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An elastic bar has a static displacement due to an applied axial load F. The force is suddenly removed, resulting in free oscillations of the bar. Derive the expression governing the displacement u(x, t) of a particle along the axis of the bar.
a. Specify the governing differential equation as well as all boundary and initial conditions necessary to solve for u(x, t).
b. Nondimensionalize the problem by introducing x* = x/L t* = t/T , where T is to be chosen for convenience.
Explain the five-steps for solving rational equations. Can any of these steps be eliminated? Can the order of these steps be changed? Would you add any steps to make it easier, or to make it easier to understand?
Select the approximate values of x that are solutions to f(x) = 0, wheref(x) = -8x2 + 6x + 5. A. {-1.60, 1.20}B. {-8, 6}
A rectangular box is to have a square base and a volume of 40 ft3. If the material for the base costs $0.30 per square foot, the material for the sides costs $0.05 per square foot
Find a 98% confidence interval for the parameter of interest. Assume the populations to be approximately normally distributed with equal variance.
Which variable in the simple interest equation I = prt represents the original amount of money borrowed or invested?
What are the four steps for solving an equation? Should any other factors be accounted for when solving an equation? Should any factors be accounted for when explaining how to solve an equation? Explain your answer.
Reduce the equation to one of the standard forms, classify the surface, and sketch it.
A is the amount of material remaining from an initial amount I at a given time t and k is negative constant determined by the nature of the material.
The metal used to make the top and bottom of a cylindrical can costs 4 cents/in^2, while the metal used for the sides costs 2 cents/in^2. The volume of the can is to be exactly 100 in^3. What should the dimensions of the can be to minimize the cos..
A sample of 13 brands of caffeinated coffee had a mean caffeine level of 119.6 mg and a standard deviation of 52.5. The population is normally distributed. Compute a 90% interval for the mean caffeine level.
Consider a rectangular box of volume 100 cubic centimters. Suppose that the base is a rectangle with sides x centimeters and 2x centimeters. Let hx give the height of the box in centimeters and let Ax be the total area of the six sides of the box.
What is the probability that fewer than 5 minutes will elapse between successive complaints?
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