A water tank initially contains 75 gallons of water, and begins draining water. The rate is given by r(t) -4 (t+1)2 gal/minute, where t is the time in minutes after the tank starts leaking. Let V (t) represent the volume (in gallons) of water in the tank at time t. a. Describe in words what the following expression means, in the context of this problem: V (0) + r(t)dt b. If the water tank starts leaking at 9:00am, find the amount of water that leaks out of the tank between 9:08am and 9:15am. Round your answer to 2 decimal places. c. Use the net change theorem to find out how long it takes for the tank to fully empty. Give your answer to the nearest minute. -t(t – 2)(t 10) t +1 d. Suppose that it was raining while the tank is leaking, so water is also filling the tank as water drains out. If V"(t) = represents the rate of change of the water in the tank, set up (but do not solve) the integral that represents the total amount of change that the volume undergoes from t = 0 tot = 7 e. Graph V'(t).Use the graph to justify your answer to the following question: If the rain were to continue forever (meaning V'(t) continues to represent the rate of change of the volume of water in the tank), will the tank eventually empty or will it overfill?
A water tank initially contains 75 gallons of water, and begins draining water. The rate is given by r(t) -4 (t+1)2 gal/minute, where t is the time in minutes after the tank starts leaking. Let V (t) represent the volume (in gallons) of water in the tank at time t. a. Describe in words what the following expression means, in the context of this problem: V (0) + r(t)dt b. If the water tank starts leaking at 9:00am, find the amount of water that leaks out of the tank between 9:08am and 9:15am. Round your answer to 2 decimal places. c. Use the net change theorem to find out how long it takes for the tank to fully empty. Give your answer to the nearest minute. -t(t – 2)(t 10) t +1 d. Suppose that it was raining while the tank is leaking, so water is also filling the tank as water drains out. If V"(t) = represents the rate of change of the water in the tank, set up (but do not solve) the integral that represents the total amount of change that the volume undergoes from t = 0 tot = 7 e. Graph V'(t).Use the graph to justify your answer to the following question: If the rain were to continue forever (meaning V'(t) continues to represent the rate of change of the volume of water in the tank), will the tank eventually empty or will it overfill?
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...
Related questions
Question
Transcribed Image Text:A water tank initially contains 75 gallons of water, and begins draining water. The rate is given by r(t)
-4
(t+1)2
gal/minute, where t is the time in minutes after the
tank starts leaking. Let V (t) represent the volume (in gallons) of water in the tank at time t.
a. Describe in words what the following expression means, in the context of this problem: V (0) + | r(t)dt
b. If the water tank starts leaking at 9:00am, find the amount of water that leaks out of the tank between 9:08am and 9:15am. Round your answer to 2 decimal places.
c. Use the net change theorem to find out how long it takes for the tank to fully empty. Give your answer to the nearest minute.
-t(t -- 2)(t - 10)
d. Suppose that it was raining while the tank is leaking, so water is also filling the tank as water drains out. If V'(t) =
represents the rate of change of the
t+1
water in the tank, set up (but do not solve) the integral that represents the total amount of change that the volume undergoes fromt = 0 to t = 7
e. Graph V'(t).Use the graph to justify your answer to the following question: If the rain were to continue forever (meaning V'(t) continues to represent the rate of change of
the volume of water in the tank), will the tank eventually empty or will it overfill?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning