## 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?

1. anonymous

@jim_thompson5910 ?

2. jim_thompson5910

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

3. anonymous

Yea solved it and got 50. Is that correct?

4. jim_thompson5910

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

5. anonymous

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

6. jim_thompson5910

oh ok

7. jim_thompson5910

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

8. jim_thompson5910

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

9. anonymous

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

10. 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

11. anonymous

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

12. jim_thompson5910

yes, simplify that fraction

13. anonymous

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

14. jim_thompson5910

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

15. anonymous

Ohh $\frac{ 30π }{ 1π }$ ?

16. jim_thompson5910

and the pi's will cancel

17. 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

18. 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 :)

19. jim_thompson5910

alright

20. anonymous

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

21. jim_thompson5910

|dw:1433458814224:dw|

22. 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|

23. jim_thompson5910

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

24. anonymous

30 seconds

25. jim_thompson5910

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

26. anonymous

15 seconds

27. jim_thompson5910

plug in t = 15 and tell me what you get

28. anonymous

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

29. jim_thompson5910

make sure you are in radian mode

30. 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?

31. anonymous

Wait

32. anonymous

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

33. jim_thompson5910

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

34. anonymous

I get 49.9?

35. jim_thompson5910

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

36. anonymous

10?

37. jim_thompson5910

yep 10

38. anonymous

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

39. jim_thompson5910

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

40. anonymous

Thank you :)

41. jim_thompson5910

you're welcome