# Problem 1 of ?

The following table describes the height of a seat on a Ferris wheel as the wheel rotates.

**Time (s)** | 0 | 5 | 10 | 15 | 20 | 25 | 30 |

**Height (m)** | 1.5 | 9.79 | 23.21 | 23.21 | 9.79 | 1.5 | 9.79 |

(a) Determine a sinusoidal regression equation for this data.

(b) Determine the radius of the Ferris wheel.

(c) For the first 25 s, determine all the times that the height of the seat will be 10 m.

**If providing a graphical solution, state the function(s) used, sketch the graph, indicate appropriate window dimensions and clearly explain how your solution is derived from the graph.**

**Solution**

A) The sinusoidal regression equation for this data is:

12 x sin(.2513X+-1.5708)+13.5

First you put Time in L_{1}, and Height in L_{2}. To do this you'd press **STAT** on your calculator, and then **ENTER** (which is the edit option).

Once you're done this, change the window settings to best suit the data. You'll see what I put, below.

Also, make sure that Plot 1 is on, and change it to scatterplot. To do this you'd go **second function**, **ENTER**. Then if the plot is off, highlight "On" and press **ENTER**.

To make the data scattered, press the down arrow and highlight the first graph. Once that's done, exit out of that by hitting **GRAPH**. You should see the data you listed.

To get the equation you'd press **STAT**, right arrow to **CALC**, and then up arrow. **SinReg** should be highlighted. Press **ENTER**. Hit **ENTER** again.

i got colored graph image, but i kinda don't no how to upload it here. will do it tomorrow. maybe Mr.K can show me how to do it.

Window Settings

XMin=0

XMax=35

Xscl=5

YMin=0

YMax=30

Yscl=5

B)The radius of the Ferris wheel can be determined by subtracting 1.5 m from 23.21 m(21.71 m)and then dividing that by 2. Therefore the radius of the Ferris wheel is 10.855 m. I found the diameter first, just by subtracting the lowest height by the highest height. :)

C) Just by looking at the data, we know that the times at which the seat will be at 10 m is slightly over 5 seconds (around 5.03 seconds), and then again slightly under 20 seconds (at around 19.93 seconds). To get this answer, I basically just played around with the value function. To get there, you press **second function TRACE** which is **CALC** and then press **ENTER**. At this point the screen will go back to the graph, and you'll notice there's **"X="** at the bottom of the screen. You'd then just enter a number, and it'll give you the Y value, which in this case is a height.

- I really hope that I explained this clearly, and that it is correct. I am a little rusty when it comes to Periodic Functions.

Correction.

For question **a** you can use this equation:

=12 sin( (2(3.14)/25) (x-1.57) ) + 13.52

a = 12

b = 2(pie=3.14)/25

c = 1.5708

d = 13.52

the equation you've used is a "SINREG"

y=a*sin(bx+c)+d

this equation is pretty accurate because its uses all the points (sinreg)

the manual equation:

y = a sin 2pie/b (x - c) + d

B. the answer for b is right.

C. the answer for c is right.

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