A gutter is to be made of a strip of metal 17.7 inches wide, with the cross section have the form of an isosceles trapezoid as shown below. Find the depth h that gives the maximum cross-sectional area. a a (b- a)/2 (b — а)/2 What is the length of a in the picture? in The depth, h, that gives the maximum cross-sectional area is in The maximum cross-sectional area is in^2

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: An architetect wants to design a semicircular tunnel so that two average trucks measuring 8 feet…

A: We have a semicircular tunnel , which looks like this ,

Q: You want to build a running track as shown in the drawing. The requirements that they ask the…

A: According to the question, The perimeter of the given field is 200 meter.…

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 cylindrical coordinate robot is to be used for palletizing a rectangular area. In order to find…

A: From the given image. It is known that, It is known that area of rectangle is lw. so, the area is,

Q: An irrigation system uses a straight sprinkler pipe r=200ft long that pivots around a central point.…

A:

Q: An architetect wants to design a semicircular tunnel so that two average trucks measuring 8 feet…

A: Given: Dimension of the truck is 8 feet wide and 12 feet tall. Horizontal distance between two truck…

Q: A rectangle is bounded by the x-axis and a parabola defined by y = 4 – x. What are the dimensions of…

A: Given that, a rectangle is bounded by the x-axis and a parabola defined by y = 4 - x2. The area of…

Q: An open box is to be made from a 21 ft by 56 ft rectangular piece of sheet metal by cutting out…

A:

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 waterway in a theme park has a semicircular cross section with diameter 11 ft. The boats that are…

A: Consider the figure for the water way and the boat. The circumference of the boat is the equation of…

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

A: Given: A Norman window has the shape of a rectangle with a semicircle on top where the diameter of…

Q: Find the dimensions of the rectangle, with the largest possible area, enclosed in the semicircle, y…

A: we use second derivative test to find out maximum area of rectangle

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: A 20 ft long water trough has ends in the form of isosceles triangles whose equal sides are 4 ft…

A:

Q: 8. Find the dimensions of the rectangular box, open at the top, which has a maximum volume if…

A: Given surface area is 18 square feet.

Q: You are given a rectangular piece of paper that has length I= 28.8 cm and height y = 14 cm. The…

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: You are given a rectangular piece of paper that has length z = 28.8 cm and height y = 14 cm. The…

A: The given data is:   Given  x=28.8 cmy=14 cm

Q: An open box is to be made from a 33 ft by 88 ft rectangular piece of sheet metal by cutting out…

A:

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 Norman window is constructed by adjoining a semicircle to the top of a rectangular window, as…

A:

Q: An open-top box is to be made by cutting congruent squares of side length x from the cor- ners of a…

A: The box is in the shape of cuboid whose sides are x , 20-2x and 25-2x

Q: A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular…

A:

Q: What is the maximum size of the window frame you can create with 20 feet of materials? The window…

A: To Find: The maximum size of the window frame you can create with 20 feet of materials.

Q: A rectangle, R, has length L = 8 and width W = 3. What is the maximum area of the rectangle, Q, that…

A: We need to find maximum area.

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: 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: Suppose that 477 ft of fencing are used to enclose a corral in the shape of a rectangle with a…

A: Given that: Length of total fencing =477ft                             NOTE: As per our answering…

Q: Starting with a 60-foot-long stone​ wall, a farmer would like to construct a rectangular enclosure…

A: So perimeter of the fence = x+w+60+x+w= 480 feet So,

Q: A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular…

A: Given: The total perimeter is 16 feet. The given window is formed by adjoining semicircle to the top…

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

A:

Q: Suppose 2700 cm² of material is available to make a box with a square base and open top. a) Show…

A:

Q: The volume of a right circular cone whose base has a radius r and that has a height of h is given by…

A: Given that: Volume of cone, V=π3r2h, h=10cm and r=30 cm and errors in height and radius = ±0.1cm

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 8 –…

A:

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: A carpenter is building a rectangular room with a fixed perimeter of 392 ft. What dimensions would…

A: Let l & b be the length and breadth of the room

Q: A rectangular page contains 65 cm? of print. The top and bottom margins of the page are each 0.5 cm…

A:

Q: Define the livable space of a building to be the volume of space in the building where a person 6…

A: As given that height of the rectangular box= 6 ft. (according to the height of person) Length of the…

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: For its beef stew, Betty Moore Company uses aluminum containers that have the form of right circular…

A: Given that an aluminium box container is in the shape of right circular cylinder and has capacity of…

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: Glenview Community College wants toconstruct a rectangular parking lot on land bordered on one…

A: What should be the dimensions of the lot if theenclosed area is to be a maximum?

Q: the area of a plane shape is given by A=(10x -2)cm². the area is not greater or equal to 12cm². it…

A: Please refer to the image below

Q: 9. Leo is building a garden against the patio walkway in his backyard as shown. He has 156 ft of…

A: The perimeter of a rectangle is the total length of all the sides of the rectangle. Hence, we can…

Q: A farmer wishes to enclose a rectangular region bordering a barn with fencing, as shown in the…

A: Assume the below figure top be the given figure as mentioned in the question. Let the length of the…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.