Evaluate the integral using integration by parts.

A. 15 sin x - x cos x + C
B. 15 sin x - 15 cos x + C
C. 15 sin x - 15x cos x + C
D. 15 sin x + 15x cos x + C


Answer: C

Mathematics

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Solve the formula for the specified variable.P = 2L + 2W for W

A. W = 
B. W = 
C. W = P - L
D. W = P - 2L

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Find the required ratio.The atomic mass of an atom of carbon is defined to be 12 u. The ratio of the atomic mass of an atom of bromine to that of an atom of carbon is . What is the atomic mass of an atom of oxygen? (The symbol u represents the unified atomic mass unit, where 1 u = 1.66 × 10-27 kg.)

A. 40 u B. 80 u C. 160 u D. 82 u

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Find the average value of the function f over the region R.f(x, y) = 4x + 10yR is the region bounded by the coordinate axes and the lines  and .

A. 13
B.
C. 26
D.

Mathematics

The function f is one-to-one. Find its inverse.f(x) = 5x - 7

A. f-1(x) = 
B. f-1(x) = 
C. f-1(x) =  + 7
D. f-1(x) =  - 7

Mathematics