Question

Just need some quick help in algebra 2 please walk me through all the steps

Answer 1

ANSWER:

30

STEP-BY-STEP EXPLANATION:

We have the following expression:

$H\mleft(t\mright)=-12\: cos\mleft(\frac{\pi t}{45}\mright)+18$

To find the maximum height, we must first calculate the time when that height is the maximum.

To calculate this, we must calculate the derivative of the function, set it equal to 0 and then solve for t, just like this:

$\begin{gathered} H^{\prime}(t)=\frac{d}{dx}\mleft(-12\cos \mleft(\frac{\pi t}{45}\mright)+18\mright) \\ H^{\prime}(t)=\frac{4\pi}{15}\sin \mleft(\frac{\pi t}{45}\mright) \\ \text{ now, we equal zero:} \\ \frac{4\pi}{15}\sin \mleft(\frac{\pi t}{45}\mright)=0 \\ \text{ We solve for t:} \\ \sin \mleft(\frac{\pi t}{45}\mright)=0 \\ t=45,90 \end{gathered}$

Now, we replace and calculate the maximum height:

$\begin{gathered} H(45)=-12\: cos\mleft(\frac{\pi\cdot45}{45}\mright)+18 \\ H(45)=-12\: cos(\pi)+18 \\ H(45)=-12\cdot-1+18=12+18 \\ H(45)=30 \end{gathered}$

The value of the maximum height of the cabin is 30