A window on a new house is designed as a rectangle with a semicircle on the top. If the window is designed to let in the maximum amount of light, and the architect fixes the perimeter of the window to be 720 cm, determine the radius r (of the semicircle) and height h of the rectangle so as to maximize the area. Enter the exact answer or round to the nearest hundredth.

Q: Suppose that 208 ft of fencing are used to enclose a corral in the shape of a rectangle with a…

A: Given:  208 ft of fencing is used to enclose a coral From given figure diameter of the semicircle is…

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

A: Let the Length of the rectangle be:  x Let the Width of the rectangle be: y It is given that the…

Q: 5. Find the dimensions of the rectangle in the figure shown below that will give the maximum…

A: let's assume length of rectangle is yfeet now, equating perimeterP of given figure with 12feet so,…

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

A: The following solution is given below:

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A: Consider x as the length and y as the breadth of the rectangle.Then area is A = xy.Since x is length…

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A: According to given,    Let x be length of the portion that is bent into a circle   Therefore, 4-x=…

Q: A rancher will use 600 m of fencing to build a corral in the shape of a semicircle on top of a…

A: Let r = radius of the semicircle Let x = the width of the rectangle 2r = length of the rectangle…

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

A:

Q: A farmer wants to fence in an area of 1.5 million square feet in a rectangular field and then divide…

A: Given query is to find the way of fency to minimize the cost.

Q: A window on a new house is designed as a rectangle with a semicircle on the top. If the window is…

A:

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

A:

Q: a. A rectangular pen is built with one side against a barn. If 2500 m of fencing are used for the…

A: Note: According to Bartleby guidelines; For more than one question asked only the first one is to be…

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

A:

Q: Given a closed box with surface area = 16 and a square bottom, what value of x will maximize the…

A:

Q: The area A of a triangle with two sides of equal length a is given by A = /P(P- a)²(P – b) where b…

A:

Q: A Norman window has the shape of a rectangle surmounted by a semicircle. Find the dimensions of a…

A: Given that the perimeter is fixed.Let us assume that the length of the rectangle part which is also…

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

A:

Q: a. A rectangular pen is built with one side against a bam. If 1100 m of fencing are used for the…

A: x=width  y=length  perimeter is given by p=2x+y here we have p=1100 1100=2x+y y=1100-2x . the area…

Q: How tall should the file be to maximize the volume that it can hold?

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Q: a rectanglar garden must be constructed so that the width is 150ft. what are the possible values for…

A: For a rectangle whose length is ‘l’ and width is ‘b’ the perimeter ‘p’ is given by the formula.

Q: A pentagon is formed by placing an isosceles triangle on a rectangle, as shown in the figure. II the…

A: The given a pentagon is formed by placing an isosceles triangle on a rectangle, as shown in the…

Q: Suppose the farmer makes the rectangular holding pen using an existing fence for one side. What…

A: Let the farmer makes the rectangular holding pen using an existing fence for one side.  let the…

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

A:

Q: A rectangular corral of 96 square meters is to be fenced off and then divided by a fence into two…

A: We use second derivative test to find dimensions where amount of fencing is minimum

Q: Suppose you are given a piece of paper which is 9 in. x 11 in. and your goal is to make the piece of…

A: Second derivative test: 1) If f'(x)=0 then x is said to be a critical point. 2) At a critical point…

Q: A piece of wire 8 m long is cut into two pieces. One piece is bent into a square and the other is…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

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

A: Let's assume length of circle is xTotal length is 7Length of square is 7-xLet's assume radius of…

Q: A window on a new house is designed as a rectangle with a semicircle on the top. If the window is…

A:

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

A:

Q: Farmer Ed has 700 700 meters of​ fencing, and wants to enclose a rectangular plot that borders on a…

A:

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

A: Here, the volume of the box is given by: V=lbh Here, for the given box, l=9-2x, w=10-2x,h=x. So,…

Q: You have a wire of length 2 m, which you can bend either into a square or a circle. You also have…

A:

Q: Suppose that 259 ft of fencing are used to enclose a corral in the shape of a rectangle with a…

A: Given, Perimeter of corral = 259 ft Then, x+2y+2πx22=259y=259-x-πx22            ... (1)

Q: Suppose that 465 ft of fencing are used to enclose a corral in the shape of a rectangle with a…

A: We are given that 465 ft of fencing is used to enclose a corral in the shape of a rectangle with a…

Q: Suppose we have 45 m² of material to build a box with a square bottom and no top. What dimensions…

A:

Q: . A window consists of an open rectangle topped by a semicircle and is to have a perimeter of 288…

A: It is given that the perimeter, P of the window is 288 inches and we have to radius of semicircle…

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: if the hypotenuse of a right triangle is 25, show that the area is a maximum of it is isosceles

A:

Q: A farmer has 100 feet of fence and wants to make a rectangular holding pen. What dimensions should…

A: Given: Length of fence available = 100 ft

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A:

Q: An isosceles triangle has a perimeter of 30cm. What is the length of the base if its area is to be…

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Q: An architect needs to design a rectangular room with an area of 89ft2 . What dimension should be use…

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Q: You want to make 3 pairs of earrings that are in the shape of isosceles triangles. Each earring will…

A: Earrings can be made of the form isosceles triangle. ie., two adjecents sides are equal. Base of the…

Q: Given that the perimeter of an isosceles triangle has 26 cm. If we want to maximized its area, what…

A:

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

A:

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: Two chicken coops are to be built adjacent to one another from 144 ft of fencing. Part: 0/ 2 Part 1…

A: Two chicken coops are to be built adjacent to one another from 144 ft of fencing To find dimensions…

Q: A rectangular building covering 6,000m2 is to be built on a lot as shown in the figure. If the…

A: Minimize area