For Exercises 29-48, use a variation model to solve for the unknown value. The amount of simple interest owed on a loan varies jointly as the amount of principal borrowed and the amount of time the money is borrowed. If $4000 in principal results in $480 in interest in 2 yr, determine how much interest will be owed on $6000 in 4 yr.
For Exercises 29-48, use a variation model to solve for the unknown value. The amount of simple interest owed on a loan varies jointly as the amount of principal borrowed and the amount of time the money is borrowed. If $4000 in principal results in $480 in interest in 2 yr, determine how much interest will be owed on $6000 in 4 yr.
Solution Summary: The author calculates the interest owed on 6000, if it varies jointly as the principal borrowed and the amount of time the money is invested.
For Exercises 29-48, use a variation model to solve for the unknown value.
The amount of simple interest owed on a loan varies jointly as the amount of principal borrowed and the amount of time the money is borrowed. If
$4000
in principal results in
$480
in interest in 2 yr, determine how much interest will be owed on
$6000
in 4 yr.
2. Consider the following:
Prove that x, x2, and 1/x are the solutions to the homogeneous equation
corresponding to x³y"" + x²y" + 2xy' + 2y = 2x4.
b. use variation of parameters to find a particular solution and complete the general
solution to the differential equation. I am interested in process. You may use a
computer for integration, finding determinants and doing Kramer's.
3. A spring is stretched 6 in. by a mass that weighs 8 lb. The mass is attached to a dashpot
mechanism that has a damping constant of 0.25 lb-sec./ft. and is acted on by an external
force of 4 cos 2t lb.
a. Set-up the differential equation and initial value problem for the system.
b. Write the function in phase-amplitude form.
C.
Determine the transient solution to the system. Show your work.
d. Determine the steady state of this system. Show your work.
e.
Is the system underdamped, overdamped or critically damped? Explain what this
means for the system.
4. Suppose that you have a circuit with a resistance of 20, inductance of 14 H and a
capacitance of 11 F. An EMF with equation of E(t) = 6 cos 4t supplies a continuous charge
60
to the circuit. Suppose that the q(0)= 8 V and the q'(0)=7. Use this information to answer the
following questions
a. Find the function that models the charge of this circuit.
b. Is the circuit underdamped, overdamped or critically damped?
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