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Form a square and a triangle from a wire 2020-04-08
From Raahim:
2. A 2 meter piece of wire is cut into two pieces and once piece is bent into a square and the other is bent into an equilateral triangle. Where should the wire cut so that the total area enclosed by both is minimum and maximum?
Answered by Penny Nom.
A relative maximum and a relative minimum 2015-12-28
From kemelo:
show for the following function f(x)=x+1/x has its min value greater than its max value
Answered by Penny Nom.
100 animals 2013-02-25
From Jessica:
You have exactly $100.00 to spend. You must get 100 animals.
The chicks cost $0.10 each.
The pigs cost $2.00 each.
The sheep cost $5.00 each.
You must get some of each animal.
How many of each animal can you get?

Answered by Penny Nom.
Lost in the woods 2012-01-12
From Liz:
I am lost in the woods. I believe that I am in the woods 3 miles from a straight road. My car is located 6 miles down the road. I can walk 2miles/hour in the woods and 4 miles/hour along the road. To minimize the time needed to walk to my car, what point on the road should i walk to?
Answered by Harley Weston.
Two max/min problems 2010-04-11
From Amanda:
1) Find the area of the largest isosceles triangle that canbe inscribed in a circle of radius 4 inches.

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

Answered by Tyler Wood.
A cone circumscribed about a given hemisphere 2010-01-19
From Neven:
The cone of smallest possible volume is circumscribed about a given hemisphere. What is the ratio of its height to the diameter of its base?
(G.F.Simmons, Calculus with Analytic Geometry, CH4 Applications of Derivatives)

Answered by Chris Fisher.
The minimum point of a quadratic 2009-12-31
From rachel:
What is the minimum point of this equation?

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

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

Answered by Penny Nom.
The optimal retail price for a cake 2009-03-25
From Shawn:
Your neighbours operate a successful bake shop. One of their specialties is a cream covered cake. They buy them from a supplier for $6 a cake. Their store sells 200 a week for $10 each. They can raise the price, but for every 50cent increase, 7 less cakes are sold. The supplier is unhappy with the sales, so if less than 165 cakes are sold, the cost of the cakes increases to $7.50. What is the optimal retail price per cake, and what is the bakeshop's total weekly profit?
Answered by Robert Dawson.
Partial derivatives 2009-01-17
From Meghan:
I have a question I've been working at for a while with maxima/minima of partial derivatives.

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

Answered by Harley Weston.
A max/min problem 2009-01-09
From Angelica:
have 400 feet of fence. Want to make a rectangular play area. What dimensions should I use to enclose the maximum possible area?
Answered by Robert Dawson.
A kennel with 3 individual pens 2009-01-06
From Jean:
An animal clinic wants to construct a kennel with 3 individual pens, each with a gate 4 feet wide and an area of 90 square feet. The fencing does not include the gates. Write a function to express the fencing as a function of x. Find the dimensions for each pen, to the nearest tenth of a foot that would produce the required area of 90 square feet but would use the least fencing. What is the minimum fencing to the nearest tenth?
Answered by Harley Weston.
How many four-legged animals are in the field? 2008-12-02
From evelyn:
Some chickens, cows and sheep are in the field. Their number of legs is 12 more than twice their number of heads. How many four-legged animals are in the field?
Answered by Harley Weston.
The minimum value of f(x)=maximum{x,x+1,2-x} 2008-09-21
From Saurabh:
The minimum value of the function defined by f(x)=maximum{x,x+1,2-x} ?
Answered by Penny Nom.
How many presses should be used? 2008-05-04
From Sarah:
Hi! I am in Calculus and this problem is on my study guide and i just cant figure it out!? A printing company had eight presses, each of which can print 300 copies per hour. It costs $5.00 to set up each press for a run and 12.5+6n dollars to run n presses for an hour. How many presses should be used to print 6000 copies most profitably? Let h equal the number of hours used to print the 6000 copies.
Answered by Harley Weston.
A lidless box with square ends 2008-04-28
From Chris:
A lidless box with square ends is to be made from a thin sheet of metal. Determine the least area of the metal for which the volume of the box is 3.5m^3. I did this question and my answer is 11.08m^2 is this correct? If no can you show how you got the correct answer.
Answered by Stephen La Rocque and Harley Weston.
Minimize the cost 2008-04-26
From A:
A power line is to be constructed from the shore of a lake to an island that is 500 m away. The closest powerline ends 4km along the shore from the point on the shore closest to the island. If it costs 5 times as much to lay the powerline underwater as along the shore, how should the line be installed to minimize the cost?
Answered by Stephen La Rocque.
A max-min problem 2008-03-27
From LSL:
show that of all rectangle with a given area, the square has the smallest perimeter.
Answered by Penny Nom.
The smallest possible perimeter 2008-01-23
From RS:
If two points of a triangle are fixed, then how can the third point be placed in order to get the smallest possible perimeter of the triangle.
Answered by Chris Fisher and Penny Nom.
Protecting a carrot patch 2008-01-03
From Kate:
A farmer has a problem with rabbits and skunks in his rectangular carrot patch that is 21m^2 in area. Determine the dimensions that will require the least amount of fencing if a barn can be used to protect one side of the garden.
Answered by Stephen La Rocque.
Smallest cone containing a 4cm radius inscribed sphere 2007-12-19
From Eva:
A sphere with a radius of 4cm is inscribed into a cone. Find the minimum volume of the cone.
Answered by Stephen La Rocque.
Animals for sale 2007-12-09
From Marion:
This question has come up and I know the answer and the equation, but how do you solve this?
Please share the proof. cows=$10, pigs=$3, chickens=$.50
In any combination buy 100 animals with $100.

Answered by Leeanne Boehm.
ln(x)/x 2007-12-07
From Nooruddin:
How can I calculate the absolute minimum of (ln x)/x?
Answered by Stephen La Rocque.
Local maxima, minima and inflection points 2007-11-13
From Russell:
let f(x) = x^3 - 3a^2^ x +2a^4 with a parameter a > 1.

Find the coordinates of local minimum and local maximum

Find the coordinates of the inflection points

Answered by Harley Weston.
f(x) = (x^4) - 4x^3 2007-07-22
From Michael:
I'm a student who needs your help. I hope you'll be able to answer my question. Here it is: Given the function f(x)=(x^4)-4x^3, determine the intervals over which the function is increasing, decreasing or constant. Find all zeros of f(x) and indicate any relative minimum and maximum values of the function.
Any help would be appreciated. Thank you for your time.

Answered by Harley Weston.
Minimum cost for a fixed volume 2007-04-18
From James:
My question goes: A silo is to be constructed and surmounted by a hemisphere. The material of the hemisphere cost twice as much as the walls of the silo. Determine the dimensions to be used of cost is to be kept to a minimum and the volume is fixed.
Answered by Penny Nom.
Minimizing a cost 2006-07-25
From Edward:
The cost of running a car at an average speed of V km/h is given by c= 100 + (V2 / 75) cents per hour. Find the average speed (to the nearest km/h) at which the cost of a 1000 km trip is a minimum.
Answered by Stephen La Rocque.
A fence around a pen 2006-03-30
From Daryl:
I hope you can help me out with the attached problem, It has been driving me crazy.
Answered by Stephen La Rocque and Penny Nom.
A max-min problem 2005-12-16
From Julie:
A car travels west at 24 km/h. at the instant it passes a tree, a horse and buggy heading north at 7 km/h is 25 km south of the tree. Calculate the positions of the vessels when there is a minimum distance between them.
Answered by Penny Nom.
A variable rectangle 2005-11-08
From Mussawar:
find the lengths of the sides of a variable rectangle having area 36 cm2 when its perimeter is minimum i do not want solution of this question. i would like to know what is mean by variable rectangle.and what is difference between rectangle and variable rectangle.also what is mean by when its perimeter is minimum.
Answered by Penny Nom.
A trig problem 2004-08-02
From A student:
Given that the maximum value of [sin(3y-2)]^2 -[cos(3y-2)]^2 is k. If y>7, Find the minimum value of y for which [Sin(3y-2)]^2 - [cos(3y-2)]^2 =k.
Answered by Penny Nom.
Maximizing the angle to the goal mouth 2004-05-15
From Yogendra:
You are running down the boundary line dribbling the ball in soccer or hockey. Investigate where in your run the angle the goal mouth makes with your position is at a maximum.
Answered by Penny Nom.
The volume of air flowing in windpipes 2003-05-02
From James:
The volume of air flowing in windpipes is given by V=kpR4, where k is a constant, p is the pressure difference at each end, R is the radius. The radius will decrease with increased pressure, according to the formula: Ro - R = cp, where Ro is the windpipe radius when p=0 & c is a positive constant. R is restricted such that:
0 < 0.5*Ro < R < Ro,
find the factor by which the radius of the windpipe contracts to give maximum flow?

Answered by Penny Nom.
Two problems 2002-10-14
From Seçkin:
i am from turkey i am a teacher in a collage i have two difficult question which i havent solve yet these are very important for me....
Answered by Claude Tardif.
A max/min problem 2002-09-21
From Evelina:
A window is the shape of a rectangle with an equilateral triangle on top. The perimeter of the window is 300 cm. Find the width that will let the maximum light to enter.
Answered by Penny Nom.
A rectangular marquee 2002-05-07
From Alyaa:
a marquee with rectangular sides on a square base with a flat roof is to be constructed from 250 meters square of canvas. find the maximum volume of the marquee. i find this topic so hard
Answered by Harley Weston.
A farmer takes 100 animals to the market to sell. 2002-02-19
From Ann:
A farmer takes 100 animals to the market to sell. All are sold and $100 is earned. The prices were $5.00 per cow, $1.00 per sheep and $.05 per pig. At least one of each kind of animal was sold. How many of each kind of animal did the farmer take to market?
Answered by Penny Nom.
Getting to B in the shortest time 2001-12-19
From Nancy:
A motorist in a desert 5 mi. from point A, which is the nearest point on a long, straight road, wishes to get to point B on the road. If the car can travel 15 mi/hr on the desert and 39 mi/hr on the road to get to B, in the shortest possible time if......

A.) B is 5 mi. from A

B.) B is 10 mi. from A

C.) B is 1 mi. from A

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

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

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

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

Answered by Harley Weston.
The smaller of a and b 2000-09-14
From Jenna:
For any two real numbers, a and b, give a mathematical expression in terms of a and b that will yield the smaller of the two numbers. Your expression should work regardless of whether a>b, a
Answered by Penny Nom.
A problem with a quadratic 2000-08-09
From David Xiao:
Find the value of a such that 4x2 + 4(a-2)x - 8a2 + 14a + 31 = 0 has real roots whose sum of squares is minimum.
Answered by Harley Weston.
Divisors of 2000 2000-06-06
From Amanda Semi :
  1. find the product of all the divisors of 2000
  2. dog trainer time has 100m of fencing to enclose a rectangular exercise yard. One side of the yard can include all or part of one side of his building. iff the side of his building is 30 m, determine the maximum area he can enclose

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

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

Minimizing the metal in a can 2000-05-02
From May Thin Zar Han:
A can is to be made to hold 1 L of oil. Find the dimensions that will minimize the cost of the metal to manufacture the can.
Answered by Harley Weston.
Nim 2000-04-04
From Sandy Daniel:
Could you please give me any information on this Math Fair topic?
Answered by Claude Tardif.
Maximize 2000-03-12
From Tara Doucet:
My question is Maximize Q=xy^2 (y is to the exponent 2) where x and y are positive integers such that x + y^2 ( y is to the exponent 2)=4
Answered by Harley Weston.
Two calculus problems 2000-03-03
From Tara Doucet:
  1. The height of a cylinder with a radius of 4 cm is increasing at rate of 2 cm per minute. Find the rate of change of the volume of the cylinder with respect to time when the height is 10 cm.

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

Answered by Harley Weston.
Slant height of a cone 2000-02-24
From Jocelyn Wozney :
I need help with this problem for my high school calculus class. Any help you can give me will be greatly appreciated-I am pretty stumped. "Express the volume of a cone in terms of the slant height 'e' and the semi-vertical angle 'x' and find the value of 'x' for which the volume is a maximum if 'e' is constant.
Answered by Harley Weston.
The shortest ladder 1999-06-26
From Nicholas:
A vertical wall, 2.7m high, runs parallel to the wall of a house and is at a horizontal distance of 6.4m from the house. An extending ladder is placed to rest on the top B of the wall with one end C against the house and the other end, A, resting on horizontal ground. The points A, B, and C are in a vertical plane at right angles to the wall and the ladder makes an angle@, where 0<@
Answered by Harley Weston.
Intersection of planes 1998-11-22
From Dave Rasmussen:
I am a teacher of secondary mathematics with a question about the uses of Three Dimensional Co-ordinate Geometry. I have been teaching my students to write equations of planes and lines, - to find the intersection of these and the distance between them. What I am having difficulty finding are good applications of these techniques to "real world" situations. Can anybody help me?
Answered by Walter Whiteley and Harley Weston.
Some Calculus Problems. 1997-10-30
From Roger Hung:
  1. What real number exceeds its square by the greatest possible amount?

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

  3. .

Answered by Penny Nom.



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