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Naomi starts the engine on her small private airplane. The engine drives a propeller with a radius of 8 feet and its centerline 13 feet above the ground. At idle, the propeller rotates at a constant speed of approximately 700 revolutions per minute. The height of one propeller tip as a function of time is given by h = 13 + 8 sin(700t), where h is the height in feet and t is the time in minutes. Use degrees to find h when t = 4 minutes.

Respuesta :

Answer:

5.13 feet

Step-by-step explanation:

Engine is driving the propeller with a radius of 8 feet and its centerline 13 feet above the ground.

And the speed is 700 revolutions per minute, the height of one propeller tip as a function of time is given by:

[tex]h=13+8 \sin(700t)[/tex]

We have been asked to find the value of height, 'h', when t=4 minutes.

Plugging the value of time, 't', in the equation, we already know that we need to use degrees (not radians) we get:

[tex]h=13+8 \sin (700 \times 4)[/tex]

[tex]h=13+8 \sin (2800)[/tex]

[tex]h=13+8 \times (-0.984)[/tex]

[tex]h=13+(-7.872)[/tex]

[tex]h=13-7.872[/tex]

[tex]h=5.128\approx 5.13[/tex]

So the height of one propeller tip at t=4 minutes is 5.13 feet.

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