[Hint: Circumference of a circle = 2ar, area of a circle = ar", where r is the radius of the circle.]

Q: A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the…

A: To determine the value of the x for the greatest amount of light is admitted.

Q: Johnny is designing a rectangular poster to contain 84 cm of printing with a 7-cm margin at the top…

A:

Q: rectangular page is to contain 32 square inches of print. The margins at the top and bottom of the…

A: Use  formula of area of rectangle  Then differentiate

Q: A rectangular poster is to contain 800 square centimeters of print. 1he margins at the top and…

A: Given that

Q: I decided to start a garden in my backyard. ree weekS ugit 80 feet of wire to enclose a rectangular…

A: It is given that the three sides has to be enclosed using 80 ft of wire. Let x be the length and y…

Q: Illustrating the Dimensions of a Box You want to make a box to be part of your designed gadget. You…

A: We have given 12 inches long and 8 inches wide rectangular sheet of cardboard.We will make a box by…

Q: Cost In redecorating an office, the cost for new carpeting is $3 per square foot and the cost of…

A: It is given that, the cost of carpeting is $3 per square foot and the cost of wallpapering is $4 per…

Q: 18. Designing a Norman Window A Norman window has the shape of a rectangle surmounted by a…

A:

Q: A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the…

A: Given:

Q: A box is in the shape of a square-based prism.  The height of the box is twice the width of the…

A:

Q: Farmer Ed has 450 meters of​ fencing, and wants to enclose a rectangular plot that borders on a…

A: To calculate the required dimensions under the given conditions

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

A: I am attaching image so that you understand each and every step.

Q: you are to construct an open rectangular box from 12 ft^2 of material. What dimensions will result…

A:

Q: 57. Minimizing cost of materials. The cost C, in dollars, to build a fence around a rectangular…

A:

Q: Illustrating the Dimensions of a Box| You want to make a box to be part of your designed gadget. You…

A: Given that: Maximum allowable volume =80 in3

Q: Another pen problem A rancher is building a horse pen on the corner of her property using 1000 ft of…

A: Diagram :…

Q: 5. An open-top box is to be made by cutting squares from a sheet of tin 4 ft. long and 2.5 ft. wide…

A: 5. Given that, An open-top box is to be made by cutting squares from a sheet of tin 4 ft. long and…

Q: A silo consists of a right circular cylinder surmounted by a hemisphere. Find the most economical…

A: Given that a silo consists of a right circular cylinder surmounted by a hemisphere. We need to find…

Q: Question A farmer is constructing three equally-sized pens against the side of a barn for his…

A: We need to find max area.

Q: A farmer plans to enclose a rectangular pasture adjacent to a river (see figure). The pasture must…

A: Given the area of the pasture in order to provide enough grass for the herdA=45,000

Q: Activity 1 Garden Arectangular garden has length 20mand breadth 8m. Different types of plants were…

A: A) option c B) 6 metres square C) 14 metres square D) 40 metres square

Q: Illustrating the Dimensions of a Box You want to make a box to be part of your designed gadget. You…

A:

Q: 41. A window consists of rectangular pane of glass surmounted by a semicircular pane of glass (see…

A: …

Q: A farmer plans to enclose a rectangular pasture adjacent to a river (see figure). The pasture must…

A:

Q: 16. Norman Windows A Norman window has the shape of a rectangle surmounted by a semicircle of…

A:

Q: 1. The perimeter of an isosceles triangle is P inches. Find the maximum area

A: Note : As per our guidelines we are supposed to answer only one question.   Since you have asked…

Q: Design a rectangular milk carton box of width w, length l, and height h which holds 464 cm3 of milk.…

A:

Q: A rectangular roller skating rink has no boundaries. If you were to take a 300-foot length of rope…

A: Given : Length of Rope to create boundaries around the rectangular roller skating rink = 300 foot…

Q: A cylinder shaped can needs to be constructed to hold 600 cubic centimeters of soup. The material…

A: Consider the Volume of the can.

Q: A rectangular box with no top and two intersecting partitions is to be constructed from 12 square…

A: Let, x be the width, y be the length and z be the height of the box. Now, given that the box is…

Q: Cost in redecorating an office, the cost for new carpeting is $5 per square foot and the cost of…

A: We can use Lagrange multipliers to answer this question.  V = xyz = f(x, y, z) ∇f(x, y, z) = λg(x,…

Q: A rectangular poster is to contain 392 square centimeters of print. The margins at the top and…

A: Let the length of the print part be x and let the width of the print part be y Then the area of the…

Q: A challenging pen problem A farmer uses 200 meters of fencingto build two triangular pens against a…

A: Dimension of triangular pens is given as x and y So, area of Triangular Pen = 12×height+base…

Q: Horse Barn Corral A horse breeder wants to construct a corral next to a horse barn that isL= 16 feet…

A:

Q: An ecologist is conducting a research project on breeding pheasants in captivity. She first must…

A:

Q: Johnny is designing a rectangular poster to contain 90 in? of printing with a 5-in margin at the top…

A:

Q: fllustrating the Dimensions of a Box You want to make a box to be part of your designed gadget. You…

A:

Q: Your new puppy needs a rectangular dog run outside. You have 50 feet of fencing and plan to use the…

A: Since one side is garage so fencing will be done for other three sides.

Q: 11. Your new puppy needs a rectangular dog run outside. You have 50 feet of fencing and plan to use…

A:

Q: Design a rectangular milk carton box of width w, length I, and height h which holds 492 cm³ of milk.…

A: Solution: We know that, l.w.h=492 cm2 h=492l×w

Q: A farmer plans to enclose a rectangular pasture adjacent to a river. (see figure). The pasture must…

A: Area of a rectangle=length × breadth

Q: puppy needs a rectangular dog run outside. You have 50 feet of fencing and plan to rall of your…

A:

Q: Cost A fence is to be built around a 200-square-foot rect- angular field. Three sides are to be made…

A: Solution:

Q: 32. A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of…

A:

Q: Question You work at a farm that wants to build three identical rectangular corrals in a row against…

A:

Q: 49. Your new puppy needs a rectangular dog run outside. You have 50 feet of fencing and plan use the…

A: Answer to the question number 49 is given below.     We want to find the maximum area.

Q: The base and sides of a container is made of wood panels. The container does not have a lid. The…

A: The volume of a cuboid is given by the formula: The total surface area of a cuboid is equal to the…

Q: A Norman window consists of a rectangle surmounted by a semicircle. What shape gives the most light…

A: A window consists of a rectangle surmounted by a semicircle. We have to find the condition that…

Q: A custom window is made by putting a semicircle on top of a rectangle (see the picture below).…

A: To find: The length l and height h of the rectangle that provides the minimal perimeter of window.…

Q: A rectangle is bounded by the x-axis and the semicircle y = 49 – x2 (see figure). What length and…

A: