You are going camping with a 10 ft. by 16 ft. tarp to use as a pup tent. You can set up the tent by splitting the tarp in half along either the shorter or longer side. will one of these choices create a larger volume or would they be the same?
thanks...im starting to get where ur coming from..but i think my teacher wants us to use derivitives...so if anyone could help show me a way to do that it would be greatly appreciated
Okey-doke then. If we set up the volume in terms of theta, then we can differentiate to find the angle that maximizes the volume. As I previously stated, it is 45 degrees. But here we show it.
The volume of the tent = area of the triangular cross-section times the length.
The area of the cross section = (1/2)hbl where h is the height, b is the base and l is the length. The width of the tarp will be called w. Using Pythagorean Thm, (2b)2=(2w)2−h2 b2=4(4w2−h2)
b2=w2−4h2
b=±w2−4h2
V=21bhl=21hlw2−4h2
Now we could substitute in w=10 and l=16 for case 1 and differentiate to determine maximum volume. Then for case 2 substitute in w=16 and l=10 and differentiate to determine maximum volume. Then we compare those results.
The volume of the tent = area of the triangular cross-section times the length.
The area of the cross section = (1/2)hbl where h is the height, b is the base and l is the length. The width of the tarp will be called w. Using Pythagorean Thm, (2b)2=(2w)2−h2 b2=4(4w2−h2)
b2=w2−4h2
b=±w2−4h2
V=21bhl=21hlw2−4h2
Now we could substitute in w=10 and l=16 for case 1 and differentiate to determine maximum volume. Then for case 2 substitute in w=16 and l=10 and differentiate to determine maximum volume. Then we compare those results.
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