5 the flight path of a drone can be modeled with the following equation: h(x)=50 - 47 cos x, where h is the…

5 the flight path of a drone can be modeled with the following equation: h(x)=50 - 47 cos x, where h is the height of the drone above the ground, in feet, and x is the horizontal distance of the drone from an arbitrarily chosen point. which of the following is equal to the maximum height reached by the drone at various times during a flight? a. 3 feet b. 47 feet c. 50 feet d. 97 feet
Answer
Explanation:
Step1: Recall cosine - value range
The range of the cosine function is $- 1\leqslant\cos x\leqslant1$.
Step2: Analyze the height - function for maximum
We have the height function $h(x)=50 - 47\cos x$. To find the maximum of $h(x)$, we want to minimize the value of $-47\cos x$. Since the minimum value of $\cos x$ is $-1$, when $\cos x=-1$, we substitute it into the function.
Step3: Calculate the maximum height
Substitute $\cos x = - 1$ into $h(x)$: [ \begin{align*} h(x)&=50-47\times(-1)\ &=50 + 47\ &=97 \end{align*} ]
Answer:
D. 97 feet