Answered

Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Join our platform to connect with experts ready to provide accurate answers to your questions in various fields. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

Suppose that 579ft of fencing are used to enclose a corral in the shape of a rectangle with a semicircle whose diameter is a side of a rectangle as the following figure:


Find the dimensions of the corral with maximum area.
x=___ft.
y=___ft.

Suppose That 579ft Of Fencing Are Used To Enclose A Corral In The Shape Of A Rectangle With A Semicircle Whose Diameter Is A Side Of A Rectangle As The Followin class=

Sagot :

raphealnwobi

The dimensions of the corral with maximum area is x = 162.15 ft and y = 81.07 ft

The perimeter (P) of the corral is:

P = y + x + y + π(x/2)

P = 2y + x + πx/2

579 = 2y + x + πx/2

y = (579 - x - πx/2) / 2 = 289.5 - x/2 - πx/4

The area (A) of the coral:

A = xy + π(x/2)²/2

A = xy + πx²/4

A = x[(579 - x - πx/2) / 2] + πx²/8

A = 579x/2 - x²/2 - πx²/4 + πx²/8

A = 579x/2 - x²/2 - πx²/8

The maximum area is at dA/dx = 0

dA/dx = 579/2 - x - πx/4

0 = 579/2 - x - πx/4

x = 162.15 ft

y = (579 - 162.15 - π(162.15)/2) / 2

y = 81.07 ft

The dimensions of the corral with maximum area is x = 162.15 ft and y = 81.07 ft

Find out more at: https://brainly.com/question/25822654

We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.