Answered: 11. (Calculator) Fluid is pumped into a…

11. (Calculator) Fluid is pumped into a tank at a rate of 8 gal/min. At the same time, the fluid is leaking out of the tank at a rate of vt +1 gal/min, where 0

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

11. (Calculator) Fluid is pumped into a tank at a rate of 8 gal/min. At the same time, the fluid is leaking out of the tank at
a rate of vt +1 gal/min, where 0<t<120 min. The tank initially contains 30 gallons of fluid.
a) Find the number of gallons of fluid that leaked out of the tank fromt = 0 to t = 3 minutes.
b) Find the number of gallons of fluid that are in the tank at exactly t= 3 minutes.
(continued)
c) Let A(t) represent the total number of gallons of fluid in the tank at any time t. Write a formula for A(t).
d) Use calculus to determine when the tank has the most fluid in it on the interval 0<t<120. Justify your answer.

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