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1. Find the roots of the polynominal equation: x^3 - 2x^2 + 2x - 15 = 0 2. Solve: sin 2x - sin x = 0 given that 0 </= x < 2pi 3. Show: sin 3x = 3 sin x - 4 sin^3 x [Hint: sin 3x = sin (2x + x)]

1. Use Cramer's rule to solve for x: {3x + 2y = 3 {6z - 2x = -1 {x + 2y + 4z = -2 2. Show: cos^2 x/1 - sin x = 1 + csc x/csc x 3. Solve cos 2x - cos x = 0 given that 0 </= x < 2 pi 4. Write the following as a single logarithm. Simplify: ln (x + y) + 2 ln z - ln (y^2z - x^2z)

1. Use Cramer's Rule to solve for y: {3x + 4y + z = 0 {y - 3z = -3 {x + y + z = 1 2. Solve sin^2 2x = 1 given that 0 degrees </= x < 360 degrees 3. Show: 2 tan x/ tan^2 x + 1 = sin 2x

1. Use Cramer's Rule to solve for y: {3x + 4y + z = 0 {y - 3z = -3 {x + y + z = 1 2. Solve sin^2 2x = 1 given that 0 degrees </= x < 360 degrees 3. Show: 2 tan x/ tan^2 x + 1 = sin 2x

Complete the statements: 1 a. A lone neutron spontaneously decays into a proton plus an _____. b. Alpha and beta rays are made of streams of particles, whereas gamma rays are streams of _____. c. An electrically charged atom is called an _____. d. Different _____ of an element are...

Solve the following equations given that 0 </= x < 2pi 1. 2 cos^2 x + cos x - 1 = 0 2. 1 - sqr. 3 tan 2x = 0 Show: 1 - cos 2x/ sec x sin 2x = sin x

1. Solve sin 2x = cos x given that 0 </= x < 2 pi 2. Show: 1 - 3 cos x - 4 cos ^2 x / sin ^2 x = 1 - 4 cos x / 1 - cos x

9. How does the number of electrons in a normal atom compare with the number of protons in its nucleus? 19. Why is more C-14 found in new bones than in ancient bones of the same mass? 20. Why would the carbon dating method be useless in dating old coins but not old pieces of adobe bricks...

Evaluate: | 2 0 1 | | 3 1 2 | | 1 2 3 |

{2x + y + 2z = 2 {2y + z = 5 {x + 3y = 2

Show: 2 sin^2 x + cos 2 x / csc x = sin x

Show: sec x sec x ____________ - __________ = 2 csc x csc x - cot x csc x + cot x (the sec x's and their denominators are separated)

0 degrees </= x < 360 degrees Solve: 2 cos^2 2x = 3 sin 2x

0 degrees </= x < 360 degrees Solve: 2 cos^2 2x = 3 sin 2x