A first class radio-telephone operator wishes to cut the wire 100 meters long into two pieces. One of the pieces will be bent into the shape of a square and the other into the shape of a circle. Where should he cut the wire so that the sum of the areas of the square and circle is maximized? Express your answers in terms of the length of the wire to be bent into the shape of a circle.

Q: 5. A piece of wire is with a length of 4 m is cut into two pieces, and the resulting two pieces are…

A: Let the length of the wire cut=xAll sides of square are same side length=yPerimeter= 4 y…

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A: Given that  John wants to enclose his rectangular garden. One side of his garden is up against his…

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A: The following solution is given below:

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Q: Where should he cut the wire so that the sum of the areas of the square and the circle is maximized?

A:

Q: 2. A rancher from above needs two equal adjacent rectangular pens that share a fence in the middle.…

A: Given that ,Rancher needs two equal adjacent rectangular pens with a fence in middle. this can be as…

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Q: A 4-pen kennel of 1,960 square feet is to be constructed as shown. The cost is $20 per foot for the…

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Q: A rectangular lot has a perimeter of 80m. If its lot area is to be maximized, what is its length?

A:

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Q: -2 Albert wants to make an open box from a rectangular piece of cardboard by cutting squares out of…

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A: To maximize the area , we use Lagrange multipliers.

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Q: A first class radio-telephone operator wishes to cut the wire 100 meters long into two pieces. One…

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Q: Your job as an engineer is to design a right circular cylinder (i.e., a soup can) whose volume will…

A: Application of Derivatives: Application of derivatives uses the derivative in order to give…

Q: A wire 7 meters long is cut into two pieces. One piece is bent into a square for a frame for a…

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Q: Bill is constructing a rectangular corral in his yard. He only has 32 ft of fencing material and…

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Q: The hypotenuse of a right triangle is 12 cm in length. Calculate the measures of the unknown angles…

A: use right angle triangle concept  pythagorean triplet use concept of maxima minima  permeter of…

Q: A 4-pen kennel of 1,440 square feet is to be constructed as shown. The cost is $20 per foot for the…

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Q: Your job as an engineer is to design a right circular cylinder (i.e., a soup can) whose volume will…

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A: Let's find.

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Q: 2. A rectangular area is enclosed with fencing on three sides, with the fourth side along a house.…

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Q: A rancher wants to create two rectangular pens, as shown in the figure, using an existing fence line…

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Q: A Norman window is a rectangle with a semicircle on top. Suppose that the perimeter of a particular…

A: Let, x denotes the half width of the rectangle.y denotes the height of the rectangle.And…

Q: You are assigned a task to design three rectangular cubicles lined up and sharing walls as in the…

A: Let, y b the length of the other side of the cubicles. So, the perimeter of the rectangular…

Q: You are assigned a task to design three rectangular cubicles lined up and sharing walls as in the…

A: We can solve the given problem by using the second derivative test.

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