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Dog freedom?


BMAD
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Chain the dog in the middle of a 100-foot wall.

In the front yard he has an 80-foot-radius semicircle of access.

When he gets to the ends of the wall, he has 30 feet of chain left.

As he walks into the back yard he gains access to a 30-foot-radius semicircle on each side.

Area [three semicircles] = pi/2 [802 + 302 + 302] = pi/2 [6400 + 900 + 900] = pi [3200 + 900] = 4100 pi ft2

General area formula (x is distance from end of wall to the chain point):

0<x<20:.. A = pi/2 [802 + (80-x)2]

20<x<50: .A = pi/2 [802 + (80-x)2 + (x-20)2]

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I see what I did wrong. I have it being quarter circles at the end of radius 30.

Chain the dog in the middle of a 100-foot wall.

In the front yard he has an 80-foot-radius semicircle of access.

When he gets to the ends of the wall, he has 30 feet of chain left.

As he walks into the back yard he gains access to a 30-foot-radius semicircle on each side.

Area [three semicircles] = pi/2 [802 + 302 + 302] = pi/2 [6400 + 900 + 900] = pi [3200 + 900] = 4100 pi ft2

General area formula (x is distance from end of wall to the chain point):

0<x<20:.. A = pi/2 [802 + (80-x)2]

20<x<50: .A = pi/2 [802 + (80-x)2 + (x-20)2]

Edited by BMAD
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