graph the function y = - cos(x) + 7. how many times does the gum return to the wall as it travels a distance…

Explanation:

Step1: Recall the period of cosine function

The general form of a cosine function is $y = A\cos(Bx - C)+D$. For the function $y =-\cos(x)+7$, the period of the cosine - related part is $T = 2\pi$ since for $y=\cos(x)$, the coefficient of $x$ is $B = 1$ and the period formula is $T=\frac{2\pi}{B}$. In the context of the problem, we assume that one full - cycle of the cosine function represents the gum returning to the same position relative to the wall.

Step2: Calculate the number of full - cycles in 60 feet

We need to find out how many full periods of the function $y =-\cos(x)+7$ occur in a distance of 60 feet. We assume that the $x$ - axis represents the distance traveled. The number of full periods $n$ is given by $n=\frac{60}{2\pi}$. [n=\frac{60}{2\pi}=\frac{30}{\pi}\approx\frac{30}{3.14}\approx9.55] Since we are interested in the number of times the gum returns to the wall (i.e., the number of full - cycles), we take the integer part of the result.

Answer:

9