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	The maximum area of a garden		2021-04-28
		Lexie pose la question : suppose you want to make a rectangular garden with the perimeter of 24 meters. What's the greatest the area could be and what are the dimensions? Penny Nom lui répond.
	Forming the largest cylinder		2020-05-20
		Amanda pose la question : How do I find the maximum surface area and volume of a cylinder made up of ONE 8.5x11 piece of paper? Penny Nom lui répond.
	Maximizing the volume of a cone		2020-05-18
		Ella pose la question : Hello, this is question - 'If you take a circle with a radius of 42cm and cut a sector from it, the remaining shape can be curled around to form a cone. Find the sector angle that produces the maximum volume for the cone made from your circle.' Penny Nom lui répond.
	Form a square and a triangle from a wire		2020-04-08
		Raahim pose la question : 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? Penny Nom lui répond.
	A cone of maximum volume		2019-08-14
		Refilwe pose la question : The slant height of a cone is 10cm. Determine the radius of the base so that the volume of the cone is a maximum Penny Nom lui répond.
	The maximum volume of a cone		2019-07-14
		A student pose la question : find the maximum volume of a cone if the sum of it height and volume is 10 cm. Penny Nom lui répond.
	Maximize monthly revenue		2019-05-23
		a student pose la question : A real-estate firm owns 100 garden type apartments. At RM400 per month, each apartment can be rented. However, for each RM10 per month increase, there will be two vacancies with no possibility of filling them. What rent per apartment will maximize monthly revenue? Penny Nom lui répond.
	A triangle of maximum area		2019-03-07
		Tom pose la question : Triangle ABC is such that AB=3cm and AC=4cm. What is the maximum possible area of triangle ABC? Penny Nom lui répond.
	A penny is thrown from the top of a building		2018-03-16
		Zoraida pose la question : A penny is thrown from the top of a 26.7-meter building and hits the ground 3.39 seconds after it was thrown. The penny reached its maximum height above the ground 0.89 seconds after it was thrown. a. Define a quadratic function, h, that expresses the height of the penny above the ground (measured in meters) as a function of the number of seconds elapsed since the penny was thrown, t. b. What is the maximum height of the penny above the ground? Penny Nom lui répond.
	The maximum area of a rectangle with a given perimeter		2017-06-02
		Bob pose la question : How would I go about finding the maximum area of a rectangle given its perimeter (20m, for example)? Penny Nom lui répond.
	Maximizing the area of a two lot region		2016-04-03
		yousef pose la question : A man wishes to enclose two separate lots with 300m of fencing. One lot is a square and the other a rectangle whose length is twice its width. Find the dimensions of each lot if the total area is to be a minimum. Penny Nom lui répond.
	A Max/Min problem with an unknown constant		2016-01-17
		Guido pose la question : Question: The deflection D of a particular beam of length L is D = 2x^4 - 5Lx^3 + 3L^2x^2 where x is the distance from one end of the beam. Find the value of x that yields the maximum deflection. Penny Nom lui répond.
	A relative maximum and a relative minimum		2015-12-28
		kemelo pose la question : show for the following function f(x)=x+1/x has its min value greater than its max value Penny Nom lui répond.
	A waste oil tank		2015-06-13
		Angela pose la question : a waste oil tank is 5 feet wide and 20 feet long, the empty tank on your truck holds 5000 gallons. If 7.48 gallons are in every cubic foot, what is the maximum depth the oil can be to completely fit into your truck? Penny Nom lui répond.
	A calculus optimization problem		2015-05-14
		Ali pose la question : Given an elliptical piece of cardboard defined by (x^2)/4 + (y^2)/4 = 1. How much of the cardboard is wasted after the largest rectangle (that can be inscribed inside the ellipse) is cut out? Robert Dawson lui répond.
	Constructing a box of maximum volume		2015-04-14
		Margot pose la question : I need to do a PA for maths and I'm a bit stuck. The PA is about folding a box with a volume that is as big as possible. The first few questions where really easy but then this one came up. 8. Prove by differentiating that the formula at 7 does indeed give you the maximum volume for each value of z. Penny Nom lui répond.
	A cone of maximum volume		2015-03-16
		Mary pose la question : 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 Robert Dawson lui répond.
	Largest cone in a sphere		2015-01-15
		Alfredo pose la question : What is the altitude of the largest circular cone that may be cut out from a sphere of radius 6 cm? Penny Nom lui répond.
	Maximizing the ticket revenue		2014-10-07
		Allen pose la question : An airplane whose capacity is 100 passengers is to be chartered for a flight to Europe. The fare is to be $150 per person, if 60 people buy tickets. However, the airline agrees to reduce the fare for every passenger by $1 for each additional ticket sold. How many tickets should be sold to maximize the ticket revenue for this flight? Chris Fisher lui répond.
	The popcorn box problem		2013-11-07
		Dave pose la question : We know that calculus can be used to maximise the volume of the tray created when cutting squares from 4-corners of a sheet of card and then folding up. What I want is to find the sizes of card that lead to integer solutions for the size of the cut-out, the paper size must also be integer. EG 14,32 cutout 3 maximises volume as does 13,48 cutout 3. I have done this in Excel but would like a general solution and one that does not involve multiples of the first occurence, as 16, 10 cutout 2 is a multiple of 8,5 cutout 1. Walter Whiteley lui répond.
	Maximize the volume of a cone		2013-10-09
		Conlan pose la question : 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. Penny Nom lui répond.
	Maximize profit		2013-01-19
		Chris pose la question : A firm has the following total revenue and total cost function. TR=100x-2x^2 TC=1/3x^3-5x^2+30x Where x=output Find the output level to minimize profit and the level of profit achieved at this output. Penny Nom lui répond.
	A max/min problem		2012-12-14
		bailey pose la question : A right angled triangle OPQ is drawn as shown where O is at (0,0). P is a point on the parabola y = ax – x^2 and Q is on the x-axis. Show that the maximum possible area for the triangle OPQ is (2a^3)/(27) Penny Nom lui répond.
	Two altitudes of a scalene triangle		2012-08-13
		grace pose la question : 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? Justify all of your conclusions. Chris Fisher lui répond.
	The maximum distance from the vertex of a triangle		2012-05-02
		David pose la question : There are three towns A,B,and C, equi-distant apart. A car is 3 miles from town A, and 4 miles from town B. (ie, somehwere outside of the triangle which the three towns form) What is the maximum distance that the car can be from town A? This was asked as quiz question in my local pub last Sunday. The answer is 7. How do I prove it? Best regards. David in Denton. Robert Dawson and Chris Fisher lui répond.
	A maximization problem		2012-04-09
		Nancy pose la question : After an injection, the concentration of drug in a muscle varies according to a function of time, f(t). Suppose that t is measured in hours and f(t)=e^-0.02t - e^-0.42t. Determine the time when the maximum concentration of drug occurs. Penny Nom lui répond.
	A max min problem		2012-02-26
		Christy pose la question : Hello, I have no idea where to start with this question. Bob is at point B, 35 miles from A. Alice is in a boat in the sea at point C, 3 miles from the beach. Alice rows at 2 miles per hour and walks at 4.25 miles per hour, where along the beach should she land so that she may get to Bob in the least amount of time? Penny Nom lui répond.
	Margie threw a ball		2012-02-16
		mary pose la question : at 9:45 Margie threw a ball upwards while standing on a platform 35ft above the ground. The height after t seconds follows the equation: h(t)= -0.6t^2 +72t+35 a) what will be the maximum height of the ball? b)how long will it take the ball reach its maximum height?? Harley Weston lui répond.
	Lost in the woods		2012-01-12
		Liz pose la question : 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? Harley Weston lui répond.
	A spherical ball in a conical wine glass		2011-10-26
		Jules pose la question : 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)). Claude Tardif lui répond.
	Maximum area of a rectangle		2011-10-04
		Lyndsay pose la question : A rectangle is to be constructed having the greatest possible area and a perimeter of 50 cm. (a) If one of the sides of the rectangle measures 'x' cm, find a formula for calculating the area of the rectangle as a function of 'x'. (b) Determine the dimensions of the rectangle for which it has the greatest area possible. What is the maximum area? Penny Nom lui répond.
	A rectangle of largest possible area		2011-09-16
		mary pose la question : Steven has 100 feet of fencing and wants to build a fence in a shape of a rectangle to enclose the largest possible area what should be the dimensions of the rectangle Penny Nom lui répond.
	Designing a tin can		2011-03-31
		Tina pose la question : A tin can is to have a given capacity. Find the ratio of the height to diameter if the amount of tin ( total surface area) is a minimum. Penny Nom lui répond.
	What is the maximum weekly profit?		2010-10-10
		Joe pose la question : A local artist sells her portraits at the Eaton Mall. Each portrait sells for $20 and she sells an average of 30 per week. In order to increase her revenue, she wants to raise her price. But she will lose one sale for every dollar increase in price. If expenses are $10 per portrait, what price should be set to maximize the weekly profits? What is the maximum weekly profit? Stephen La Rocque and Penny Nom lui répond.
	Maximizing the volume of a cylinder		2010-08-31
		Haris pose la question : question: the cylinder below is to be made with 3000cm^2 of sheet metal. the aim of this assignment is to determine the dimensions (r and h) that would give the maximum volume. how do i do this? i have no idea. can you please send me a step-to-step guide on how t do this? thank you very much. Penny Nom lui répond.
	A max min problem		2010-08-19
		Mark pose la question : a rectangular field is to be enclosed and divided into four equal lots by fences parallel to one of the side. A total of 10000 meters of fence are available .Find the area of the largest field that can be enclosed. Penny Nom lui répond.
	Maximize the floor area		2010-07-07
		shirlyn pose la question : A rectangular building will be constructed on a lot in the form of a right triangle with legs of 60 ft. and 80 ft. If the building has one side along the hypotenuse, find its dimensions for maximum floor area. Penny Nom lui répond.
	A max/min problem		2010-06-12
		valentin pose la question : What is the maximum area of an isosceles triangle with two side lengths equal to 5 and one side length equal to 2x, where 0 ≤ x ≤ 5? Harley Weston lui répond.
	An optimization problem		2010-05-23
		Marina pose la question : Hello, I have an optimization homework assignment and this question has me stumped..I don't even know A hiker finds herself in a forest 2 km from a long straight road. She wants to walk to her cabin 10 km away and also 2 km from the road. She can walk 8km/hr on the road but only 3km/hr in the forest. She decides to walk thru the forest to the road, along the road, and again thru the forest to her cabin. What angle theta would minimize the total time required for her to reach her cabin? I'll do my best to copy the diagram here:                              10km Hiker_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _Cabin       \                           |                              /        \                          |                             /      f  \                      2km                          /          \                        |                           / theta   \___________________________ /                             Road Penny Nom lui répond.
	A rectangular garden		2010-04-25
		Billy pose la question : Tanisha wants to make a rectangular garden with a perimeter of 38 feet. What is the greatest area possible that tanisha can make the garden? Penny Nom lui répond.
	Two max/min problems		2010-04-11
		Amanda pose la question : 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. Tyler Wood lui répond.
	A max min problem		2010-04-06
		Terry pose la question : 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. Harley Weston lui répond.
	The maximum area of a rectangle		2010-01-03
		Mohammad pose la question : determine the maximum area of a rectangle with each perimeter to one decimal place? a)100 cm b)72 m c)169 km d)143 mm Penny Nom lui répond.
	Maximizing the area of a rectangle		2009-12-17
		rachel pose la question : A rectangular field is to be enclosed by 400m of fence. What dimensions will give a maximum area? Penny Nom lui répond.
	Maximize profit		2009-11-14
		Willie pose la question : Profit is the difference between Total Revenue and Total Cost. Therefore, to MAXIMIZE PROFIT you must maximize Total Revenue. True or False? Explain answer. Penny Nom lui répond.
	A max/min problem		2009-10-12
		avien pose la question : a rectangle has a line of fixed length Lreaching from the vertex to the midpoint of one of the far sides. what is the maximum possible area of such a rectangle? SHOW SOLUTION USING CALCULUS Penny Nom lui répond.
	The maximum number of right angles in a polygon		2009-10-05
		Bruce pose la question : 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? Chris Fisher lui répond.
	A rectangular pen		2009-08-13
		Kari pose la question : A rectangular pen is to be built using a total of 800 ft of fencing. Part of this fencing will be used to build a fence across the middle of the rectangle (the rectangle is 2 squares fused together so if you can please picture it). Find the length and width that will give a rectangle with maximum total area. Stephen La Rocque lui répond.
	Maximum Volume of a Cylinder Inscribed in a Sphere		2009-06-18
		Jim pose la question : Hello I have a hard time finishing this question: A right circular cylinder has to be designed to sit inside a sphere of radius 6 meters so that each top and bottom of the cylinder touches the sphere along its complete circular edge. What are the dimensions of the cylinder of max volume and what is the volume? Janice Cotcher lui répond.
	Application of Derivatives of Trig Functions		2009-05-21
		Alannah pose la question : I have a word problem from my Calculus textbook that I can't figure out. Triangle ABC is inscribed in a semicircle with diameter BC=10cm. Find the value of angle B that produces the triangle of maximum area. I am supposed to set up an equation for the area of the triangle A=b x h/2 using Trig functions based on angle B to represent the base and height but I'm not sure how to do this when the side length given is not the hypotenuse. Janice Cotcher lui répond.
	Maximum profit		2009-05-11
		Sally pose la question : a manufacturer of dresses charges $90 per dress up to 100 units and the average production cost is $60 per dress. to encourage larger orders the company will drop the price per dress by .10 for orders in excess of 100. I need to find the largest order the company should allow with the special discount to realize maximum profit. Harley Weston lui répond.
	A discount on a charter plane		2009-05-06
		karen pose la question : a charter plane company advertises that it will provide a plane for a fare of $60. if your party is twenty or less and all passengers will receive a discount of $2 per person if the party is greater than 20. what number of passengers will maximize revenue for the company Stephen La Rocque lui répond.
	A max-min problem		2009-04-20
		Charlene pose la question : A fixed circle lies in the plane. A triangle is drawn inside the circle with all three vertices on the circle and two of the vertices at the ends of a diameter. Where should the third vertex lie to maximize the perimeter of the triangle? Penny Nom lui répond.
	The optimal retail price for a cake		2009-03-25
		Shawn pose la question : 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? Robert Dawson lui répond.
	A max-min problem		2009-03-24
		Jay pose la question : Determine the area of the largest rectangle that can be inscribed between the x-axis and the curve defined by y = 26 - x^2. Harley Weston lui répond.
	Partial derivatives		2009-01-17
		Meghan pose la question : 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)" Harley Weston lui répond.
	A maximum area problem		2009-01-13
		Kylie pose la question : Help me please! I don't know how or where to start and how to finish. The problem is: A window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 15 ft., find the dimensions that will allow the maximum amount of light to enter. Harley Weston lui répond.
	What is the maximum revenue?		2009-01-09
		Kristy pose la question : A skating rink manager finds that revenue R based on an hourly fee x for skating is represented by the function R(x) = -200x^2 + 1500x What is the maximum revenue and what hourly fee will produce maximum revenues? Harley Weston lui répond.
	A max/min problem		2009-01-09
		Angelica pose la question : have 400 feet of fence. Want to make a rectangular play area. What dimensions should I use to enclose the maximum possible area? Robert Dawson lui répond.
	A sphere in a can of water		2008-12-12
		Meghan pose la question : A cylindrical can open at the top has (inside) base radius equal to 1. The height of the can is greater than 2. Imagine placing a steel sphere of radius less than 1 into the can, then pouring water into the can until the top of the sphere is just covered. What should be the radius of the sphere so the volume of water used is as large as possible? Harley Weston lui répond.
	Taxes in Taxylvania		2008-10-22
		April pose la question : Taxylvania has a tax code that rewards charitable giving. If a person gives p% of his income to charity, that person pays (35-1.8p)% tax on the remaining money. For example, if a person gives 10% of his income to charity, he pays 17 % tax on the remaining money. If a person gives 19.44% of his income to charity, he pays no tax on the remaining money. A person does not receive a tax refund if he gives more than 19.44% of his income to charity. Count Taxula earns $27,000. What percentage of his income should he give to charity to maximize the money he has after taxes and charitable giving? Harley Weston lui répond.
	Maximize revenue		2008-10-08
		Donna pose la question : A university is trying to determine what price to charge for football tickets. At a price of 6.oo/ticket it averages 70000 people per game. For every 1.oo increase in price, it loses 10000 people from the average attendance. Each person on average spends 1.5o on concessions. What ticket price should be charged in order to maximize revenue. price = 6+x, x is the number of increases. ticket sales = 70000- 10000x concession revenue 1.5(70000 - 10000x) I just do not know what to do with the concession part of this equation (6+x) x (70000 - 10000x) I can understand but not the concession part please help. thx. Penny Nom lui répond.
	The biggest right circular cone that can be inscribed in a sphere		2008-09-08
		astrogirl pose la question : find the volume of the biggest right circular cone that can be inscribed in a sphere of radius a=3 Harley Weston lui répond.
	Largest Inscribed Rectangle		2008-09-03
		astrogirl pose la question : find the shape and area of the largest rectangle that can be inscribed in a circle of a diameter a=2 Janice Cotcher lui répond.
	The maximum range of a projectile		2008-07-22
		kwame pose la question : the range R of projectile fired with an initial velocity Vo ,at an angle of elevation (@ )theta from the horizontal is given by the equation R = (Vo(squared) sin2theta)/g. where g is the accelation due to gravity . Find the angle theta such that the projectile has maximum range . Harley Weston lui répond.
	A square and a circle		2008-07-20
		kobina pose la question : 4 ft of a wire is to be used to form a square and a circle. how much of the wire is to be used for the square and how much should be used for the square in order to enclose the maximum total area Harley Weston lui répond.
	What is the greatest area she can have for her garden?		2008-05-12
		angie pose la question : Mary has 12 wood boards, each board is 1 yard long. She wants her garden to be shaped like a rectangle. What is the greatest area she can have for her garden? Penny Nom lui répond.
	How many presses should be used?		2008-05-04
		Sarah pose la question : 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. Harley Weston lui répond.
	A lidless box with square ends		2008-04-28
		Chris pose la question : 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. Stephen La Rocque and Harley Weston lui répond.
	At what value of t is the maximum acceleration?		2008-04-25
		Mary pose la question : Velocity of a function (which is the first derivative of its position) is defined over the interval 0 to 12 using the following piecewise function: v(t)=-1 from 0 to 4, v(t)=x-5 from (4 to 8 and v(t)=-x+11 from (8 to 12. At what value of t is the maximum acceleration? Stephen La Rocque lui répond.
	An open box		2008-04-23
		Le pose la question : Metal Fabrication; If an open box is made from a tin sheet 8 in square by cutting out identical squares from each corner and bending up the resulting flaps, determine the dimensions of the largest box that can be made. Harley Weston lui répond.
	f(x) =ax^blnx		2008-04-13
		charles pose la question : supposef(x) =ax^blnx is a real- valued function. Determine exact values(not decimal approximations) fro nonzero constants a and b so that the function f has a critical point at x=e^3 and a maximum value of 1/2e Harley Weston lui répond.
	The maximum area of a pizza slice		2008-04-12
		charles pose la question : A slice of pizza in the form of a sector of a circle has a perimeter of 24 inches. what value for the radius of the pizza makes the slice largest[when o is the central angle in radians, the area of the sector is given by A= r^20/2and the length on the circle is given by s=r0 Harley Weston lui répond.
	What point on the graph y = e^x is closest to the origin?		2008-03-03
		elvina pose la question : What point on the graph y = e^x is closest to the origin? Justify your answer. Stephen La Rocque lui répond.
	A Norman window		2008-02-25
		Jason pose la question : If the perimeter of a Norman window is 20 feet, what is the maximum area of the window? Stephen La Rocque lui répond.
	A ball bearing is placed on an inclined plane		2008-02-15
		Leah pose la question : A ball bearing is placed on an inclined plane and begins to roll. The angle of elevation of the plane is x. The distance (in meters) that the ball bearing rolls in t seconds is s(t) = 4.9(sin x)t^2. What is the speed of the ball bearing, and what value of x will produce the maximum speed at a particular time? Penny Nom lui répond.
	Maximize income		2008-01-18
		Chris pose la question : Lemon Motors have been selling an average of 60 new cars per month at $800 over the factory price. They are considering an increase in this markup. A marketing survey indicates that for every $20 increase, they will sell 1 less car per month. What should their new markup be in order to maximize income? Stephen La Rocque and Harley Weston lui répond.
	Maximum volume of a box		2008-01-15
		Rajesh pose la question : A square piece of a cardboard of sides ten inches has four equal peices are removed at the corners, then the sides are turned up to form an open box. What is the maximum volume such a box can have? Stephen La Rocque lui répond.
	Maximize the product		2007-11-25
		David pose la question : Hi i have this site call calcchat.com, but i dont understand how they explained this can you take a look? The question is: Direction: Find two positive numbers that satisfy the given requirements. The sum is S and the product is a maximum this is what they did 1) Let x and y be two positive numbers such that x + y = S 2)P = xy 3) = x (S - x) 4) =Sx - x^2 5)...etc. the thing i dont get is how did they go from step 2 to step 3 and also i know this sound dumb but how did they get step 2? =) Harley Weston lui répond.
	A rectangular plot of farmland		2007-11-25
		Christy pose la question : A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a single-strand electric fence. With 800m of wire at your disposal, what is the largest area you can enclose, and what are its dimensions? Harley Weston lui répond.
	The maximum area of a rectangle		2007-11-23
		Christy pose la question : Question from Christy, a student: Show that among all rectangles with an 8m perimeter, the one with the largest area is a square. I know this is simple but I'm not sure if I'm doing it correctly. Here is what I did. 1. A = xy 2. 8 = 2x+2y 3. y = 4-x 4. A = x(4-x) = 4x-x^2 Not sure what to do from this point because I don't know if its right. Harley Weston lui répond.
	A rectangle in an ellipse		2007-11-18
		David pose la question : I need to find the max area of a rectangle inscribed in an ellipse with the equation x^2+4y^2=4.. What I have so far is f(x,y)=4xy g(x,y)=x^2+4y^2-4=0, y=sqrtx^2-4/4 f'(x)=2x^2/sqrt-4x^2+2(sqrt-4+x^2). What I need to know is how to finish the problem and find the actual mas area of the rectangle. David Penny Nom lui répond.
	Local maxima, minima and inflection points		2007-11-13
		Russell pose la question : 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 Harley Weston lui répond.
	Maximize his profit		2007-11-12
		apoorva pose la question : During the summer months Terry makes and sells necklaces on the beach. Last summer he sold the necklaces for $10 each and his sales averaged 20 per day. When he increased the price by $1, he found that he lost two sales per day. a. Find the demand function, assuming it is linear. b. If the material for each necklace costs Terry $6, what should the selling price be to maximize his profit? Penny Nom lui répond.
	Maximize profit		2007-10-22
		Dina pose la question : A meat market purchases steak from a local meat packinghouse. The meat is purchased on Monday at a price of $2 per pound, and the meat market sells the steak for $3 per pound. Any steak left over at the end of the week is sold to a local Zoo for $0.50 per pound. The demand for steak and the probabilities of occurrence are as follows: Demand Probability       20          10%       21          10%       22          15%       23          20%       24          20%       25          15%       26          10% Determine the amount of stock to maximize the profit. Draw the graph and explain. Penny Nom lui répond.
	Maximizing profits II		2007-10-05
		a student pose la question : Suppose there are three firms with the same demand function. The function is Q=1000-40P. Each firm also a a cost function. Firm 1: 4000+5Q, Firm 2: 3000+5Q, Firm 3: 3000+7Q. What price should each firm charge if it wants to maximize profits. Harley Weston lui répond.
	Maximizing profit		2007-10-05
		a student pose la question : Use the following equation to demonstrate how a firm that produces at MR=MC can also maximize its total profit. The equations to use are P=170-5Q TC=40+50Q+5Q^2 Harley Weston lui répond.
	The range of a projectile		2007-09-18
		Claudette pose la question : This is a maximum minimum problem that my textbook didn't even try to give an example of how to do it in the text itself. It just suddenly appears in the exercises. Problem: The range of a projectile is R = v^2 Sin 2x/g, where v is its initial velocity, g is the acceleration due to gravity and is a constant, and x is the firing angle. Find the angle that maximizes the projectile's range. The author gives no information other than the formula. I thought to find the derivative of the formula setting that to zero, but once I had done that, I still had nothing that addressed the author's question. Any help would be sincerely appreciated. Claudette Stephen La Rocque lui répond.
	Find the dimensions of the rectangle that will contain the greatest area		2007-08-06
		Julirose pose la question : The perimeter of a rectangle is 38 meters. Find the dimensions of the rectangle that will contain the greatest area. Penny Nom lui répond.
	f(x) = (x^4) - 4x^3		2007-07-22
		Michael pose la question : 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. Harley Weston lui répond.
	The isosceles triangle of largest area with perimeter 12cm		2007-07-16
		sharul pose la question : find the dimension of isosceles triangle of largest area with perimeter 12cm Harley Weston lui répond.
	Using Heron's Formula to help maximize the area of a triangle		2007-06-27
		Claire pose la question : Given one side of a triangle is 4 cm and the ratio 1:3 for the other 2 sides. What is the largest area of the triangle? Stephen La Rocque and Harley Weston lui répond.
	Maximizing the volume of a cone given the slant length		2007-05-14
		Christina pose la question : 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. Stephen La Rocque and Kerstin Voigt lui répond.
	Optimization - carrying a pipe		2007-05-05
		A student pose la question : A steel pipe is taken to a 9ft wide corridor. At the end of the corridor there is a 90° turn, to a 6ft wide corridor. How long is the longest pipe than can be turned in this corner? Stephen La Rocque lui répond.
	Maximum area		2007-04-29
		fee pose la question : Given a perimeter of 24cm, calculate the maximum area using quadratics. Penny Nom lui répond.
	Maximize the volume of a cone		2007-04-27
		ashley pose la question : hello, I've been stumped for hours on this problem and can't quite figure it out. The question is: A tepee is a cone-shaped shelter with no bottom. Suppose you have 200 square feet of canvas (shaped however you like) to make a tepee. Use calculus to find the height and radius of such a tepee that encloses the biggest volume. Can you help?? Stephen La Rocque and Penny Nom lui répond.
	A cylinder inside a sphere		2007-04-25
		Louise pose la question : i need to find the maximum volume of a cylinder that can fit inside a sphere of diamter 16cm Penny Nom lui répond.
	Minimum cost for a fixed volume		2007-04-18
		James pose la question : 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. Penny Nom lui répond.
	Find the maximum revenue		2007-04-05
		Megan pose la question : The weekly revenue for a company is R= -3p+60p+1060, were p is the price of the company's product. Find the maximum revenue for this company. Stephen La Rocque lui répond.
	Maximize revenue		2007-03-08
		San pose la question : A movie theatre sells tickets for $8.50 each. The manager is considering raising the prices but knows that for every 50 cents the price is raised, 20 fewer people go to the movies. The equation R= -40c^2+84c describes the relationship between the cost of the tickets, c dollars, and the amount of revenue, R dollars, that the theatre makes. What price should the theatre charge to maximize revenue? This question comes from my gr.11 corresponding study homework and I not yet solve it. Please help! Thank you, I will appreciate your help. Stephen La Rocque lui répond.
	Maximize the area of the yard		2007-02-08
		Andy pose la question : I have 60 m to construct a fence adjacent to my house. What are the values of x and y that maximize the area of the yard? Penny Nom lui répond.
	Maximizing profit		2007-01-23
		Denise pose la question : Total Profit= Total Revenue-Total Cost P(x)=R(x)-C(x) Where x is the number of units sold. Find the maximum profit and the number of units that must be sold in order to get that profit. R(x)=5x C(x)=.001x^2+1.2x+60 Stephen La Rocque lui répond.
	A Norman window		2006-11-30
		Joe pose la question : a norman window is a rectangle with a semicircle on top. If a norman window has a perimeter of 28, what must the dimensions be to find the maximum possible area the window can have? Stephen La Rocque lui répond.
	How much labor should the firm employ?		2006-10-28
		Christy pose la question : A dressmaking firm has a production function of Q=L-L(squared)/800. Q is the number of dresses per week and L is the number of labor hours per week. Additional cost of hiring an extra hour of labor is $20. The fixed selling price is P=$40. How much labor should the firm employ? What is the resulting output and profit? I am having a difficult time with this, HELP! Stephen La Rocque lui répond.
	A fence around a pen		2006-03-30
		Daryl pose la question : I hope you can help me out with the attached problem, It has been driving me crazy. Stephen La Rocque and Penny Nom lui répond.
	The box of maximum volume		2006-02-01
		Elizabeth pose la question : A box factory has a large stack of unused rectangular cardboard sheets with the dimensions of 26 cm length and 20 cm width. The question was to figure what size squares to remove from each corner to create the box with the largest volume. I began by using a piece of graph paper and taking squares out. I knew that the formula L X W X H would give me volume. After trial and error of trying different sizes I found that a 4cm X 4cm square was the largest amount you can take out to get the largest volume. My question for you is two parts First: Why does L X H X W work? And second, is their a formula that one could use, knowing the length and width of a piece of any material to find out what the largest possible volume it can hold is without just trying a bunch of different numbers until you get it. If there is, can you explain how and why it works. Penny Nom lui répond.
	A max-min problem		2005-12-16
		Julie pose la question : 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. Penny Nom lui répond.
	Mrs. Faria lives on an island		2005-12-15
		Julie pose la question : Mrs. Faria lives on an island 1 km from the mainland. She paddles her canoe at 3 km/h and jogs at 5 km/h. the nearest drug store is 3 km along the shore from the point on the shore closest to the island. Where should she land to reach the drug store in minimum time? Penny Nom lui répond.
	A field with the largest possible area		2005-09-25
		Louise pose la question : A FARMER HAS FENCING OF 1000M AND WANTS A FIELD WITH THE BIGGEST POSSIBLE AREA HOW DO I GO ABOUT DOING THIS Penny Nom lui répond.
	Maximizing revenue		2005-05-13
		Jackie pose la question : 1.The manager of a 100-unit apartment complex knows from experience that all units will be occupied if the rent is $400 per month. A market survey suggests that, on the average, one additional unit will remain vacant for each $5 increase in rent. What rent should the manager charge to maximize revenue? 2.During the summer months Terry makes and sells necklaces on the beach. Last summer he sold the necklaces for $10 each and his sales averaged 20 per day. When he increased the price by $1, he found that he lost two sales per day. a. Find the demand function, assuming it is linear. b. If the material for each necklace costs Terry $6, what should the selling price be to maximize his profit? Penny Nom lui répond.
	Gasoline in a cylindrical tank		2005-03-23
		Jennifer pose la question : Gasoline is stored in a tank which is a cylinder on its side. Height of fuel is "h" meters and the diameter is "d". The length is "l". I need to find the amount of gas in the tank when the height is h and also to calculate the fraction of how full it is. Also, the part I am really confused on is this one, E(h/d) is the error of the function of h/d, when h/d is used to measure how full the tank is. For what value of h/d is the error maximal? Penny Nom lui répond.
	Largest square inside a circle		2004-10-25
		Bob pose la question : my granddaughter asked what is the largest size square in inches would fit in a 60 inch circle? I believe it to be around 42.3 inches but would like to teach her how to do it mathematically. Penny Nom lui répond.
	Maximize income		2004-10-24
		Connie pose la question : A company that sells x units of a product generates an income (I, in dollars) which is a function of x. The income generated is described by the equation I = (-1/2)x^2 + 100x. Discuss how to determine the number of units that must be sold so that the company can maximize its income. What is the maximum income? Penny Nom lui répond.
	A trig problem		2004-08-02
		A student pose la question : 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. Penny Nom lui répond.
	Maximizing the angle to the goal mouth		2004-05-15
		Yogendra pose la question : 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. Penny Nom lui répond.
	Percent difference		2004-04-10
		A parent pose la question : For a school science project, my son Alex is taking measurements of plant growth at regular intervals. As part of the data, he must provide the maximum percent difference observed in the categories his team has identified. So, for example he has six plants with four measurements each. (He has more, but I'll keep it simple) For the first plant he measured 2mm, 2.4mm, 2.9mm, and 3.2mm. For the 2nd, 3rd, and 4th plants, he has similar numbers. Is there a way to calculate the maximum percent difference between any two plants in his measurements during the project? Doing it for each combination would be tedious. Penny Nom lui répond.
	Maximizing the area		2004-03-27
		Petey pose la question : Please could you tell me why for my coursework (where I have to find the largest area that a fence 1000m long can cover) why I should only test equilateral and isoceles triangles? We were told NOT to do right angled triangles but I was wondering why not? Penny Nom lui répond.
	Which one has the most factors?		2003-10-31
		Kristi pose la question : Of all the whole numbers less than or equal to 5000, which one has the most factors? Claude Tardif lui répond.
	The volume of air flowing in windpipes		2003-05-02
		James pose la question : 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? Penny Nom lui répond.
	A max/min problem		2002-09-21
		Evelina pose la question : 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. Penny Nom lui répond.
	A rectangular marquee		2002-05-07
		Alyaa pose la question : 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 Harley Weston lui répond.
	a+b=10 and ab=40		2002-04-27
		April pose la question : What two numbers add to ten and multiply to forty? (a+b=10, a*b=40) I think the answer includes radicals and/or imaginary numbers. Penny Nom lui répond.
	Getting to B in the shortest time		2001-12-19
		Nancy pose la question : 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 Penny Nom lui répond.
	A lighthouse problem		2001-11-02
		A student pose la question : 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? Harley Weston lui répond.
	Where is the fourth point?		2001-10-24
		Mike pose la question : Four points are placed at random on a piece of paper. Connect the three points of the triangle of the largest area. What is the possibility that the fourth point is in the triangle? Penny Nom lui répond.
	Dividing a circle		2001-10-17
		Ahmeen pose la question : I am having a hard time figuring out how a circle can be divided into 11 equal parts with only 4 cut allowed? My teacher gave this to us and I still can't cut my pie into eleven equal parts with only four cuts. Walter Whiteley lui répond.
	Maximize the area		2001-10-13
		Mike pose la question : I have no clue how to do this problem. Here is what the professor gave to us: A=LW C=E(2L+2W) + I(PL) Where P = # of partitions E= cost of exterior of fence I = cost of interior of fence C = total cost of fence . . . Harley Weston lui répond.
	Maximize profit		2001-05-09
		Brian pose la question : The marginal cost for a certain product is given by MC = 6x+60 and the fixed costs are $100. The marginal revenue is given by MR = 180-2x. Find the level of production that will maximize profit and find the profit or loss at that level. Harley Weston lui répond.
	An emergency response station		2001-03-29
		Tara pose la question : 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? Claude Tardif and Penny Nom lui répond.
	Airflow in windpipes		2001-03-25
		Ena pose la question : 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? Harley Weston lui répond.
	Pillows and Cushions		2000-09-27
		Fiona pose la question : The following problem was given to grade eleven algebra students as a homework assignment. To manufacture cushions and pillows, a firm uses two machines A and B. The time required on each machine is shown. Machine A is available for one full shift of 9.6 hours. Machine B is available for parts of two shifts for a total of 10.5 hours each day. Harley Weston lui répond.
	Divisors of 2000		2000-06-06
		Amanda Semi pose la question : find the product of all the divisors of 2000 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 Claude Tardif lui répond.
	Thearcius Functionius		2000-05-03
		Kevin Palmer pose la question : 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). Harley Weston lui répond.
	Minimizing the metal in a can		2000-05-02
		May Thin Zar Han pose la question : 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. Harley Weston lui répond.
	An integer max-min problem		2000-03-13
		Paul Servic pose la question : Maximize Q = xy 2 where x and y are positive integers such that x + y 2 = 4 Penny Nom lui répond.
	Maximize		2000-03-12
		Tara Doucet pose la question : 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 Harley Weston lui répond.
	Two calculus problems		2000-03-03
		Tara Doucet pose la question : 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. 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? Harley Weston lui répond.
	Slant height of a cone		2000-02-24
		Jocelyn Wozney pose la question : 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. Harley Weston lui répond.
	The isoperimetric theorem		2000-02-24
		Raj Bobal pose la question : How can you prove Mathematically that the maximum area enclosed by a given length is a circle? Chris Fisher lui répond.
	Area of a circle and an inequality		1999-10-30
		Adam Anderson pose la question : I have two problems. The first: prove that the area of a cirlce is pi times radius squared without using calculus. The second: show that ln(x) < x - 1 for all x > 0. Harley Weston lui répond.
	The shortest ladder		1999-06-26
		Nicholas pose la question : 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<@ Harley Weston lui répond.
	Some Calculus Problems.		1997-10-30
		Roger Hung pose la question : What real number exceeds its square by the greatest possible amount? The sum of two numbers is k. show that the sum of their squares is at least 1/2 k^2. . . . Penny Nom lui répond.

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