Homework Help is Here – Start Your Trial Now!
Math
Calculus
Water is draining out of a tank so that the height of the water, h m , in time t minutes, satisfies the differential equation dh k h dt = − , where k is a positive constant. The initial height of the water is 2.25 m and 20 minutes later it drops to 1 m. a) Show that the solution of the differential equation can be written as ( )2 60 1600 t h − = . b) Find after how long the height of the water drops to 0.25 m.  In

Water is draining out of a tank so that the height of the water, h m , in time t minutes, satisfies the differential equation dh k h dt = − , where k is a positive constant. The initial height of the water is 2.25 m and 20 minutes later it drops to 1 m. a) Show that the solution of the differential equation can be written as ( )2 60 1600 t h − = . b) Find after how long the height of the water drops to 0.25 m.  In

Calculus: Early Transcendentals
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...
See similar textbooks
icon
Related questions
Question

Water is draining out of a tank so that the height of the water, h m , in time t minutes,
satisfies the differential equation
dh k h
dt
= − ,
where k is a positive constant.
The initial height of the water is 2.25 m and 20 minutes later it drops to 1 m.
a) Show that the solution of the differential equation can be written as
( )2
60
1600
t
h
−
= .
b) Find after how long the height of the water drops to 0.25 m. 

In the attached image the prof. solves the equation. Please note the part in the rectangle. What is he doing here. Seems very slick!

 

de =kp? (a) dt o whn teo P: bo0 I=B dP= k dt (000 At + P lo00 p*dP = Jkdt tet P= Z000 -p°= kt + C : 44 + 200 kt t C 4A = - a Att B | %3D 8000 lo00 8 -t 8000 P = BooD 8-t 6) If t-8 P becomts mfinit- P becomts negutivt -la ta a 4.
Transcribed Image Text:de =kp? (a) dt o whn teo P: bo0 I=B dP= k dt (000 At + P lo00 p*dP = Jkdt tet P= Z000 -p°= kt + C : 44 + 200 kt t C 4A = - a Att B | %3D 8000 lo00 8 -t 8000 P = BooD 8-t 6) If t-8 P becomts mfinit- P becomts negutivt -la ta a 4.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
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: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS