Hi, My name is Alan. Grade: 12 (AP Calculus BC) Who: Student I have 2 questions that are very new to me, they were included on a quiz and the material was never covered. Our teacher never explained the purpose and detailed explanation of how to solve the problem. Could you help? Thanks. Question 1: A ball is falling 30 feet from a light that is 50 feet high. After 1 sec. How fast is the shadow of the ball moving towards the light post. Note that a ball moves according to the formula S=16t^2 Question 2: How many trapezoids must one use in order for the error to be less than 10^-8 if we want to find the area under the curve Y=1/X from 1 to 2. Find the exact area, Graph the function and use the trap rule for the "N" that you found. I would appreciate a succinct explanation with minor work, not something real detailed or something you have to labor over. I just would like to see how to conceptualize the problem by setting it up and the answer I should get. Thank you for your help. Hi Alan, Question 1 In the diagram below L is the light, B is the ball, P is the position of the shadow, s is the height of the ball from the ground ans x is the distance from the base of the light post to the sahdow. By similar triangles 50/x = s/(x-30) or 50x - 1500 = xs x and s are both functions of time, t in seconds, so differentiating with respect to t gives, 50 dx/dt = s dx/dt + x ds/dt Since s = 16 t2, ds/dt = 32 t and thus when t = 1 sec ds/dt = 32 feet, s = 50 - 16 = 34 feet and, using the similar triangles expression x = 1500/16 feet. Substituting into the equations above gives dx/dt = -1500/8 = 187.5 feet/sec. Question 2 The expression for approximating an integral with trapezoids is where and The error E satisfies where for all x between a and b. For problem function f"(x) = 2/x3 a = 1 and b = 2 and hence |f"(x)| is bounded by 2 on [1,2] so you can take K = 2. Let E = 10-8 and solve for n. Make sure that you round up. I hope this helps, Harley Go to Math Central