Express the statement as an equation involving the indicated variables.The surface area S of a sphere is 4 times ? times the square of the radius r.

A. S = 4?r
B. S = ?r2
C. S = 4? 
D. S = 4?r2

Answer: D

Mathematics

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Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C.F = ln (x2 + y2)i + tan-1 j; C is the region defined by the polar coordinate inequalities 4 ? r ? 8 and 

A. 80 B. -8 C. 96 D. 0

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Mathematics

Express the integrand as a sum of partial fractions and evaluate the integral. 

A. 27ln 4 - 9ln 3 + 
B. 27ln  - 
C. 36ln  - 
D. 9ln 4 - 

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Mathematics

Solve the problem.Boyle's law states that if the temperature of a gas remains constant, then PV = c, where P is the pressure, V is the volume, and c is a constant. Given a quantity of gas at constant temperature, if V is decreasing at a rate of 12 in.3/s, at what rate is P increasing when P = 50 lb/in.2 and V = 80 in.3?

A.  lb/in.2-s
B.  lb/in.2-s
C.  lb/in.2-s
D.  lb/in.2-s

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Mathematics

Add.-9.1 + 5.6

A. 14.7 B. 3.5 C. -14.7 D. -3.5

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Mathematics