Hi,
My name is Alan. 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:
Question 2: 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
or
x and s are both functions of time, t in seconds, so differentiating with respect to t gives,
Since s = 16 t^{2}, 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/x^{3} 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,
