I will medal and fan
I need help with part 2
Xavier is riding on a Ferris wheel at the local fair. His height can be modeled by the equation H(t) = 20cosine of the quantity 1 over 15 times t + 30, where H represents the height of the person above the ground in feet at t seconds.
Part 1: How far above the ground is Xavier before the ride begins?
Part 2: How long does the Ferris wheel take to make one complete revolution?
Part 3: Assuming Xavier begins the ride at the top, how far from the ground is the edge of the Ferris wheel, when Xavier's height above the ground reaches a minimum?

- anonymous

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- anonymous

@jim_thompson5910 ?

- jim_thompson5910

So the H(t) function is this
\[\Large H(t) = 20\cos\left(\frac{1}{15}t+30\right)\]
right?

- anonymous

Yea solved it and got 50. Is that correct?

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## More answers

- jim_thompson5910

so the +30 is definitely inside the parenthesis and not outside?

- anonymous

\[H(t)=20 \cos \left( \frac{ π }{ 15 }t \right)+30\] that's the equation

- jim_thompson5910

oh ok

- jim_thompson5910

So yes, plugging in t = 0 gives 50 as the output

- jim_thompson5910

at t = 0 seconds, he is at a height of 50 ft

- anonymous

Okay, what exactly do I do for the second part? That part confuses me

- jim_thompson5910

The part in red represents the coefficient for the t variable
\[\Large H(t)=20 \cos \left( {\color{red}{\frac{ π }{ 15 }}}t \right)+30\]
this is the value of B. To find the period you would use the formula
T = 2pi/B

- anonymous

So it would be \[\frac{ 2π }{ \left( \frac{ π }{ 15 } \right) }\]

- jim_thompson5910

yes, simplify that fraction

- anonymous

We can take out the pi's right? so we would now have \[\frac{ 2 }{ 15 }\]

- jim_thompson5910

\[\large \frac{ 2π }{ \left( \frac{ π }{ 15 } \right) } = \frac{2\pi}{1} \times \frac{15}{\pi} = ???\]

- anonymous

Ohh \[\frac{ 30π }{ 1π }\] ?

- jim_thompson5910

and the pi's will cancel

- jim_thompson5910

so T = 30 is the period
t is in seconds, which means the period is 30 seconds
that means the ferris wheel completes a cycle every 30 seconds

- anonymous

Okay thank you :) I'll try and see if I can get part three on my own and if not I'll let you know :)

- jim_thompson5910

alright

- anonymous

Okay I'm confused as to what the question is asking exactly

- jim_thompson5910

|dw:1433458814224:dw|

- jim_thompson5910

"Part 3: Assuming Xavier begins the ride at the top, how far from the ground is the edge of the Ferris wheel, when Xavier's height above the ground reaches a minimum?"
at time t = 0, he starts at this point here
|dw:1433458873515:dw|

- jim_thompson5910

how long does it take to go around the full circle?

- anonymous

30 seconds

- jim_thompson5910

so how long does it take to go from the very top, to the very bottom?

- anonymous

15 seconds

- jim_thompson5910

plug in t = 15 and tell me what you get

- anonymous

I get a decimal when I plug it into my calculator
92.83185307

- jim_thompson5910

make sure you are in radian mode

- anonymous

\[H(15)=20\left( \frac{ π }{ 15 }15 \right)+30\] \[\frac{ π }{ 15 }\times \frac{ 15 }{ 1 }=\frac{ 15 }{ 15 }=1\] \[20\left( 1 \right)+30=50\] correct?

- anonymous

Wait

- anonymous

\[H(15)=20\left( \frac{ π }{ 15 }15 \right)+30 \] \[\frac{ π }{ 15 }\times \frac{ 15 }{ 1 }=\frac{ 15π }{ 15 }=1π?\]

- jim_thompson5910

so you'll have 20*cos(pi) + 30 = ???

- anonymous

I get 49.9?

- jim_thompson5910

you should find cos(pi) = -1
try again

- anonymous

10?

- jim_thompson5910

yep 10

- anonymous

Okay so the edge of the Farris wheel is 10ft from the ground when Xavier's height above the ground reaches a minimum

- jim_thompson5910

yep the lowest it goes is 10 ft off the ground
|dw:1433460789409:dw|

- anonymous

Thank you :)

- jim_thompson5910

you're welcome

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