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8. Evaluat 3 tan x - 2cos x dx. COS X A. 3 sec x + 2 sin x + C B. 3 sec x - 2 sin x + C C. -3 secx + C D. 2 sinx + C 9. Evaluate (cot2x + 2 tan? x - 5) dx. A. cot x - 2 tan x + 4x + C C. - cot x + 2 tan x + 4x + C B. cot x + 2 tan x + 4x + C D. - cot x - 2 tan x - 4x + CFor number 10-12 What is the particular solution of the differential equation determined by the given initial condition ? 10. ly = x2- 2x - 4; y = - 6 when x = 3 dx A. y = x3 - x2 - 4x + 6 C. 1 3 3X-x-4x+6 B. V= - 2 3+x+4x+6 D. )= 3 x+x+4x+6 11. dy cos 3x =-x when x=-* dx sin 2y 2 A. 4 sin 3x - 6 cos 3y + 7 =0 C. 4 sin 2x + 6 cos 3y + 7 = 0 C. 4 sin 3x - 6 cos 27 -7 =0 D. 4 sin 3x + 6 cos 2y + 7 = 0For question # 13 & 14 If there are 200 bacteria after 2 hours and 800 bacteria after 5 hours, 13. How many bacteria were present initially? A. $70.37 bacteria B. ~89.37 bacteria C. ~79.37 bacteria D. 80.73 bacteria 14. After how many hours will the bacteria be 50,000? A.~13.95 hours B. $12.59 hours C.~11.90 hours D. 10.95 hours 15. The rate of decay of a certain substance is directly proportional to the amount remaining. The half-life of this substance is 150 days. After how many days will the sample have disintegrated 90%? If the sample initially weighs 30 grams. What is the decay rate of change of this new sample on its 100" day? A. ~ 401 days and decay rate of change ~ -.09532 B. ~ 468 days and decay rate of change ~ -.05642 C. ~498 days and decay rate of change ~ -.08732 D. ~448 day's and decay rate of change ~ -. 09237