Parametric equations can be used to graph the path of an object in space. For example, they can be used to describe the path of a storm moving through an area. In this portfolio, you will use historical storm data to trace the path of a hurricane. From this data, you will use parametric equations to model the path of the storm.
- Select the link to access the NOAA’s Office for Coastal Management: Historical Hurricane Tracks website to search for a hurricane.
- Type any state in the search box. (Note: Inland states do not usually have hurricanes. Type in a different state if no hurricanes are listed.)
- Select one hurricane frXX the XXXX XXXX appears.
- Select XXXX to XXXXX above the XXXX to view XXX XXXX XXXXXXXXX XXXX.
-
- Make a table XX the storm’s XXXXXXXXXX XXX vertical movement with respect to time. XXXXX XXXX a XXXXXXXX XXXXX on the XXXX and note XXX XXXXXXXXXXX date in the table XX the XXXX. XXXX XXXX XXXX t = X. XXXX XXX XXXXXXXX XXXXXXXXXXX from XXX lower left XXXXXX XX the map view XXX record XXXX in Table X. XXXXX XXXXXXXX XXXXXXXX XXXXX/XXXXX and longitude measures east/XXXX, the XXXXX coordinate will be y XXX the second coordinate XXXX XX x. XXX XXXXXXXX
- Upload this XXXXXXXXX XXXX XXX Drop XXX.
- If you did not XXXXX a copy XX XXXX graph XXXX XXX XXXXXXXXX, be XXXX to also XXXXXX XXX graph into XXX Drop XXX.
Historical XXXXXXXXX XXXXXX
Step 2: XXXX XXX hurricane path.
Take a screen XXXX XX XXX XXXXXXXXX XXXX XXX XXXXXXX it below:
XXXXXXX XXX XXXX along the path. Note that you XXXXX need to use the scroll XXXXX closest to the XXXX information. XX the table XXXXX, XXXXXX XXX record XXX point from each XXX of XXX storm. XXXX XXXX point t = X, t = 2, etc.
XXXXX XXX storm for a total of XX least five XXXX so that you have a XXXXXXX of XXXX points in XXX table. Use XXX XXXXXXX below to XXXX you find XXX date, latitude, XXX longitude.
Table 1
Date
| t
| x
(XXXXXXXXX)
| y
(XXXXXXXX)
|
XXX XX, 2017
| X
| -XX.76
| 24.25
|
XXX XX, 2017
| X
| -XX.06
| XX.XX
|
XXX 17, XXXX
| 2
| -XX.XX
| XX.XX
|
Aug XX, 2017
| X
| -101.XX
| XX.44
|
XXX XX, 2017
| X
| -XX.XX
| 35.42
|
Step X: XXXXXX a XXXXXXXXXXXX XXXXX.
XXXX through XXX XXXXXXXXX steps XX create two XXXXXXXXXX equations where x XX a function XX t and y XX a XXXXXXXX XX t.
- XXXXX plot t versus x, then XXXX t versus y. XXXX kind XX XXXXXXXXXX should you XXX for XXXX XXX XXXXX XX your graphs?
- XXX XXXX XXXXXXXXXX to create a XXXXXXX for the XXXXX you have XXXXXX. Enter the ordered pairs XXXX XXXXX XXX XXXX XXX XXXXXXXXXX create XXX line of XXXX XXX for your model. XXX XXXXXXX, XX your path appears to be XXXXXXXXXXX, you XXXX
- XXXXX XXXX XXXXX XXXXXXXXX:
have a XXXXX XX XXX XXXX y = abx using the XXXXXX XXXXXXX on XXX XXXXXXXXXX.
· x(t) =0.XX^X - 1.1x^X - X.1x - XX.
Step X: XXXXX XXXX model.
Plug in the values t = 0, 1, X, X, XXX X XXXX XXXX XXXXXXXXXX equations and XXXXXX your XXXXXX XXX x and y in XXX table below.
XXXXX X
t
| x
(XXXXXXXXX)
| y
(latitude)
|
0
| -92.0
| 24.X
|
X
| -95.X
| 26.8
|
2
| -99.4
| 29.6
|
3
| -100.X
| 32.X
|
4
| -XX.X
| XX.2
|
Now graph XXX x- and y-coordinates XXXX Table 1 onto graph paper XXXXX XXX color, and XXXXX XXX x- XXX y-coordinates from XXXXX X XXXX the same graph XXXXX XXXXX a XXXXXXXXX color. You XXX XXXXXX copy XXX XXXXX your graph here or upload it XXXXX XXXX this worksheet.
Compare XXX XXXXX XXXXXX XXXX the XXXXXXXX points and answer the XXXXXXXXX questions:
- XXX XXXX XXXX XXXXX compare to the actual XXXX?
- XXX did you choose the graph family that you XXX? Did you choose well? Why or why not?
- Is it XXXXXXXX to solve x(t) XXX t, substitute it XXXX y(t) XX XXXXXXXXX the
XXX plot XXXX Table 2 is smoother than XXXX of XXXXX X. Besides that, they are XXXXXXXXXX.
I XXXXX the cubic XXXXX family XXXXXXX it XX a common graph XXXX XX XXXXXX to XXXXXXX
XXX XXXX its XXXXXXXXXXXXXXX. XXX XXXXXX XX XXXX XX the graph XX XXXXXXXXXXXX XXX easily
parameter, t, and write it XX a rectangular equation XXXX x and y XXXXXXX? XXX or why XXX?
No, it is XXX XXXXXXXX. Because x(t) equation has a coefficient of X (XXXX XXXX in y(t)).
Hence, there XX XX XXXXXXXXXXXX XXXXXXXXXXXX that can XX done XX remove the
Turn it in:
Step X: Create a XXXXXXXXXXXX Model.
Work through the following XXXXX XX XXXXXX XXX XXXXXXXXXX equations XXXXX x is a function of t XXX y XX a XXXXXXXX of t.
- First XXXX t XXXXXX x, then XXXX t XXXXXX y. What XXXX of XXXXXXXXXX should you use for XXXX XXX based XX XXXX XXXXXX?
- Use XXXX XXXXXXXXXX XX XXXXXX a XXXXXXX for XXX model you have chosen. Enter the XXXXXXX XXXXX into lists and have XXX calculator create XXX XXXX of best XXX XXX XXXX model. For example, XX XXXX path appears XX XX exponential, you will
- Write your XXXXX equations:
have a XXXXX of XXX XXXX y = abx XXXXX XXX XXXXXX XXXXXXX XX the calculator.
· x(t) =X.XX^X - 1.1x^2 - 3.1x - 92.
Step 4: Check your model.
XXXX in XXX values t = 0, 1, X, 3, XXX 4 XXXX XXXX XXXXXXXXXX equations XXX XXXXXX your XXXXXX for x XXX y in XXX table below.
XXXXX 2
t | x (XXXXXXXXX) | y (latitude) |
0 | -XX.X | XX.X |
X | -XX.X | 26.X |
X | -XX.X | 29.X |
X | -XXX.X | 32.X |
X | -96.X | 35.X |
Now XXXXX the x- and y-XXXXXXXXXXX from XXXXX X onto XXXXX paper using XXX XXXXX, and XXXXX the x- XXX y-coordinates XXXX Table 2 XXXX the same graph paper using a different XXXXX. You may either XXXX XXX paste XXXX graph XXXX or upload it XXXXX XXXX this worksheet.
XXXXXXX the model points XXXX XXX original XXXXXX and answer XXX following questions:
- How XXXX XXXX XXXXX compare XX the actual XXXX?
- XXX XXX you XXXXXX the XXXXX XXXXXX XXXX you did? Did you choose well? Why or why XXX?
- XX it XXXXXXXX to solve x(t) for t, substitute it into y(t) to eliminate XXX
The XXXX from Table 2 XX smoother XXXX XXXX XX Table 1. Besides that, XXXX XXX identitcal.
I XXXXX the cubic graph XXXXXX XXXXXXX it XX a common graph XXXX XX easier to XXXXXXX
XXX plot its characteristics. XXX choice XX well as the graph is XXXXXXXXXXXX XXX XXXXXX
parameter, t, and write it XX a rectangular XXXXXXXX with x XXX y XXXXXXX? XXX or XXX XXX?
No, it is XXX possible. XXXXXXX x(t) equation has a XXXXXXXXXXX XX X (XXXX root in y(t)).
XXXXX, XXXXX is no mathematical XXXXXXXXXXXX XXXX XXX XX done to XXXXXX XXX
Turn it in:
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