a.) By using Pythagorean Theorem, we have...
x2+902=z2; when x=45ft; z=√452+902=45√5ft
Taking the derivative with respect to time,
2xdxdt+0=2zdzdt
xdxdt=zdzdtdzdt=xzdxdt
Plugging in all the values we have,
dzdt=\cancel45\cancel45√5(24)dzdt=24√5 or 24√55fts
The distance of the battler from the second base is decreasing at a rate of 24√55fts
b.)
Again, by using Pythagorean Theorem,
x2+902=z2; when x=45ft; z=√452+902=45√5ft
Taking the derivative with respect to time,
0+2xdxdt=2zdzdtxdxdt=zdzdtdzdt=xzdxdt
Plugging all the values we obtain,
dzdt=4545√5(24)dzdt=24√5 or 24√55fts
Thus shows that the distance of the batter from the third base is increasing at a rate equal to the decreasing rate of the batter's distance from the second base.
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