A farmer would like to construct a cage to separate farm animals. He has 600 meters of materials to use and the design that he is going to construct is as shown in the figure. What is the maximum area for the cage?

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: The volume of an open box with a square base is 4000 cm3. Find the dimensions of the box if the…

A: Given that volume =4000cm3 find the dimensions of the box that minimize the amount of material used…

Q: A packaging company is going to make open-topped boxes out of 20 cm by 20 cm rectangles of cardboard…

A:

Q: The perimeter of an isosceles triangle is 38 m. Find the length of the sides of the triangle of…

A: Let's find.

Q: A standard elevator in a midrise building can hold a maximum weight of about 3 2/3 tons. Assuming an…

A: We first convert tons into pounds

Q: What are the dimensions of a rectangle with perimeter 160 cm and the maximum area' What is the…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: A farmer buys 120 m of fence. He wants to make 2 cages of 4 rectangles with the same length for his…

A: Let x and y be the  length and width of cage respectively (equals to dimensions of rectangle) total…

Q: Imagine you want to enclose a field in the shape of a rectangle with a semicircle on one end. If you…

A: Imagine you want to enclose a field in the shape of a rectangle with a semicircle on one end. If you…

Q: A goat is tethered to a stake In the ground by a rope that is 10 feet long in terms of pi, what is…

A:

Q: Jim wants to build a rectangular parking lot along a busy street but only has 2,800 feet of fencing…

A: This question is related to application of derivative.

Q: An open-top box with a square base is to have a volume of 32 cubic feet. Find the dimensions of the…

A: To determine the dimension of the box which minimize the amount of material used.

Q: A Norman Window has the shape of a rectangle surmounted by a semicircle. If a Norman window is to…

A: Given, The perimeter of the window = 28 ft  Height of rectangular part = y width of rectangular part…

Q: You have 268 feet of fencing to enclose a rectangular region. What is the maximum area of the…

A: maximum area of the rectangle

Q: You are given a rectangular piece of paper that has length x=35.4x=35.4 cm and height y=28y=28 cm.…

A:

Q: Jim wants to build a rectangular parking lot along a busy street but only has 1,600 feet of fencing…

A:

Q: An open-top box is to be made from a 36 in. by 27 in. piece of cardboard by removing a square from…

A:

Q: An open box is to be made of a piece of cardboard 10cm x 16cm by cutting equal squares out of the…

A:

Q: A rectangular garden is to be constructed using a rock wall as one side of the g and wire fencing…

A: We are asked to find dimensions of the rectangle.

Q: A rancher has 400 feet of fencing with which to enclose two adjacent rectangular corrals (see…

A:

Q: An animal shelter has 160 feet of fencing to enclose two adjacent rectangular playpenareas for dogs.…

A: Sketch the adjacent rectangular playpen areas for dogs as shown below.

Q: Suppose that 202 ft of fencing are used to enclose a corral in the shape of a rectangle with a…

A: Given that 202 ft of fencing are used to enclose a corral in the shape of a rectangle with a…

Q: A cardboard box without a lid is to have a volume of 4000cm3. Find the minimum amount of cardboard…

A:

Q: If a gun is fired with and a =30o and V0 = 500m/s, whenwill the bullet hit the ground? How far from…

A:

Q: 2) Angelina is building a garden in the centre of her backyard as shown. She has 46 m of fencing…

A:

Q: A cow is tethered to one corner of a square barn, 20 feet by 20 feet, with a rope 100 feet long.…

A:

Q: A box with an open top is to be constructed from a square piece of cardboard that is 4 feet wide by…

A: Square piece of cardboard of 4 feet wide. Let x feet be cut off from each corner of the square piece…

Q: A rancher has 200 feet of fencing with which to enclose two adjacent rectangular corrals (see…

A: Total fencng = 200 feetTotal fencing = 4x+3y=200 feet  — (i)Area = 2x×yFrom eqn - i - y =200-4x3Area…

Q: You have 40 feet of fence to enclose a rectangular garden with two subdivisions. What is the maximum…

A:

Q: A farmer wants to fence in two rectangular corrals, equal in area, using an inner fence as shown in…

A: Given;

Q: A farmer wants to create four rectangular corral's to separate his livestock. He has 750m of fencing…

A: Let the dimension of the each rectangular corral be, x m by y m.The perimeter of one rectangular…

Q: Paula plans to build a rectangular closure for her dogs using 140m of fencing. What is the maximum…

A:

Q: Find the maximum area that can be formed by a series of small pens next to a river with separate…

A: The area of a rectangle is the product of its length and breadth. For a parabola of the form…

Q: Jim wants to build a rectangular parking lot along a busy street but only has 2,100 feet of fencing…

A:

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: A window is in the shape of a rectangle surrounded by a semicircle. If the perimeter of the window…

A:

Q: 8. A rancher has 200 feet of fencing with which to enclose two adjacent rectangular corrals (see…

A: A rectangular figure is given. Let, the length of parallel side of division be y and the length of…

Q: A box with no top has a square base. If 64 squared centimeter of material is used, what is the…

A: A box with no top has a square base and 65 cm^2 of material is used

Q: A farmer with 120 meters of fencing needs to enclose a rectangle area into three equal pens with…

A:

Q: The size of the rectangle that can be made from 200 cm long wire so that the area is maximum is ….

A: We have to find the maximum area of given rectangle.

Q: (EX) Max wishes to enclose a rectangular garden, using one side of his house as shown below. What is…

A: We use second derivative test to find out dimensions of rectangular garden have maximum area

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

A:

Q: Suppose that 404 ft of fencing are used to enclose a corral in the shape of a rectangle with a…

A: Area of the shape=Area of the semicircle+Area of rectangle .Area of semicircle=πx22x12…

Q: A farmer wants to make a rectangluar enclosure using a wall of a barn as one side and 160 ft of…

A: Let x ,in feet, be the length of side of rectangular enclosure which is along the wall of barn and y…

Q: Find the rectangle of the maximum area that can be inscribed in a right triangle with legs of length…

A:

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: The sum of the dimensions of a box with a sqaure base is 48 m. Find the maximum volume of the box.

A: Volume

Q: Find the dimensions of the rectangle in the figure shown below that will give the maximum area, if…

A:

Q: A carpenter is building a rectangular room with a fixed perimeter of 116 ft. What dimensions would…

A:

Q: You are given a rectangular piece of paper that has length x=35.4 cm and height y=28 cm. The lower…

A: Since, we have been given a rectangular piece of paper that has lengthx=35.4 cm and height y=28 cm.…

Q: An open topped box is to be made from a rectangular piece of metal 18cm x 48 cm by cutting off…

A: