21 mark for review a pendulum swings back and forth, toward and away from a point on a wall. the motion of…

21 mark for review a pendulum swings back and forth, toward and away from a point on a wall. the motion of the pendulum is periodic. the distance, in inches, from the point on the wall at time t seconds is modeled by (f(t)=15sin(pi t)+18). what is the least interval of time between the moments when the pendulum is farthest from the point on the wall? a the least interval of time is the period of the function, which is 1 second, because the coefficient of t is (pi) and the period is (pi) divided by this coefficient. b the least interval of time is the period of the function, which is 2 seconds, because the coefficient of t is (pi) and the period is (2pi) divided by this coefficient. c the least interval of time is the period of the function, which is (pi) seconds, because the coefficient of t is (pi) and the period is that coefficient. d the least interval of time is the period of the function, which is (2pi) seconds, because the coefficient of t is (pi) and the period is 2 times that coefficient.

21 mark for review a pendulum swings back and forth, toward and away from a point on a wall. the motion of the pendulum is periodic. the distance, in inches, from the point on the wall at time t seconds is modeled by (f(t)=15sin(pi t)+18). what is the least interval of time between the moments when the pendulum is farthest from the point on the wall? a the least interval of time is the period of the function, which is 1 second, because the coefficient of t is (pi) and the period is (pi) divided by this coefficient. b the least interval of time is the period of the function, which is 2 seconds, because the coefficient of t is (pi) and the period is (2pi) divided by this coefficient. c the least interval of time is the period of the function, which is (pi) seconds, because the coefficient of t is (pi) and the period is that coefficient. d the least interval of time is the period of the function, which is (2pi) seconds, because the coefficient of t is (pi) and the period is 2 times that coefficient.

Answer

Explanation:

Step1: Recall period formula

The general form of a sine - function is $y = A\sin(Bt - C)+D$, and its period $T$ is given by the formula $T=\frac{2\pi}{B}$.

Step2: Identify the value of B

In the function $f(t)=15\sin(\pi t)+18$, the coefficient of $t$ is $B = \pi$.

Step3: Calculate the period

Substitute $B=\pi$ into the period formula $T=\frac{2\pi}{B}$. We get $T=\frac{2\pi}{\pi}=2$. The least interval of time between the moments when the pendulum is farthest from the point on the wall is equal to the period of the function.

Answer:

B. The least interval of time is the period of the function, which is 2 seconds, because the coefficient of $t$ is $\pi$ and the period is $2\pi$ divided by this coefficient.