8. A right triangle has a fixed base of length 11 meters and a height that is in

Question

8. A right triangle has a fixed base of length 11 meters and a height that is increasing at a rate of 3 meters/second. At what rate is the length of the hypotenuse increasing when the height is 14 meters? 9. The volume of a sphere formula is known to be: V-4 ·r' . If a snowball is melting (decreasing) at a rate of- in) /hr, what is the rate orchange of the radius when the radius is 5 in? 10. Gravel is being dumped from a conveyor belt at a rate of 25 ft'hr and its coarseness is such that it forms a pile in the shape of a right cone whose increasing when the pile has the height of 15t? Htint: Use Formula

Explanation / Answer

8. h2= b2+l2

h2=112+142

h2=121+196 =317

h= sqrt 317

h2=b2+l2

2h (dh/dt) = 2l(dl/dt)

2 sqrt 317(dh/dt) = 2(14) (dl/dt)

dh/dt= 14/sqrt317 =0.786m/s

9. V=(4/3) pi r3

dV/dt= 4 pi r2(dr/dt)

(1/2) pi = 4 pi (25) (dr/dt)

(1/2)*(1/100) = dr/dt

dr/dt= 1/200 in/hr =0.005 ln/hour

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