BRIEF ANSWERS FOR TEST 1

1. T or F?
   1. F. Since 2^(1/12) is less than 3^(1/19), tripling is better.
   2. F. If a = 2 and b = c = 4, then the left side equals 2 while the right side equals 1/2.
   3. F. log_2(1/2) = -1, which is less than zero.
   4. F. The statement is nonsense. You can't divide a law by another law.
   5. F. If x = 0, then the left side equals 0 while the right side equals 1.
2. e is the limit of (1 + (1/n))^n as n goes to +infinity.
3. 1. log_3(11) is approximately 2.183
   2. cot(11*Pi/6) = - square_root(3)
4. Must find h if .4 = 2^(-10000/h). Answer: h = -10000/lg(.4) = approximately 7565 years.
5. 1. x = 4/7.
   2. x = 5. (Note: x = 0 is an apparent solution, but it does not satisfy the original equation.)
6. Amplitude = 2, Period = 3*Pi, Phase Shift = 3*Pi/8.
7. • Draw a nice picture.
   • Distance 1 = 1464 m. (Use Law of Sines.)
   • Distance 2 = 1793 m. (Use Law of Sines.)
   • Distance traveled = 536 m. (Use Law of Cosines.)
8. 1. tan(15 degrees) = 2 - square_root(3)
   2. cos(105 degrees) = (square_root(2) - square_root(6))/4.