HELLO. I NEED HELP ASAP WITH THIS QUESTIONS. NEED AN EXCELLENT EXPERT ON CALCULUS FOR THIS. STEP BY STEP EXPLANATION FOR EACH QUESTION SEPARATE

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The difference in length of a spring on a pogo stick from its non-compressed length when a teenager is jumping on it after 9 seconds can be described by the function f(0)= nine-+5. PartA: Determine all values where the pogo stick's spring will be equal to its noncompressed length. (5 points) Part B: lithe angle was doubled, that is 6 became 26, what are the solutions in the interval [0, 211)? How do these compare to the original function? (5 points) Part C: A toddler is jumping on another pogo stick whose length of their spring can be represented by the function g(0) =100829+ J5 At what times are the springs from the original pogo stick and the toddler's pogo stick lengths equal? (5 points) Students were asked to prove the identity (sec x)(csc x) = cot x + tan x. Two students' work is given. Student A Student B Step 1: 1 1 Step 1: sec xcscx = COS X sin x = cot x + tan x cos x sinx sin x COS X Step 2: 1 = cotx + tan x Step 2: secxcscx = cos * x sin x cos x sin x cos xsin x cosxsinx Step 3: cos x + sin2 x = cot x + tan x Step 3: sec xcscx = cos x + sin2 x cos x sin x cos x sin x Step 4: cos x sin x = cotx + tanx Step 4: sec xcsc x = 1 cos x sin x cos x sin x cos x sin x Step 5: cosx sinx = cotx + tan x Step 5: sec xcscx = (- sin x COS X cos x )( sinx ) Step 6: cot x + tan x = cot x + tan x Step 6: sec x csc x = sec x CSC X Part A: Did either student verify the identity properly? Explain why or why not. (10 points) Part B: Name two identities that were used in Student A's verification and the steps they appear in. (5 pointsA curve, described by x2 + y:2 + 12y = 0, has a pointAat (6, -6) on the curve. Part A: What are the polar coordinates of A? Give an exact answer. Part B: What is the polar form of the equation? What type of polar curve is this? Part C: What is the directed distance when 3 = 2\"? Give an exact answer. A polar curve is represented by the equation r1 = 3 + 3sin 6. Part A: What type of limacon is this curve? Justify your answer using the constants in the equation. Part B: Is the curve symmetrical to the polar axis or the line a = g? Justify your answer algebraically. Part C: What are the two main differences between the graphs of r1 = 3 + 35in 9 and r2 = 8 + 3005 6? Points z, and z2 are shown on the graph. Timaginary Axis 21 N Real axis, -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 Z2 Part A: Identify the points in standard form and find the distance between them. Part B: Give the complex conjugate of z2 and explain how to find it geometrically. Part C: Find Z2 - 21 geometrically and explain your steps.A baseball is hit, following a path represented by x = 140f and y = 3.1 + 40t 161' 2 for 0 5 ts 3. Part A: Find the ordered pairs, (x, y}, when t = 0.2, 1.2, and 2.4. Part B: The fence, which is 10 feet tall, lies 320 feet away from home plate. Does the baseball travel over the fence? Justify your answer mathematically. Part C: Write a rectangular equation to represent the plane curve