My question 7. You are given a ferris wheel rotating at two revolutions per minute and the hub has a center. Oh, and the diameter is 16 meters, so the radius is 8 meters. A person's view is at the precision such that SP is X and the angle is Theta. Using the cosine rule, it can be shown that X squared is equal to 12 + 8-1 2a cosine Theta. Now, let's examine this triangle. By applying the sine rule, we have X squared equals a squared plus X squared minus 2 times X times a times cosine Theta. However, this formula seems to have a negative sign error, so we need to rectify it in order to obtain the required result. Moving on, we can evaluate DX DT as 64 sine Theta over X. To do this, we differentiate the expressions we obtained earlier and square them. Consequently, we have 2X DX DT equals -128 sine Theta times d Theta/dt. Rearranging the expressions, we achieve the required result. Next, we move on to Part C. We have to find d Theta/dt, which represents the rate of change of the angle. By observing the rotation, we are given that the change in angle is two revolutions per minute. Since one revolution is equal to 2 pi, this implies that d Theta/dt is 4 pi. Finally, we need to find the rate at which SP is changing. We can obtain this by calculating DX DT. Using the expressions we derived from Part B and the information from Part C (d Theta/dt = 4 pi), we substitute these values and evaluate. Furthermore, in the given question, it is stated that SP is 8 meters above point P. By substituting the value of Theta into the expressions, we obtain X when X equals 28 meters, which...
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