adjacent rectangular corrals (see figure). 85. (a) Write the area A of the corrals as a function of x. (b) Construct a table showing possible values of x and the corresponding areas of the corral. Use the table to estimate the dimensions that will produce the maximum enclosed area. (c) Use a graphing utility to graph the area function. Use the graph to approximate the dimensions that will produce the maximum enclosed area. (d) Write the area function in standard form to find analytically the dimensions that will produce the maximum area. (e) Compare your results from parts (b), (c), and (d). 82. Geometry An indoor physical fitness room consists of a rectangular region with a semicircle on each end. The perimeter of the room is to be a 200-meter single-lane running track. (a) Draw a diagram that gives a visual representation of the problem. Let x and y represent the length and width of the rectangular region, respectively. (b) Determine the radius of each semicircular end of the room. Determine the distance, in terms of y, around the inside edge of each semicircular part of the track. (c) Use the result of part (b) to write an equation, in terms of x and y, for the distance traveled in one lap around the track. Solve for y. (d) Use the result of part (c) to write the area A of the rectangular region as a function of x. What dimensions will produce a rectangle of maximum area? . Maximum Revenue A small theater has a seating capacity of 2000. When the ticket price is $20, attendance is 1500. For each $1 decrease in price, attendance increases by 100. (a) Write the revenue R of the theater as a function of ticket price x. (b) What ticket price will yield a maximum revenue?
adjacent rectangular corrals (see figure). 85. (a) Write the area A of the corrals as a function of x. (b) Construct a table showing possible values of x and the corresponding areas of the corral. Use the table to estimate the dimensions that will produce the maximum enclosed area. (c) Use a graphing utility to graph the area function. Use the graph to approximate the dimensions that will produce the maximum enclosed area. (d) Write the area function in standard form to find analytically the dimensions that will produce the maximum area. (e) Compare your results from parts (b), (c), and (d). 82. Geometry An indoor physical fitness room consists of a rectangular region with a semicircle on each end. The perimeter of the room is to be a 200-meter single-lane running track. (a) Draw a diagram that gives a visual representation of the problem. Let x and y represent the length and width of the rectangular region, respectively. (b) Determine the radius of each semicircular end of the room. Determine the distance, in terms of y, around the inside edge of each semicircular part of the track. (c) Use the result of part (b) to write an equation, in terms of x and y, for the distance traveled in one lap around the track. Solve for y. (d) Use the result of part (c) to write the area A of the rectangular region as a function of x. What dimensions will produce a rectangle of maximum area? . Maximum Revenue A small theater has a seating capacity of 2000. When the ticket price is $20, attendance is 1500. For each $1 decrease in price, attendance increases by 100. (a) Write the revenue R of the theater as a function of ticket price x. (b) What ticket price will yield a maximum revenue?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:adjacent rectangular corrals (see figure).
85.
(a) Write the area A of the corrals as a function of x.
(b) Construct a table showing possible values of x and
the corresponding areas of the corral. Use the table
to estimate the dimensions that will produce the
maximum enclosed area.
(c) Use a graphing utility to graph the area function.
Use the graph to approximate the dimensions that
will produce the maximum enclosed area.
(d) Write the area function in standard form to find
analytically the dimensions that will produce the
maximum area.
(e) Compare your results from parts (b), (c), and (d).
82. Geometry An indoor physical fitness room consists
of a rectangular region with a semicircle on each end.
The perimeter of the room is to be a 200-meter
single-lane running track.
Transcribed Image Text:(a) Draw a diagram that gives a visual representation of
the problem. Let x and y represent the length and
width of the rectangular region, respectively.
(b) Determine the radius of each semicircular end of the
room. Determine the distance, in terms of y, around
the inside edge of each semicircular part of the track.
(c) Use the result of part (b) to write an equation, in
terms of x and y, for the distance traveled in one lap
around the track. Solve for y.
(d) Use the result of part (c) to write the area A of
the rectangular region as a function of x. What
dimensions will produce a rectangle of maximum
area?
. Maximum Revenue A small theater has a seating
capacity of 2000. When the ticket price is $20,
attendance is 1500. For each $1 decrease in price,
attendance increases by 100.
(a) Write the revenue R of the theater as a function of
ticket price x.
(b) What ticket price will yield a maximum revenue?
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