Question

the blades of a wind turbine are 135 feet long and are attached to the top of a 262 - foot tower. the turbine completes 17 revolutions per minute. suppose the tip of one of the blades starts at its maximum height above the ground. which function represents the height, in feet, of the tip of this blade after t minutes? f(t)=270 cos(17πt)+262 f(t)=135 cos(17πt)+262 f(t)=270 cos(34πt)+262 f(t)=135 cos(34πt)+262

Explanation:

Step1: Determine the amplitude

The length of the blade is 135 feet. The amplitude $A$ of the cosine - function representing the height variation is equal to the length of the blade. So $A = 135$.

Step2: Calculate the angular frequency

The turbine completes 17 revolutions per minute. One revolution is $2\pi$ radians. So the angular frequency $\omega$ (in radians per minute) is $\omega=17\times2\pi = 34\pi$.

Step3: Determine the vertical shift

The top of the tower is at a height of 262 feet. This is the vertical - shift $D$ of the cosine function. The general form of a cosine function for this situation is $y = A\cos(\omega t)+D$.
Since the blade starts at its maximum height, the function is $f(t)=135\cos(34\pi t)+262$.

Answer:

$f(t)=135\cos(34\pi t)+262$ (corresponding to the fourth option)