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WARRIOR [948]
3 years ago
15

Solve the following for the specified variable Z=s/2(P+p); for P

Mathematics
1 answer:
lapo4ka [179]3 years ago
6 0

Answer:

\boxed{\sf P = \frac{2Z}{s} - p}

Step-by-step explanation:

\sf Solve \ for \ P: \\ \sf \implies  Z = \frac{s}{2} (P + p) \\ \\ \sf Z = \frac{s}{2} (P + p) \ is \ equivalent \ to \ \frac{s}{2} (P + p) = Z: \\ \sf \implies \frac{s}{2} (P + p) = Z \\ \\  \sf Divide \ both \ sides \ by \ \frac{s}{2} : \\ \sf \implies P + p = \frac{2Z}{s} \\ \\ \sf Substrate \ p \ from \ both \ sides: \\ \sf \implies P = \frac{2Z}{s} - p

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<em>[using calculus] </em>When the function h(t) reaches its maximum value, its first derivative will be equal to zero (the first derivative represents velocity of the ball, which is instantaneously zero). We have h'(t) = -32t + 48, which equals zero when t = 3/2 = 1.5. The ball therefore reaches its maximum height when t = 1.5. To find the maximum height, we need to find h(1.5), which is 64 feet.

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