MHB Solving Minute Hand Distance from Ground Graph Problem

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To solve the minute hand distance from the ground problem, first determine the initial height of the minute hand tip at 10 a.m., which is 66 inches plus the 6-inch length of the minute hand, totaling 72 inches. The graph representing this motion will be periodic, reflecting the circular movement of the minute hand. Options (A) and (C) are ruled out because (A) does not account for the return to the original height, and (C) incorrectly represents the motion with straight lines. This leaves options (B) and (D), with (B) being the correct choice due to its smooth curve, while (D) suggests an unrealistic sudden change in direction. Understanding the cosine function and its graph is crucial for visualizing this periodic motion.
jshayhsei
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I'd like to know how to solve this. I'm pretty lost as to how to solve this. I want to say that the graph would look periodic because of the graph of the time would go down and then go back up again, but I really don't have anything concrete.

The question states:

The circular clock has a diameter of 14 inches and its minute had has length 6 inches. It is placed on the wall so that the center of the clock is 66 inches above the ground. Which of the following graphs could represent the distance from the tip of the arrow of the minute hand to the ground with respect to time from 10 a.m. to 11 a.m.?

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Hi, and welcome to the forum.

Can you figure out the initial position (height above the ground) of the minute hand tip at 10 a.m.? Also, do you know what cosine is and what its graph looks like?
 
(A) isn't possible because the minute had will have returned to its original height after 60 minutes.
(C) isn't possible because it has straight lines while the minute hand in moving in a circle.
That leaves (B) and (D) and the most obvious difference between the is that (B) is "smooth" while (D) has a cusp at the bottom. (D) implies a sudden change in direction which cannot be the case in circular motion.
 
Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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