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anonymous
 one year ago
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
 one year ago
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?

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jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1So the H(t) function is this \[\Large H(t) = 20\cos\left(\frac{1}{15}t+30\right)\] right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yea solved it and got 50. Is that correct?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so the +30 is definitely inside the parenthesis and not outside?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[H(t)=20 \cos \left( \frac{ π }{ 15 }t \right)+30\] that's the equation

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1So yes, plugging in t = 0 gives 50 as the output

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1at t = 0 seconds, he is at a height of 50 ft

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, what exactly do I do for the second part? That part confuses me

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1The 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
 one year ago
Best ResponseYou've already chosen the best response.0So it would be \[\frac{ 2π }{ \left( \frac{ π }{ 15 } \right) }\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yes, simplify that fraction

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0We can take out the pi's right? so we would now have \[\frac{ 2 }{ 15 }\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1\[\large \frac{ 2π }{ \left( \frac{ π }{ 15 } \right) } = \frac{2\pi}{1} \times \frac{15}{\pi} = ???\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ohh \[\frac{ 30π }{ 1π }\] ?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1and the pi's will cancel

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so 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
 one year ago
Best ResponseYou've already chosen the best response.0Okay thank you :) I'll try and see if I can get part three on my own and if not I'll let you know :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay I'm confused as to what the question is asking exactly

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1433458814224:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1"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
 one year ago
Best ResponseYou've already chosen the best response.1how long does it take to go around the full circle?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so how long does it take to go from the very top, to the very bottom?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1plug in t = 15 and tell me what you get

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I get a decimal when I plug it into my calculator 92.83185307

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1make sure you are in radian mode

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[H(15)=20\left( \frac{ π }{ 15 }15 \right)+30\] \[\frac{ π }{ 15 }\times \frac{ 15 }{ 1 }=\frac{ 15 }{ 15 }=1\] \[20\left( 1 \right)+30=50\] correct?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[H(15)=20\left( \frac{ π }{ 15 }15 \right)+30 \] \[\frac{ π }{ 15 }\times \frac{ 15 }{ 1 }=\frac{ 15π }{ 15 }=1π?\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1so you'll have 20*cos(pi) + 30 = ???

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you should find cos(pi) = 1 try again

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay so the edge of the Farris wheel is 10ft from the ground when Xavier's height above the ground reaches a minimum

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yep the lowest it goes is 10 ft off the ground dw:1433460789409:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you're welcome
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