Find two numbers whose sum is a, if the product of one by the cube of the other is to be a maximum. Find the dimensions of a rectangle of maximum perimeter inscribed in a circle. Figure

Q: Among all pairs of numbers whose sum is 20, find a pair whose product is as large as possible. What…

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Q: Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter:…

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Q: Of all rectangles with a perimeter of 32, which one has the maximum area? (Give the dimensions.) The…

A: Here we have to find the length and width of the rectangle that has perimeter of 32 with maximum…

Q: Find the length and width of a rectangle that has the given area and a minimum perimeter. Area: 81…

A: Find the length and width of a rectangle that has the given area and a minimum perimeter. Area: 81…

Q: Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter:…

A: Let the length of the rectangle = LLet the breadth of the rectangle = BPerimeter of the rectangle =…

Q: Of all rectangles with a perimeter of 11, which one has the maximum area? (Give the dimensions.) The…

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Q: 9. A rancher has 400' of fencing with which to enclose two adjacent rectangular corrals. What…

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Q: A farmer has 480 meters of fencing with which to build two animal pens with a common side as shown…

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Q: Find the Maximum height of h(x) = -4x^2 + 320x + 100.

A: The given height function is h(x)=-4x2+320x+100

Q: Use calculus to find two numbers whose product is -16 and such that the sum of the squares of the…

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Q: An open-top box is to be made from a 30-inch by 54-inch piece of plastic by removing a square from…

A: Given:Dimension of plastic board=30inch by inch

Q: The back of Jill's property is a creek. Jill would like to enclose a rectangular area, using the…

A: Given,          The back of Jill's property is a creek. Jill would like to enclose a rectangular…

Q: Of all rectangles with a perimeter of 5, which one has the maximum area? (Give the dimensions.) The…

A: The area of a rectangle is: A=l×w Where, l is the length of the rectangle. w is the width of the…

Q: A rectangle is bounded by the x-axis and the semicircle y = √(25 − x2). What length and width should…

A: Given, A rectangle is bounded by the x-axis and the semicircle y=25-x2. The figure,

Q: An architect is asked to design a game room in the shape of an isosceles trapezoid where the non…

A: Let's find fourth side length for maximum area.

Q: Of all rectangles with a perimeter of 32, which one has the maximum area? (Give the dimensions.) The…

A: To find the length and width of the rectangle that has perimeter of 32 with maximum possible area.…

Q: A farmer wants to fence in three sides of a rectangular field shown below with 1,120 feet of…

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Q: Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter:…

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Q: Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter:…

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Q: Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter:…

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Q: Find two numbers whose sum is 10, and the sum of whose squares is a minimum. Please put the…

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Q: Find the length and width of a rectangle that has the given area and a minimum perimeter. Area: 49…

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Q: Of all rectangles with a perimeter of 28​,which one has the maximum​ area? (Give the​ dimensions.)

A: We can find the dimensions as below.

Q: A rectangle is bounded by the x-axis and the semicircle  y = square root of (49-x^2)  (see figure).…

A: Let the length along the x axis is = 2x So the height= 49-x2 So the area is: A=2x49-x2

Q: Of all the numbers whose sum is 52, find the two that have the maximum product.

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Q: A rectangle has a perimeter of 40m. What could be the maximum area of the rectangle?

A: A rectangle has a perimeter of 40 m. Let x and y be the length and width of the rectangle. Now…

Q: The back of Jill's property is a creek. Jill would like to enclose a rectangular area, using the…

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Q: find the dimensions of a rectangular plot of land such that the perimeter is 80 meters and the area…

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Q: The area of a rectangle is represented by 12x - x² where x is a side of the rectangle. For what…

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Q: A farmer plans to make 3 identical and adjacent rectangular pens, using an existing wall as one…

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Q: a rancher has 720 feet of fencing to construct six corrals, find the dimensions that maximized the…

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Q: A gardener is building a garden shaped like a rectangle. If he has 100 meters of fencing to go…

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Q: An open-top box is to be made from a 37 in. by 27 in. piece of cardboard by removing a square from…

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Q: Amoung all pairs of numbers with a sun of 149, find the pair whose product is a maximum

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Q: Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter:…

A: The given Perimeter P = 48 m Let length of rectangle l = x  Width = b

Q: Find two numbers whose sum is "a", if the product of one to the square of the other is to be a…

A: sum of two numbers is 'a', the product of one to the square of the other is to be maximum

Q: The perimeter of a rectangle is to be no less than 72 centimeters and the width must be 17…

A: In the question we have to find minimum length of the rectangle.

Q: A farmer has 480 meters of fencing with which to build two animal pens with a ... common side as…

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Q: The longest side of a triangle is 3 times the shortest side and the third side is 2 cm shorter than…

A: Let the shortest side= x cm  so the longest side= 3x cm  third side= 3x-2 cm

Q: Find the length and width of a rectangle that has the given perimeter and a maximum area Perimeter:…

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Q: A shipping company will ship a box only if the sum of its length and girth (distance around) does…

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Q: A farmer has 2, 000 feet of fence and wishes to build two identical rectangular enclosures, as in…

A: Given query is to find the dimensions of the sides to maximize the area.

Q: A rancher has 480 feet of fencing with which to enclose two adjacent rectangular corrals (see…

A: Total fencing needed in that given picture is= x+x+x+x+y+y+y=4x+3y Given that the rancher has 480…

Q: framer has 160 feet of fencing to enclose two adjacent rectangular pens. what dimensions should he…

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Q: The base of a three-dimensional figure is bound by the semi-circle y = √9-x². Vertical cross…

A: Given: Let us consider the given semi-circle, y=9-x2 Let's determine the Area of the square.

Q: A farmer has 1,300 feet of fence and wishes to build two identical rectangular enclosures, as in the…

A: Given: A farmer has 1,300 feet of fence and wishes to build two identical rectangular enclosures as…

Q: A farmer has 480 meters of fencing with which to build two animal pens with a ... common side as…

A: Let us assume that both pens have same dimensions.

Q: Find the dimensions of a rectangle of maximum area having a perimeter of 36 feet

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Q: The back of Jake's property is a creek. Jake would like to enclose a rectangular area, using the…

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