Rania is riding the ferris wheel. Her vertical height H(t) (in m ) off the ground as a function of time t (in seconds) can be modeled by a sinusoidal expression of the form a*cos(b*t)+d. At t=0, when she starts moving, she is at a height of 10m off the ground, which is as low as she goes. After 20 pi seconds, she reaches her maximum height of 30m. Find H(t). t should be in radians. H(t)=

Initial Height Determination: Rania's lowest height is 10m at t=0, so d=10.Amplitude Calculation: The maximum height is 30m, so the amplitude a is half the difference between max and min height, a=(30-10)/2=10.Period Calculation: Since the ferris wheel takes 20 pi seconds to complete a full cycle, the period T is 20 pi seconds. The value of b is found using b=2*pi/T, so b=2*pi/(20*pi)=1/10.Function Derivation: The function H(t) is H(t)=a*cos(b*t)+d. Substituting the values of a, b, and d, we get H(t)=10*cos((1/10)*t)+10.

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Rania is riding the ferris wheel.
Her vertical height
H(t) (in
m ) off the ground as a function of time
t (in seconds) can be modeled by a sinusoidal expression of the form
a*cos(b*t)+d.
At
t=0, when she starts moving, she is at a height of
10m off the ground, which is as low as she goes. After
20 pi seconds, she reaches her maximum height of
30m.
Find
H(t).

t should be in radians.

H(t)=

Rania is riding the ferris wheel. $\newline$ Her vertical height $H(t)$ (in $\mathrm{m}$ ) off the ground as a function of time $t$ (in seconds) can be modeled by a sinusoidal expression of the form $a \cdot \cos (b \cdot t)+d$ . $\newline$ At $t=0$ , when she starts moving, she is at a height of $10 \mathrm{~m}$ off the ground, which is as low as she goes. After $20 \pi$ seconds, she reaches her maximum height of $30 \mathrm{~m}$ . $\newline$ Find $H(t)$ . $\newline$ $t$ should be in radians. $\newline$ $H(t)=$

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Q. Rania is riding the ferris wheel.

\newline

Her vertical height

H(t)

(in

\mathrm{m}

) off the ground as a function of time

t

(in seconds) can be modeled by a sinusoidal expression of the form

a \cdot \cos (b \cdot t)+d

\newline

t=0

, when she starts moving, she is at a height of

10 \mathrm{~m}

off the ground, which is as low as she goes. After

20 \pi

seconds, she reaches her maximum height of

30 \mathrm{~m}

\newline

Find

H(t)

\newline

t

should be in radians.

\newline

H(t)=

Initial Height Determination: Rania's lowest height is $10\,\text{m}$ at $t=0$ , so $d=10$ .
Amplitude Calculation: The maximum height is $30\,\text{m}$ , so the amplitude $a$ is half the difference between max and min height, $a=(30-10)/2=10$ .
Period Calculation: Since the ferris wheel takes $20 \pi$ seconds to complete a full cycle, the period $T$ is $20 \pi$ seconds. The value of $b$ is found using $b=2\pi/T$ , so $b=2\pi/(20\pi)=1/10$ .
Function Derivation: The function $H(t)$ is $H(t)=a\cdot\cos(b\cdot t)+d$ . Substituting the values of $a$ , $b$ , and $d$ , we get $H(t)=10\cdot\cos((1/10)\cdot t)+10$ .