Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
A tank initially holds 100 gallons of brine solution containing 20 lbs. of salt. At t = 0, fresh water is poured into the tank at the rate of 5 gal/min., while the well- stirred mixture leaves the tank at the same rate. Find the amount of salt in the tank at any time t.

A tank initially holds 100 gallons of brine solution containing 20 lbs. of salt. At t = 0, fresh water is poured into the tank at the rate of 5 gal/min., while the well- stirred mixture leaves the tank at the same rate. Find the amount of salt in the tank at any time t.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
100%
1. A tank initially holds 100 gallons of brine solution containing 20 lbs. of salt. At t = 0, fresh water is poured into the tank at the rate of 5 gal/min., while the well- stirred mixture leaves the tank at the same rate. Find the amount of salt in the tank at any time t. 2. A tank 100 gallon capacity is initially full of water. Pure water is allowed to run into the tank at a rate of 1 gallon per minute, and at the same time containing one-fourth pound of salt per gallon flows into the tank also at a rate of 1 gallon per minute. The mixture flows out at a rate of 2 gallons per minute (it is assumed that there is perfect mixing). Find the amount of salt in the tank after t minutes. 3. The rate of growth of an investment is proportional to the amount of the investment at any time t. The initial investment is $1000 and after 10 years the balance is $3320.12. What is the particular solution? 4. The limiting capacity of the habitat of wildlife herd is 750. The growth rate dN/dt of the herd is proportional to the unutilized opportunity for the growth. As describe by differential equation dN/dt = k(750 – N). When t = 0, the population of the herd is 100. After two years the population has growth to 160. Write the population N as a function of t. What is the population of the herd after 4 years? %3D 5. An apple pie with an initial temperature of 170 °C is removed from the oven and left to cool in a room temperature of 20 °C. Given that the temperature of the pie initially decreases at a rate of 3.0 °C/min., how long will it take for the pie to cool to a temperature of 30 °C? 6. A circuit consists of an inductance of 0.05 henry, a resistance of 5 ohms, and a condenser of capacitance 4 x 10-4 farad. If q = i = 0 when t = 0, find q and i in terms of t when (a) there is a constant emf = 110 volts, (b) there is an alternating emf = 200 cos100t.
Transcribed Image Text:1. A tank initially holds 100 gallons of brine solution containing 20 lbs. of salt. At t = 0, fresh water is poured into the tank at the rate of 5 gal/min., while the well- stirred mixture leaves the tank at the same rate. Find the amount of salt in the tank at any time t. 2. A tank 100 gallon capacity is initially full of water. Pure water is allowed to run into the tank at a rate of 1 gallon per minute, and at the same time containing one-fourth pound of salt per gallon flows into the tank also at a rate of 1 gallon per minute. The mixture flows out at a rate of 2 gallons per minute (it is assumed that there is perfect mixing). Find the amount of salt in the tank after t minutes. 3. The rate of growth of an investment is proportional to the amount of the investment at any time t. The initial investment is $1000 and after 10 years the balance is $3320.12. What is the particular solution? 4. The limiting capacity of the habitat of wildlife herd is 750. The growth rate dN/dt of the herd is proportional to the unutilized opportunity for the growth. As describe by differential equation dN/dt = k(750 – N). When t = 0, the population of the herd is 100. After two years the population has growth to 160. Write the population N as a function of t. What is the population of the herd after 4 years? %3D 5. An apple pie with an initial temperature of 170 °C is removed from the oven and left to cool in a room temperature of 20 °C. Given that the temperature of the pie initially decreases at a rate of 3.0 °C/min., how long will it take for the pie to cool to a temperature of 30 °C? 6. A circuit consists of an inductance of 0.05 henry, a resistance of 5 ohms, and a condenser of capacitance 4 x 10-4 farad. If q = i = 0 when t = 0, find q and i in terms of t when (a) there is a constant emf = 110 volts, (b) there is an alternating emf = 200 cos100t.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS