handwrit/e and show all work and steps

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Be sure to show and explain all work. 10 points each Part 1 - Application The magnitude R (on the Richter scale) of an earthquake of Intensity I is defined as R = log I . =minimum intensity used for comparison. Ms. Cohen felt an earthquake in Los Angeles that had an intensity of (5 x 10 ) (1 ). What was its magnitude, to one decimal place, on the Richter scale? Be sure to show and explain your work. Part 2 - Find the error(s) and solve the problem correctly. Solve. Be sure to show and explain your work. log (x + 3) + log , (x - 3) = 2 Answer: log , (x + 3) + log , (x - 3) = 2 log (x + 3 + x - 3) = 2 log (2x) = 2 4 2= 2X 16 = 2x 8 = x Part 3 - Discussion Question How do we know that e "and In x are inverses of each other?Be sure to show and explain all work. 10 pointseach Part 1 - Application A mass oscillating up and down on the bottom of a spring (assuming perfect elasticity and no friction or air resistance) can be modeled as harmonic motion. If the weight is displaced a maximum of 6 cm, find the modeling equation if it takes 4 seconds to complete one cycle. Be to show, illustrate and explain your work. Part 2 - Find the error(s) and solve the problem correctly. Be sure to explain and show your work. Where did the "wrong answer" come from? Sin 52 Answer: sin 52 = .9866 Part 3 - Discussion Question Name 4 other angles whose cosine is the same as cos %. Explain using mathematical language how you know this is true. (calculations only using a calculator is not considered mathematical language). Is this statement true or false? Explain your answer. Aft angles that have the same cosine will have the same sine