Question

On a hot day, a fan has a mark on the tip of one blade. The equation y

=20cos(x) + 25 represents the height of the mark, y centimeters, above the
table x seconds after the fan is turned on. What is the height of the mark
above the table when it is closest to the table?

Answer 1

Answer: 5 cm

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Step-by-step explanation:

Recall that the range for cosine is from -1 to 1, including both endpoints. The smallest cosine value is what we're after, since we want the height to be as small as possible (to allow the blade be closest to the table).

Effectively, this means we replace the cos(x) with -1 so that it's as small as possible. Then we compute to get:

20*cos(x)+25

20*(-1) + 25

-20 + 25

5

The height of the fan tip is 5 cm when it is the closest to the table.

Side note: On the flip side, the furthest away the fan tip can get is 20*(1) + 25 = 45 cm. Therefore, the range of y values is
`5 \le y \le 45`