Answer:
40 feet.
Step-by-step explanation:
The height of the Ferris Wheel is modeled by:
[tex]\displaystyle H(t)=-16\cos\Big(\frac{t}{45}\Big)+24[/tex]
Where H(t) is the height (in feet (assuming)) and t is the time in seconds.
Remember that the value of cosine, regardless of the input, will always be between -1 and 1. That is:
[tex]-1\leq \cos(t)\leq 1[/tex]
So, we can use the two maximums. Testing -1 and 1, we get:
[tex]H(t)=-16(1)+24=8[/tex]
And:
[tex]H(t)=-16(-1)+24=40[/tex]
Therefore, the maximum height of a cabin of the Ferris Wheel will be 40 feet in the air.
Notes:
And the minimum height will be 8 feet.
We are not asked to find t. To do so, however, set H(t) = 40 and find the general solution for t.
