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 illustrates the problem. Let x and y represent the length and width of the rectangular region, respectively. (b) Determine the radius r, in terms of y, of the semicircular ends of the track. Determine the distance d, in terms of y, around the inside edge of the two semicircular parts of the track. d= (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 y (d) Use the result of part (c) to write the area A of the rectangular region as a function of x A= (4) Use a graphing utility to graph the area function from part (d). Use the graph to approximate the dimensions that will produce a rectangle of maximum area. (Round your answers to two decimal places) m
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 illustrates the problem. Let x and y represent the length and width of the rectangular region, respectively. (b) Determine the radius r, in terms of y, of the semicircular ends of the track. Determine the distance d, in terms of y, around the inside edge of the two semicircular parts of the track. d= (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 y (d) Use the result of part (c) to write the area A of the rectangular region as a function of x A= (4) Use a graphing utility to graph the area function from part (d). Use the graph to approximate the dimensions that will produce a rectangle of maximum area. (Round your answers to two decimal places) m
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Pls solve this question correctly instantly in 5 min i will give u 3 like for sure
Transcribed Image Text: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 illustrates the problem. Let x and y represent the length and width of the rectangular region, respectively.
(b) Determine the radius r, in terms of y, of the semicircular ends of the track.
re
Determine the distance d, in terms of y, around the inside edge of the two semicircular parts of the track.
d=
(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
YH
(d) Use the result of part (c) to write the area A of the rectangular region as a function of x.
A=
(e) Use a graphing utility to graph the area function from part (d). Use the graph to approximate the dimensions that will produce a rectangle of maximum area. (Round
your answers to two decimal places)
m
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
