Water flows into a tank at the rate of $\sqrt { 2 t + 5 }$ ft³/min. If the tank is empty when t = 0, how much water does it contain 6 minutes later? Express the answer to two decimal places. A) 0.63 ft³ B) 19.64 ft³ C) 32.08 ft³ D) 24.74 ft³

Question

Quizplus · Accepted Answer

To find the amount of water that flows into the tank over 6 minutes, we integrate the rate of flow from t = 0 to t = 6. The integral of $\sqrt{2t + 5}$ with respect to t gives us the volume of water. The integral is $\frac{2}{3}(2t + 5)^{3/2}$ evaluated from 0 to 6. Plugging in the values, we get $\frac{2}{3}(2(6) + 5)^{3/2} - \frac{2}{3}(2(0) + 5)^{3/2}$, which simplifies to $\frac{2}{3}(17)^{3/2} - \frac{2}{3}(5)^{3/2}$. Calculating this gives approximately 19.64 cubic feet.

Water Flows into a Tank at the Rate Of 2t+5\sqrt { 2 t + 5 }2t+5​

Water Flows into a Tank at the Rate Of $\sqrt { 2 t + 5 }$