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.
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.
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
x and s are both functions of time, t in seconds, so differentiating with respect to t gives,
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.
The expression for approximating an integral with trapezoids is
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,