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let h(x) = sin(ax). let H^(n)x denote the n:th derivative, ie. ex. n=2 means the second derivative. Show that the equation h^(n)x = h^(n+2)x has two distinct general solutions depending on whether n is odd or even and solve the equation in each cases.
If Tom Bombadil's house is 30 miles east of Hobbiton and 16 miles south, what is the straight line distance (omit units)?
In triangle ABC, a = 8, b = 9, and m<C = 135 degree. What is the area of triangle ABC?
Show that if sum a_n converges absolutely then sum a^2_n also converges absolutely Does this proposition hold without absolute converge
A square garden plot measures 125 square feet. a second square garden plot measures 405 square feet. how many more feet of fence will the second garden plot require over that required for the first garden plot.
Tom and Jim decided to play the following game for points. A single die is rolled. If it shows a non-prime number, Tom receives points equal to two times the number of dots showing
at the instant when the water is 5 m deep find the rate at which the water is leaking out if the water level is falling at the rate of 0.1 m/hr.
Refer to wage data, which reports information on annual wages for a sample of 100 workers. Also included are variables relating to industry, years of experience, and gender for each worker.
an aircraft flew four hours with the wind. the return trip took 5 hours with the wind. if the speed of the plane in still air is 144 miles per hour more than the speed of the wind find the wind speed and the speed of the plane in still air.
Determine the area of the region totally enclosed by the lines y = 3x, x = 3y, and 3x + y = 30. Your problem solution submission must include, on graph paper, the graphs of each of the lines with the (x, y) coordinates
The componets of v=180i+450j represent the respective number of one-day and three day videos rented from a video store. the componets of w=3i+2j represent the prices to rent the one day and three day videos,respectively
Suppose that N and M are two normal subgroups of G and that N intersection M = (e). Show that for any n belongs to N, m belongs to M, nm = mn.
A rancher needs to enclose two adjacent rectangular corrals, one for cattle and one for sheep. If the river forms one side of the corrals and 420 yd of fencing is available, find the largest total area that can be enclosed.
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