Please show me how to get to the answer. 7. Water leaks out of a tank through a square hole with 1-inch sides. At time \( t \) (in seconds), the velocity of water flowing through the hole is \( v = g(t) \) ft/sec. Write a definite integral that represents the total amount of water lost in the first minute. The expression shown is an integral problem commonly found in calculus and mathematical analysis:\[ \int_{0}^{60} \frac{1}{144} g(t) \, dt \, \text{ft}^3 \]This represents the definite integral of the function \(\frac{1}{144} g(t)\) with respect to \(t\), from the lower limit of 0 to the upper limit of 60. The result of this integration will be in cubic feet (\(\text{ft}^3\)), suggesting it might be a problem related to volume or accumulation over time.

Name: Please show me how to get to the answer. 7. Water leaks out of a tank
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Please show me how to get to the answer. 7. Water leaks out of a tank through a square hole with 1-inch sides. At time \( t \) (in seconds), the velocity of water flowing through the hole is \( v = g(t) \) ft/sec. Write a definite integral that repre

Given that water leaks out of a tank through a square hole with 1 inches side. At time t the velocity of flow of water is given by g(t) feet/second. We need to write a definite integral to represent the total amount of water in the first minute. Since t is given in minute we need to convert t in to seconds. 1 minute=60 seconds So t varies from 0≤t≤60 Since the sides is measured in inches , we need to convert it into feet. 1 feet =12 inches. 1 inches =1/12 feet. Since water is flowing at a constant velocity , so the amount of water which has passed through some time dt can be viewed as rectangle solid of height g(t)∆t feet and area with side 1/12 feet. So total amount water lost is represented as V=∫t=060(112)2g(t)dtV=∫t=060(1144)g(t)dt