Find the integral using an appropriate trigonometric substitution.


Mathematics

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Solve the problem.The population of a particular city is increasing at a rate proportional to its size. It follows the function  where k is a constant and t is the time in years. If the current population is 22,000, in how many years is the population expected to be 55,000? Round to the nearest year.

A. 6 yr B. 76 yr C. 11 yr D. 5 yr

Mathematics

Solve the problem. Use ? ? 3.14.The foundation for a cylindrical water tank is a cylinder 21 m in diameter and 3 m high. What volume of concrete is needed to build the foundation? Round your answer to the nearest tenth if necessary.

A. V ? 4154.2 m3 B. V ? 2077.1 m3 C. V ? 395.6 m3 D. V ? 1038.6 m3

Mathematics

Find the absolute value. 

A.  
B. -  
C. 0
D.  

Mathematics

Simplify. Assume that all variables represent positive real numbers.

A. 4a2
B. 4
C. 4a 
D. 256a 

Mathematics