Concept explainers
Chemical Mixture A tank contains 30 gallons of a solution composed of 80% water and 20% alcohol. A second solution containing half water and half alcohol is added to the tank at the rate of 6 gallons per minute. At the same time, the well-stirred solution is withdrawn at the same rate, as shown in the figure.
(a) Find the amount y (in gallons) of alcohol in the solution as a function of t by solving the differential equation
(b) Find the amount of alcohol in the tank after 10 minutes.
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Chapter 11 Solutions
Calculus: An Applied Approach (Providence College: MTH 109)
- The kinetic energy E of an object varies jointly with the object’s mass m and the square of the object’s velocity v . An object with a mass of 50 kilograms traveling at 16 meters per second has a kinetic energy of 6400 joules. What is the kinetic energy of an object with a mass of 70 kilograms traveling at 20 meters per second?arrow_forwardFind the constant of proportionality. y is directly proportional to x. If x=30, then y=15.arrow_forwardHand write plsarrow_forward
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- INVESTMENT PLAN An investor makes regular deposits totaling D dollars each year into an account that earns interest at the annual rate r compounded continuously. Explain why the account grows at the rate dV/dt=rV+D where V(t) is the value of the account t years after the initial deposit. Solve this differential equation to express V(t) in terms of r and D. Amanda wants to retire in 20 years. To build up a retirement fund, she makes regular annual deposits of $8,000. If the prevailing interest rate stays constant at 4% compounded continuously, how much will she have in her account at the end of the 20-year period? Ray estimates he will need $800,000 to retire. If the prevailing rate of interest is 5% compounded continuously, how large should his regular annual deposits be so that he can retire in 30 years?arrow_forwardSolve the differential equation:arrow_forwardSolve it quickly pleasearrow_forward
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