Answer:
531.5 feet
Step-by-step explanation:
You have the equation H(t) = 70 * sin(2pi / 7) * (t - 1.75) + 80
H(t) is similar to f(x) but with different letters.
It is defined that t is the time in minutes. And H (the output) is the height in feet.
The question is asking you how far off the ground you will be when t = 10. It is asking you what is the result of H(10).
To do this, we will replace t with 10.
H(t) = 70 * sin(2pi / 7) * (t - 1.75) + 80 becomes
H(10) = 70 * sin(2pi / 7) * (10 - 1.75) + 80
Put 70 * sin(2pi / 7) * (10 - 1.75) + 80 into a calculator, you will get: 531.50768112.
So, H(10) = 531.50768112
Since the question tells you to round to the nearest tenth of a foot, our final answer is 531.5 feet.
Where did I get t = 10 from?
"If you are loaded onto the gondola at 11 AM, how far off the ground will you be at 11:10?" The difference between 11 AM and 11:10 AM is 10 minutes. Since it's defined that t is in minutes, we simply plug in t with 10.
If, for example, it was defined that t is in seconds, we would have to multiply 10 by 60. But since it didn't ,we just plug it in.
