1. ## related rates help:

A baseball diamond is 90ft on a side. (It is really a square). A man runs from first base to second base at 25 ft/sec. At what rate is his distance from the third base decreasing when he is 30ft from the first base?

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A baseball diamond is 90ft on a side.
A man runs from first base to second base at 25 ft/sec.
At what rate is his distance from the third base decreasing when he is 30ft from the first base?
Of course, you made a sketch . . .
Code:
                    B
*
*   * x
*       *  A
90 *           o
*       o       *
*   o    y          *
C o                       *
*                   *
*               *
*           *
*       *
*   *
*

The man is at A.
His distance from second base is: .x = AB
. . That distance is decreasing at 25 ft/sec: .dx/dt = -25

His distance from third base is: .y = AC
. . We want dy/dt

From right triangle ABC, we have: . .= .x² + 90²

Differentiate with respect to time: .2y·(dy/dt) .= .2x·(dx/dt)

. . and we have: .dy/dt .= .(x/y)·(dx/dt) .[1]

When he is 30 feet from first base, x = 60
. . And: . .= .60² + 90² . . y = 30√13
And we know that: .dx/dt = -25
. . . . . . . . . . . . . . . . . . . . . . . . . . .__
Substitute into [1]: .dy/dt .= .60/(30√13) · (-25) . .-13.9 ft.sec