A) Basketball and Football
B) Soccer
C) ???
Answer: x=6
Step-by-step explanation:
Just think about how the problem is half
Pretty low, it’s exactly 0.175
Here L = W, but H can be different.
The sum L+H+W must be less than or equal to 192 cm.
We can solve L + H + W = 192 for H: H = 192 - W - L. Remembering that W = L, the formula for H becomes 192 - 2W.
The formula for volume would be V = L*W*H.
This becomes V = W*W*H, or V = W^2*(192-2W)
Multiplying this out: V = w^2*192 - 2W^3
Two ways of determining W:
1) graph V = 192W^2 - 2W^3 and determine the value of W at which V is at a max with the constraint W + L + H is equal to or smaller than 192.
2) Differentiate V with respect to W and set the result equal to zero:
384W - 6W^2 = 0. Solving for W: W(384 - 6W) = 0.
W = 0 is trivial, so just solve 384 - 6W = 0 for W: 6W = 384, and W = 64.
The width is 64 cm, the length is 64 cm also, and the height is (192-2W) cm, or 64 cm.
These dimensions produce the max volume.
