Use calculus to find the dimensions of the box that give the maximum possible volume. Also calculate the maximum volume. Indi- cate your final answers by either writing them in the provided blanks or clearly labeling them so it’s clear which are which. x= y= Maximum Volume:

Q: A window is in the form of a rectangle surrounded by a semi-circular opening. The total perimeter of…

A: This question can be solved by applying the concept of maxima and minima.

Q: Consider the following rectangular piece of tinplate. An open-top cake tin is to be made by cutting…

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Q: A ball with a 20 cm diameter fits exactly into a container that is a cylinder. What is the maximum…

A: A ball spherical in shape is to be fitted on a cylindrical container given the diameter of ball is…

Q: A cylindrical coordinate robot is to be used for palletizing a rectangular area. In order to find…

A: From the given image. It is known that, It is known that area of rectangle is lw. so, the area is,

Q: A point P needs to be located somewhere on the line AD so that the total length L of cables linking…

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Q: Find the points on the circle x? + y? = 1 in which f(x, y) = 4xy has an absolute maximum and the…

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Q: Suppose a snow cone has a paper cone that is 8 centimeters deep and has a diameter of 5 centimeters.…

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Q: Q17 An open storage bin with a square base and vertical sides is to be constructed from a given…

A: In question amount of metal is not given So i assume 108 ft ^2 Then i calculate

Q: 1) The volume of an open box with a square base is 4,000 cu.cm. Find the dimensions of the box if…

A: First the base is given as square so assume that the sides of the square base is x then the width…

Q: Let A be a positive real number. If the absolute minimum value of f(x) Ar5 35x on [0, oo) occurs at…

A: If the absolute minimum value of f(x)=Ax5-35x3 on [0,∞) occurs at x=cAk. Where A be a positive real…

Q: Becausd of terra in difficuties, 2 Sides of a fence Loa be built foc$3 Per tt, while the (ther 2…

A: Given fencing needed for the field below. The cost for two sides is $7 per feet and $3 per feet for…

Q: The convex surface area of a cylinder is at maximum. Determine its dimension in order to be…

A: The convex surface area of a cylinder is at maximum. We have to determine its dimension in order to…

Q: If ƒx(a, b) = ƒy(a, b) = 0, must ƒ have a local maximum or minimum value at (a, b)? Give reasons for…

A: Given fxa,b=fya,b=0

Q: (c) cut from each corner of length x cm, a maximum volume for the resulting open-top cake tin will…

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Q: Find the absolute maximum of f(x,y) = 4x²y² + 3y? 5x2 bounded by y = x, y = 0 and x = 3. + Answer:

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: The dimensions of a closed rectangular box are measured as 21 cm, 17 cm and 11 cm, respectively with…

A: Given the dimension of the closed rectangular box 21 cm, 17 cm and 11 cm

Q: A piece of cardboard measuring 8 inches by 14 inches is formed into an open-top box by cutting…

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Q: (c) A race track 400 m long is to be built around an area that is a rectangle with a semicircle,…

A: In this question we have to find the value of x where area of trangular region is maximum.

Q: A tube of lip balm has a height of 2.75 inches and a diameter of 0.75inches.  a. if the cap on the…

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Q: An open rectangular box is to be constructed by cutting square corners out of a 29- by 29- inch…

A: An open rectangular box to be constructed by cutting square corners out of a 29 by 29 inch piece of…

Q: Postal regulations require that for priority mail the length and girth of a rectangular parcel…

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Q: An open rectangular box is to be constructed by cutting square corners out of a 16 by 16 cm piece of…

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Q: (a) The total surface area of an open cylinder is 27 cm³ given that radius, rcm. i. Show that the…

A: Given that; Total surface area of am open cylinder is 27pi cm^3. Radius r cm.

Q: ind the dimensions of the rectangle of maximum area with sides parallel to the coordinate axes that…

A: Given that the ellipse equation is 75x2+3y2=75 find length and width

Q: Find a formula for the volume of the box in terms of æ V(x) = Find the value for æ that will…

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Q: A square sheet of metal has squares cut from its corners as shown. a сm What sized square should be…

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Q: A rectangular base box must be constructed, with a sheet of cardboard 40 cm wide and 50 cm long,…

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Q: Consider the following rectangular piece of tinplate. An open-top cake tin is to be made by cutting…

A: This question is based on application of Derivatives.

Q: . Calculate the area of the beach Abcd in square meters b. The beach area is covered in sand to a…

A: Answer and explanation is given below...

Q: An open box is to be made from a 3 ft by 8 ft rectangular piece of sheet metal by cutting out…

A: We need to find maximum volume.

Q: A piece of cardboard measuring 8 inches by 11 inches is formed into an op squares with side length a…

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Q: The volume of traffic for a collection of intersections is shown in the figure below. A X3 10 50 40…

A: The minimum number of vehicles go through C to A is 20 vehicles

Q: ONotes Evaiuate A box with an open top is to be constructed out of a rectangular piece of cardboard…

A: topic - application of derivatives

Q: e. Find the second derivaitve. f''(x) = f. Use parts b through e to identify maximums as points. g.…

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Q: (b) A vacuum flask for keeping water hot is modelled as closed cylinder in which the internal radius…

A: Volume for a closed cylinder = πr2h In our case, πr2h = 1000 The total internal surface area of the…

Q: Please

A: If we fold it we will get a cuboid with l=10-2x cm, b=8-2x cm and h=x cm Volume V for a cuboid = lbh

Q: Let R be a rectangle with sides measuring x > 0 and y > 0 and perimeter equal to 14. What is the…

A: x = length of rectangle R ; x>0y = width of rectangle R; y>0A = Area of RA = xy…

Q: Suppose you make napkin rings by drilling holes with different diameters through two wooden balls…

A: SOLUTION-

Q: Solve the following maxima and minima problems: A silo consists of a right circular cylinder…

A: When we place right circular cone on top of a cylinder, the curved surface…

Q: Glenview Community College wants toconstruct a rectangular parking lot on land bordered on one…

A: What should be the dimensions of the lot if theenclosed area is to be a maximum?

Q: An Architect Plans To Build A Triangular Enclosure With A Fence On Two Sides And A Wall On The Third…

A: The given triangle is sketched below.

Q: An architect plans to build a triangular enclosure with a fence on two sides and a wall on the third…

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Q: An open box is to be made from a 33 ft by 88 ft rectangular piece of sheet metal by cutting out…

A: Solve the given problem.

Q: 9. If 1200 square centimeters of material is available to make a box with a square base and an open…

A: Use second derivative test

Q: If an open box has a square base and a volume of 103 in.3 and is constructed from a tin sheet, find…

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Q: Find the absolute maximum of f(x,y) = 7x²y² + 4y? + 4x² bounded by y = x, y = 0 and x = 1. Answer:

A: Here is the solution of the given problem.

Q: Given that a right circular cylinder is inscribed within a sphere, what is the least possible volume…

A: First we draw the figure as per the given information, Now, we will assume the following : Let,…

Q: A cone is to be constructed so that, if its radius is r, its height must be h = 100 – r2. We wish to…

A: the volume of a cone is given by ...............(1) the equation of the height is…

Q: 8a. A rectangle is bounded by the x-axis and the semicircle y = \4 – x². What length and width…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.