Question

On a hot day, a fan has a mark on the tip of one blade. The equation y = 16cos(x) + 36 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? Round to the nearest centimeter.

Answer 1

Approximately 52 centimeters

Explanation:

To find the height of the mark when it is closest to the table, we need to determine the minimum value of the function y = 16cos(x) + 36. The minimum value of a cosine function occurs when the cosine function is at its maximum value, which is 1.

In this case, the maximum value of cos(x) is 1, so we can rewrite the equation as:

y = 16(1) + 36

y = 16 + 36

y = 52

Therefore, the height of the mark above the table when it is closest to the table is approximately 52 centimeters (rounded to the nearest centimeter).