See attached image. For part b, my answer is , and for part c I think the coffee pot is empty at t=41.231, although I'm not sure about these answers.

a) shown

b) h = [sqrt(17) - (5/2)t]²

c) t = 2sqrt(17)/5 seconds

Step-by-step explanation:

V = pi × r² × h

V = pi × 5² × h

V = 25pi × h

a) dV/dt = dV/dh × dh/dt

-5pi × sqrt(h) = 25pi × dh/dt

dh/dt = -sqrt(h)/5

b) 1/sqrt(h) .dh = -5. dt

2sqrt(h) = -5t + c

t = 0, h = 17

2sqrt(17) = 0 + c

c = 2sqrt(17)

2sqrt(h) = -5t + 2sqrt(17)

sqrt(h) = [2sqrt(17) - 5t] ÷ 2

sqrt(h) = sqrt(17) - (5/2)t

Square both sides

h = [sqrt(17) - (5/2)t]²

c) empty: h = 0

0 = [sqrt(17) - (5/2)t]²

sqrt(17) - (5/2)t = 0

(5/2)t = sqrt(17)

t = 2sqrt(17)/5

t = 1.64924225 seconds

sqrt: square root

for ex: the reciprocal of 3/4 is 4/3. it is the opposite.

reciprocal definition:

a mathematical expression or function so related to another that their product is one; the quantity obtained by dividing the number one by a given quantity.

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step-by-step explanation: