Water is leaking out the bottom of a hemispherical tank of radius 9 feet at a rate of 2 cubic feet per hour. the tank was full at a certain time. how fast is the water level changing when its height h is 6 feet? note: the volume of a segment of height h in a hemisphere of radius r is pi h squared left bracket r minus left parenthesis h divided by 3 right parenthesis right bracket.

The water level changing by the rate of -0.0088 feet per hour ( approx )

Step-by-step explanation:

Given,

The volume of a segment of height h in a hemisphere of radius r is,

Where, r is the radius of the hemispherical tank,

h is the water level, ( in feet )

Here, r = 9 feet,

Differentiating with respect to t ( time ),

Here,

And, h = 6 feet,

Thus,

a) y = -3x +2

b) y = 1/2x -6

these 2 can be combined into one equation.

-3x +2 = .5x -6

8 = 3.5x

x = 8 / 3.5 = 2.2857142857

y = -3 * (8 / 3.5) +2

y = (-24 / 3.5) + 2

y = -4.8571428571

step-by-step explanation: