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Use partial decomposition to integrate.
(2x^2-x-20)/(x^2+x-6 )
(sint)(4cos^2t-1)/(cost)(1+2cos^2t+cos^4t)
(x+pi )/(x^2-3pix+2pi^2)
What does the final row of the augmented matrix in echelon form (the above description) tell you about the solution to the system of 5 linear equations?
Find number of ways using permutation
Evaluate the area of the rectangle - Write a polynomial that represents the area.
Let E be an open and convex subset of R^n and let f in C^1(E). Show that f satisfies the Lipschitz condition on E if and only if its derivative Df is bounded on E, that is, there exists a constant M => 0 such that the norm of
A company is constructing an open-top, square-based, rectangular metal tank that will have a volume of 66 ft^3. What dimensions yield the minimum surface area? Round to the nearest tenth, if necessary.
Suppose K is a conjugacy class of S_n (the symmetric group), with K consisting of even permutations. Suppose that x in K. Show that K splits into two conjugacy classes
We may think that this is similar to a Fresnel Integral (sin(x^2)). In that case, we would set z=e^(iz)^2, and then integrate over the special contour with regions I: 0 to R, II:
Suppose a machine has three independent components with Exp(.1) lifetimes. Compute the expected lifetime of the machine if it needs all three components to function properly
Solve the following system of equations using the Substitution method: Solve the following system of equations using the elimination method:
The following pairs of functions, graph each one together in Desmos, show on your graph and find the area between them bounded by the given values of x.
A recent study reported that college students study for an average of four hours per day. You believe this figure is too large & you decide to conduct your own test. Find the p value & explain its meaning.
Find all values of: tan^(-1) * (1 + i). The format for the final answer should be similar to this one:
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