question 5 1 pts the average annual snowfall in a certain region is modeled by the function s(t)=20 +…

question 5 1 pts the average annual snowfall in a certain region is modeled by the function s(t)=20 + 10cos(π/5t), where s represents the annual snowfall, in inches, and t represents the number of years since 1970. what is the maximum annual snowfall, in inches, for this region? o 20 o 10 o 30 o none of these

question 5 1 pts the average annual snowfall in a certain region is modeled by the function s(t)=20 + 10cos(π/5t), where s represents the annual snowfall, in inches, and t represents the number of years since 1970. what is the maximum annual snowfall, in inches, for this region? o 20 o 10 o 30 o none of these

Answer

Answer:

C. 30

Explanation:

Step1: Recall cosine - function range

The range of the cosine function $y = \cos(x)$ is $[- 1,1]$, i.e., $-1\leqslant\cos\left(\frac{\pi}{5}t\right)\leqslant1$.

Step2: Find maximum of $S(t)$

We have $S(t)=20 + 10\cos\left(\frac{\pi}{5}t\right)$. To find the maximum of $S(t)$, we consider the maximum value of $\cos\left(\frac{\pi}{5}t\right)$. When $\cos\left(\frac{\pi}{5}t\right)=1$, we calculate $S(t)$: [ \begin{align*} S(t)&=20+10\times1\ &=20 + 10\ &=30 \end{align*} ] So the maximum annual snow - fall is 30 inches.