Access Ramp A wooden access ramp is being built to reach a platform that sits 30 inches above the floor. The ramp drops 2 inches for every 25 -inch run. Write a linear equation that relates the height y of the ramp above the floor to the horizontal distance x from the platform. Find and interpret the x -intercept of the graph of your equation. Design requirements stipulate that the maximum run be 30 feet and that the maximum slope be a drop of 1 inch for each 12 inches of run. Will this ramp meet the requirements? Explain. What slopes could be used to obtain the 30 -inch rise and still meet design requirements?
Access Ramp A wooden access ramp is being built to reach a platform that sits 30 inches above the floor. The ramp drops 2 inches for every 25 -inch run. Write a linear equation that relates the height y of the ramp above the floor to the horizontal distance x from the platform. Find and interpret the x -intercept of the graph of your equation. Design requirements stipulate that the maximum run be 30 feet and that the maximum slope be a drop of 1 inch for each 12 inches of run. Will this ramp meet the requirements? Explain. What slopes could be used to obtain the 30 -inch rise and still meet design requirements?
Access Ramp A wooden access ramp is being built to reach a platform that sits
30
inches above the floor. The ramp drops
2
inches for every
25
-inch run.
Write a linear equation that relates the height y of the ramp above the floor to the horizontal distance
x
from the platform.
Find and interpret the
x
-intercept of the graph of your equation.
Design requirements stipulate that the maximum run be
30
feet and that the maximum slope be a drop of
1
inch for each
12
inches of run. Will this ramp meet the requirements? Explain.
What slopes could be used to obtain the
30
-inch rise and still meet design requirements?
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?
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Linear Equation | Solving Linear Equations | What is Linear Equation in one variable ?; Author: Najam Academy;https://www.youtube.com/watch?v=tHm3X_Ta_iE;License: Standard YouTube License, CC-BY