# math

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a bootlenose dolphin jumps out of the water. the path the dolphin travels can be modeled by h=-0.2d^2+2d, where h represents the height of the dolphin in feet and d represents the horizontal distance.

What is the maximum height the dolphin can jump?

• math -

Assuming this is a calculus question and not a graphical one, you need to solve a simple differential equation in d:

h = 2d - (d^2)/5, so
dh/dd = 2 - 2d/5 = 0 at the maximum, so d=5. But at d=5, h= 2*5 - (5^2)/5 = 10 - 5 = 5. So the maximum height is 5 feet. Not very high, is it? Do check it and see if you agree.

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