







Running in opposite directions around a circular track 
20200511 

From Alessandra: 2. Alan and Brian are two runners. Alan runs at 6.6 m/s and Brian runs at 8.4 m/s. They start from
the same place on a circular 400 m track and run in opposite directions round and round the
track.
(a) How far has Brian run when they pass each other for the first time?
(b) After they pass each other for the second time, how much further does Brian need to run
in order to complete two laps (800 m)? Answered by Penny Nom. 





Running around a circular track in opposite directions 
20190224 

From carmi: how many times will lita and rose pass each other in 15 minutes if lita and rose start jogging on a 110 meters circular track. they begin at the same point but in opposite direction. lita at 8/3 meters per second and rose at 7/3 meters per second. Answered by Penny Nom. 





The price of a watermelon 
20180707 

From errin: the price of the watermelon is directly proportional to its weight. If a watermelon that weighs 22 pounds cost $5.40, how much will a 17.5 pound watermelon cost? Answered by Penny Nom. 





Travelling in opposite directions 
20151206 

From Roselyn: Jenny and Mark commute to work, travelling in opposite directions. Jenny leaves the house at 8 AM, and averages 35 kph. Mark leaves at 8:15 AM, and averages 40 kph.At what time will they be 40 kilometers apart? Answered by Penny Nom. 





The derivative of x^1/3 
20151108 

From omar: hi can help me
am teacher ask me about x^1/3 Derivation definition . Answered by Penny Nom. 





The train fares are proportional to the square root of distance traveled 
20140111 

From manish: train fares are proportional to the sq .root of distance traveled. the train fare is Rs. 24.4 for a distance of 140 kms. by how much % does the total fare increase if the same distance is covered by breaking the journey after every 35 kms. 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. 





If 4 cooks can bake 8 pies in 6 hours????? 
20130318 

From Kenneth: Hello:
I want to determine which quantities are directly and inversely proportional in order to determine the answer for the following:.
If 4 cooks can bake 8 pies in 6 hours, 2 cooks can bake how many pies in 4 hours?
Answer: 2 2/3 pies
Can someone fully explain what I need to know in order to determine what is directly and inversely proportional in the example above?
I thank you for your reply. Answered by Robert Dawson. 





If x ix directly proportional to y then ... 
20120219 

From Crystal: I understand that we say x and y are proportional, then y = kx.
Generally when we say x is proportional to y, we think that when x increases y increases.
Now I am questioning whether that is actually true.
If k is negative, then when x increases, y DECREASES.
My question is does this mean this statement is incorrect:
If x is proportional to y, when x increases, y increases proportionally.
Is it more correct to say:
If x is proportional to y, when x increases, y either increases proportionally or decreases proportionally.
Along the same line of reasoning, when x is inversely proportional to y,
we think that when x increases y decreases, but that is true only if k is positive.
Is that correct? Answered by Harley Weston. 





The derivative of f(x) = (x+1)^1/2 
20110905 

From Carla: Find the derivative using the limit process of
f(x) = (x+1)^1/2 Answered by Harley Weston. 





I need to make $1000 profit 
20110328 

From Kat: I need to make $1000 profit selling plants for $3 each. My direct cost is $2 per plant and my overhead is $5oo. How many pots (plants = 1 per pot) do I need to make $1000? Answered by Penny Nom. 





Using the limit definition 
20100606 

From Meagan: Using the limit definition find the derivative of 3/(2x^2) Answered by Harley Weston. 





The adjacency matrix of an undirected graph 
20100115 

From Bhavya: Let Cn be the undirected graph with vertex set V = {1,2,3,...,n} and edge set E = {(1,2), (2,3), (3,4),.... , (n1,n), (n,1)}. Let An be the adjacency matrix of Cn.
a. Find the determinant of An.
b. Find (An)^2 Answered by Robert Dawson. 





Proportionality 
20091103 

From Nazrul: If x is proportional to y , how can I prove that (x^2y^2) is proportional to xy.
Please explain the process. Answered by Penny Nom. 





Proportionality 
20090629 

From Nazrul: If x is proportional to y and y is proportional to z , how can I prove that (x^2+y^2)^3/2 is proportional to z^3 Answered by Harley Weston. 





Direct and inverse relationships 
20090406 

From allison: A piece of string is cut into n pieces of equal lengths L
(1) does n vary directly or inversely with L Answered by Penny Nom. 





Direct, inverse and indirect proportionality 
20090304 

From Brian: My 14 year old is confused about indirectly proportional and inversely proportional. On searching on the internet we were directed to:
http://mathcentral.uregina.ca/QQ/database/QQ.09.00/ellis1.html
Here leanne starts explaining indirectly proportional and ends up describing inversely proportional. Has Leanne got it wrong ?
What is indirectly proportional.
Thanks
Brian Answered by Chris Fisher. 





The parabola with vertex (7,2) and directrix y = 3 
20090121 

From Deann: Find an equation of the parabola with vetrex (7,2) and directrix y =(3) Answered by Penny Nom. 





y varies jointly as x and the square of z and... 
20090105 

From peter: I don't really get the terms in this problem. Could you explain it: If y varies jointly as x and the square of z and inversely as the cube of w, by what factor is y increased when z is doubled and w is divided by 3 and x remains the same? Answered by Harley Weston. 





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. 





A force vector 
20080828 

From moumita: F=20N...this force is acting along a vector A=4j+3k.what is F? Answered by Penny Nom. 





What angle should he turn? 
20071201 

From Jasmine: Bob is traveling due north he then turns left 45 degrees followed by four 20 degree turns to the right
What is his new heading if he needed to turn so his heading was SSW what direction and what angle should he turn? Answered by Walter Whiteley. 





Direct and inverse variations 
20071127 

From Julie: Please Help I do not understand this question. X varies directly as the square of S and inversely as T. How does X change when S is doubled ? When both S and T are doubled ? I appreciate your help with this problem. Answered by Stephen La Rocque. 





Variation 
20071029 

From deeqa: 1. A car traveled 175mi at a certain speed. If the speed had been 20mph faster,
the trip could have been made in 1hr less time. Find the speed
2. The average weekly allowance A of children varies directly as their grade level, G.
If the average allowance of an 8thgrade student is $8.56 per week, what is the average
weekly allowance of a 5thgrade
The time T required to do a job varies inversely as the number of people P working. It takes 2hr for 4
working. It takes 2 hrs for 4 volunteers to distribute flyers to a neighborhood. How long would it take 12
volunteers to complete the job? Answered by Penny Nom. 





Direct variation 
20071007 

From Kimberly: If y is directly proportional to the square of x,
and x=2 when y=12, then what is the value of y when x=3? Answered by Penny Nom. 





The derivative of f(x)=1/(x1) 
20070921 

From Michelle: im having trouble finding the derivative of f(x)=1/(x1) using the f(x+h)f(x)/h method. Answered by Stephen La Rocque. 





Direct variation 
20070507 

From Jennifer: assume that y varies directly as x. find y when x = 54 if y =1/4 when x=3/2 Answered by Stephen La Rocque. 





Direct and inverse Variation 
20070403 

From liz: how do you tell if an equation varies Directly or Inversely? ex.
x= 2y or
xy+12=3
i know that if you have three numbers (x. y, z) that it varies jointly but how do you tell if it is Inverse or Direct?
Thanks for the Help!
liz Answered by Stephen La Rocque. 





What is the intensity 5m below the surface? 
20070331 

From david: I have this question which I am supposed to set it up and solve as a differential equation. I know how to solve the diffrential equation but I am having hard time understanding this question. Here is the question: The intensity of light in the ocean decreases the deeper you dive. In fact, the rate at which the intensity decreases is proportional to the current intensity. Setup the corresponding differential equation and solve for I(Y), the intensity I as a function of current intensity Y. If the light intensity 2m below the surface is 25% of the intensity at the surface, what is the intensity 5m below the surface. Can you please explain to me what does it mean by current intensity and how do I set this equation up. Thanks for the help. Answered by Penny Nom. 





Direct and inverse variation 
20070303 

From Rene: Hi I'm Rene, I'm stuck with some problems in direct and inverse variation.
I know how to solve direct and inverse problems when only one variation is in a question at a time.
EX: p varies inversely as the square root of q, and when p=12, q=36 find p when q=16
12*6 =p*4 72=4p 18=p
But how would you solve a problem like.....
If s varies directly as r and inversely as t, and s=10 when r=5 and t=3, for what value of t will s=3 when r=4 ? Answered by Penny Nom. 





What is the diameter of the planet? 
20061207 

From Niall: In April 2005, scientists claimed to have captured light from an extrasolar planet orbiting a brown dwarf in the constellation Hydra some 230 lightyears from Earth. The scientists believe the planet is about five times the mass of Jupiter.
Assume the planet has the same density as Jupiter. What is the diameter of the planet? Answered by Stephen La Rocque. 





Direct variation 
20061105 

From Johann: The perimeter of regular octagon varies directly with the length of one side of the octagon Answered by Stephen La Rocque. 





Direct and Inverse variation 
20061027 

From Vishalinee:
i'm not sure how to use the words direct variation and inverse variation to describe thre relationship between: a. speed and distance b.speed and time c. distance and time. and then i need to create equations using the descriptions. i am really messed up with direct and inverse variation. Answered by Karen McIver. 





livinia the housefly finds herself caught in the oven 
20060627 

From Danielle:
livinia the housefly finds herself caught in the oven at the point (0,0,1). the temperature at the points in the oven is given by the function
T(x,y,z) = 10 (xe^{(y2)} + ze^{(x2)})
where the units are in degrees celsius.
(i.)so if livinia begins to move towards the point (2,3,1) at what rate in deg/cm does she find the temp. changing?
(ii.)in what direction should she move in order to cool off as rapidly as possible?
(iii.)suppose that livinia can fly at a speed of the square root of 2 (cm/sec.) if she moves in the direction of part (ii) at what rate will she find the temp. to be changing?
Answered by Penny Nom. 





Equations of two lines 
20060405 

From Wael: Determine a cartesian equation of the line passing through A and V as a direction vector?
1 A (2;1) and V = j
2 A (2;3) and V = i Answered by Penny Nom. 





A proof by contraposition 
20060316 

From Eban:
1)by mathematical induction prove that 1^{2} + 3^{2 }+ 5^{2 }+ ...... + (2k1)^{2} = (1/3)k(2k1)(2k+1) for all positive integers k.
2)show that the contrapositive of the following statement is true. if 1 + M^{7} is even, then M is odd.
Answered by Stephen La Rocque. 





The equation of an ellipse 
20050717 

From Allan: I working on a problem that asks me to give the equation of an ellipse when only the location of the directrix and the length of the latus rectum are given. No other points on the ellipse are given. Again, the only "givens" are:
Length of latus rectum = 12
Location of directrix is x = 16
If I could determine the eccentricity, I could proceed from there by taking the ratio of the distance from a focus to the latus rectum point to the distance of the point from the directrix, but I lack the x coordinate of c. I've searched the text, and feel I've "missed something" somewhere! I note that the latus rectum segment is unique in one respect in that it is parallel to the directrix, where any other line segment on the ellipse to the focus would not be. Please indicate where I'm going wrong. Answered by Chris Fisher. 





Direct and inverse variation 
20041005 

From Abraham: Given that y varies inversely as x and x varies directly as z.If z is doubled then y is halved.Why is that true.Please explain.I'm having trouble understanding the different types of variation Answered by Penny Nom. 





X is due north of Y ... 
20040811 

From A student: X is due north of Y and 2km distant. Z is due east of Y and has a bearing of S35°12'E from X. How far, to the nearest metre, is Z from X? Answered by Penny Nom. 





A linear function 
20020909 

From Chad: If y = 9x  13 does it represent a linear function? And if it does what is its slope and is it a direct variation? Answered by Peny Nom. 





Why do you flip the inequality sign? 
20011026 

From Sean: I have a question about an inequality problem. Here it is: Solve and graph 5  3x => 17. (=> is greater than or equal). Please tell me why you flip the inequality sign when divinding by a negative number. Answered by Penny Nom. 





Proportionality: direct and indirect 
20010118 

From Nancy Ellis: What is the difference between directly proportional and indirectly proportional? Answered by Leeanne Boehm. 





Direct and inverse variation 
20001212 

From Ashley: I'm stuck on this unit of direct and inverse variation..please and my problems and show me how to do each PLEASE!!! Assume that y varies directly as x If y= 4 when x = 2, find y when x= 6 Assume that y varies inversely as x If y =4 when x=2, find y when x =6 Answered by Penny Nom. 





Reversing the direction of an inequality. 
19990306 

From Mallory White: If the Problem was 4a plus 5 is less than or equal to 14, why would you change the sign to greater than or equal to? Answered by Jack LeSage and Harley Weston. 





Parabolas 
19980724 

From Danica: how do you find the focus, vertex, and directrix of 4xy^22y33=0 Answered by Penny Nom. 





The twodigit numbers from 1099 
19980121 

From Alexis Riddle: My name is Alexis. I'm a student in 8th grade and I'm taking Algebra I Honors. My question is: In a string of numbers, two adjacent digits are considered as a twodigit number. For instance, the string 11012 contains the numbers 10, 11, and 12. What is the number of digits in the smallest string that contains all of the twodigit numbers from 1099? Please help and thank you for any assistance you can give me. Answered by Penny Nom. 





Parabolic Mirrors 
19970128 

From Megan Wennberg: Consider a ray of light that passes through a chord of a parabola (the chord is above the focus and parallel to the directrix), hits the parabola at a point (x,y) and is reflected through the focus. If d1 is the distance from the chord to the point of incidence (x,y) and d2 is the distance from (x,y) to the focus, can you prove that the sum of the distances d1+d2 is constant, independent of the particular point of incidence. Answered by Penny Nom. 

