A pendulum is swinging back and forth. After t seconds, the horizontal distance from the bob to the place where it was released is given by H(t)=7-7cos((2pi(t-2))/(20)). How often does the bob cross its midline? Give an exact answer. Every seconds

Crossing Midline: The midline is crossed when H(t) equals 7, which is the average of the maximum and minimum values of H(t).Set Equation: Set H(t) equal to 7 to find when the bob crosses the midline: 7 = 7 - 7cos((2pi(t-2))/20).Simplify Equation: Simplify the equation: 0 = -7cos((2pi(t-2))/20).Isolate Cosine Function: Divide both sides by -7 to isolate the cosine function: 0 = cos((2pi(t-2))/20).Find Zeroes of Cosine: The cosine function equals zero at pi/2 + k*pi, where k is an integer.Solve for t: Solve for t: (pi/2 + k*pi) = (2pi(t-2))/20.Multiply and Solve: Multiply both sides by 20/(2pi) to solve for t: t = 10/pi * (pi/2 + k*pi) + 2.Simplify Equation: Simplify the equation: t = 5 + 20k + 2.Combine Like Terms: Combine like terms: t = 7 + 20k.Period of Cosine Function: The bob crosses the midline every 20 seconds, which is the period of the cosine function.

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A pendulum is swinging back and forth. After
t seconds, the horizontal distance from the bob to the place where it was released is given by

H(t)=7-7cos((2pi(t-2))/(20)).
How often does the bob cross its midline? Give an exact answer.
Every seconds

A pendulum is swinging back and forth. After $t$ seconds, the horizontal distance from the bob to the place where it was released is given by $\newline$ $H(t)=7-7 \cos \left(\frac{2 \pi(t-2)}{20}\right) .$ $\newline$ How often does the bob cross its midline? Give an exact answer. $\newline$ Every $\square$ seconds

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Area of quadrilaterals and triangles: word problems

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Q. A pendulum is swinging back and forth. After

t

seconds, the horizontal distance from the bob to the place where it was released is given by

\newline

H(t)=7-7 \cos \left(\frac{2 \pi(t-2)}{20}\right) .

\newline

How often does the bob cross its midline? Give an exact answer.

\newline

Every

\square

seconds

Crossing Midline: The midline is crossed when $H(t)$ equals $7$ , which is the average of the maximum and minimum values of $H(t)$ .
Set Equation: Set $H(t)$ equal to $7$ to find when the bob crosses the midline: $\newline$ $7 = 7 - 7\cos\left(\frac{2\pi(t-2)}{20}\right)$ .
Simplify Equation: Simplify the equation: $0 = -7\cos\left(\frac{2\pi(t-2)}{20}\right)$ .
Isolate Cosine Function: Divide both sides by $-7$ to isolate the cosine function: $\newline$ $0 = \cos\left(\frac{2\pi(t-2)}{20}\right)$ .
Find Zeroes of Cosine: The cosine function equals zero at $\frac{\pi}{2} + k\pi$ , where $k$ is an integer.
Solve for t: Solve for t: $\newline$ $\left(\frac{\pi}{2} + k\pi\right) = \frac{2\pi(t-2)}{20}$ .
Multiply and Solve: Multiply both sides by $\frac{20}{2\pi}$ to solve for $t$ : $\newline$ $t = \frac{10}{\pi} \cdot \left(\frac{\pi}{2} + k\pi\right) + 2.$
Simplify Equation: Simplify the equation: $t = 5 + 20k + 2$ .
Combine Like Terms: Combine like terms: $t = 7 + 20k$ .
Period of Cosine Function: The bob crosses the midline every $20$ seconds, which is the period of the cosine function.