Question

The flight path of a fighter plane can be modeled with the following equation: h(x) = 30,000 − 5,000 sin x, where h is the height of the jet above the ground, in feet, and x is the horizontal distance of the jet from an arbitrarily chosen point. Which of the following is equal to the maximum height reached by the jet at various times during a flight? A. 25,000 feet B. 30,000 feet C. 35,000 feet D. 40,000 feet

Answer 1

The maximum height reached by the fighter jet is found when the sine function in the equation is at its minimum value. Since the sine function subtracts from 30,000 feet, the maximum height is 35,000 feet when sin x equals -1.

Step-by-step explanation:

The fighter plane's flight path is given by the equation h(x) = 30,000 − 5,000 sin x, where h represents the height of the jet above the ground in feet, and x is the horizontal distance from a chosen point. To find the maximum height the jet reaches at various times during flight, we need to consider the maximum value of the sine function, which is 1. Therefore, the maximum height is obtained when sin x=1:

h(x) = 30,000 − 5,000 × 1 = 25,000 feet.

However, since the sine function subtracts from 30,000 feet, the actual maximum height reached by the jet would be when the sine function is at its minimum, which is −1. So we have:

h(x) = 30,000 − 5,000 (−1) = 30,000 + 5,000 = 35,000 feet.

Thus, the correct answer is C. 35,000 feet.