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A baseball diamond is 90 feet square (NOT 90 square feet!). Coach Jack Handley runs from first base to second base at 25 feet per second. How fast is he moving away from home plate when he is 30 feet from first base (Problem #3)? How fast is he moving away from home plate when he is 45 feet from first base (Problem #4)? Answers should be expressed in terms of feet per second.

Respuesta :

Answer:

dx/dt = 5√5/2

Step-by-step explanation:

Given:

dx/dt = 25 feet per second

According to Pythagoras theorem:

x² + 90² = y²

We know that x = 30 ft

So,

x² + 90² = y²

30² + 90² = y²

y = 30√10

So,

x² + 90² = y²

By taking differentiate:

2x dx/dt = 2y dy/dt

[x/y][dx/dt] = dy/dt

dx/dt = 5√5/2

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