Question

A 6,000​-liter cistern is empty when water begins flowing into it​ (at t = ​0) at a rate​ (in L/min) given by Q`(t) = 9 √t, where t is measured in minutes.
a. How much water flows into the cistern in 1.75 hours?
b. Find and graph the function that gives the amount of water in the tank at any time t.

Answer 1

Answer:

a) 6,455 L

b) V(t) = (18/3) * t^(1.5)

Step-by-step explanation:

Part a

Integrating the given relation from t = 0 to t= 105 mins

$V = \int {9 * \sqrt{t} } \, dt\\V = {\frac{9*2}{3}*t^(1.5) = \frac{18}{3}*t^(1.5)\\\\V = \frac{18}{3}*105^(1.5)\\\\\\V = 6,455L$

Part b

$V(t) = \frac{18}{3} * t^(1.5) + C\\Since V = 0 @ t = 0 ; hence, C = 0\\\\V(t) = \frac{18}{3} * t^(1.5)$