like to know formula for searching a combination of 4 digit. eg.
I knew my Phone Lock combination is my car plate number 4230. But
this time, i used another way around instead of 4230.
But I am sure, there is only this 4 digits only. 4 & 2 & 3 & 0 Answered by Penny Nom. 





Sinx=logx+x^2 
20121128 

From yasmin: Sinx=logx+x^2 Answered by Harley Weston. 





5<2x+1<1 
20121111 

From Rahul: How does 5<2x+1<1 changes to 1<2x+1<5. What is the rule?
Can we apply absolute value function throughout the first inequality i.e. can we say 5<2x+1<1. But then it becomes 5<2x+1<1 which is impossible because 5 is not less than 1. Answered by Penny Nom. 





What's your secret? 
20121111 

From ryan: Tuscan school has a fair. At the fair, Pia plays "what's your secret?
The game starts with 3 players who are told the same secret.
Each of those 3 players tells another 3 player, and so on.
At the end of the 3rd round, everyone who knows the secret
will compare what they have heard. What number in exponent form
represents the number of people who know the secret after 3 rounds?
How many people is that?
Thank you very much.
P.S. I got 3 cube. which is 27
But when i map it out I end up with 39. Answered by Penny Nom. 





How fast is the distance between the aircraft and the car increasing? 
20121024 

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. 





A label to cover a plastic cup 
20121023 

From Kevin: I'm trying to make a label to cover the entire outer area or a plastic cup. I know there must be a way to figure out the dimensions needed, but I can't seem to figure it out. The circumference of the bottom of the cup is 21.4cm and the circumference at the top of the cup is 29.8cm. The cup is 14.5cm tall. What should the height of the arc from the plane connecting the two ends of the 21.4cm arc. I attached a diagram where x is the value I'm looking for. I'm guessing there is some simple relationship between the length of a line and the arc needed to turn that line into a perfect circle, but I don't know what it is. Can you figure this out and share it with me? Thanks.
Kevin Answered by Penny Nom. 





A proof by contraposition 
20121019 

From Rahul: I am not able to understand the following,
To prove that if for all e>0, x0, then x>=e. I understand the approach very well but I do not understand why if x=e then x>=e. If it is so then why not x=
Thanks in advance!'
Rahul. Answered by Penny Nom. 





The nth term of a sequence 
20121019 

From Emily: I don't understand how to do this question:
Nth term for 9, 7, 5, 3, 1
Is there a fast way to do nth term for this question? Or in fact any question? Answered by Penny Nom. 





Composition of functions and one to one 
20121017 

From Ariana: If f o g are one to one function,does it follow that g is one to one? Give reasons for your answers Answered by Penny Nom. 





A tank with an inner walled compartment 
20121012 

From don: I have a tank 20 feet diameter, 19' 8" tall with an inner walled compartment that has a 7' 6" radius arc with in the tank. I need to figure out the volume of the inner area and the volume of the larger area. Answered by Harley Weston. 





A word problem involving a fraction 
20121012 

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. 





GST in New Zealand 
20121010 

From Colleen: I work out my claimable gst each month but need to know the total sales or purchases amounts for filling in my six monthly paper work. How do I do that. I tried doing the opposite of calculating the gst i.e. x3 and /23 but it is slightly different to my total. Answered by Penny Nom. 





A problem that yields a linear equation 
20121007 

From Eshraj: one fourth of a whole number is three more than one fifth of the next whole number.find the whole number Answered by Penny Nom. 





Changing the sign of an inequality 
20120919 

From Bryauna: Why do you change the signs in inequalities?! Answered by Penny Nom. 





Functions 
20120918 

From nayeem: I tried with many functions but I am not getting the exact values please help me
A give an example of a function whose domain equals the set of real numbers and whose range equals the set the set {1,0,1}?
B Give an example of a function whose domain equals (0,1)and whose range equals [0,1]
C.Give n example of a function whose is the set of positive integers and whose range is the set of positive even integers
D. Give an example of a function whose domain is the set of positive even integers and whose range is the set of positive odd integers
E give an example of function whose domain is the set of integers and whose range is the set of positive integers.
F. Give an example of function whose domain is the set of positive integers and whose range is the set of integers.
please show me the work
Please give me the trick of finding such functions Answered by Robert Dawson and Harley Weston. 





Functions 
20120918 

From nayeem: I tried with many functions but I am not getting the exact values please help me
A give an example of a function whose domain equals the set of real numbers and whose range equals the set the set {1,0,1}?
B Give an example of a function whose domain equals (0,1)and whose range equals [0,1]
C.Give n example of a function whose is the set of positive integers and whose range is the set of positive even integers
D. Give an example of a function whose domain is the set of positive even integers and whose range is the set of positive odd integers
E give an example of function whose domain is the set of integers and whose range is the set of positive integers.
F. Give an example of function whose domain is the set of positive integers and whose range is the set of integers.
please show me the work
Please give me the trick of finding such functions Answered by Robert Dawson and Harley Weston. 





Cones, pyramids, cylinders and prisms 
20120913 

From Roy: I read on this page that a pyramid is a special kind of cone, but a cone is not a pyramid. Does this apply to cylinders. Is a prism a special kind of cylinder, but a cylinder is not a prism? Answered by Robert Dawson. 





Row echelon form 
20120905 

From Jennifer: Hello, my name is Jennifer. I am a 12th grader in PreCalculus and I was wondering if you may help me with Row Echelon Form.
x + 2y  3z = 5
2x  4y  6z = 10
3x + 7y  2z = 13 Answered by Penny Nom. 





A tangent to f(x) = 1/x 
20120904 

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. 





Exponential form 
20120904 

From angie: How do i write 9^5 in exponential form? Answered by Penny Nom. 





Exponntial form 
20120830 

From Robin: My math teacher has asked the question:
"Write mmmxxjmyy2 in exponential form"
How would you solve this problem? Answered by Penny Nom. 





Making a wind sock 
20120828 

From John: I am trying to build a wind sock and need to be able to lay the shape
out on cloth. I need the wind sock front opening (diameter) to be
3 1/2" and the rear opening diameter to be 1". The windsock needs
to be 9 1/2" long. I tried using the example of the person trying to
make a crayfish trap but got confused and could not figure out my
numbers. Any help would be greatly appreciated.
Thanks
John Answered by Penny Nom. 





Problem solving 
20120815 

From Sugavanas: If length of a rectangle exceeds its width by 5 m. if the width is increased by 1m and the length is decreased by 2 m, the area of the new rectangle is4 sq m less than the area of the original rectangle. Find the dimensions of the original rectangle. Answered by Penny Nom. 





The exponential function form f(x)=a^x 
20120813 

From Lucy: Hi,
Why does the "a" value in the exponential function form f(x)=a^x have to be negative? Answered by Penny Nom. 





A plane travelling with the wind and against the wind 
20120803 

From Gwen: The time of a plane trip of 450 miles, with the wind is 3/5 the time of the return trip against the wind. If the plane travels 120 mph in still air, what is the wind speed? Answered by Penny Nom. 





John's electronic store 
20120725 

From Jora: Electronic Store
John opened an electronic store in December. During his first month,
He sold 10 LCD TVs and 20 Plasma TVs. His income during that
month was $12800. In January, he sold 25 LCD TVs and 40 Plasma
TVs for an income of $27600.
In February he projects to sell 30 LCD TVs and 50 Plasma TVs.
If John expenses are $28900 in February, how much money will he
have after paying the expenses? Answered by Penny Nom. 





A pile of topsoil 
20120723 

From Perry: I have a pile of topsoil that is 42ft long and 16ft tall shaped like a cone how many yards of topsoil do I have. Answered by Penny Nom. 





Fence post holes 
20120719 

From Gerry: Hello, I'm digging 30 8" dia holes, 5 ft deep for fence posts that are 4"x 4" Can you please help me figure out how much stone dust I should order for all 30 holes. Thanks Answered by Penny Nom. 





A truncated cone: the central angle 
20120717 

From Tom: I have researched several sites, including this one and am fairly confident I can do the calculations required to produce the two radii and the slant height for a truncated cone.
I a somewhat confused by the central angle. Some sites indicate that it should never exceed 180 degrees while others do not. Different examples on your site seem to use this in two different ways in constructing a truncated cone.
Sometimes the angle seems to indicate the section to be removed, while in other examples the angle seems to indicate the section to be saved. Since the two angles will always total 360 I am confused about how to use the info to
calculate the minimum rectangle required to contain the pattern. I'm guessing that in some cases I may need to use the chord or sagitta to determine the desired height and width of the material. Any help is greatly appreciated.
Thank you.
Tom Answered by Penny Nom. 





2x+underroot2=3x43underroot2 
20120709 

From Eshraj: 2x+underroot2=3x43underroot2 Answered by Penny Nom. 





Expanded exponential form? 
20120612 

From Ramon: express the numbers 990 614 000 005 in expanded exponential form. Answered by Harley Weston. 





The position of an aircraft relative to the airport 
20120608 

From Dennis: "Air traffic controllers usually describe the position of an aircraft relative to the airport by altitude, horizontal distance, and bearing. Suppose an aircraft is at altitude 500m, distance 15km, and bearing 35 degrees east of north. What are the x,y, and z components (in meters) of the position vector. The xaxis is east, the yaxis is north and the zaxis is vertical. Answered by Penny Nom. 





A lamp shade 
20120515 

From Fleur: I am helping my child make a cone lampshade, the measurements are as follows in "cm's"
21 cm = height
8 cm = top diametre
40 cm = bottom diametre
Please could you give the pattern (cut out) dimensions for final cut. Answered by Penny Nom. 





cos(theta/30) = 1 
20120514 

From Hope: cos (theta / 30 = 1
I am very confused as to how to solve it. Can you help? Answered by Penny Nom. 





An equation of the form y=mx 
20120417 

From Samiya: what would be an equation of the form y=mx with the points (2, 6) and (1, 3) for the line? Answered by Penny Nom. 





Using Newton's Method to find a root 
20120409 

From Nancy: Use Newton's method to find the real root function, accurate to five decimal places
f(x) = x^5+2x^2+3 Answered by Penny Nom. 





The spread of a rumor 
20120409 

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. 





Radioactive decay 
20120402 

From Christy: Hello, how do I go about answering this question?
Should I be using the formula Ce^(kt)?
Given that the decay constant for Radium is .000428/year, how long, to the nearest year, does it take a sample to decay to 15% of its present mass? Answered by Penny Nom. 





The equation of a line 
20120326 

From Danielle: Hello, could you help me figure out what the equation of the line is in the form of Ax+By=C with the points (2,0) and (0,3)?
Thank You! Answered by Penny Nom. 





A cubic inequality 
20120325 

From Victoria: The flight path of a bumblebee above the ground can be modelled by the function f(x)= 2x^3 17x^2+ 11x + 130. Where x is the time in seconds and f(x) represents the height in inches above the ground. The entrance to the bee's hive is located 100 inches above the ground. Determine when the bumblebee's height is greater than 100 inches. The bee's height was monitored from 0 to 25 seconds inclusive. (over the domain 0 Answered by Penny Nom. 





A vertical line passing through (10,4) 
20120316 

From Isabelle: Hi! My question is this:
Write the equation of each line described:
A vertical line passing through (10,4)
I would really appreciate your help!
Thanks,
Isabelle Answered by Penny Nom. 





Forming a triangle from 3 line segments 
20120315 

From rustom: A point X is selected at random from a line segment AB with midpoint 0. Find the probability that the line segments AX, XB, and A0 can form a triangle. Answered by Penny Nom. 





A water tank is in the shape of a truncated cone 
20120308 

From Victoria: Suppose you have a water tank in the shape of a truncated cone. The larger diameter is K, the smaller diameter is K/2, and the height is also K (all measured in meters). The force of gravity on an object of mass, m, is F=9.8m (measured in Newtons). The density of the water is 1000 kilograms per cubic meter. What is the volume of the tank and how much mass will the tank have when it is full? Answered by Penny Nom. 





81+8 to the 3 power 
20120308 

From KiMesha: 81+8 to the 3 power Answered by Penny Nom. 





2x^3*2x^2/3x^2 
20120306 

From hope: 2x^3*2x^2/3x^2 Answered by Penny Nom. 





The dimensions of a conical tent 
20120304 

From yash: a conical tent is to accommodate 11 people.Each person must have 4m square of space on the ground and 20m cube at air to breathe.Find the height and radius of the conical tent.26202 Answered by Penny Nom. 





Integral 1/(25x^2)^3/2 
20120222 

From John: Integral 1/(25x^2)^3/2 Answered by Harley Weston. 





A cylindrical container 
20120214 

From KRIS: YOU ARE PaCKAGING 4 EQUAL SIZED PAINT CANS WITH A RADIUS 8CM AND A HEIGHT OF 20CM, IN A CIRCULAR CONTAINER.What is the surface area of the packing container? Answered by Penny Nom. 





The curvature of the earth 
20120208 

From sean: Question from sean, a student:
Two people 1.8 metres tall walk directly away from each other until they can no longer see each other (due to the curvature of the earth, which has a radius of about 6378 km).
A) Find a function relating the height of two identical objects with the distance between them using the scenario above as an example.
B) Sketch this function (you may use Graphmatica if you wish). Over what domain and range does the function exist?
C) Describe this relation in practical terms. Answered by Harley Weston. 





Building a tipi 
20120129 

From Lacy: Hi there!
We are building a tipi for our children. We want to build a large one about 15ft tall with a base of about 15 feet diameter. I am trying to figure out how much canvas we need to accomplish this. I graduated about 20 years ago and am struggling. Please help if you can. Answered by Penny Nom. 





Tangent of theta 
20120117 

From stahl: explain what the 'tangent of theta' means. Draw and label a diagram to help with your explanation. Answered by Harley Weston. 





Exponential form 
20120115 

From Helen: How do you write (1/x) in exponential form? Answered by Penny Nom. 





Four apples and two oranges cost Rs. 30... 
20120113 

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? Answered by Harley Weston. 





An equilateral triangle and some circles 
20120110 

From tushar: draw an equilateral triangle with side 6cm.draw 3circles with radii 3cm on each angular point of triangle.draw common tangent on each of two circles Answered by Penny Nom. 





A straight line distance 
20120106 

From Margaret: If you traveled 300 miles east and 275 miles north, how many miles would you save by going in a straight line? Answered by Penny Nom. 





The volume of a frustum of a cone 
20111224 

From CV: If I know the height, taper, and volume of a frustum cone,
what are its Radii?
Calculating frustum cone volume is straight forward.
v=Pi/3*h*(R*R+r*r+R*r) where;
v=volume;
h=frustum height;
R=major radius;
r=minor radius;
Pi=3.1415926;
t=taper, ('slant angle' where t=0 is a disk)
Here is the tricky part.
Knowing 'h', 't', & 'v';
Calculate one or both of 'R' & 'r'.
Specifically, what is the formula for 'R=' or 'r='? Answered by Penny Nom. 





Three sides of a triangle 
20111224 

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 
20111219 

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. 





Augmented matrix 
20111214 

From Britney: Write Augmented matrix and use row reduction to solve.
I need major help with this problem! Tomorrow is my semester test and I have no idea how to do this.
2x+5y=8
yx=10 Answered by Robert Dawson. 





Exponential form 
20111212 

From Zoey: What is the exponential form of 1/8?? Answered by Penny Nom. 





A railway bridge over a road is in the shape of a parabola 
20111123 

From Brennen: A railway bridge over a road is in the shape of a parabola,
and the bridge is 3 m high in the middle and 6 m wide at its base.
A truck that is 2m wide is approaching the bridge.
What is the maximum height that the truck can have and
still pass under the bridge? Explain.
Thank you!! Answered by Penny Nom. 





I started with Euler's identity and manipulated it 
20111114 

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 
20111111 

From Reuchen: Find equations of the lines tangent to y^2=4x and containing (2,1). Answered by Penny Nom. 





A log equation in exponential form 
20111111 

From Sarah: Express the equation in Exponential form
log2 to the 16th power=4 Answered by Penny Nom. 





The slope of a line 
20111110 

From Sara: Line k lies in the xyplane.
The xintercept of line k is 4.
And line k passes through the midpoint of the line segment whose endpoints are (2,9) and (2,0).
What is the slope of line k?
Give the answer as a fraction. Answered by Penny Nom. 





A spherical ball in a conical wine glass 
20111026 

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. 





Linear equations 
20111006 

From Hannah: I am confused about a question on my homework, here is an example on what I need to do:
You own a sightseeing boat tour. Kids' admission costs $5, adults' admission costs $8.
During that day you get (madeup number) $521 with 71 admissions.
How many of each passenger boarded?
I tried something like
5x + 8y = 521
x + y = 71
But, I still don't understand how to solve it! Help? Answered by Penny Nom. 





Exponential form? 
20110830 

From Emily: I have a 6th grader that needs to find out what is the exponential form of 461,885,811 Answered by Penny Nom. 





A pattern for a cone 
20110830 

From Izzy: I need to create a cone as a prop and my math is not good enough to create the pattern.
Here are my instructions :
The diameter is 2'5" and it has to be 4 feet tall. It is a giant cone. I want it to be pointy at the end, not truncated. Answered by Penny Nom. 





Exponential form 
20110823 

From kiara: The African bush elephant is the largest land animal and
weighs about 8 tons . Write the amount in exponential form . Answered by Robert Dawson. 





Two line segments in the plane 
20110815 

From Tim: For this problem I actually have tried to visualise the image in my head many times. This question makes my head spin.
Four points lie in a plane. They are partitioned into two pairs so that the sum of the lengths of the segments joining the points of each pair has the minimal possible value.
Prove that these segments have no common points. Answered by Chris Fisher. 





A sequence 
20110814 

From intesar: how do i figure this out 0,1/6,2/9,3/12 Answered by Penny Nom. 





The third term of a sequence 
20110813 

From sammantha: Find the 3rd term of the sequence, an=1.5(4)n  1. Answered by Penny Nom. 





A cone with an oval as a base 
20110803 

From Emily: Hi, I was wondering how to calculate the surface area of a cone with an oval as a base (which I think is referred to as an elliptic cone or something like that). I have the both the maximum and minimum radius as well as the height, but I don't have a slant height and I'm not sure how to calculate it and then calculate surface area. I would really appreciate some help. Thanks! Answered by Robert Dawson. 





An equation in the form Ax+By=C 
20110728 

From Mike: I need to write an equation in the form Ax+By=C
The points I was given are (5,0) and (3,5)
I know how to find the slope I got 5/8 and wrote it out as y=(5/8)x+b however I'm not quite sure where to go from here.
Any help would be greatly appreciated. Answered by Penny Nom. 





A stained glass lamp 
20110725 

From Guy: Like Kay, I also work in stained glass, but in 3dimensions. I am
frequently asked to replicate lamp shades in stained glass where the
diameter of the top is different (narrower) from the diameter of the
bottom (which is wider). Some people want 5, 6, 7, 8, 10, 12, 16, ,,,
nsided shades. Is there a formula I can use to determine the width
of the sides using the angle, if I remember correctly, I think it's
called theta. In other words, is there a formula where I can plug
in the angle which describes the arc of the circle. For instance, if
someone asks for a 7 sided shade, plugging in 51.43 (360/7). I
could then use that to determine the width at the top and bottom
rings to create the appropriate trapezoids. I've visited a few sites
so the formula looks like its a function of sin & cos but they are
presented like proofs for teaching. Your site appears to want to
actually answer questions without making the inquirer feel stupid. Answered by Harley Weston. 





A linear equation with fractions 
20110713 

From Simon: I would like to ask if you would be able to explain : linear equation: 2 1/2 (X1)  x+3 /3 = 4 , the first step shows multiplying by 2 then multiplying by 3. etc. What I don't understand is where the 2 in multiplying by 2 comes from? ( the three is pretty obvious being x+3 /3 (to get rid of the divided by) ) .
Thanks for your help. Answered by Penny Nom. 





A line tangent to f(x)=1/x 
20110605 

From Michael: A line tangent to f(x)=1/x in the first quadrant creates a right triangle
with legs the xaxis and the yaxis. Prove that this triangle is always
2 square units regardless of where the point of tangency is. Answered by Penny Nom. 





Exponential form 
20110518 

From Kara: How do I write this in exponential form?
log 1/8 = 3 Answered by Penny Nom. 





Numbers with a digit 9 
20110513 

From Veronica: How many numbers between 200 and 750 have a 9 for at least one of the digits? Answered by Penny Nom. 





An exclusion zone around a triangle II 
20110503 

From Aishwarya: A long time ago Mr gibson found an island shaped as a triangle with three straight shores of length 3km, 4km and 5km. He declared an exclusion zone around his island and forbade anyone to come within 1km of his shore. What was the area of his exclusion zone?
This question was answered but did not understand the explanation. Answered by Robert Dawson. 





The nth term 
20110430 

From Samantha: predict the general term, or the nth term, An for the sequence.
1/2,2/3,3/4,4/5,5/6 Answered by Penny Nom. 





The radius of a cylinder 
20110427 

From Jazmin: Hi, I don't understand how to find the radius in a cylinder with only the surface area (143.7) and the height (0.8)? I know that the formula is 2pir2+2pirh, but I don't see how to isolate the r? I appreciate your help. Answered by Penny Nom. 





(27^r^1)^2/3 
20110424 

From YungJu: (27^r^1)^2/3 Answered by Penny Nom. 





Cone story problem 
20110416 

From Chelsea: There is a cone with a story problem that states only that the radius is the same as the altitude and that the slant height of the cone is 6cm. I have no idea how to figure this problem out. Answered by Penny Nom. 





The volume of a flower pot 
20110407 

From kp: I have 2 flower pots with the following dimensions that I am trying to calculate the
volume of Soil I will need to fill them. pot #1 29"tall, top of pot 31.5 inches across( radius of 15.5") the bottom of the pot is 21"across (radius 10.5)
Pot #2 29"tall, top of pot 26 across (radius 13") the bottom of the pot 17'"a cross (radius 8.5")
thank you
KP Answered by Penny Nom. 





Eliminate y 
20110407 

From Lynn: 2x + y = 8
y + 3z =5
z + 2w =1
5w + 3x = 9
Form three equations with y eliminated Answered by Penny Nom. 





A conical container and a spherical balloon 
20110406 

From Steven: Water is running out of a conical container 12 feet in diameter and 8 feet deep (vertex down) and filling a spherical balloon.
At the instant the depth of the water in the cone is 4 feet, the radius of the sphere is approximately 4 feet.
The rate of change of the depth of the water in the cone at the instant is approximately ______________ times the rate of change of the radius of the balloon. Answered by Penny Nom. 





A transversal 
20110330 

From Jillian: I don't understand finding angels in a transversal Answered by Penny Nom. 





sin x = 0.25 
20110329 

From Wayne: How do you solve for x in the equation sin x = 0.25
the answer is 3.394 and 6.030 but I don't know the steps they used to calculate this Answered by Penny Nom. 





New Brunswick hst 
20110325 

From andy: what is the short formula to get the hst 13% out of the total price of an item Answered by Penny Nom. 





Linear inequalities 
20110325 

From Alice: OK. I'm in algebra 1 and the linear inequality is
y<2x1
y>2
I don't completely know how to graph y>2 and I'm getting really frustrated
Please help me in any way possible!
Thank You! Answered by Penny Nom. 





The number of points on a line is equivalent to that of a surface 
20110324 

From Gary: I I was reading about how the number of points on a line is equivalent to that of a surface. This was done by taking any point on a line then taking alternating digits and making them as points on an x and y axis therefore points on a surface.The problem is as i see it if you just take a line then hold it over a surface you have just put the points on the line in a one to one correspondence with the points directly under it on the surface.Now you have all the rest of the surface which cannot be mapped onto the line since it is already used up.What am i missing? Answered by Penny Nom. 





What is x to the power of 0? 
20110323 

From Jason: What is x to the power of 0? Answered by Robert Dawson. 





6 faces and 8 corners 
20110304 

From noemi: jeff made a figure with 6 faces the figure has 8 corners all of the faces are the same size and shape what figure did jeff make Answered by Penny Nom. 





A camera's line of sight 
20110226 

From MJ: A rocket that is rising vertically is being tracked by a ground level camera located 3 mi from the point of blast off when the rocket is 2 mi high its speed is 400mph At what rate is the (acute) angle between the horizontal and the camera's line of sight changing Answered by Penny Nom. 





At what rate is the grain pouring from the chute? 
20110226 

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. 





Cutting the top off a conical tent 
20110222 

From tom: how far from the top must you cut a conical tent in order to cut the
cloth in half... Answered by Penny Nom. 





Making a truncated cone 
20110218 

From lisa: We need to make a cone that has the following dimensions.
143/8" diameter on large end
133/8" diameter on small end
4" tall
What are the dimensions I need to cut in order to make a cone with one seam? Answered by Stephen La Rocque. 





Two conical tanks 
20110217 

From rustom: Two vertical conical tanks (both inverted) have their vertices connected by a short horizontal pipe.
One tank, initially full of water, has an altitude of 6 ft. and a diameter of base 7 ft.
The other tank, initially empty, has an altitude of 9 ft., and a diameter of base 8 ft.
If the water is allowed to flow through the connecting pipe, find the level to which
the water will ultimately rise in the empty tank (Neglect the water in the pipe.) Answered by Penny Nom. 





Points on a graph 
20110215 

From Maggie: Which set of ordered pairs can be used to graph y = 2x1.
A.(5,9),(1,3),(4,9) B. (2,5),(1,1),(5,9)
C.(2,5),(0,1),(4,3) D. (5,9),(2,3),(4,9)
I cannot figure it out. Could you help me? Answered by Penny Nom. 





The equation of a circle 
20110214 

From Cristela: find the equation and all the information in General Form and Standard Form of the Circle that will passed trough the point (2,3) (6,1) (4,3) Answered by Stephen La Rocque. 





Calibrating a conical tank 
20110205 

From Bill: Hi, I have a round tank with tapered sides where I know the diameter at the top and bottom. Is there a formula I can use to calculate the volume by measuring from the bottom up the side (at the angle of the side) to any given point? Thanks, Bill Answered by Stephen La Rocque and Penny Nom. 





The nearest one and a half and the nearest inch 
20110202 

From Miranda: REASON:sarah gave the same answer when asked to round 4 seven eighth inches to the nearest one and a half and the nearest inch. explain why sarah is correct? Answered by Penny Nom. 





A cone with a specific angle 
20110201 

From John: Hi my daughter came with a seemingly easy question (which to me it was not)
How to make/calculate a cone of a specific angle from top to bottom radius. Answered by Penny Nom. 





(7cubed * 8(exponent6))exponent 6 
20110129 

From Shalaine: What is the exponential form of (7cubed•8(exponent6))exponent 6? Answered by Penny Nom. 





The sequence 2,3,5,5,8,7,11 
20110119 

From taylor: number relationship in number sequence 2,3,5,5,8,7,11 Answered by Chris Fisher and Penny Nom. 





Points with distance 5 from the point (2, 1) 
20110119 

From Alexa: Find all points having a xcoordinate of 2 whose distance from the point (2, 1) is 5. Answered by Penny Nom. 





Flipping a cone over 
20110117 

From Fionna: The height of your cone is "x".
Holding the cone so that the vertex is at the bottom, fill it half full with water. The depth of the water is "1/2x".
Put a lid over the top, and flip it over.
What is the new depth of the water, now that the cone is flipped? Answered by Penny Nom. 





What is next in the sequence? 
20110113 

From jodi: what is next in the sequence 1, 1/4, 1/9, 1/16, 1/25 Answered by Penny Nom. 





The angle between a line and a plane 
20110112 

From tom: what are the angles of the diagonal of a rectangular parallelepiped 2in by 3 in by 4 in
makes with the faces...
You know this is a problem that I can't figure out ...I don't know where
the angle and the diagonals where? can you help me with this one? Answered by Penny Nom. 





Line segments 
20110104 

From Izsak: What is the formula to find the number of segments that can be named by a given number of points on a line? Answered by Penny Nom. 





A tangent line 
20110103 

From Amanda:
Question from Amanda, a student:
an equation of the line tangent to y=x^3+3x^2+2 at its point of inflection is
(A) y=6x6
(B) y= 3x+1
(C) y= 2x+10
(D) y=3x1
(E) y=4x+1 Answered by Penny Nom. 





Exponential form 
20110102 

From jumana: find any five examples of exponential form from real life situation Answered by Penny Nom. 





A truncated cone 
20101231 

From jagjeet: dear suppose i have cone of 50cm radius at base and 100cm radius at top at a height of 80cm. now keeping base radius of 50cm and height of 80cm i want to increase top radius to 150cm how will i do that. plz height m talking abt is vertical height not slant height Answered by Penny Nom. 





An inequality 
20101213 

From jimmy: 1.7b1.1 <2.3 Answered by Stephen La Rocque. 





A water tank has the shape of a right circular cone 
20101207 

From mike: A water tank has the shape of a right circular cone with height 12 feet and radius 8 feet. Water is running into the tank so that the radius r (in feet) of the surface of the water is given by r=0.75t where t is the time (in minutes) that the water has been running. the volume V of the water is given by V=1/3 pi r^2h. Find V(t) and use it to determine the volume of the water when t=5 minutes. Answered by Penny Nom. 





Simultaneous equations 
20101205 

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. 





Can determine if it is scalene, isosceles, or equilateral 
20101201 

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. 





Linear inequalities with absolute values 
20101201 

From ryan: Good day!
We we're given this assignment in algebra concerning linear inequalities with absolute value.
In this number I'm confused how to isolate the absolute value, considering there is a variable in the absolute value and there is a variable in the outside.
2+5 43t+t ≤ 34t Answered by Penny Nom. 





What is its speed in still air? 
20101128 

From Shelby: An Airplane flies a certain distance in 3 hours going WITH a 40km/hr wind. It travels the same distance in 5 hours when going against the wind. What is it's speed and how long would it take to travel the same distance in still air? Distance = speed x time Answered by Penny Nom. 





How long will you and your friend be able to talk? 
20101123 

From beket: you and your friend leave your home town at the same time your friend travels by train 45 mph directly east while you travel by train 50 mph going directly south you are talking on cell phone but you plan charges extra if the phones are 100 miles apart. How long will you and your friend be able to talk before the charges increase? Answered by Penny Nom. 





How far must the pitcher travel to get to the ball? 
20101104 

From ken: A baseball player bunts a ball down the first base line. It rolls 35ft at an angle of 26 degrees with the first base path. The pitchers mound is 60.5 ft from the plate. How far must he travel to get to the ball. Answered by Penny Nom. 





What is the speed of each car? 
20101104 

From Jennifer: two cars are 420 miles apart and traveling towards each other along the same road. They meet in 3.5 hours. One car is traveling 15mph slower than the other. What is the speed of each car?
This must be solved using a system of equation, I have no idea? Answered by Stephen La Rocque. 





Two algebraic expressions 
20101029 

From chaptay: what is the difference between x(n^2) and x(n)^2 Answered by Penny Nom. 





A rectangle with rounded corners 
20101021 

From Connie: How do you find surface area if the rectangle is 100ft. by 200ft. with quarter circles in the corners with a radius of 20ft. ? Answered by Penny Nom. 





Powers 
20101020 

From dylan: how do you write 20736 in exponential form .same for 1728 and 50625.
is there a formula to figure out how to express large know numbers in exponential form. Answered by Penny Nom. 





An exponential equation 
20101019 

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
0500
1600
2720
3864
41037
51244
61493
71792
82150
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. 





The equation of a line 
20101019 

From Sava: I have to write an equation and sketch a graph for the line that meets the given conditions:
A line with slope 15/5 that passes through the point (2.5,4.5) Answered by Penny Nom. 





The angles in an mgon and genrealizations 
20101016 

From Michael: Hello:
In answer to a student's question, someone named Penny from
your organization provided a proof that the sum of the interior
angles of a triangle in the plane is pi radians (or 180 degrees).
I am interested (and I'm sure many other people would be too) in
3 potential generalizations of this basic fact in plane geometry: Answered by Walter Whiteley. 





A linear system 
20101015 

From Sandy: HARD!! algebra (Linear Systems) question?
An Airplane cruises at 120km/h in still air. One day, when the wind was blowing steady from the west, the airplane travelled west (flying into the wind) and landed at its desination after 1.5h. The airplane's return trip (flying with the wind) was only 1.0 h long. On both legs, the airplane travelled at its cruising speed. (meausred with respect to the air surrounding the airplane).
Part A
Write a System of equations that would allow you to determine the speed of the wind blowing that day and the distance travelled each way
Part B
When solving the system of equations graphically, what equations would you enter into the equation editior (to make graphs on your calculator)
Part C
Indicate what the X and the Y represent Answered by Stephen La Rocque. 





Two jets leave denver at 9 am. 
20101015 

From Carl: two jets leave denver at 9 am. One flying east at a speed of 50 km per hour greater than the other which is traveling west. At 11 am the planes are 2500 km apart. Find their speeds. Answered by Stephen La Rocque. 





Mathematics and medicine 
20101013 

From Dixie: need equations used in medicine for medicine and intravenous administration Answered by Penny Nom. 





Can a function be both even and one to one? 
20101009 

From Tracy: Can a function be both even and one to one? Answered by Harley Weston. 





Exponential form 
20101006 

From celina: what is the exponential form of 4x*4x Answered by Penny Nom. 





rat sequence 
20100924 

From Vishal: this is known as rat sequence. I want to know the logic pf this :
1,2,4,8,16,77,145 Answered by Chris Fisher. 





A Squared Number That's Negative 
20100922 

From David: What is the only number that when it's squared becomes negative? Answered by Stephen La Rocque. 





Limits 
20100920 

From rodrigo: what's the limit of x+1/x1, when x tends to 1? Answered by Janice Cotcher. 





Six nines 
20100916 

From Steph: It's sort of one question. We have to use six nines to get the numbers 130. I got all but 22, 23, 24, and 30. Like 15 is 9+9(9+9+9)/9. Answered by Penny Nom. 





A strip of land 
20100915 

From Walter: How many linear feet of strip of land 15 feet wide does it take to make 1 acre? Answered by Penny Nom. 





La racine carrée et l'exposant une demie 
20100914 

From Alain: Bonjour.
Je cherche une explication sur l'équivalence entre les exposants
fractionnaires et les racines ničme.
Par exemple, comment prouvet'on que la racine carrée correspond ŕ
l'exposant une demie?
merci Answered by PierreLouis Gagnon et Claude Tardif. 





(5xy)^5 
20100910 

From ana: (5xy)^5 Answered by Penny Nom. 





A building and a flag pole 
20100909 

From paul: A flag pole and a building stand on the same horizontal level. From the point p at the bottom of the building,the angle of elevation of the top t of the flag pole is 65 degrees. From the top q of the building the angle of elevation of the point t is 25 degrees.If the building is20 meters high. Calculate the distance pt Answered by Penny Nom. 





A logarithmic equation 
20100908 

From Rohit: x^2 + k*ln(x)  c  k = 0
Where k and c are constants. Answered by Penny Nom. 





What is 2^2? 
20100825 

From alex: I know that (2)^2 is 4 but what is 2^2? Answered by Robert Dawson and Penny Nom. 





Exponential form 
20100824 

From Courtney: What the Exponential form? For Ex. X2*X5*X4?? Answered by Penny Nom. 





Remainders 
20100717 

From GARY: WHAT NUMBER DIVIDED BY 11 LEAVES 1, DIVIDED BY 13 LEAVES 8, AND DIVIDED BY 17 LEAVES 3. Answered by Chris Fisher. 





A play tent 
20100628 

From Susan: Hi!!!
I am making a play tent as seen at the link below and need to figure out how to get the dimensions for the cone shape. The one shown has 4 different seams, but I guess I can get away with just one seam to sew it together (?) I need it to go over a hula hoop as that is what I am using for the round support at the top. My hula hoop is
35" in diameter from outside edge to outside edge. I would like the height of the teepee to be around 30" from the center to the peak.
Thanks so much, oh my gosh, I have been fretting for 2 days about this and my hair is about to fall out!!!!
Please contact me if you need any additional info.
~Susan
http://www.landofnod.com/family.aspx?c=52&f=4100 Answered by Penny Nom. 





The intersection of two graphs 
20100627 

From Austin: In depth explanation of how to find the intersection points of functions y=4t+300 and y=4.9(t5)^2+300 Answered by Stephen La Rocque. 





Volume of a styrofoam cup 
20100623 

From Stacy: how do you find the volume of a truncated cup with height of 3, top diameter of 2.5, and a bottom diameter of 2 Answered by Penny Nom. 





A linear relationship 
20100622 

From Laura: The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it cost her $300 to drive 480 miles and in June it cost her $460 to drive 800 miles.
Question: Express the monthly cost C as a function of the distance driven d, assuming that a linear relationship gives a suitable model. Answered by Robert Dawson. 





Exponential form 
20100616 

From charlotte: what is the exponential form of 6x6x6x5x5x5x5= Answered by Robert Dawson. 





My phone is "sim locked" 
20100610 

From Daniel: Question from daniel:
got a phone that says sim locked, it requires 09 digit code to get in, how many combinations could there be if you could please list the possibilities, the number can be repeated. Answered by Penny Nom. 





Graphical Representation of Complex Numbers 
20100608 

From Anas: why do we write complex number a+ib as (a,b)? Answered by Janice Cotcher. 





4 > 3m7 >= 2 
20100605 

From pamela: The question is
4>3m7>=2 Answered by Penny Nom. 





graph y=(2x^23x)e^ax 
20100531 

From James: graph y=(2x^23x)e^ax Answered by Robert Dawson. 





x/a +y /b =a+b : x/a^2+ y/b^2 =2 
20100530 

From smithu: x/a +y /b =a+b : x/a2+ y/b2 =2 solve by using elimination method ,
cross multiplication, substitution method Answered by Penny Nom. 





More on a truncated cone 
20100528 

From Mike:
Question from Mike, a parent:
I was reviewing this question and answer:
http://mathcentral.uregina.ca/QQ/database/QQ.02.06/phil1.html
But I have trouble with this part:
Now if we express the radius of the inside circle as r and the outside circle's radius is R, then this means r/R is 911/1728. But earlier we said that the outside radius R is simply w more than the inside radius r, so R = r + 282. That means that r/R = r/(r + 282). Now we can simply solve the equation for r:
r/(r+282) = 911/1728
This means r = 314 mm (with rounding).
Can I get more detail on the method to solve for r?
Thank you,
Mike Answered by Penny Nom. 





Graphing a linear inequality 
20100526 

From Valeie: When graphing a linear inequality, how do you know if the inequality represents the area above the line. Answered by Penny Nom. 





Which values of x satisfy (x2) / (x+4) <7 
20100523 

From Rocco: Which values of x satisfy (x2) / (x+4) <7 Answered by Harley Weston. 





Extraneous solutions 
20100522 

From Joe:
Question from Joe, a parent:
w+3 2w
   = 1
w21 w1
W2 is = w squared
4
The answer is w= 
3
but have no idea how this was solved. any help is appreciated. Thanks. Answered by Penny Nom. 





Line of sight 
20100506 

From David: I live in St. Joseph, Michigan and there is an ongoing argument regarding lineofsight over the horizon.
Standing on a 200 foot high bluff here, people swear they can see the top of the Willis (nee Sears) Tower in Chicago, which is about 1653 feet high.
It is my contention that this is actually a "refracted reflection" and not directlineofsight.
So, to settle the argument, I'd sure like some simple explanation for this, even ifand I hope notI am incorrect.
David Answered by Harley Weston. 





The "vertex" of a cone 
20100427 

From Tom: By definition a vertex is a point where three edges meet in a 3 dimensional object.
My ten year old son argues that the point at the top of a cone is not a vertex since it does not fit the definition. He got the answer wrong on a test recently but insists that he is right. I need a mathematician to answer this for him. Answered by Robert Dawson and Chris Fisher. 





A champagne tower 
20100416 

From gabriel: thanks for having something like this up online. My question is how do i build a Champagne Tower that has 290 glasses and 15 stories high.
Please help me out. this is for a clarity function. Answered by Robert Dawson. 





A tangent line to a circle 
20100415 

From Rhonda: The Greek method for finding the equation of the tangent line to a circle used the fact that at any point on a circle the line containing the reauis and the tangent line are perpendicular. Use this method to find an equation of the tangent line to the circle x^2+y^2=9 at the point (1,2 square root of 2). Answered by Penny Nom. 





A sequence 
20100413 

From Essence: hello,
I am having trouble doing my math homework. It asks me to write the first five terms of each sequence .I can not figure it out because it is a fraction.
The Problem Is:
{2n+1/2n} Answered by Penny Nom. 





A conical pile of gravel 
20100413 

From Chassity: The gravel pile is 120' around at the base and goes up 20' high at the peak. How many tons or yards of gravel in that pile? Answered by Penny Nom. 





Exactly two lines of symmetry 
20100411 

From debbie: i am looking for a quadrilateral with exactly two lines of symmetry. please help! thank you. Answered by Tyler Wood. 





If a third is a fourth of a number, what is the number? 
20100408 

From larry: If a third is a fourth of a number, what is the number? Answered by Penny Nom. 





A max min problem 
20100406 

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. 





A system of equations 
20100330 

From samantha: the equations of two lines are 6xy=4 and y=4x +2.what is the value of x in the solution for this system of equations? Answered by Penny Nom. 





The sides of a 306090 triangle 
20100329 

From maris: Find the sides of a 306090 triangle whose perimeter is 6. The solution must use systems of equations using 3 variables. Answered by Penny Nom. 





A radio tower 
20100326 

From Alex: The height of a radio tower is 450 feet, and the ground on one side of the tower slopes upward at an angle of 10 degrees. How long should a guy wire be if it is to connect to the top of the tower and be secured at a point on the sloped side 110 feet from the base of the tower? Answered by Harley Weston. 





A negative times a negative 
20100325 

From priya: why is minus into minus plus? Answered by Harley Weston. 





The angle of intersection between two lines 
20100325 

From Madhumitha: How to find the angle of intersection between a line x=249 and another line which is of the form y=m*x+c; Line1 has a slope of infinity so what does the angle of intersection turn out to be? Or how can i find it? Answered by Chris Fisher. 





The line passing through (2,6) and (2,9) 
20100324 

From antoinette: the equation of a line passing through the points (2,6) and (2,9)? Answered by Penny Nom. 





A champagne pyramid 
20100322 

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. 





A quadrilateral with 4 known sides and 1 known angle 
20100319 

From samuel: Name: Samuel
Status: Student
I have a quadrilateral with 4 known sides and 1 known angle, and I'm trying to evaluate the other angles of my quadrilateral.
By the law of cosines, I can easily find my opposite angle (using the diagonal as a basis for the equation).
However, to find the two remaining angles, I have found no other way so far than to use the other diagonal, which can be found with the equation attached (from geometry atlas).
Is there any simpler way? Answered by Robert Dawson and Harley Weston. 





A quadratic equation 
20100315 

From rachelle: under certain condition, it is found that the cost of operating an automobile as a
function of speed is approximated by a quadratic equation. use the data shown
below to find the function. then use the function to determine the cost of operating
the automobile at 60mph.
speed
(in miles per hour) 
operating cost
per mile(in cents) 
10 
22 
20 
20 
50 
20 
Answered by Penny Nom. 





Arc length and Chord length 
20100313 

From Darryl: Is there a formula to determine the chord length of an arc knowing only the arc length and the arc depth (sagitta)? I know you can't find the radius with only these two inputs, but can you find the chord length? Answered by Harley Weston. 





Cooling 
20100307 

From Lori: If a house is always at 20 degrees celsius.
Water (tea) boils at 100 degrees celsius.
5 minutes later the tea was 70 degrees celsius.
Use an equation to predict the temperature after 20 minutes. Answered by Tyler Wood. 





The line joining (3,4) and (5,6) 
20100306 

From Patric: Find the condition that the point (x,y) may lie on the line joining the points
(3,4) and (5,6) Answered by Penny Nom. 





The test for some disease is 99% accurate 
20100224 

From baaba: Assume that the test for some disease is 99% accurate. If somebody tests positive for that disease, is there a 99% chance that they have the disease? Answered by Chris Fisher. 





A linear relationship 
20100224 

From Mel: This table shows the linear relationship between an aeroplane's height (above sea level) and the outside air temperature.
h (cm) 
120 
340 
480 
600 
1040 
T (degrees C) 
14.28 
12.96 
12.12 
11.4 
8.76 
Find the gradient and vertical intercept of the function. Write the formula for T. Answered by Penny Nom. 





A geometric sequence 
20100222 

From Kelsey: _, 2, _, _, 250, _
i don't know how to fill in the missing terms Answered by Penny Nom. 





Frank makes picture frames 
20100220 

From Carol: Frank makes picture frames his revenue from sales is R=$13.60x for frames sold. The cost making frames is C=$5.80x+$120 for frames made. What is the minum number of frames Frank must make and sell in order for his revenue to be greater than his costs. Answered by Penny Nom and Melanie Tyrer. 





Substitution method 
20100217 

From Melodie: 7x  4y = 10
4y= x2 Answered by Tyler Wood. 





Can a line segment curve over two planes? 
20100214 

From Graham: I am working on a math fair project.
Can a line segment curve over two planes?
Such as, if I had a three dimensional L bracket and I drew a line segment
on it with a marker starting on the bottom of the L and had it curve
around the corner and up the top, would it still be considered one line
segment? Or is that two line segments?
Is there a rule that a line segment can only occupy one plane?
Thank you.
Graham Answered by Chris Fisher. 





Substitution 
20100214 

From Izayah: what is 3 ways to find the meeting point of y=2x+4 and 3x+y=7
by making 2 table and using a graph Answered by Stephen La Rocque. 





The angle at which the road is inclined 
20100210 

From abeth: a mountain road drops 5 m for every 22 m of road. Calculate the angle at which the road is inclined to the horizontal to the nearest degree. Answered by Penny Nom. 





1/a + 1/b + 1/c < 1 
20100201 

From Mrityun: suppose a,b and c are natural numbers such that 1/a + 1/b + 1/c < 1. Prove that
1/a + 1/b + 1/c < = 41/42. Answered by Penny Nom and Claude Tardif. 





A 3D cardboard cupcake 
20100130 

From Margaret: Hi,
I'm an art student and I'm attempting to build a 3D cupcake out of cardboard.
I want it to have a circular base of 8.5 inches and sides that are 7'' tall and slope outward so the top of the base is 29'.
The top with the frosting would be a detachable lid made from a cone with a base circumfrance of 29".
My problem is how to cut the side so they will slope out, I'm pretty sure there needs to be a curve, however I don't how to calculate the degree of it.
Ideally I want the sides to be a single piece of cardboard.
I also don't know how to calculate the arc needed to make a cone who's circular base's circumfrence is 29''.
Thanks,
Margaret Answered by Stephen La Rocque. 





Linear growth 
20100127 

From S.: I. Linear Growth:
Suppose that the town has a fixed increase in population growth number of population increase each year.
Choose the amount of population growth each year = 200
(Hint: Choose a whole number for your growth rate, rather than a percent.)
a) Fill in the following chart:
Year (t) Population (P)
t = 0
(2010) 1000
t = 1
(2011) 1000+200=1200
t = 2
(2012) 1000+400=1400
t = 3
(2013) 1000+600=1600
b) Find a linear equation in the form P = mt + b (y = mx + b), which gives the population, P, t years from 2010.
. . .
Answered by Melanie Tyrer. 





A sequence 
20100127 

From Haku: if there are 8 dots in the first shape, 13 in the second, 19 in the third, and 26 in the fourth, then what is the formula? Answered by Penny Nom. 





Growth rates 
20100126 

From Bhavya: Dear Sir/Ma'am,
I read in the text book that the growth rates of these 3 functions are as below
n^{2/3} < n/lg n < n^{0.99}
I tried the substitution method to check the correctness of this. But it gets really tough as n increase.
Is there any simpler way to understand the correctness of these growth rates?
Thanks and Regards,
Bhavya Answered by Robert Dawson. 





A tunnel from Toronto to Montreal 
20100125 

From Dave: I want to make a tunnel from Toronto to Montreal (for example)
Something like this
http://mathcentral.uregina.ca/QQ/database/QQ.09.09/h/grant1.html

My coordinates are 45.442455,73.861340 (Montreal) and 43.442455, 79.861340 (Toronto)
I need to know how to find arc distance, chord distance and radius
What websites can i find for this subject
Google has many but they are useless (blah blah) websites
LOL
Thanks Answered by Chris Fisher and Robert Dawson. 





Solving a triangle 
20100125 

From Paige: how do i solve a triangle with one angle of 73 degrees,
one angle of 32 degrees, and one side of 23cm? Answered by Harley Weston. 





A sequence 
20100122 

From brahmaji: 0 7 26 63 _ 215 342 fill the blank? find the missing number Answered by Robert Dawson. 





A 4digit phone code 
20100121 

From pat: my daughter can`t remember her 4digit code to unlock her phone. she is pretty sure it starts with a 4. can you help us? my brain is locked up Answered by Robert Dawson. 





The cube of an integer 
20100120 

From Shankar: Can the cube of an integer end with 1985 ones ? Answered by Robert Dawson. 





Angle of incline 
20100120 

From Alan: how do I fnd the angle of an incline with a measurement of 0.042 with an adjacent of 1.2mtrs?. Thank You Answered by Penny Nom. 





A cone circumscribed about a given hemisphere 
20100119 

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 linear equation with the variable on both sides 
20100116 

From dog: 4x9=7x+12 Answered by Penny Nom. 





Percentage increase from a negative to a positive 
20100112 

From Greg: If a company had a net lost in 2005 of $11,234 and net income of $3231 in 2006, what is the percentage annual growth in income between the two years? Answered by Robert Dawson. 





The triangle inequality 
20100111 

From Nazrul: If A and B are any two vectors, then how can I prove that magnitude of (A+B)<=magnitude of A+magnitude of B. Please show me the process in details. Thank you. Answered by Robert Dawson. 





The intervals where the function is positive and negative 
20100110 

From Ron: Hello
I'm trying to find out the intervals where the function is positive and negative.
It's for a polynomial function y= (x+2)^2 (x2) and y= (x+1)(x+4)(x3)
I have tried the right and left side of each xintercepts, but I still don't understand the
results
thank you for your help Answered by Penny Nom. 





A pair of simultaneous equations 
20100109 

From Yumiko: Solve the following pair of simultaneous equations.
x^2 4x = y^24
3y=2x  3 Answered by Penny Nom. 





A networking event 
20100107 

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. 





A linear equation with fractions 
20091231 

From Michelle: How would I solve: (2)(1/2x + 5) = (2)(8)? Answered by Penny Nom. 





The volume of a frustum 
20091229 

From dave: I have a frustum top 1.7r bottom .55r and 2.14 h
I have to calculate cement in a silo every week.
I am not very good at maths but i have been adding the top and bottom
to get an average so as to turn it into a cylinder and i come up with
8.5m3 I know that the correct volume is 9.24 m3. Can you tell me why
getting an average width on the top and bottom of a frustum doesn't work.
Thank you. Answered by Chris Fisher. 





Linear programming using the Simplex Method 
20091228 

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. Answered by Janice Cotcher. 





The acute angle formed by intersecting lines 
20091217 

From Katie: To the nearest tenth of a degree, find the size of the acute angle formed by the intersecting lines 3x + 2y = 12 and x  2y = 2. Was is necessary to find the intersection point? Answered by Robert Dawson. 





A pile of sand 
20091216 

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. 





A trig question 
20091215 

From A trig question: Hey, my name is Candle
I'm in academic math10 and am stuck on my trig... one question I thought I had right because i used the cosine law I got wrong and can't figure out why... here's a copy of the question. (i guessed it was D... but my teacher said it's B)
Thanks
Candle Answered by Robert Dawson. 





Energy in calories 
20091215 

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. 





A telephone pole on a slope 
20091214 

From Marissa: A 10 meter telephone pole casts a 17 meter shadow directly down a slope when the angle of elevation of the sun is 42 degrees. Find the angle of elevation of the ground. Its a law of sines problem. Answered by Penny Nom. 





A number base that's not a positive integer 
20091211 

From Nick: Is it possible for a number to have a base that's not a positive integer?
Base 1 gives a result that's meaningless but possible. I have no concept of a base 0, a negative base, or a fractional base, never mind any other base. I think there isn't any base that's not a positive integer, but, knowing that math keeps jumping ahead and sometimes has inventions before anyone knows how to exploit them, I think I'd better ask.
Thank you.
Nick Answered by Robert Dawson and Claude Tardif. 





e = m c^2 
20091209 

From Jim: Please explain the following formula:
E=MC2 (squared) Answered by Robert Dawson. 





How fast is the distance between the two cars decreasing? 
20091208 

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. 





7 36 14 18 28 9 56 x y 
20091206 

From lisa: what is the sequence of x and y
7 36 14 18 28 9 56 x y Answered by Penny Nom. 





A magic/math trick 
20091204 

From Valentin: What is the explanation for the following math trick: you think of any four digit number add those digits take that sum and subtract it from the first number then you say three of those new numbers in any order and the other person guesses the last digit.
How does he do it? Answered by Claude Tardif. 





Airline routes 
20091201 

From Kapilan: Please answer the following question:
From A to B there are four possible air routes. From B to C there are five
possible air routes. From C to D there are three possible air routes. How many
different trips can be taken from A to D and back without taking the same route on any
section of the return trip? Answered by Penny Nom. 





A line through the yintercepts 
20091201 

From Rogerson: Find the equation of the line through yintercept of the lines 3x + 4y = 12 and 3x  y = 9. Answered by Penny Nom. 





What number comes next? 
20091125 

From Mark: Can someone help and give me the break down of how to solve. 5,3,1,1 Answered by Penny Nom. 





Solving two equations, one with a square root 
20091123 

From kacie: y = square root of x+3
x4y = 7
im having trouble with this problem...i have to find where they intersect. Answered by Harley Weston. 





The point of intersection of the pair of straight lines 
20091119 

From Stephanie: Find the point of intersection of the pair of straight lines:
y=3x9
y=4x+2
x = _______ and y = ________
I am totally confused. Please help Answered by Robert Dawson. 





Oneeighth of one million dollars 
20091116 

From Jarrett: what is 1/8 equal to out of a million dollars. Answered by Penny Nom. 





Three angles and one side of a triangle 
20091116 

From Esther: How do i find the sides of an acute triangle if i know the angels are 60,45,75 and i only know one side which is 10? Thanks! Answered by Penny Nom. 





Excluded values 
20091114 

From Janie: I have to State the excluded values for this equation and then solve, but not sure how to do this. Here is the problem
(x+6)/x+3=(3)/(x+3)+2 Answered by Harley Weston. 





A truncated cone 
20091111 

From Lucian: I need to calculate the bottom inside diameter of a truncated cone.
The top insdie diameter is 1450mm.
The material is 6mm thick
The cone angle is 20 degrees
The slant length is 152mm
I would like a formula so that I can build a spread sheet Answered by Penny Nom. 





What's the next term? 
20091103 

From bharat: if
1=5
2=25
3=325
4=4325
5=? Answered by Robert Dawson and Penny Nom. 





The intersection of two graphs 
20091030 

From asma: by using the suitable scales,draw both the graph of x/2 + y/4 =3 and y=2 on the same graph paper.Find the points of intersection of the two graph. Answered by Penny Nom. 





Is it a rectangle? 
20091029 

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. 





Two non zero vectors 
20091027 

From Nazrul: Given that a and b are two non zero vectors and ma+nb=0 where m and n are two scalars. How can I prove that m=n=0. Answered by Robert Dawson. 





A word problem 
20091024 

From Ryan: Two times one number plus 7 times another number is equal to 17. the first number plus the second number is equal to 25. What are the two numbers? Please Help! Answered by Penny Nom. 





e^pi and pi^e 
20091022 

From Natalie: Question from natalie, a student:
Without using your calculator, prove which is bigger: e^pi or pi^e
we talked about ad absurdum in class, so I'm assuming that is how I approach this question, but since neither of them have a variable( like the examples we actually solved in class), I'm not quite sure how to solve it.... Answered by Harley Weston. 





Forming a square 
20091021 

From christianah: Two parallel lines have the equations y=x+4 and y=x2.Two additional lines are drawn to form a square.What is the side length of the square?Write possible equations for the additional lines.Explain and justify your reasoning. Answered by Penny Nom. 





A sequence 
20091020 

From Alyce: The rule of this sequence is k=1/8n. Find the 8th term of the sequence.
1/8, 1/4, 3/8, 1/2, ...
Thanks! Answered by Penny Nom. 





A linear system 
20091020 

From marissa: Solve this linear system
2xy=5
3x+y=9 Answered by Penny Nom. 





A line and a circle 
20091019 

From Renson: Determine whether the line x2y=0 cuts,touches or fail to meet the circle x^2+y^28x+6y15=0.If it touches or cuts ,find the coordinates of the point(s) of contact Answered by Harley Weston. 





The next three terms 
20091016 

From Shawn: I'm a parent and don't know how to help my 6th grader solve for this problem.
Name the next tree terms in this sequence and tell the rule used to find each:
1,0,1,0,1,2,3,8,25,..... Answered by Chris Fisher. 





541.39(1 + i)^15 = 784.09 
20091014 

From Fitore: Hi, I noticed that this question was already posted up, however I was hoping I could solve it without having to use logs. Can you please help me? The equation is:
541.39(1 + i)^15 = 784.09 Answered by Penny Nom. 





Integration of cos (x^2) dx 
20091012 

From Venkat: How do you evaluate the integration of cos (x^2) dx ? Answered by Harley Weston. 





$6.25 in nickels quaters and dimes 
20091010 

From miriam: a piggy bank contains $ 6.25 in nickles quaters and dimes.
there are 65 coins all together and there are four times as many nickles as quaters
find the number of coins of each kind Answered by Penny Nom. 





Two rectangles 
20091008 

From Lillian: A rectangle is 5cm longer than twice its width.
The width of another rectangle is 3cm less
than the width of the first rectangle and its length is 6cm more than 3 times its
width. If the perimeters are equal, find the dimensions of both rectangles Answered by Penny Nom. 





Elimination method 
20091008 

From Kenty: How do I solve this problem using the elimination method?
3x7y=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. Answered by Penny Nom. 





Two jets are traveling towards each other 
20091005 

From jake: two jets are traveling towards each other and are 4000 km apart. the rate of one jet is 100 km/h faster than the rate of the other. if the jets pass each other after 2.5 hrs what is the rate of speed of the faster jet? Answered by Penny Nom. 





The maximum number of right angles in a polygon 
20091005 

From Bruce: Is there way other than by trial and error drawing to determine the maximum number of right angles in a polygon? Secondary question would be maximum number of right angles in a CONVEX polygon. Is there a mathematical way to look at this for both convex and concave polygons? Or are we limited to trial and error drawing? Answered by Chris Fisher. 





What is the next term? 
20091004 

From julia: patterns
18 46 94 63 52 61 what is the next one? Answered by Penny Nom. 





Evaluating x^2 + (yz  3)^2 
20090928 

From Kathy: My daughter and I are having trouble solving this equation:
x˛+ (yz – 3)˛
if x=4,y=2 and z=0
We are having difficulty with the x˛ part of the equation. Thanks Answered by Penny Nom. 





Extraneous solutions 
20090920 

From iyana: what is an extraneous solution? what must you do to determine whether a extraneous solution? Answered by Stephen La Rocque and Harley Weston. 





Exponential form 
20090918 

From karen: Q: Write the following in exponent from: a * a * a * a * * * a, where there are n 1 a's
note: *asterisk means times. Answered by Penny Nom. 





how many ones are in 1 million 
20090917 

From djuan: how many ones are in 1 million Answered by Harley Weston. 





The method of substitution 
20090917 

From laura: ok! i really need help with this question plz help!!
x=  4y +5
x+2y = 7 Answered by Penny Nom. 





10x8 /3 =6x+24 /5 
20090916 

From Heidi: 10x8 /3 =6x+24 /5.....I know the answer is 7/2 but how do I get there? Answered by Penny Nom. 





A sequence 
20090915 

From Derek: what are the next four numbers in this sequence 1/8, 1/4, 3/8, 1/2... Answered by Penny Nom. 





A trillion grains of rice 
20090914 

From akaila: can 1trillion rice grains fit in a classroom with the area of 144.4m3 Answered by Penny Nom. 





The slopeintercept form 
20090911 

From Shelby: Write an equation in slopeintercept form of the line that is parallel to the graph of 3y4x=1 and passes through (0,6) Answered by Penny Nom. 





Exponential form 
20090908 

From hanna: hi,
well i am really bad in math and i have a math paper and i was just
wondering what 3x3x3x3x3 was in exponential form and what is
exponential in a way a person like me would understand? Answered by Penny Nom. 





Airline overbooking 
20090903 

From Nikita: An airline company knows that 8% of it's passengers will not show up for their scheduled flights. A plane has 175 seats.
a) What is the probability that 10 passengers or fewer will not show up?
b) What is the probability that 10 to15 passengers will not show up?
c)What is the probability that exactly 10 passengers will not show up?
d) What is the probability that more than 19 passengers will not show up? Answered by Robert Dawson. 





What is 8 tons in exponential form? 
20090901 

From Tyler: what is 8 tons in exponential form Answered by Penny Nom. 





The sum of digits of 4444^4444 
20090831 

From SHIVDEEP: The sum of digits of 4444^4444 is A .The sum of digits of A is B .
Find the sum of digits of B ? Answered by Claude Tardif. 





Exponential form 
20090831 

From cecil: what is the exponent form 564000? Answered by Stephen La Rocque and Harley Weston. 





Simultaneous equations 
20090828 

From onias: solve 3/a  2/b = 1/2 , 5/a + 3/b = 29/12 Answered by Robert Dawson. 





y=2x+1 and y=2x1 
20090828 

From MARICELA: Need help of how to work this problems
y=2x+1 and y=2x1
First of all what is the difference?
Second I think is easy just to work with the X y with the line in the middle
but how do you get the numbers for each side. Answered by Penny Nom. 





2(x4)>4+2x 
20090827 

From jorna: 2(x4)>4+2x Answered by Penny Nom. 





Linear equations 
20090823 

From shwetha: The length of a rectangle is greater than the breadth by 18 cm. If both length and breadth are increased by 6 cm then area increases by 168 cm square. Find the length and breadth of the rectangle. Answered by Stephen La Rocque. 





Graph 2x3y+15=0 
20090820 

From Diem: Graph 2x3y+15=0 Answered by Leeanne Boehm. 





Making a cone 
20090819 

From angela: how can i make a cone with a 6cm of heigth and has 2cm radius in the opening?? Answered by Stephen La Rocque. 





Find the central angle 
20090818 

From Larissa: In a circle, the length of a chord AB is 4 cm and the length of the arc AB is 5 cm. Find the central angle theta, in radians, correct to four decimal places. Then give the answer to the nearest degree. I think I'm supposed to use Newton's method, but am not sure how to start with this problem. Answered by Harley Weston. 





The median is greater than the mean 
20090814 

From Shawna: If the median is greater than the mean on a set of test scores, describe the situation. Answered by Robert Dawson. 





Fitting the curve y=a*exp(b*x)+c 
20090812 

From aika: Could one show me the complete algorithm and formula for finding the coefficients (a,b, and c) in exponential regression model
y=a*exp(b*x)+c Answered by Robert Dawson. 





The volume of a telephone pole 
20090811 

From robert: 12.5"@ base x 7" @ top and 40' height. How would I find the volume in cubic feet for a telephone pole with these dimensions? Answered by Harley Weston. 





Exponential form 
20090805 

From motaz: Let x = log_2 1/8 Write the exponential form of the equation and solve the equation for x Answered by Stephen La Rocque. 





A cone with the top cut off 
20090802 

From Paul: I am making a cone with a diameter of 1300, a base of 500, a side length
800. I need to workout so I can draw it out flat, cut it out, and make into
a cone. Answered by Harley Weston. 





Two equations in two unknowns 
20090730 

From Alicia: I need help with the following equation please show me the steps to complete so that I will know how to do this my self.
2xy=2 5x+y=5 Thanks for the help Answered by Penny Nom. 





Inequalities Proof 
20090724 

From ABOU: good morning.......a b c are real positive no zero......proof that
sq root(2a/(a+b))+sq root(2b/(b+c))+sq root(2c/(c+a))inferior or equal 3
thank you Answered by Janice Cotcher. 





Circular Measures 
20090724 

From onyeka: find the equation of a circle with point [3,7][5,5] and wich center lies on the line x4y=1 Answered by Robert J. Dawson. 





Inequalities 
20090722 

From Sindhu: prove that
4^79 < ( (2^100) + (3^100) )< 4^80 ? Answered by Robert Dawson. 





Finding the Line Joining Perpendicular Feet 
20090716 

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 3x3y4= 0 and 3x+y6=0. Answered by Janice Cotcher. 





The lateral area of a cone 
20090715 

From ashley: What is the radius of a cone with the lateral area being 443.3 mm^2 and the slant height being 14.7 mm. Answered by Penny Nom. 





A sequence 
20090711 

From jamie: what is the next number in the sequence and what is the relationship of the numbers? 36,16,20,10,12, _ Answered by Penny Nom. 





Fractional Exponents 
20090707 

From bob: 2^5/2  2^3/2 Answered by Janice Cotcher. 





Simultaneous Equations 
20090706 

From Mukulu: Solve the equation simultaneously X/5=(Y+2)/2= (Z1)/4 ……………….eqt 1
3X+4Y+2Z25=0 ………………eqt 2 Answered by Janice Cotcher. 





Vector spaces 
20090705 

From Nazrul: How can I prove that m(a+b)=ma+mb where a and b are two vectors.
Thank you. Answered by Harley Weston. 





Parallel lines 
20090701 

From chris: Write the slope of a line that is parallel to each line.
1.y=2x5
2.y=x+2
3.3x+y=10
4.5xy=11
5.x+2y=6
6.2x3y=9
7.4x+y=3
8.x+2y=14 Answered by Brennan Yaremko. 





The product of gradients between 2 perpendiculars lines 
20090611 

From Alister: how do i prove that the product of gradients between 2 perpendiculars lines equal to 1.... Answered by Penny Nom. 





Vectors and the Law of Cosine 
20090608 

From lauren: once force of 20 pounds and one force of 15 pounds act on a body at the same point so that the resultant force is 19 pounds. Find, to the nearest degree, the angle between the two original forces Answered by Janice Cotcher. 





Properties of Inequality 
20090605 

From Nazrul: We know that if a>b then (1/a)<(1/b)
But why 5> 2 implies (1/5)>(1/2) .
Thank you in advance for your help. Answered by Robert J. Dawson. 





At what speed does an automobile start to hydroplane? 
20090603 

From Don: How do you figure at what speed does an automobile start to hydroplane when driving on a wet surface. Answered by Robert Dawson. 





An aeroplane flying in a wind 
20090602 

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. 





Extraneous solutions 
20090602 

From Ayana: solve and check for extraneous solutions.
3x+6/ x˛4 = x+1/ x2
x can not = {2,2} Answered by Penny Nom. 





Two equations 
20090531 

From tony: y = 1.2x  32.7,
y = 0.7x + 46.15
can you please solve this for me? i am not able to figure it out... thank you
tony Answered by Penny Nom. 





Draw a net for a rectangular prism? 
20090529 

From Mohamad: Draw a net for a rectangular prism?
Last week when we were studying for our finals we came across a section about drawing nets I would really appreciate it if you gave me some help on it Answered by Robert Dawson. 





A sequence 
20090526 

From Jay: what is the equation that would give me the next 3 numbers in this progession: 0,1,5,14,20 Answered by Stephen La Rocque. 





Find out the length of a cup when its volume is halved 
20090525 

From Thomas: I'm having trouble with a question.
What kind of formula would i use to find out the length of a cup when its volume is halved? Answered by Stephen La Rocque. 





Nickels, dimes and quarters 
20090525 

From Amy: Coming from South Africa I find working with nickels, dimes and quarters confusing.
How many dimes are in a nickel and how many quarters are in a dime? Answered by Penny Nom. 





The dimensions of a larger cup 
20090523 

From Elizabeth: Hey
If i have a cup that holds a volume of 477mL and the bottom radius is 2.8cm and the top radius is 4.9cm and the height is 10cm. If i increase the volume by one and a half times what is the new measurements if the cup is directly proportional to the first one.
Thank you Answered by Stephen La Rocque and Penny Nom. 





(x + 1) / 3 + (x + 2) / 7 = 2 
20090522 

From MzDonna: Question from MzDonna, a parent:
We can't seem to get an answer for this problem:
X + 1 X + 2
_____ + _____ = 2
3 7
The book gives the answer as 10 ; But, we struck. Please help us.
___
21
Thanks in advance for your assistance. Answered by Stephen La Rocque. 





The volume of a cone 
20090520 

From Lillian: okay! so my math question is about the volume of a cone! my work sheet gave me the volume and base of the cone and asked me for the height! please help me discover the height of a cone when the volume is 78.54 cm (cubed obviously) and the base is 6 centimeters. thanks so much :) Answered by Penny Nom. 





Two equations 
20090518 

From Bob: solve the system:
x/2  2y= 8
3x + 2/3y= 10 Answered by Stephen La Rocque. 





1/(x+1) <1 
20090516 

From Nazrul: What is the solution of absolute value of (1/(x+1))<1? Please explain. Answered by Stephen La Rocque. 





Rewriting an Expression with Positive Exponents 
20090513 

From lynda: (4x)to the 0 power times x squared over 3to the 3 power i have to rewrite the expression with pos exponents Answered by Janice Cotcher. 





Finding an Array to an Integer Linear Programming Problem 
20090512 

From Debbie: how to make an array for 3 box of juice for 25 students and 2 teacher. 1 pack of juices
hols 3boxes the answer is 9 packages but how do you make array for this Answered by Janice Cotcher. 





Solve 1<52x<10 for x 
20090512 

From Helen: solve the following inequality for x
1<52x<10 Te less then sign by the one, should be less then or equal to. Answered by Stephen La Rocque and Penny Nom. 





A number sequence 
20090508 

From alicia: what is the next number 1,2,6,42,1806? is it 1954? Answered by Robert Dawson, Chris Fisher, Penny Nom and Claude Tardif. 





Perpendicular lines 
20090507 

From shabnam: the line presented by y= 3x2 and a line perpendicular to it intersect at R(1,1). Determine the equation of the perpendicular line Answered by Stephen La Rocque. 





Stairway construction 
20090502 

From Olivia: Hi, I'm Olivia and I'm in 8th grade studying algebra 1. I'm having some trouble with my math project. It has to do with rules of stairway construction. It says that there are two generally accepted rules to building stairs.
Rule 1: x+y=43 and x+y=46 (cm)
Rule 2: 2y+x=61 and 2y+x=64 (y is the riser and x is the tread length)
I cant figure out how to graph them...it says they're supposed to intersect to make a square which is like the safety zone for building stairs (the stairs' rise and tread lengths are plotted as points) any points outside of that square are considered unsafe.
Did i explain it ok? Thanks for your help.
olivia Answered by Penny Nom. 





Percent increase from a negative number to a positive number 
20090421 

From Brian: I have no problem calculating year over year net profits but am having trouble when it comes to a negative.
2007 Net Profit = 110,333.00
2008 Net Profit = 66,054.00
Brian Answered by Harley Weston. 





1/(square root 16) 
20090421 

From Conor: Hi Guys!
I dont have a square root sign so im just gonna use the ^ symbol :)
I am just wondering if
1/(16^a)
when rewritten can it be
1/16 to the power 1/2
Thanks :) Answered by Penny Nom. 





A perpendicular line in standard form 
20090421 

From Kristy: Can you help me with this equation?
Find the equation, in standard form of the line perpendicular to 2x3y=5 and passing through
(3,2) With the equation in standard form with all integer coefficient. Answered by Stephen La Rocque. 





12 oz. cup 
20090419 

From Tom: I am a ceramic teacher and wanted my students to make a 12 oz. cup, what formula should we use? Answered by Chris Fisher. 





Exponential form 
20090416 

From Pete: Hi,
How do you express ł√h^4 in exponential form. I am having a lot of
trouble with this one.
thanks
Pete Answered by Stephen La Rocque. 





Parallel and perpendicular lines 
20090408 

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. 





A large, hollow, ice cream cone 
20090403 

From Darah: A manufacturer is making a large, hollow, ice cream cone to serve as an ad for a local BaskinRobbins. The ice cream cone is made up of a cone with height 8 feet, topped by a hemisphere with radius 6 feet. How much ice cream could the hollow object hold? If a gallon is 0.13368 cubic feet, how many gallons does it hold? If 3 gallons of BaskinRobbins heavy cream chocolate blend weighs 24 pounds, how much would the ice cream cone weigh, excluding the weight of the construction material? Answered by Stephen La Rocque. 





Grain of rice on a chess board 
20090330 

From andy: Is there an easy way for my students to find out 8 to the power of 21 to solve the grains of rice doubling investigation on a chessboard? Any suggestions welcome. Thanks very much Answered by Robert Dawson and Claude Tardif. 





Octagonal panels for a horse pen 
20090325 

From Tony: I am building a pen for my horse. I am going to use 12' panels in the shape of an octagon. How many feet will he have from side to side using 12' panels.
Thanks,
Tony Answered by Robert Dawson and Penny Nom. 





Comparing positive and negative fractions 
20090324 

From Christyrose: Hello. I am a sixth grade math student and i need help on how to compare negative and positive fractions.
Here is is:
3/4 2/3 7/10 5/6
I'm not sure how to do the negative parts because i was absent for a couple days. Thank you!
Christyrose Answered by Penny Nom. 





An infinite number of solutions 
20090324 

From Sean: this is a linear equations problem;
first:
3535.5 + Fbd (.866) + Fbc (.5)  Fab (.5) = 0
and
3535.5  Fab (.866)  Fbc (.5)  Fbd (.5) = 0 Answered by Harley Weston. 





An equation for a line with a changing slope 
20090321 

From Ben: Is there anyway to write an equation for a line with a changing slope.
e.g. A cell [hone company has a initial fee of 50$ paying for the first 100 minutes,
the rate then increases to 10 cents per minute, then at 500 minutes the rate is 5 cents
per minute.
If so please tell how.
Thanks Answered by Penny Nom. 





A dead fly is stuck to a belt that passes over two pulleys 
20090321 

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. 





The volume of water in a cone 
20090317 

From Freddie: A ball of diameter 20cm rests in a conical container whose angle with the slant height and the vertical axis is 25degrees. if water is poured into the container just enough to touch the bottom of the ball, find the quantity of water in the container. Answered by Penny Nom. 





A plane cuts a line segment 
20090317 

From Manis: Find the ratio in which the line joining (2,4,16) and (3,5,4) is divided by the plane 2x3y+z+6=0. Answered by Robert Dawson. 





A slopped table top 
20090316 

From anthony: A perfect circle with radius 100m is supported by four legs, 50m long. The circle is flat when all four legs are 50m long, and tilted when the legs are different in length. The four legs are spread evenly 90 degrees apart at 0, 90, 180, and 270. Find the high and low points in degree and height when the legs are 55m at 0 degree, 70m at 90 degree, 45m at 180 degree, and 30m at 270 degree.
Not sure if they can be calculated using only 2 or 3 legs.
I have tried by picking the two adjacent highest legs (55m and 70m) so I know the high point falls into the first quadrant. Then I tried using ratio to determine where the high point is, which I think high point should be closer to the 70m leg, I am not sure. If I can find the high point, the low point should be opposite to it. Answered by Chris Fisher and Harley Weston. 





How many ball bearings can you make from a cone? 
20090314 

From Vatsal: there is a sum in my maths book which states the following:
how many ball bearings of diameter 2.5 cm. can you get by
melting a solid metalic cone of radi. 20cm and a Hight of 5 meters?
how do i do this please tell me even the minute things like cancellatoins and where to
use = , ; or any such thing because Im a bit weak in maths Answered by Harley Weston. 





Express 13 mills as a decimal part of $1.00. 
20090313 

From Kenneth: Hello:
I read the following in an old business mathematics textbook:
"Express 13 mills as a decimal part of $1.00."
I can determine the answer as follows: There are 1000 mills in or per
$1.00. 13 mills divided by 1000 mills/$1.00 equals $0.013, the answer.
My question is as follows: What does "...as a decimal part of $1.00"
indicate or represent from "Express 13 mills as a decimal part of
$1.00."?
Is (a decimal part of $1.00) any decimal less than $1.00 with the decimal having a dollar sign
before it.
I thank you for your reply. Answered by Harley Weston. 





A linear system 
20090313 

From Rasanga: Use the row echelon form of the augmented matrix to solve the following linear system.
X1+2X2+X4=6
X3+6X4=7
X5=1 Answered by Harley Weston. 





The equation of a line 
20090311 

From Teresa: Write an equation in slopeintercept form that has a horizontal intercept of 7/3 and a vertical intercept of 7/9 Answered by Harley Weston. 





Related rates 
20090309 

From Megan: A plane flying with a constant speed of 330 km/h passes over a ground radar station at an altitude of 3 km and climbs at an angle of 30°. At what rate is the distance from the plane to the radar station increasing a minute later? Answered by Harley Weston. 





An inequality with logs 
20090306 

From Indrajit: (x/10)^(logx  2)<100..........how to solve this one?? Answered by Stephen La Rocque. 





If 5 to the power of y = 625, what is y? 
20090302 

From Charlene: If 5 to the power of y = 625, what is y? Answered by Penny Nom. 





Comparing 2^3^4^5 ; 2^5^4^3 ; 5^4^3^2 etc. 
20090301 

From JIM: WHICH WOULD BE LARGEST USING THE NUMBERS 2,3,4,5 :
2^3^4^5 ; 2^5^4^3 ; 5^4^3^2 : ETC. OF ALL THE POSSIBLE
COMBINATIONS ? IS THERE A GENERAL FORMULA ? I AM
UNABLE TO FIND A COMPUTER THAT CAN HANDLE SUCH LARGE
CALCULATIONS . I ALSO DO NOT THINK IT IS AS STRAIGHT
FORWARD AS FIRST APPEARS . THANKYOU , JIM Answered by Stephen La Rocque, Robert Dawson and Harley Weston. 





Find the resultant of this displacement pair 
20090222 

From katydidit: Find the resultant of this displacement pair:
500 miles at 75 degrees east of north and
1500 miles at 20 degrees west of south.
How do I graph this and how do I solve this problem? Answered by Penny Nom. 





The graph of y = 6 
20090221 

From Barb: I was given the problem that says "graph the line y = 6" how do I find all the set points that have a y coordinate of 6? I am so lost lost and have no clue how to start. Can you help me please? thanks. Answered by Penny Nom. 





Find an expression for the nth term 
20090220 

From Dawn: Find an expression for the nth term:
x= 1 2 3 4...n
y=11 8 5 2...?
I think it's a linear relation but don't know the equation that goes with it. Answered by Stephen La Rocque. 





Linear systems 
20090220 

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. Answered by Penny Nom. 





The substitution method 
20090218 

From Nicolette: I am working on linear programming problems that I need to solve pairs of linear equations for. I am confused and am not sure how to solve these problems!
5x+3y=7 y=x3 How can i solve this using the substitution method? Answered by Penny Nom. 





A line parallel to a given line 
20090218 

From Lisa: I'm having a hard time understanding the concept of how to write an
equation of the line containing the given points and parallel to the given line.
Express the answer in the form of y=mx+b.
(7,9); 2x+5y=4. i would appreciate it alot if someone can show ne how
to do this. Thank you, Lisa Answered by Penny Nom. 





A conical sleeve 
20090217 

From Jonathan: I'm having a hard time making a design pattern for a cone sleeve, the thing is the cone sleeve is 22 degrees, how can i know the angle of this when it is flat on paper, based on my calculations, it should be around 66  69, but i want it to be exact can anybody help? Answered by Penny Nom. 





A fraction with negative exponents 
20090214 

From Gabriel: What does the line seperating the top from the bottom mean? what does it tell you to do and what is the answer to the question?
Question 3
Simplify. Write the answer using only positive exponents. Assume all variables represent nonzero numbers.
(x^5)^4(x^1y)^3
________________
(xy^4)^3 Answered by Penny Nom. 





Large exponents 
20090212 

From Dan: I would like to know how to calculate a whole number as the base that
has a large exponent;Such as 7 to the 23rd.power=. Otherwise if I use a calculator
it goes off the scale. Answered by Stephen La Rocque. 





6^x = y 
20090212 

From Jamie: Find x:
6^x=y Answered by Harley Weston. 





Cubic feet gas to grams of gas 
20090211 

From tim: I was trying to convert cubic feet gas to grams of gas. Is there a formula to complete this task? Answered by Robert Dawson. 





A sphere in a cone 
20090210 

From Shubham: An upturned conical vessel of radius 6cm and height 8cm is completely
filled with water. A sphere is lowered in the conical vessel filled with
water and the size of sphere is such that it just touches the sides of
cone and is just immersed. What fraction of water overflows? Answered by Harley Weston. 





Solving an equality 
20090210 

From Deborah: 2(v+10)<18 Answered by Penny Nom. 





Are these lines parallel? 
20090206 

From Conor: are these lines parallel?
y = 3x 2 and 6y = 3x +2 Answered by Stephen La Rocque. 





Congruent line segments 
20090205 

From casie: marica drew oneline segment on a graph with endpoint of (0,9) and (0,4). she drew another line segment with endpoints (1,1) and (6,1). are the line segment congruent?explain Answered by Penny Nom. 





A point on 8x^2+5xy+y^3=149 
20090204 

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. 





Fertilizer in a bin 
20090203 

From Todd: Hello I am looking for a formula to figure out the fertilizer volume in a hopper bottom bin not only when it is full but part full as well. When you are filling it is heaped up in the middle to make a cone and when you are emptying the bin the cone is inverted so it would be nice to be able to quickly figure out the tonnes partly filled and when full.
Lets say the bin is 32 feet high from top of bin where you fill to the bottom where the product goes out and it is 16 feet in diameter. I know how to calculate the cylinder it is the cones on the top and bottom of the bin I have the main question on. Answered by Harley Weston. 





Simultaneous equations with an xy term 
20090201 

From angelee: xy+5x2y10=0
2x+y=1 Answered by Penny Nom. 





The intersection of two lines 
20090130 

From kaylee: how do you find and graph the intersect of these two equations:
y=2x4 (and) 2y=x
thanks,
kaylee Answered by Stephen La Rocque. 





Missing three digits in a phone number 
20090130 

From Elmer: I have part of a phone number. the first 3 digits are 212, the last digit is four, and the three missing digits are all odd, how many numbers will I have to call to get the right number?
212 _ _ _ 4? Answered by Stephen La Rocque and Penny Nom. 





The vertical line test 
20090126 

From bob: what is a Vertical line test Answered by Stephen La Rocque. 





Linear speed 
20090126 

From Hom: A semi is driving cross country at 70mph. The tires on the semi have a 3 foot diameter. What is the linear speed in feet per minute? Answered by Robert Dawson. 





Using y = mx + b 
20090126 

From Caroline: How do you write a symbolic representation using the y=mx+b method? Answered by Robert Dawson. 





How fast is the visible surface of the earth decreasing? 
20090124 

From Ray: A dive bomber loss altitude at a rate of 400 mph. How fast is the visible surface of the earth decreasing when the bomber is one mile high? Answered by Harley Weston. 





Water flowing from a cone to a cylinder 
20090123 

From Ray: Water is passing through a conical filter 24 cm deep and 16 cm across the top into a cylindrical container of radius 6 cm. At what rate is the level of water in the cylinder rising when the depth of the water in the filter is 12 cm its level and is falling at the rate of 1 cm/min? Answered by Harley Weston. 





20 miles of gasoline 
20090118 

From Roger: I used the volume formula and found that a cylinder with a 3" radius X 8.75" height yields just over 231 cu. in. (one gallon) doesn't seem right, but that's what I got. Then found the percent that 8.175" is to one foot and multiplied that into the number of feet in 20 miles. I'm not good at math, so I'm starting to lose myself here. The short story is I get a cylinder that is 20 miles long and only .0000387" in diameter. Is this even close to the mark? Answered by Harley Weston. 





The point of intersection of the straight lines 
20090118 

From Kieran: Find the point of intersection of the straight lines
y=2x+4, and y+2x16=0 Answered by Robert Dawson and Penny Nom. 





How far is the airplane from the control tower? 
20090117 

From Murtaza: An aircraft is vertically above a point which is 10 km west and 15 km north of a control tower. The aircraft is 4000 m above the ground, how far is it from the control tower? Answered by Penny Nom. 





Solve for x 
20090116 

From maritza: 5=3(x2)= Answered by Penny Nom. 





0.0708 lbs per linear yard 
20090116 

From Kevin: If I know that my product is .0708lbs per linear yard how do I calculate how many Linear yards are in a lb? Answered by Penny Nom. 





A line is perpendicular to another line 
20090116 

From Greg: A line is perpendicular to the line y=2x+3 and has the same xintercept 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 
20090115 

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. 





The volume of a cone 
20090113 

From ab: the area of the base of the cone shown is 314 cm and it's height is 12 cam what is the volume? Answered by Penny Nom. 





Negative rate of change 
20090112 

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. 





The table of values for y=3x10 
20090109 

From Jade: How can I know the value of x for y=3x10 in this table of values pls. include the deatails
if x=2 y=16
if x=3 y=1
but how if y=2 what is x Answered by Penny Nom. 





The top half of a cone vs. the bottom half of the same cone 
20090108 

From Tammy: What is the ratio of the volume of the top half of a cone vs. the bottom half of the same cone? Is it seven times larger, or four times larger? and is the ratio consistent regardless of the size of the cone opening? Answered by Penny Nom. 





50 coins with a value of $1.00 
20090108 

From Ana: you have 50 coins which have a total value of 1.00. What are the coins and how many of each do you have? Answered by Robert Dawson. 





A kennel with 3 individual pens 
20090106 

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 of a region in the plane 
20090103 

From Rogerson: Find the area, S, of the shaded region enclosed by the given cureve, the given line and the xaxis.
y = x^2 + 1
line x = 2 Answered by Harley Weston. 





The radius of a cone 
20090102 

From kalpaj: A conical funnel holds 100ml. If the height of the funnel is 10 cm, determine
its radius, to the nearest tenth of a centimeter. Answered by Penny Nom. 





Solving an inequality 
20090102 

From jarred: 3x+8>2 Answered by Penny Nom. 





What is i^i? 
20081227 

From randomness: i have learnt that 'i' is square root of 1. What is then i^i ? It baffles my maths teacher... Answered by Robert Dawson and Penny Nom. 





Solving an equation for D 
20081218 

From Darrin: In his finance class, my son is being asked to take the following equation and solve for "D":
1 / [1  (1 + D/12)^T] = (1 / D) * [((12*B) / (P*T)) + Y + ((12N * Z) / (360T))]  [(12Z) / (360T)] * F Answered by Robert Dawson. 





The 2 rightmost digits 
20081218 

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. 





The angle between two lines 
20081217 

From abhi: how to calculate the angle between two lines, given the length of the lines..
angle should vary from 0  360 in the counterclockwise direction Answered by Robert Dawson and Harley Weston. 





The nth power 
20081212 

From Kellie: I am taking a 9th grade course yet im in 7th grade. I do not understand the nth power
and i have no clue what it is. could you explain to me what it is? Answered by Robert Dawson. 





A wine decanter 
20081210 

From Suzanne: I am trying to buy a wine decanter for my dad for Christmas. One big
problem I am having shopping online is finding the right size. Wine is sold
by metric ml, with a standard bottle holding 750ml of wine. Decanters are
measured by oz, and the sizes are all over the place, with one site alone
having sizes 25oz, 26 1/2oz, 50oz, 59 1/8oz, and 68oz.
Can you help me with metric conversions so I can figure out how much wine
these decanters hold? Like everybody else, I need this as soon as possible
so I can get it shipped in time for Christmas. (I'm disabled & don't drive, so
online shopping is my only way to get gifts.)
Thanks for your help!
Suzanne Answered by Chris Fisher and Robert Dawson. 





A quadrilateral with exactly 1 pair of parallel sides and no congruent sides 
20081210 

From alie: a quadrilateral with exactly 1 pair of parallel sides and no congruent sides is what? Answered by Robert Dawson. 





Electrical energy 
20081209 

From ROHAN: A lamp consumes 1000J of electrical energy in 10s. what is its power Answered by Stephen La Rocque. 





A line in slope intercept form 
20081208 

From laurie: the question: Write and equation of the line that passes through the point
and has the give slope. Then rewrite the equation in slope intercept form.
(2, 5 ) m= 3 Answered by Penny Nom. 





The sides of a rectangle 
20081208 

From Mitchell: The perimeter of rectangle ABCD (represented on a Cartesian plane) is 52cm.
The equation associated with segment AD is 3x+4y60=0
Point C is at (18, 14).
What is the length of segment AD? Answered by Penny Nom. 





Ratio of Volumes of a Cylinder and a Cone 
20081206 

From rohan: A CYLINDER IS WITHIN THE CUBE TOUCHING ALL THE VERTICALS FACES . A CONE IS INSIDE THE CYLINDER.IF THEIR HEIGHT ARE SAME WITH SAME BASE ,FIND THE RATIO OF THEIR VOLUMES. Answered by Janice Cotcher. 





Three onedigit numbers 
20081206 

From JOANNA: Could you please tell me what Adding Three OneDigit Numbers += 15 19 without using any number twice Answered by Penny Nom. 





The volume of a cone 
20081203 

From Tamriko: Hi! Help me, please to solve the following problem: The diameter of an icecream cone is 6 cm and the slant height is 10 cm. What volume of icecream would fit inside the cone? Thanks! Answered by Penny. 





What is so important about quadratics? 
20081129 

From zoe: what is so important about quadratics? Answered by Harley Weston. 





Four nines to make 100 
20081127 

From jane: use 4 nines in a math equation that will give you an answer of 100 Answered by Penny. 





Related rates 
20081126 

From Lyudmyla: How fast is the volume of a cone increasing when the radius of its base is 2 cm and growing at a rate of 0.4 cm/s, and its height is 5 cm and growing at a rate of 0.1 cm/s? Answered by Harley Weston. 





Solve 3x +5= 4x10 
20081122 

From Nikko: HELP please how do I solve these type of questions? 3x +5= 4x10 or 4x +10= 6x8 Answered by Penny Nom. 





The nth term of a sequence 
20081120 

From kim: Find the next 2 terms of the sequence.
11n+2.5 Answered by Harley Weston. 





The path of a small sailboat 
20081119 

From jane: a sailor in a small sailboat encounters shifting winds. she sails 2.00 km East
then 3.40 km North East, then an additional distance in an unknown direction. Her final position
is 6.68 km directly east of the starting point. find the magnitude & direction
of the third leg of the voyage. Answered by Harley Weston. 





How do you solve " (x4)^3/2 = 6 "? 
20081117 

From Jim: How do you solve " (x4)^3/2 = 6 " ? Answered by Penny Nom. 





The nth term of a sequence 
20081116 

From Robin: How do I solve for the next term in the following sequence, I just don't want the answer...I want how to do it to. x,x 1, x 2
Also, how do I solve for the nth term? I can't understand the explanations I've found. He has numbers subscripted in his equations. Answered by Victoria West. 





The midpoint o a line segment 
20081115 

From Jane: The vertices of a triangle are at (1,7), (6,1) and (0,3). Find the coordinates of the midpoints of the sides. Answered by Penny Nom. 





How far are the boats apart? 
20081114 

From dom: Two boats leave port at the same time. They leave at 150 degree angle. One boat travels at 10mph and the other at 20mph. After two hours how far are the boats apart? Answered by Penny Nom. 





What is 5x+3y=24? 
20081113 

From Robert: What is 5x+3y=24??????? Answered by Stephen La Rocque. 





The angles and sides of a triangle 
20081113 

From JAMIE: a triangle with a side(b)37m an angle(C)70degrees and (a)79m find values of angles A and B and length of side c Answered by Stephen La Rocque. 





The volume of a cyclone 
20081113 

From Dianna: I need to figure the cubic yards of a cyclone. 144" down to 48" 60" high Answered by Penny Nom. 





A conical funnel 
20081112 

From Rachael: Hello, I am a 10th grader in AP Calc, and can not figure out this question:
Water is running out of a conical funnel at the rate of 1 inch^3/sec. If the radius of the base of the funnel is 4 in. and the altitude is 8 in., find the rate at which the water level is dropping when it is 2 in. from the top. Answered by Harley Weston. 





Liquid in a drum 
20081110 

From RAY: How can I determine the exact amount of liquid in an overturned drum? Answered by Penny Nom and Victoria West. 





How fast is the distance between the airplanes decreasing? 
20081110 

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. 





1/8, 2/7, 1/2, 4/5, ..., ... 
20081106 

From katie: Inductive reasoning, what 1/8, 2/7, 1/2, 4/5, what would be the next two in th sequence. Answered by Penny Nom. 





A belt drives a pulley 
20081103 

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. 





The prime factorization of one billion 
20081102 

From Alta: The prime factorization of 1000 is 2 cubed times 5 cubed. How do you write the prime factorization of one billion using exponents? Answered by Penny Nom. 





A circle tangent to a line and with its centre on another line 
20081101 

From liza: Find the equation of the circle of radius squareroot 26 tangent to the line 5x+y=13 and having its center on the line 3x+y+7=0. Answered by Chris Fisher. 





Equations with the variable in the exponent 
20081028 

From fari: Solve for x
5 * 4^x3=40
5^x=25^(x+8) Answered by Penny Nom. 





Tangent line 
20081027 

From Maddie: Find a general equation for a line that touches, but does not pass through the function Y=X2(X squared) + BX+C. Answered by Stephen La Rocque and Victoria West. 





A sequence 
20081026 

From Nicole: what is the rule to this sequence 3,6,12,24,48..... Answered by Penny Nom. 





The sequence 49,48,46,43,39... 
20081026 

From Kyle: What number comes next in the series 49,48,46,43,39...? Answered by Stephen La Rocque. 





The sequence 6,1,6,2,6,4,6,8,6, 
20081026 

From Kyle: What number comes next in the series 6,1,6,2,6,4,6,8,6,? Answered by Stephen La Rocque. 





Water is leaking from a conical tank 
20081024 

From Kimberly: Water is leaking out of an inverted conical tank at a rate of 12000 cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of 20 cm/min when the height of the water is 2 m, find the rate at which water is being pumped into the tank. Answered by Stephen La Rocque. 





Put in lowest terms 6a^2c/8ab 
20081024 

From hana: put in lowest terms 6a^2c/8ab Answered by Stephen La Rocque. 





A linear system 
20081022 

From Tiffany: solve:
x + y + z = 4
2x  3y  z = 1
4x + y  2z = 16 Answered by Penny Nom. 





nth term 
20081022 

From jen: what is a nth term and how do i find the nth term of any sequence Answered by Penny Nom. 





Exponential form 
20081021 

From layla: how we wite 256 in exponential form Answered by Harley Weston. 





A falling block 
20081018 

From KOBINA: A 50 kg block being held at rest 20m above the ground is released. the block falls (no friction). how fast is the block traveling (in m/sec) when it has lost 40% of its original potential energy. Answered by Stephen La Rocque. 





The slope of a tangent line 
20081018 

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 
20081017 

From Dushayne: Please help me in solving this problem:
a. 3x4y=32
5x+2y=10
b. 2x+3y=11
4x+3y=10 Answered by Penny Nom. 





A geometric construction 
20081017 

From M: Given any 3 parallel lines on a plane, how to construct an equilateral triangle with each vertex on each line? Answered by Chris Fisher. 





Using the augmented matrix 
20081017 

From Karlena: I am supposed to write the augmented matrix of the system and use the matrix method to solve the system. I must show my work algebraically
x+y+2z=30
2x+3y+2z=53
x+2y+3z=47 Answered by Harley Weston. 





A tangent line to f(x) = 1/(x  1) 
20081016 

From Amanda: If f(x)=1/(x1) then what is the slope of the tangent line at x=2? Answered by Harley Weston. 





Perpendicular lines 
20081016 

From Hailey: In the xyplane,
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. 





The volume of a slice from a wedge 
20081016 

From Jeff: If I have a wedge shaped object (ie, a triangle of nonspecific type
extruded along a length) and it is sliced from the twocorner base at
one end to the onepoint tip at the other, what is the volume of the
upper (smaller) part as a percentage of the whole? I hope I have
explained it clearly enough. Thanks. Answered by Harley Weston. 





The rate of change of the volume of a cone 
20081015 

From Barbara: Suppose that both the radius r and height h of a circular cone change at a rate of 2 cm/s.
How fast is the volume of the cone increasing when r = 10 and h = 20? Answered by Harley Weston. 





A cone shaped pile 
20081010 

From Nadine: I have a pile of wheat in the shape of a cone. I would like to know how much
wheat I have. I have found the equation "V=1/3 pie r squared h" , but it dosn't
work! The pile is 7 feet high, diameter is 50 feet, circumference is 185 feet.
I also measured the slope 19feet. (Probably not needed) You need to know that
wheat weighs 60 pounds per bushel, and I would like to know how many bushels
I have. Even if I could receive the # of Volume Bushels, I could convert that.
Can you help me?? Answered by Stephen La Rocque. 





Nets of SquareBased Pyramids 
20081010 

From Miss: How many different nets does a squarebased pyramid have? Answered by Janice Cotcher. 





Linear and Angular Velocity 
20081010 

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 inequalities 
20081008 

From s: 3y > 4x
2x3y>6 Answered by Stephen La Rocque. 





A linear equation with fractions 
20081007 

From Christopher: 1/6(x18)+1/8(x+8)=x9 Answered by Penny Nom. 





The rise over the run 
20081007 

From Mak: what is the ratio of the rise to run? Answered by Penny Nom. 





Logs and exponentials 
20081006 

From Charles: I seem to remember you could solve exponential problems using natural logs quite simply without calculators, such as the fifth root of 400 or 33 to the 4th power. All you did was convert the number to its natural log and then just divide by 5 or multiply by 4 and then convert it back. I just remember how to do this. Thanks. Answered by Harley Weston. 





A product of positive and negative numbers 
20081003 

From kaylou: Suppose you were given 13 numbers and asked to find their product.
Seven of the numbers were positive, and the rest were negative.
Would your product be positive or negative? Why? Answered by Penny Nom. 





4^x = 2^x + 12 solve for x 
20081002 

From Dave: 4^x = 2^x + 12 solve for x. Answered by Harley Weston. 





Lines that pass through a point 
20080930 

From Abigail: what is the name for a point that a group of lines pass through that contains the letters c e n p i l? Answered by Penny Nom. 





The vertices of a triangle 
20080927 

From T.: how do you find the coordinates of the vertices of the triangle with the sides determined by the graphs of the following equations:4x+3y+1=0,4x3y17=0,4x9y+13=0? Answered by Harley Weston. 





The standard form Ax+By=C 
20080926 

From Susan: I am having difficulty changing the pointslope form of the equation of the line yy1=m(xx1) to the standard form Ax+By=C. You must express A,B,C in terms of the constants m,x1,y1. I have been able to insert numbers and switch easily from the general to the point slope equation, but I am stumped on how to convert it this way. Answered by Penny Nom. 





5 units from (1,2) and 5 units from yaxis 
20080926 

From Shaun: Find the points (x,y) in the plane that are 5 units from (1,2) and 5 units from yaxis.
I am more interested in the approach, in general terms, than the numerical values. Answered by Penny Nom. 





Extraneous solutions 
20080925 

From crystal: /6x+7/=5x+2 Answered by Penny Nom. 





Exponential form 
20080925 

From Pat: The African bush elephant is the largest land animal and weighs about 8 tons. Write this amount in exponential form. Answered by Penny Nom. 





Exponential form 
20080916 

From shawn: Write the product in exponential form: 5.5.5.2 Answered by Penny Nom. 





What is the derivative of (2^sinx)/(logbase4(2x+1))? 
20080916 

From Jesse: What is the derivative of (2^sinx)/(logbase4(2x+1)) Answered by Harley Weston. 





Solving Exponential Equations Using Logarithms 
20080915 

From Todd: 7(6^x)=6e^2x Answered by Janice Cotcher. 





The nth term of a sequence 
20080913 

From lavett: what is the Nth term in the sequence when the sequence is 2,4,8,16... and the term numbers are 1,2,3,4... Answered by Stephen La Rocque. 





A line through two points 
20080910 

From Conor: Find the equation of the straight line which passes through the points (2,14) and (8,1) Answered by Penny Nom. 





An ice cream cone 
20080909 

From olivia: Judy has a sugar cone and wants to know how many cubic inches of ice cream it will hold if it is filled completely to the top of the cone and no more. The cone has a height of 4.5 inches and a radius of 1.5 inches. Answered by Penny Nom. 





Collinear 
20080908 

From Patrick: On page 17 of my son's 9th grade math book Geometry by Jurgensen, Brown, and Jurgensen (copyright 2004),
the authors state from the diagram that you can conclude the points A, B, and C are collinear.
In the diagram, the points A, B, and C appear to be situated on a straight line; however,
nothing in the diagram states that it is a straight line. I told him that you can't conclude they are collinear
because angle ABC could be 179.9 degrees instead of 180 degrees since nothing in the diagram states otherwise.
His teacher marked his answer incorrect on a test but I still believe that I am correct. How do conclude points are
collinear if nothing tells you that they are situated on a line? Answered by Harley Weston. 





The biggest right circular cone that can be inscribed in a sphere 
20080908 

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 exclusion zone around a triangle 
20080907 

From Awrongo: A long time ago Mr Gibson found an island shaped as a triangle with three straight shores of length 3 km,4 km and 5 km. He declared an 'exclusion zone' around his island and forbade anyone to come within 1 km of his shore. What was the area of his exclusion zone? Answered by Stephen La Rocque and Penny Nom. 





2^x = 1,000,000 
20080906 

From Peter: How do I solve for "x" in the following equation: "2 to the power of x = 1,000,000" ? Answered by Penny Nom. 





A tangent to a circle 
20080906 

From Jake: Find an equation of the line that is tangent to the circle x^2 + y^2 = 3 at the point (1,√2) Answered by Penny Nom. 





Parallel and perpendicular lines 
20080906 

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. 





The square root of 2 the the X power 
20080905 

From Peter: How can I rewrite the expression: The square root of 2 the the X power? Answered by Penny Nom. 





The selling price 
20080904 

From Robert: Client wants to sell his property providing he is left with 100000.00$ net.
How do I calculate selling price if commission is 6% and taxes on the commission 6% Fed and 7.5%prov.
I'm taking the real estate class and this one really got me. Answered by Penny Nom. 





A line parallel to y= 1/2x + 5 
20080903 

From Michelle: Find the equation of a line parallel to y= 1/2x + 5 if the required line passes through ( 3,4) Answered by Penny Nom. 





1,679,616 as a power of 6 
20080903 

From Denise: express 1,679,616 in exponential form as a power of 6. Answered by Penny Nom. 





A word problem with three numbers 
20080902 

From Wanda: "Jabari is thinking of three numbers. The greatest number is twice as big as the least number. The middle number is three more than the least number. The sum of the three numbers is 75. Find the numbers." Answered by Victoria West. 





A cardboard spaceship 
20080831 

From Lee: I am building a "cardboard" spaceship for my 4 year old grandson.
The cabin is a dishwasher box with a cool control panel and elipse shaped
windows.
I really need help designing the cone or"nosecone".
The diameter of the base is 26", 24" tall, with a 6" diameter opening
at the top.
Thank you for the help!
Lee Answered by Penny Nom. 





The flight of an airplane 
20080829 

From kobina: You are traveling on an airplane that is moving at 500 mph in a direction 40deg north of west.Therefore , You are travelling (due to the plane ) at how many mph toward the west. Answered by Stephen La Rocque. 





Solve e^x + e^(x+1) = 250 
20080825 

From Laura: "solve this equation correct to three decimals"
e^x + e^x+1= 250 Answered by Penny Nom. 





Radii and Chords Create a NonRight Triangle 
20080822 

From Beary: AOC is a diameter of circle O. Line AB is 12, and lines OA and OC (the radii) are 10. Find the length of line BO and chord BC. Answered by Janice Cotcher. 





Function or Not? 
20080822 

From Katie: Determine whether y is a function of x:
[(x^2)y](x^2)+(4y)=0
....thx Answered by Janice Cotcher. 





Angular & Linear Speed from a Sine Graph 
20080819 

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. 





Joining vertices in a polygon 
20080818 

From Megan: I'm trying to develop a relationship between the number of points of a regular polygon and the
(a) number of lines you could draw between those points,
(b) number of triangles you could draw,
(c) number of quadrilaterals,
etc. Answered by Penny Nom. 





Solving for Shared Height of Two Right Triangles 
20080817 

From Heidi: find the height of a triangle, which can be split into two right triangles, but the base (50m) is not split equally in half. one end of the base is 40 degrees, while the other is 30 degrees. Answered by Janice Cotcher. 





How do you solve for x when (x^4)x is greater than or equal to 0? 
20080814 

From Katie: How do you solve for x when (x^4)x is greater than or equal to 0? Answered by Penny Nom. 





BEDMAS 
20080812 

From Rebecca: I have 3 questions.
1) I don't really understand BEDMAS.Im going in to the 6th grade and im
kind of nervis about it.?
2)When you're doing BEDMAS what does the small 3 or 2 above the
other numerals mean?
3)How would you answer this:5+2 x 9  9 x 12= ?? Answered by Janice Cotcher. 





A linear function 
20080807 

From Warren: What are the conditions of the numerical coefficients of the standard form Ax+By=C in Linear Function?
How will you transform y=square root of 3 x + 1 in standard form Ax+By=C? Answered by Penny Nom. 





Arclength and sectorangle 
20080806 

From Benson: If chord length, radius are given, How to find the sector angle and arclength Answered by Janice Cotcher. 





A cone on the end of a cylider 
20080805 

From Jerry: Hi.
I need to make a plastic cone to fit on the end of a cylinder. The only dimension i have is the diameter of the cylinder.
This 553 mm.
I need to find the formulae required and how much material will be required. Answered by Penny Nom. 





Find the product of 2^35 and 5^38 in sci. notation. 
20080803 

From Peter: I am preparing for a competition and a lot of the noncalculator problems are like find the product of 2^35 and 5^38 in sci. notation. How would you do that? Answered by Penny Nom. 





Two equations in two unknowns 
20080801 

From James: Question from james, a student:
3x+2y=9;24x2y=18
My math teacher says that it is (2,4)
Can someone please explain how to figure this out by graphing? Answered by Victoria West. 





Right Sided Limit of an Exponential Function 
20080729 

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. 





Going to Neptune 
20080729 

From mariah: how fast would you be going per hour if you wanted to get to neptune in 1 week ? Answered by Penny Nom. 





Trigonometric 
20080728 

From kiran: In triangle , Sin@ = ? Answered by Penny Nom. 





Braking Distance Relationship 
20080723 

From Mr.Adjetey: you are travelling at 30km/h.According to the rule of thumb,the braking distance is 9 metres when braking normally.How long is the braking distance under the same conditions when travelling at 60km/h? Answered by Janice Cotcher. 





Simultaneous equations 
20080723 

From Franco: Solve
3 D + E  F = 10
2 D  F = 4
3 D  4 E  F = 25
Franco Answered by Penny Nom. 





The midpoints of the sides of a quadrilateral 
20080722 

From JOEL: A QUADRILATERAL A,B,C,D HAS THE CO ORDINATE [2,5],[8,7],[10,3]&[0,1] RESPECTIVLY [B,E,G,H] ARE THE MID POINTS OF THE SIDES AB,BC,CD&DA RESPECTIVLY FIND THE MID POINTS OF [FG]&[FH] Answered by Penny Nom. 





The number of digits in a really big exponent 
20080721 

From Pete: how would you find the number of digits in a really big exponent without a calculator? Answered by Penny Nom. 





A cube inscribed in a right cone 
20080716 

From Steven: A cube is inscribe in a right cone of radius 2 and height 5. What is the volume of the cone? Answered by Victoria West and Harley Weston. 





A reflected line segment 
20080714 

From Peter: Segment AB has endpoints A(1,2) and (3,1). Segment AB is reflected over the yaxis such that A becomes A' and B becomes B'. What is the positive difference between the lengths of segment AA' and segment BB'? Answered by Janice Cotcher. 





Overbooking flights 
20080710 

From DON: Overbooking by Airlines
This is a simplified version of calculations used by airlines when they overbook
flights. They realize that a certain percentage of ticketed passengers will cancel
at the last minute. Therefore, to avoid empty seats, they sell more tickets than
there are seats, hoping that just about the right number of passengers show up.
We will assume that the noshow rate is five percent.
For a flight with 220 seats, the airline wants to find how sensitive various
probabilities are to the number of tickets it issues. In particular, it wants to
calculate
a) the probability that more than 225 passengers show up
b) the probability that more than 220 passengers show up
c) the probability that at least 215 seats will be filled
d) the probability that at least 210 seats will be filled.
To assess the benefits and drawbacks of issuing various numbers of tickets on an
airline flight with 220 seats, create a table showing as many different scenarios
as possible (table only on one page when printed) and use a second page for
your analysis and recommendation to the airline. Which are the good cases,
which are the bad cases for the airline? Answered by Janice Cotcher. 





Making Change 
20080709 

From Peter: In how many ways can you make 30 cents with quarters, nickels, and pennies? Answered by Penny. 





Exponential form 
20080703 

From Kent: How to write 8 365 005 106 in expanded and exponential form? May I request you also to explane how does it solve. Answered by Stephen La Rocque. 





Units digit 
20080702 

From seemachauhan: How to find unit digit of various numbers and what are unit digits? Answered by Penny Nom. 





Some phone numbers 
20080630 

From star: What do you think the probability of finding the last 3 digits of a telephone number if the 1st digit begins with 7? Answered by Janice Cotcher and Harley Weston. 





A rectangular room 
20080630 

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. 





Write log_2 (1/8) = 3 in exponential form 
20080627 

From Jaime: how do you write log2 (1/8) = 3 in exponential form?
the 1/8 is a fraction and the 2 is a base of 2 Answered by Penny Nom. 





How many face does a cone have? 
20080621 

From Vanessa: How many face does a cone have? Answered by Harley Weston. 





A line which is perpendicular to another line 
20080618 

From Emily: How do you solve perpendicular bisectors with a slope and a point? Answered by Penny Nom. 





(2b^1c^3)^3 (b^4c^2)^0 
20080605 

From ashley: Simplify this expression
(2b^1c^3)^3 (b^4c^2)^0
Please help me. I not sure about the zero on the outside of parentheses. Answered by Penny Nom. 





A quadratic equation 
20080603 

From Drew: A solution of x^28x=17 is
4 or 4+I or 4 or 4+i Answered by Janice Cotcher. 





Substitution method 
20080530 

From taquicia: 2yx=3
x=5+y Answered by Janice Cotcher. 





x/4 = 3 1/2 
20080530 

From Kelsey: How do you solve for "X" in the problem below?
X
 = 3 1/2
4
Kelsey Answered by Victoria West. 





Liquid is being pored into the top of a funnel 
20080525 

From Stella: Liquid is being pored 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 in the bottom where the liquid is flowing out at a rate of 20cm^3/s. How fast is the height of the liquid changing when the liquid in the funnel is 15cm deep?
At the instance when the height of the liquid is 25cm, the funnel becomes clogged at the bottom and no mo re liquid flows out. How fast does the height of the liquid change just after this occurs? Answered by Stephen La Rocque. 





Net weight 
20080523 

From Leticia: Hello, My name is Leticia,
I am having trouble with Net weight and I need your help.
When I am in class my friends answer questions that they say are easy,but I have no clue what's happening, we are going to have a test soon so please send me fast. Answered by Janice Cotcher. 





A 9 team flag football tournament 
20080522 

From James: I like to run a 9 team flag football tournament where each team is guaranteed 3 games prior to playoffs. All games must have playoff implications and must not be a consolation game. Answered by Victoria West. 





A season schedule for 9 teams 
20080522 

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. 





Nine digit numbers 
20080521 

From Alex: List of Nine digit numbers, that can be divided by nine? Answered by Janice Cotcher. 





The cube of 2y in exponential form 
20080519 

From Xiu: I dont get this question..
Write "the cube of 2y" in exponential form. I know the answer is (2y)^2 but i really don't understand why. Can you explain how to do this whole problem for me? Answered by Leeanne Boehm. 





Guy wires for a tower 
20080519 

From larissa: a radio tower 500 feet high is located on the side of a hill ( the hill has an inclination to the horizontal of 5 degrees.) How long should two guy wires be if they are connected to the top of the tower and are secured at two points 100 feet directly above ( up the hill ) and directly below the base of the tower? Answered by Penny Nom. 





Elevation gain 
20080518 

From Mark: How do you calculate elevation gain on a treadmill? e.g. 5.0 miles (26,400ft) @ 15% incline.
I have been estimating it as 26,400 x .15 = 3,960 ft of elevation gain.
Hopeful Mount Rainier Climber Answered by Victoria West. 





How old are the sisters? 
20080511 

From George: Theresa is four years older than her younger sister Joni. Twelve years ago, she was twice as old as her sister.
Find the present age of the two siblings. Answered by Penny Nom. 





A linear model 
20080509 

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. 





A net for a hemisphere 
20080506 

From Julie: how would you draw the net of a hemisphere? Answered by Walter Whiteley. 





The inverse of a function 
20080503 

From keith: please help me find the inverse of this function:
h(t) = 2 + 4 ln(15t) Answered by Stephen La Rocque. 





5x < 25+10 
20080425 

From Courtney: What is the answer to 5x<25+10 Answered by Stephen La Rocque. 





15 + 0.10n = 0.25n, solve for n 
20080424 

From monica: 15 + 0.10n = 0.25n
Solve for n. Answered by Penny Nom. 





What is the altitude of the plane? 
20080423 

From tiana: If a plane is taking off and its climbing at 380 feet per minute at 205 MPH, what is the altitude of the plane after it traveled 115 miles? Answered by Penny Nom. 





How is the square root of 3/4 is greater than 3/4? 
20080422 

From Serena: How is the square root of 3/4 is greater than 3/4? Answered by Penny Nom. 





The isoperimetric inequality 
20080421 

From Dutch: I'm searching for the proof that the sphere has the smallest volume of any figure and maximizes the volume of any figure. Answered by Chris Fisher. 





x/3 5 = 3(x2) 
20080420 

From Mrs: I am having trouble helping my son solve the following equation:
x/3 5 = 3(x2) Answered by Penny Nom. 





The volume of a stone 
20080417 

From sara: a rectangular tank 30 cm long and 20 cm wide is filled with water to a depth of 8 cm. When a stone was put in, the water level rose to 11 cm. Find the volume of the stone. (Assume that the stone is completely under water.) Answered by Penny Nom. 





A parallel line to a given line 
20080412 

From john: A parallel line to a given line through a given point not on the a given line Answered by Harley Weston. 





The slope intercept form 
20080411 

From Dave: Hi, why is there a yintercept in the slope intercept form?What does the yintecept have to do with the equation? Answered by Penny Nom. 





A truncated cone 
20080411 

From jason: i need to know how to figure the cubic feet of a cone that the top is 72" wide the bottom is 25" wide and it is 48" tall.
is there a specific formula for this? Answered by Penny Nom. 





The amount of a washing machine 
20080407 

From Eddy: we have a washing machine with a specific cylinder size, which we could calculate the volume as a regular cylinder formulas. The question is, if we fill the washer cylinder with water at a specific height on water , example 15 cm height, how can we find the volume of water at that specific height? Answered by Penny Nom. 





1(1P)^75=0.05 
20080405 

From Amy: 1(1P)^75=0.05 Answered by Stephen La Rocque and Penny Nom. 





The shortest distance from a point to a line 
20080403 

From Katherine: How do I find the shortest distance from the point (3,5) to the line x = 2 Answered by Stephen La Rocque. 





Two consecutive odd numbers 
20080401 

From prinsilla: of all pairs of consecutive odd integers whose sum is greater than 75. find the pair whose sum is least? Answered by Stephen La Rocque. 





The exponential form of x radical y to the third power 
20080330 

From Jennifer: what is the exponential for of x radical y to the third power Answered by Penny Nom. 





The nth term 
20080316 

From ryan: need help figuring nth term for 1, 2, 5, 14, 41...... could you please help Answered by Penny Nom. 





1, 1, 2, 3, 5, 8, 13, ___ ___ ___ 
20080313 

From Karen: What is the rule for the following pattern, and what would come next?
1, 1, 2, 3, 5, 8, 13, ___ ___ ___ Answered by Penny Nom. 





Estimate the cube root of 270 
20080311 

From Tom: (a) By plotting suitable graphs, estimate to one decimal place the cube root of 270.
(b) With reference to your answer to part (a), use 8 iterations of a Bisection Search to refine your estimate. Use the nearest whole numbers either side of your estimate from part (a) as starting values.
(c) Using either of your starting values from part (b) as first guess, use the NewtonRaphson method to find the true value of the root (to 6 decimal places). Repeat using the other starting value from part (b) and compare the two results. Answered by Harley Weston. 





A linear system 
20080310 

From sandhiya: one group of people purchased 10 hotdogs and 5 soft drinks at a cost of
$12.50. a second group bought 7 hotdogs and 4 soft drinks a ta cost of $9.00
find the cost of a single hot and a single soft drink.(using the row echelon form to solve) Answered by Penny Nom. 





Two perpendicular lines 
20080307 

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. 





How large is a container that will hold 3.5 cu meters? 
20080305 

From Robert: If a company allows you to ship personal belongings while on an over seas assignment and the figure is 3.5 cubic meters. Just how much is the total area in square feet?? 10X10X10 or??? I just wanted to understand the size of a container that would hold 3.5 cubic meters!! Answered by Harley Weston. 





The angles of a triangle 
20080301 

From Allen: How to find the other two angles of a scalene triangle if one angle is given Answered by Steve La Rocque and Penny Nom. 





Simultaneous equations 
20080229 

From CONOR: I was wondering if you could help me with this problem
7x  5y = 1
3y = 4x Answered by Penny Nom. 





A package of supplies is dropped from a plane 
20080229 

From beth: An airplane flies west at a speed of 200m/s. A package of supplies is dropped from the plane to some campers. if the plane is at an altitude of 1000meters, how far from the campers should the package be dropped to land near them? ignore wind resistance. Answered by Stephen La Rocque. 





A line drawn between 2 vertices 
20080226 

From Arshad: what is a line drawn between 2 vertices which are not next to each other called. Answered by Penny Nom. 





A fractional inequality 
20080220 

From ed: solve the inequality
(x+3)^2 (2x)
___________ < 0
(x+4) (x^2  4)
Answered by Penny Nom. 





Find the next terms 
20080220 

From Darrin: I was given a number sequence and can't figure out the next terms to this
2,9,20,35,66,91...... Answered by Penny Nom. 





A complex quadratic 
20080218 

From Ash: z^2(6+2i)z+(8+6i)=0
Solve for Z Answered by Steve La Rocque and Penny Nom. 





The equation of a line 
20080217 

From Jennifer: Given the point A(3,2)B(5,8) find the equation of the line AB ( in standard form ) Answered by Penny Nom. 





The slope intercept form of a line 
20080217 

From chris: find the slope and y intercept of the line (2x+4)3y=11(x1)
is this equation in slope point form. Answered by Penny Nom. 





Exponential form 
20080216 

From annna: i already got the answer for what is the prime factorization of 648 which is 2x2x2x3x3x3x3
but how do i write that answer in exponential form? Answered by Penny Nom. 





The length of the third side of a triangle 
20080216 

From mary: I have an angle of 72 degrees and each of the sides are 5' long. What is the distance from each of the ends of the 5 feet to form a triangle. Answered by Stephen La Rocque. 





Growth factor and growth rate 
20080213 

From william: what is the difference between growth factor and growth rate? Answered by Stephen La Rocque and Harley Weston. 





Classifying a triangle 
20080207 

From kevin: scalene triangle 8 ft base right side 9.5 left side 12 ft what is the angles Answered by Penny Nom. 





Why is the number 1 neither prime nor composite? 
20080207 

From ronni: why is the number 1 neither prime nor composite? Answered by Harley Weston. 





Two spinners 
20080205 

From Kim: Zack has two spinners with numbers on them. the probability of spinning
a 7 on both spinners is 3/20. if the probability of spinning a 7 on the first
spinner alone is 1/4 what is the probability of getting a 7 on the second
spinner alone? Answered by Penny Nom. 





A inear system 
20080203 

From Kelly: is (1,5) a solution of each system? y=x+4 y=1/5x Answered by Penny Nom. 





Two equations in x and y 
20080201 

From leslie: 6x+8y=40 4x+5y=25 Answered by Penny Nom. 





The standard form of a line 
20080130 

From Thomas: I'm attempting to get this in standard form
slope=3;(1,5) Answered by Penny Nom. 





Negative Exponents 
20080129 

From Bill: t to the negative fourth power inside parenthesis to the ninth power
OVER
t to the negative fourth power inside parenthesis to the third power
I am confused on how to start the problem. What I did was invert the Ts to make them positive and I then multiplied the powers. I am not sure if this is the correct process. Answered by Harley Weston. 





Belledout pier 
20080128 

From Gina: I need to know how to find the total yards needed to fill a concrete pier that is 54"/ 108" and 26' deep.
That is...54" @ the top of the pier belled to 108" @ the bottom...26' deep. Answered by Stephen La Rocque. 





How do I convert mcg to ml? 
20080127 

From David: How do I convert mcg to ml? Answered by Stephen La Rocque. 





O.T.T.F.F.S.S 
20080125 

From Omar: What is the next letter in the following sequence:
O.T.T.F.F.S.S Answered by Penny Nom. 





Linear feet to metres 
20080125 

From Jillian: i have a measurement of something in linear feet. i dont know what a linear foot is so i want to convert it to meters to have an idea.
how do i convert. Answered by Penny Nom. 





The standard form of a line 
20080124 

From James: I need to put it in Standard from ax+by=c the problem is
(4,0); parallel to y=2+1 how can I put this in Standard from Answered by Stephen La Rocque. 





x^3 y^(6) 
20080124 

From Bill: I need help completing this negative exponents problem:
x to the power of 3 multiplied by y to the power of negative 6.
What would the process to solving this problem be? Answered by Penny Nom. 





Find the slope of the line with equation 73y=2x 
20080123 

From nell: Find the slope of the line with equation 73y=2x Answered by Stephen La Rocque. 





A linear system 
20080122 

From Lisa: I am supposed to use augmented matrices to solve this system of equations. x  3y = 5; 4x  12y = 13. I think it is unsolvable but I want to be sure I am not just giving up. Thanks in advance for your help! Lisa. Answered by Stephen La Rocque and Brennan Yaremko. 





1/2, 1/2, 3/8, 1/4, 5/32, 3/32, 7/128 
20080122 

From Neil: Find the next two terms in the following number sequence
1/2, 1/2, 3/8, 1/4, 5/32, 3/32, 7/128
Find a general rule for the nth term of the sequence Answered by Penny Nom. 





The cosine of an angle 
20080121 

From Kristine: Find measure of unknown side
cosA=0.5 Answered by Harley Weston. 





The equation of a line 
20080120 

From Sara: The question is:
Write the equation of a line that is parallel to y=3x2 through the point (5,9).
I think the correct equation for this is y=3x+24.
But I have to write it in standard form, and I can't seem to figure out how to do that. Please answer soon! Thanks! Answered by Stephen La Rocque and Penny Nom. 





The line through (22 ;1) and (23, 2) 
20080120 

From Zachery: i have a slope that equals 1/1 and my coordinates are (22;1) and (23;2) and i am trying to change it into the equation y=mx+b and the farthest that i've gotten is y=1x_ (i can not find out how to find b.) So i was wondering if you could help me find out what b is because i have got no clue!!!!! Answered by Penny Nom. 





The angles of a triangle given the three sides 
20080117 

From Lucy: Is there a way to find the angles of a triangle just by knowing the lengths of it's sides?
It seems like the would be a relationship between the two, but I'm not sure. Answered by Stephen La Rocque and Harley Weston. 





How many rolls of stock do I need to buy? 
20080116 

From Dan: How many rolls of stock do I need to buy?
Given:
The rolls are 40" wide, 20" roll o.d., 4" core o.d., gauge is 0.008"
I need to cut these master rolls in 6" strips (4" of waste per master roll)
and I need 1,270,500 linear feet of this strip. Answered by Stephen La Rocque. 





Two solutions using the law of sines 
20080114 

From Kate: I am working on the Law of Sines and I have a problem that says: Find a value for b so that the triangle has 2 solutions.
I am given that A = 36 degrees and a = 5. Now, I learned that for a triangle to have 2 solutions, h < a < b.
BUT...my answer key says the answer is: 5 < b < 5/sin 36. I can't figure out how to make this fit with h < a < b. Answered by Harley Weston. 





Linear systems 
20080110 

From Sandra: I have two questions. Please solve both. Thank you.
1.) In your chemistry class, you have a bottle of 5% boric acid solution and a bottle of 2% boric acid solution. You need 60 milliliters of a 3% boric acid for an experiment. How much of each solution do you need to mix them together?
2.) You plant a 14inch hemlock tree in your backyard that grows at a rate of 4 inches per year and an 8 inch blue spruce that grows at a rate of 6 inches per year. In how many years after you plant the trees will the trees be the same height? How tall will each tree be?
Thank you. I did not understand neither problem, so I could not show any work. Please help. Answered by Stephen La Rocque and Harley Weston. 





Forces on an inclined plane 
20080110 

From Ron: A body that weighs 540lbs is caused to slide up an inclined plane with a uniform velocity by a force that acts parallel to the plane. For each foot of horizontal distance, there is a vertical rise of 2in. If the coefficient of sliding friction is 0.16, what force is required to move the body? Answered by Stephen La Rocque. 





How do I write the following in exponential form? 
20080109 

From Mandy: How do I write the following in exponential form?
( square root of a^2 b)^5 Answered by Penny Nom. 





Exponential form 
20080108 

From liam: i was wondering if anyone could help me with this question and tell me how and what the did; exponetial form of 4 326 180 501 Answered by Stephen La Rocque. 





Donuts and bagels for the first period class 
20080108 

From Karen: Mr. Pace bought breakfast for his first period class. Ten donuts and fifteen bagels
cost a total of $15.75. Mrs. Pace bought breakfast for her class. Five donuts and twenty
bagels cost a total of $17.00. Set up and solve a system of linear equations to determine the cost
of one donut and one bagel. Answered by Penny Nom. 





How far is the jet from the lighthouse? 
20080107 

From Natalie: Question: A ship spots a lighthouse that is 53m high, at an angle of elevation of 7 degrees that is directly north of the ship. The same ship spots a jet travelling N62E at an altitude of 1500m with an angle of elevation of 15 degrees. How far is the jet from the lighthouse?
Natalie Answered by Harley Weston. 





The radius of a planet 
20080106 

From Ben: Two people who are both h feet tall are standing on a spherical planet. One person walks a distance d in feet away from the the other person. At this point, the person walking turns around and can no longer see the top of the other persons head. What is the radius of the planet? Answered by Stephen La Rocque and Harley Weston. 





What is the speed of the plane in still air? 
20080105 

From oscar: A plane flies 400 miles with the wind and 340 miles against the wind
in the same length of time. If the speed of the wind is 24mph, what is
the speed of the plane in still air? Answered by Penny Nom. 





The shortest distance to a line 
20080104 

From nana: 3y+4x12=0 is the equation of the line AB on a graph......the line AB joins both y and x axises together.....point A is on y axis and its value is 3....point B is on x axis and its value is 4.....Question : from point O(0,0).find the point ont the line AB Answered by Stephen La Rocque. 





Multiplying exponentials 
20080102 

From jessie: Can you please explain how to put x^3 y^2 times x^1 y^3 in simplest exponential form? Answered by Penny Nom. 





Radicals in exponential form 
20080102 

From Andre: The title of the section in my textbook is to write each of the following
radicals in exponential form.
My question is how do u write the squareroot of 10 in exponential form? Answered by Penny Nom. 





How would one find the radius? 
20071229 

From Ned: Given an arc with length of 192 inches (don't know chord length),
and arc height of 6 inches, how would one find the radius? Answered by Stephen La Rocque and Harley Weston. 





Finding the equation of a line from its graph 
20071225 

From ken: I have a graph and it is asking me to find the slope of each line, and
then write its equation. the graph show a negative slope. Would
appreciate the answer if you could show me how to do this question.
Kind regards: Ken Answered by Stephen La Rocque. 





Smallest cone containing a 4cm radius inscribed sphere 
20071219 

From Eva: A sphere with a radius of 4cm is inscribed into a cone. Find the minimum volume of the cone. Answered by Stephen La Rocque. 





Linearize a graph 
20071219 

From Justene: My daughter has a physics lab where she must linearize a graph of acc vs. mass. I have no idea how to help her. Answered by Stephen La Rocque. 





Negative numbers 
20071214 

From mannal: what negative integers do we use in the real world? like 30 temperature? Answered by Penny Nom. 





Solve sin(x)=x^2x 
20071211 

From ming: is there anyway you can solve
sin(x)=x^2x without a calculator? Answered by Stephen La Rocque. 





A math trick 
20071210 

From Megan: I need to write a mathematical explanation of why this works!
Start with a four digit number. (a positive integer, and all digits can NOT be the same. At least one must be different)
Rearrange that four digit number.
Subtract the smaller 4digit number from the larger.
Now circel one digit. (canNOT be zero, because that is already a circle)
Now rewrite that number excluding the circled digit.
Compute the sum of the digits.
Now write down the next multiple of 9 that is larger than the sum.
Subtract the Sum from the multiple. (multiple  sum of digits)
Report Difference = to number circled.
The resulting number should be the number that originally circled. Answered by Penny Nom. 





Plotting a function 
20071206 

From Paula: My son has a problem that says plot the point:
2x3y=9
I have explained to him that there must be a function for y in order to plot that point, but he doesn't think so. The question above that one says find the function for y, and I assume we should use that function. Am I wrong? Can we plot a point without a y function. Answered by Stephen La Rocque. 





System of equations 
20071206 

From Jenn: change the equation,xy=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 
20071205 

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. 





Ramp height 
20071203 

From Steve: I need to find the height of a angle.
23 degree angle at 12 feet of length is how high from the ground? Answered by Stephen La Rocque. 





Exponential form 
20071130 

From Sasha: How do I write the number 127398 in exponential for? Answered by Penny Nom. 





An augmented matrix 
20071129 

From Beth: I am having troubles fiinding this augnmented matrix. I know how to do it
but everytime i do it it get a different answer and its not the right answer.
Could you help me to make sure I do it right?
Here is the problem:
4x  3y = 5
2x +9y = 6 Answered by Harley Weston. 





Multiplying an inequality by a negative number 
20071127 

From Lisa: Why is it that you have to switch the sign of the inequality when you divide or multiply by an negative number to solve for a variable? Answered by Penny Nom and Walter Whiteley. 





Straight lines 
20071126 

From Divyansh: hello
i am in eleventh class and am, preparing a project on straight lines
i cant really find uses of straight lines and its equations in daily life
i am also thankful to you in advance and am waiting for your answer eagerly because i need to submit my project only this week
thanking you Answered by Penny Nom. 





The definition of the sine function 
20071122 

From Indrajit: I need a explanation in this theory.......if sinθ = p/h...then
sin 90 deg. = p/h
or 1 = p/h
or p=h .....how can a perpendicular be equal to a hypotenuse.??? Answered by Harley Weston. 





Exponential Growth 
20071119 

From lisa: Hi i am a 8th grader who is learning about algebra
and we are having test on exponent and i don't really get it
i asked my teacher and she told me i should pay more attention
so i want to know what exponential Growth means Answered by Penny Nom. 





The vertex of a cone 
20071118 

From miriam: how many verticies does a cone have Answered by Penny Nom. 





Two lines 
20071118 

From Kate: represent qraphically the equations of these lines and their intersecting points
xy=2
3x+y=11 Answered by Penny Nom. 





Exponential form 
20071116 

From ashley: write a sentence for exponential form. Answered by Penny Nom. 





Why do they use the letter b in y=mx+b? 
20071115 

From virginia: why do they use the letter b in y=mx+b?
im asking this because my math teacher said he will give extra points to anyone who finds this out first
and i was hoping you guys would be the ones who could help. Answered by Penny Nom. 





x^2 + x^3 = n^2 
20071114 

From Rapin: x and n are the whole number and less than 100 , x^2 + x^3 = n^2,
please help to solve this equation. Answered by Penny Nom. 





A particle moves in the xyplane 
20071112 

From Russell: A particle moves in the xyplane with
X = 2t^3  12t^2 + 18t
Y = 3t^4  28t^3 + 72t^2
find an equation of the line tangent to the given curve at t_0_ = 1
note: t_0_ is t subscript 0 Answered by Harley Weston. 





The sequence 3,12,26,45.... 
20071112 

From Tra: I can seem to find the realtionship in these sequence of numbers, I am looking for the next three. How can I determine that, I have tried everything??!!!
3,12,26,45.... Answered by Penny Nom. 





Cones and pyramids 
20071110 

From Eric: I have a question regrading the differences between a cone and a pyramid.
In my son's Maths workbook, a cone is always referred to as a pyramid,
which confuses me very much. I understand that a pyramid is a special case of a
cone and therefore you can refer a pyramid as a cone but not the other way around.
Am I correct? Answered by Harley Weston. 





Distributing prize money 
20071108 

From Barbara: Question from Barbara, a student:
In writing competition, the first place winner receives 1/2 of the prize money. The second runner up receives 1/4 of what the winner won.
what was the total amount of prize mone distributed if the winner receives $6,000? Answered by Penny Nom. 





Why is the number 1 neither prime nor composite? 
20071108 

From amarilis: why is the number 1 neither prime nor composite? Answered by Penny Nom. 





I have a piece of material 44 inches by 78 inches 
20071102 

From Marianne: I have a piece of material 44 inches by 78 inches. How many linear yards can I get from it? Answered by Penny Nom. 





The sum of the ones 
20071029 

From Hangsun: When 2 two digit numbers are added what is the greatest possible sum of the ones? Answered by Penny Nom. 





Constantly accelerated motion 
20071029 

From Priyanka: A, B and C are three points lying in that order on a straight line. A body is
projected from B towards A with speed 3 m/s. The body experiences an
acceleration of 1 m/s^2 towards C. If BC =20 m, find the time taken to reach C and
the distance travelled by the body from the moment of projection until it reaches C. Answered by Stephen La Rocque. 





collinear points 
20071026 

From Carl: the points H,S,D,K,L, and B are collinear.
KS+SB=KB
DH+HS=DS
DH+HK=DK
point L and B are not between any other labeled points on the line.
<> Answered by Penny Nom. 





A graph with 100 vertices 
20071024 

From amarjeet: let g be a graph with 100 vertices numbered 1 to 100. Two vertices i and j are adjacent only if ij=8 or ij=12. The number of connected components
in g are:
1. 8
2. 12
3. 4
4. 25 Answered by Penny Nom and Victoria West. 





A line parallel to a given line 
20071020 

From Samaira: Given Y=2/3 + 3/4x
Give the equation that is parallel to the given one and which touches the xaxis in x=3 Answered by Leeanne Boehm and Stephen La Rocque. 





Stanley Cup costume (truncated cone pattern) 
20071019 

From Janet: You hockey fans will love this question. I am making a Stanley Cup halloween costume and need a flat pattern for the bowl portion. I believe a truncated cone will work nicely. Base circumference needs to be 32" (10.19 diameter). Top circumference needs to be 44" (14 diameter). It needs to be 8" high. Thanks for your help. Answered by Stephen La Rocque. 





0 = (1/t)  [ln(1+r) ln(t)] 
20071018 

From Brandi: Objective: solve for t, where r = 0.05
0 = (1/t)  [ln(1+r) ln(t)] Answered by Penny Nom. 





Surface area of an openended cone 
20071016 

From Lorne: What is the surface area of an open ended cone? Measured at 10' high,
16' diameter on the bottom and 2' diameter at the top. Answered by Stephen La Rocque. 





Four triangles in a square 
20071015 

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. 





Domain and range 
20071012 

From Dawn: Hi, I've been out of school for 8 years and recently picked up a math correspondence course. I'm having trouble trying to figure out the range and domain of a linear function. I've read everything I can find in my text, lessons and on your site and I still can't figure out what I'm suppose to be doing. The function is y=2x+1. Please help. Answered by Penny Nom. 





A dinner club schedule 
20071012 

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. 





77,49,36,18,... 
20071011 

From Kim: Find a pattern and predict what comes next in this sequence 77,49,36,18,________________. Answered by Penny Nom. 





Substitution method 
20071011 

From Kevin: 3xx+2y=36y=11 Answered by Stephen La Rocque. 





Area of a quadrilateral 
20071010 

From Courtney: how would i find the area of a quadrilateral..
the sides are a (/) is 6cm, b (—) is 9 cm, and c (\) is 7 cm..
the angle between a and b is 140 degrees and b and c is 115 degrees.. Answered by Stephen La Rocque. 





Coin jar 
20071007 

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. 





Doubling every day 
20071007 

From Jerrie: Patti saved pennies for 10 days. The first day she saved 1 cent. Every day after that she saved twice as much as the day before. How much money did Patti save altogether? Answered by Stephen La Rocque. 





Solving four simultaneous equations (system of four linear equations) 
20071007 

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. 





Find the equation of a line given two points 
20071005 

From Tiffany: The equation for the line through the points (11,2) and (18,12) can be written in the form Ax+By=C.
Find A and B. Answered by Victoria West. 





Equation of a tangent line to a function 
20071004 

From Princess: If f ' (x) = 3x^2 +1, find the equation of
the tangent line to f(x) = x^3 + x at x= 1. Answered by Stephen La Rocque. 





how do you get 9^59^4/8 to equal 9^4 
20071001 

From nathen: how do you get 9^59^4/8 to equal 9^4 Answered by Stephen La Rocque. 





Two power expressions 
20070929 

From James: find the values for a and b
(a*x to the power of 1*y)(1/2*x*y to the power of b)=6*y to the power of 6
please show me how to do this. Can I begin by taking out the powers? Answered by Leeanne Boehm. 





Size of a sphere fitting inside a cone 
20070927 

From Juan: I am supposed to find the largest sphere that
will fit into a cone. I am assuming is a maximizing problem, but I am not sure
of what relation (between a cone and a sphere) to use. Answered by Penny Nom and Stephen La Rocque. 





Exponents 
20070926 

From Calvin: Exponential form
5 3exponent x 5 4exponent divide 5 2exponent Answered by Stephen La Rocque. 





Nine dots 
20070925 

From al: Connect the dots.
There is nine dots, three across and three down.
Connect the nine dot with the pencil only using four line and never lifting the pencil off of the paper. Answered by Stephen La Rocque and Harley Weston. 





Exponential regression 
20070924 

From Anonymous: I need help in finding this. Find a formula for exponential regression.
Determine how to calculate a and b in the formula.
Y = ba^x
where y is as a function of x. Answered by Penny Nom. 





Large exponents 
20070924 

From Kira: Is there an easy way to calculate a number with a large exponent? For example, 2(10)^35. Answered by Stephen La Rocque and Victoria West. 





12 men can complete a work in 8 days 
20070923 

From farah: 12 men can complete a work in 8 days. 3 days after they started working, 3 more men joined. In how many days will all of them together complete the remaining work. Answered by Stephen La Rocque. 





Finding equations, intersection point of two lines at right angles 
20070922 

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 coordinates of D. Answered by Stephen La Rocque. 





The incline of my yard as it slopes away from my house 
20070922 

From Janet: I need to calculate the degree (or is it percent?) of incline of my yard as it
slopes away from my house. Do I visualize a right angle formed by a
level line from the bottom of the slope to the side of the house, and then
compare the line of the slope against the right angle to get the degree?
Or is an incline calculated by the measurement of the rise in 100 feet? For
instance, if the ground rises 3 feel in a distance of 100 feet, is that a 3%
incline? And if it rises 4 feet in a distance of 25 feet, is that a 16% incline?
Thanks so much. Answered by Stephen La Rocque. 





Two equations in two unknowns 
20070922 

From Mary: Having problems doing this problem, looking for a solution with the work. I would like to see how you got your answer, to see what I was doing wrong.
solve using the substitution method, is there "no solution" or "infinitely many solutions"
4x+y=4
2x+8y=0 Answered by Stephen La Rocque and Leeanne Boehm. 





Points that are 15 units from the origin 
20070920 

From Paula: Find the coordinates of any point(s) 15 units away from the origin with an
xcoordinate of 9.
I was given the answer: (9,12) and (9,12), but I do not understand how these numbers
were calculated. Thank you for your help! Answered by Stephen La Rocque. 





Solving an equation with fractions 
20070920 

From Len: I am having a brain cramp or maybe I just forgot some basic math,
but I am having trouble solving for "r" in your truncated cone example
where r/(r+w)=r/R or r/(r+282)=911/1728. Could you refresh my memory
by showing the steps to solve for "r"? Answered by Harley Weston. 





Tens and ones 
20070916 

From julia: My son has come home with a math question "what i know about 10s and 1s" we're totally stumped any information you can provide would be greatly appreciated Answered by Harley Weston. 





The contents of a silo 
20070914 

From Steven: I need to know how to find the weight of the contents of a silo that is 4 feet across and is funnel shaped at 60 degrees Answered by Penny Nom. 





Exponential form 
20070912 

From Ericha: How do I express 1,679,616 in exponential form as a power of 6 using a calculator? Answered by Stepehe La Rocque and Penny Nom. 





What are the next two terms? 
20070911 

From Sassy: I can't figure out what the next two integers in this pattern are 3,9,6,12,9 are. Answered by Stephen la Rocque. 





Segments on a line 
20070910 

From Cathy: This question was on my daughter's geometry assignment. Write a general rule of formula for finding the number of segments that can be named by a given number of points on a line. For example, 2 points on a line = 1 line segment; 3 points on a line = 3 segments; 5 points on a line = 10 segments. Answered by Penny Nom. 





nth term in this series 
20070907 

From danii: im trying to solve the nth term for this pattern.
1 3 6 10 15 21 28
any help would be appretiated Answered by Stephen la Rocque. 





The next term 
20070907 

From Ariel: Please explain to me why 3^2 is a 9. One calculator give me an answer of positive 9.
WHAT IS THE NEXT TERM IN Each sequence/ What is its term number?
1/2, 2/3, 3/4, 5/6 6/7
1, 1/4, 1/9, 1/16 Answered by Stephen la Rocque. 





The slope of a line 
20070906 

From Danielle: Hello. I need some help with this: i am supposed to find the equation of a line with a point
(2/3,5) and (5/6,4) the answer in the book says y=6x+1. My question is how did they get
for the slope? Answered by Penny Nom. 





Perpendicular lines 
20070906 

From dinesh: we know that for two perpendicular lines
m1*m2=1perpendicular
but this is not true for xaxis and yaxis? Answered by Harley Weston. 





Prime factors in exponential form 
20070906 

From Michelle: how would you write this: factor 48 as a product of primes written in exponential form Answered by Stephen La Rocque. 





Exponential form 
20070905 

From jeanette: the African bush elephant is the largest animal and weighs 8 tons. write this amount in exponential form. Answered by Stephen la Rocque and Penny Nom. 





X^3 = 3/10 
20070905 

From ioana: If we have X at power 3 that result equally with 3/10 haw much X is ?? Answered by Penny Nom. 





Variable expressions  part 2 
20070904 

From lisa: how do I write a variable expression for word phrase example x less than =
2 or 2 less than p
4 fewer than job please help Answered by Penny Nom. 





Exponential form 
20070831 

From Victoria: The cost of each space shuttle is about $10,000,000.
Write this amount in exponential form. Answered by Stephen La Rocque. 





Exponential form 
20070829 

From Emily: Write the Exponential Form of 125 x 25 and 81 x 27. Answered by Stephen La Rocque. 





Rotational energy needs 
20070829 

From will: how much energy in KW do i need to start and subsequently rotate a 4 ton fly wheel of 1 metre radius at 12 rpm? Answered by Stephen La Rocque. 





2,6,7,21,22,66,67 
20070828 

From EDWIN: this doesnt make any sense to me....... i cant find the pattern...
2,6,7,21,22,66,67 Answered by Leeanne Boehm and Stephen La Rocque. 





A truncated cone 
20070824 

From JUAN: i need to create a template for a cone that has a 4 " opening at top, a 14" base and 12" tall.Can u tell me how to achieve this ?
u have similar problems but when i try to do it , is not coming up right , please help.. Answered by Harley Weston. 





Twocolumn proof for a circle geometry problem 
20070824 

From Kendra: i have to prove that tangents to a circle at the endpoints of a diatmeter are parallel by stating whats given, whats to prove and a plane, then write a two column proof i dont understand this Answered by Stephen La Rocque. 





Two coplanar lines 
20070821 

From Robin: I am going two show that the two lines are coplanar:
(x5)/4=(y7)/4=(z+3)/5
(x8)/7=y4=(z5)/3
I know I have to find a point that lie on both lines, but dont really get it. Answered by Stephen La Rocque and Penny Nom. 





How much would 3 yards of stone cost? 
20070821 

From Sue: If it costs $13.50 a ton of 3/4" stone, how much would 3 yards of stone cost? Answered by Steve La Rocque. 





A geometry problem 
20070820 

From samhita: ABC is a triangle. Let D be a point on side BC produced beyond B such that BD=BA. Let M be the midpoint of AC. The bisector of angle ABC meets DM at P. Prove that angle BAP=angle ACB. Answered by Chris Fisher. 





Pointslope form 
20070816 

From jenny: write an equation in the pointslope form and the intercept form
slope=4,passing through (1,3)
slope=8,passing through (4,1)
slope= 5,passing through (4,2)
slope= 2,passing through(0,3) Answered by Leeanne Boehm. 





The length of the third side of a triangle 
20070815 

From Brooklyn: What is the equation to find the length of the third side of a triangle if you have the length of A, B, and the angles(s)? Answered by Stephen La Rocque. 





Circle Geometry 
20070814 

From Robin: In a triangle ABC, angle A=75 and B=60. A circle circumscribes the triangle. The tangents of the at points A and B meet in a point D outside the circle. Show that ABD is an isosceles triangle with a right angle at D. Diagram included. Answered by Stephen La Rocque. 





A nonlinear system 
20070814 

From Marsia: Explain how the solution of a nonlinear system could be just a point, or two points. Sketching these may make it easier Answered by Penny Nom. 





The swaying of a building in the wind 
20070811 

From San: During a strong wind, a tall builing, such as the CN Tower, can sway
back and forth as much as 100cm, with a period of 10 seconds.
Please help me to determine the equation for this function, in the form
y=asinkx Answered by Stephen La Rocque. 





Linear systems and inverses 
20070806 

From Marsia: explain how inverses are used to solve linear systems. Answered by Penny Nom. 





Logs and exponentials 
20070731 

From Marsia: Explain how the functions of exponents and logarithms relate to each other. Answered by Penny Nom. 





Equation of a perpendicular line 
20070728 

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 
20070726 

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 realworld 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)024
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)024
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. 





A cone with two fruits 
20070726 

From Meg: You have a cone shaped bag. At the bottom of the bag is an orange with
radius r. On top of the orange is a melon with radius R. It touches the
orange and fits snugly in the bag, touching it in a ring around the orange.
Its top is at the same level as the top of the bag. What is the radius of the
cone? Answered by Stephen La Rocque. 





A one to one function 
20070724 

From Marsia: Explain what it means for a function to be one to one. Answered by Harley Weston. 





Calculating the area (acreage) of a four sided lot 
20070718 

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. 





Trig functions for angles not between 0 and 90 degrees 
20070716 

From Tim: My question: Why is the value of a trigonometric function, the same, for an angle over 90 degrees and its reference angle?
How are the angle and its reference related? Do they both form a triangle that has equal sides? Answered by Penny Nom. 





Proving a quadrilateral is a rectangle 
20070714 

From Sonja: I was having this discussion with another teacher and we need a third opinion. When you are trying to prove a quadrilateral is a rectangle which method should you use:
 Prove the shape is a parallelogram by doing slope 4 times by stating that parallel lines have equal slopes. Then proving a right angle by stating that perpendicular lines have negative reciprocal slopes.
 Doing the slope 4 times and stating that the shape is a rectangle because opposite sides are parallel because of equal slopes and it contains a right angle because of negative reciprocal slopes.
I guess the real question is do you have to first state that the shape is a parallelogram? Answered by Stephen La Rocque. 





Any regular polygon inscribed in a circle 
20070712 

From DJ: Circle with r=12" is inscribed in a regular octagon. What is the length of each octagon segment?
Note: Our answer works for any regular polygon inscribed in any circle. Answered by Stephen La Rocque. 





Discount percentage 
20070711 

From Greg: List Price: $50.00
Discount: 33 1/3%
What would the net price be? Answered by Stephen La Rocque. 





Calculating sales taxes 
20070711 

From Tonya: Hi, Im having trouble calculating GST and PST
I know that in this province, GST is 6% and PST is 7%, I have a total of $275, and GST is 0.06, and PST is 0.07, so do I add those two and multiply them by the total, $275? Answered by Stephen La Rocque. 





Finding the radius of an inscribed circle 
20070705 

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. 





The lock code for my phone 
20070630 

From Amanda: okay so i forgot my lock code for my phone its four digits but i know it doesn't have a 1 or a 0 in it so it has to be from numbers 2 to 9 i need to know all the four digit combinations asap cause i cant use my phone till can someone please help me Amanda Answered by Penny Nom. 





If A is 1 and Z is 26 
20070629 

From Sue: If A is 1 and Z is 26 is there a word that when you multiply all the numbers instead of letters adds up to a million? Answered by Chris Fisher and Harley Weston. 





A linear system 
20070629 

From Kim: solve for x,y,z
xy+z=4
2x+2yz=2
x2y+2z=7 Answered by Harley Weston. 





Splitting the profits unequally 
20070627 

From Maci: We recently hosted a fundraiser.
Not everyone will receive a whole share of the profits
because they did not participate the entire time.
Several will receive only 1/2 or 1/3 share.
How do I divide the profits? Answered by Stephen La Rocque. 





sinx and cosx 
20070625 

From Mac: Can anyone tell me whether sinx and cosx 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 
20070625 

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. 





The substitution method 
20070623 

From mary: solve the system by the method of substitution:
5x+2y=15
4xy=9 Answered by Stephen La Rocque. 





Exponential form: x^y 
20070622 

From Kishor: whats the easy way to calculate X raised to Y where y is much greater than x. Answered by Stephen La Rocque. 





Rewrite 2x+4y+2=3y+5 in general form 
20070621 

From dawn: how do you rewrite 2x+4y+2=3y+5 in general form? Answered by Stephen La Rocque. 





Simultaneous equations : the Elimination method 
20070621 

From Patricia: I need to find the value of X and Y using the Elimination method.
5/x + 3/y=4
25/x2/y=3 Answered by Stephen La Rocque. 





Factor X^6  64 
20070620 

From Krystal: How do I Factor X^6  64 into linear factors? Answered by Penny Nom. 





Simultaneous inequalities 
20070618 

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. 





An inequality 
20070616 

From jerry: Two real numbers a and b satisfy the equation ab=1.
i) Prove that a^6 + 4b^6 >4
ii) Find out whether the inequality a^6 + 4b^6 >4 holds for all a and b such that ab = 1 Answered by Stephen La Rocque. 





A system of linear equations 
20070614 

From Alfredo: A student club sponsored a jazz concert and charged $3 admission for students, $5 for faculty, and $8 for the general public. The total ticket sales amounted to $2542.
Three times as many students bought tickets as faculty. The general public bought twice as many tickets as did the students. Set up the equations that determine how many
tickets were sold to each group and solve. Answered by Stephen La Rocque and Penny Nom. 





Angles of depression 
20070613 

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. 





How high does the ladder reach? 
20070611 

From Madi: A ladder 8 ft long resting on a house makes a 60 degree angle with the ground. how far up the house does it reach? Answered by Stephen La Rocque. 





The area of a quadrilateral 
20070610 

From Lucy: Calculate the area of the quadrilateral ABCD.
AB= 4.1cm, BC = 7.6cm, AD= 5.4 cm, CD= ?
Angle ABC = 117, Angle ADC = 62.
Give your answer correct to 3 significant figures. Answered by Stephen La Rocque and Penny Nom. 





The law of sines 
20070609 

From Felicia: A parallelogram has one side that is 12.0 cm and one angle that is 65°. The shorter diagonal is 25.0 cm. To the nearest tenth of a centimetre, how long is the other side of the parallelogram? Use the sine law. Answered by Penny Nom. 





Two tangent lines to y=x^3 
20070607 

From stephanie: find the equations of two tangent lines to the y=x^3 function through the point (2,8) Answered by Penny Nom. 





What happens when you have zero's on both sides? 
20070605 

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. 





Equation of a line 
20070603 

From Mahrukh: Hi i would like to know how to find the equation of a line, when you are given a piont (3, 1) and the x intercept which is 1? Answered by Penny Nom. 





Points in a plane 
20070601 

From Gabrielle: In general how many planes are there which contain two given points, three given points, and four given points? Answered by Steve La Rocque and Walter Whiteley. 





The intersection of two planes 
20070531 

From Sarim: How to find a intersection of two planes? Answered by Penny Nom. 





Volumes of cones and cylinders 
20070529 

From George: 1. The volume of a cylinder is 1353cm3
A) What is the volume of a cone with the same radius as the cylinder
but double the hieght of cylinder?
B) What is the volume of a cone with the same height as the cylinder
but with three times its radius? Answered by Steve La Rocque and Walter Whiteley. 





y=mx+b 
20070529 

From molly: Im having a problem with the y=mx+b for our homework we have a table that goes from 0 to 6 , 1 to 7 and 2 to 8 and we have to make a equation of that. Please help. Answered by Penny Nom. 





The distance between parallel lines 
20070528 

From Kristie: I can't figure out how to determine the distance between parallel lines I am taking
linear algebra and vector geometry. I was given two lines in the form #x+#y =#
told they were parallel and asked to find the distance between them??
Please help
Thanks Answered by Penny Nom. 





System of equations 
20070524 

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. 





Solve for I 
20070523 

From Mark: A=4.9(B)*C^(.00925(D.542))* E^(.015(D))*E^(.013(F))* (G/B)^(.00825(D.225))* H^.877*(I/B)^.511*(J/B)^.319 Answered by Stephen La Rocque. 





Set up two simultaneous equations 
20070521 

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. 





Constant rate of sand falling in a cone 
20070520 

From Nhi: Sand is falling into a conical pile . After 5 min. the pile has radius 24 and height 26 . After 7 min. tell how far the point c. is from the top of the cone (A). Answered by Stephen La Rocque. 





Lateral area of a right cone 
20070517 

From Crystal: In my homework the question says the lateral area of a right cone is 226.08 cm cubed.
the slant hieght is 12 cm. Find the total surface area. How do I do that? Answered by Stephen La Rocque. 





Altitudes of scalene triangles 
20070517 

From Chris: Two of the altitudes of a scalene triangle ABC have length 4 and 12.
If the length of the third altitude is also an integer, what is the biggest
that it can be? Answered by J. Chris Fisher. 





Maximizing the volume of a cone given the slant length 
20070514 

From Christina: A coffee filter for a new coffee maker is to be designed using a conical filter. The filter is to be made from a circle of radius 10cm with a sector cut from it such that the volume of coffee held in the filter is maximised. Determine the dimensions of the filter such that the volume is maximised. Answered by Stephen La Rocque and Kerstin Voigt. 





Prisoners 
20070512 

From Ryan: Last monday, the county jail had 200 prisoners. Of these, 130 were accused of felonies, and 121 were accused of misdemeanors. How many prisoners were accused of both a felony and a misdemeanor? Answered by Stephen La Rocque. 





Exponents and geometry 
20070512 

From Cynthia: Hi is (x^6)(x^4)1/2 = 5
And
How does 1/2(3.14)(4.1) =26.3917 Answered by Penny Nom and Stephen La Rocque. 





Find the equation of a line passing through two given points 
20070512 

From Kenzie: I am having problems solving an equation of the line passing through (2,4) and (6,0) Answered by Penny Nom and Stephen La Rocque. 





Finding the hypotenuse without Pythagorus 
20070511 

From Shelbie: How do i find the hypotenuse of a right traingle not using the pythagorean thereom if i have the measurements of the legs? Answered by Stephen La Rocque. 





Linear growth 
20070511 

From Rebecca: What is the definition of linear growth? Answered by Penny Nom. 





Understanding log equations 
20070510 

From Sean: The number, N, of people who have heard a rumor spread by mass media at time, t, in days is modelled by N (t) = a / 1+ be^ kt. If 50 people have heard the rumour initially and 300,000 people hear the rumour eventually, find a and b. If the rumour is initially spreading at the rate of 500 people per day, find k. Answered by Penny Nom. 





