Answered

Select the correct answer.

Two friends are sitting on a seesaw at the park. The height, [tex]$h(t)$[/tex], of the left seat, in inches above the ground, is modeled by a sine function. Let [tex]$t$[/tex] represent the time, in seconds, since the friends started seesawing.

[tex]\[
\begin{array}{|c|c|c|c|c|c|c|c|}
\hline
t & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
h(t) & 24 & 48 & 24 & 0 & 24 & 48 & 24 \\
\hline
\end{array}
\][/tex]

If the friends start seesawing with the plank in a level position, how long does it take for the friend in the left seat to move upward, downward, and then back to the initial position?

A. 3 seconds
B. 2 seconds
C. 6 seconds
D. 4 seconds



Answer :

GinnyAnswer
To determine how long it takes for the friend in the left seat to move upward, downward, and then back to the initial position, we need to look at the height function [tex]$h(t)$[/tex] values provided in the table over time.

[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|} \hline t & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline h(t) & 24 & 48 & 24 & 0 & 24 & 48 & 24 \\ \hline \end{array} \][/tex]

1. At [tex]\(t = 0\)[/tex], the height [tex]\(h(t)\)[/tex] is 24 inches.
2. At [tex]\(t = 1\)[/tex], the height [tex]\(h(t)\)[/tex] is 48 inches, indicating that the left seat has moved upward.
3. At [tex]\(t = 2\)[/tex], the height [tex]\(h(t)\)[/tex] is 24 inches again, indicating the left seat has moved back to the initial position (24 inches).
4. At [tex]\(t = 3\)[/tex], the height [tex]\(h(t)\)[/tex] is 0 inches, indicating the left seat is now at the lowest position (downward).
5. At [tex]\(t = 4\)[/tex], the height [tex]\(h(t)\)[/tex] is back to 24 inches, showing the left seat has returned back to the initial position.

Examining these values, we see that from [tex]\(t = 0\)[/tex] to [tex]\(t = 3\)[/tex], the function rises, returns, and falls to a new position, taking a total of 3 seconds.

Thus, it takes 3 seconds for the left seat to move upward, downward, and then back to the initial position.

The correct answer is:

A. 3 seconds