Answering questions Mathematics & Economics Research
Kindly I need answers for the last 3 questions on this project. I will provide you with the previous tasks because they are related to each other.
Water Park Project Part 2
TASK 5: Calculating the Distance
A team of surveyors is trying to determine how large a space they will need to design your park. You have been asked to determine, using the distance formula, how far away certain attractions are from one another. This will provide them with the information they need to expand the park from your scaled blueprint to actual dimensions. Calculate the distance in unit dimensions by applying your selected attraction points (Task 2) and the distance formula,
D =
Show your work in the space provided!
Help Center to Water Slide #1 |
Toddler Area to Concessions
|
Gift Shop to Restrooms |
Security Desk to Water Slide #2
|
Lazy River to Large Whirlpool
|
Help Center to Gift Shop |
Restrooms to Water Slide #3
|
Concessions to Lazy River
|
Water Slide #1 to Water Slide #2 |
Water Slide #2 to Water Slide #3
|
Task 6: Converting to Actual Dimensions
Your water park design has been drawn as a blueprint, but to build it, you will need actual dimensions in lieu of the unit dimensions. A large rectangular plot of land has been selected for development, and the city has given approval for construction. Knowing that the actual dimensions for the land is 301m x 196 m in size, determine the scale of your coordinate system.
1st: count the number of spaces along the length of your paper: ___________ spaces.
2nd: set a ratio equal to _________ spaces per 301m.
Now, use this ratio to solve for the actual unknown distances by setting up a proportion and calculating. Show your work!
Show your work in the space provided!
Help Center to Water Slide #1
|
Toddler Area to Concessions
|
Gift Shop to Restrooms |
Security Desk to Water Slide #2
|
Lazy River to Large Whirlpool |
Help Center to Gift Shop
|
Restrooms to Water Slide #3 |
Concessions to Lazy River
|
Water Slide #1 to Water Slide #2 |
Water Slide #2 to Water Slide #3
|
Task 7: Writing Linear Equations.
In task 3 you identified direct paths between various park attractions by drawing them in with red lines. Now, you will show off your skills by writing equations for each of those red lines.
- Use the linear equation, y = mx +b and solve for B (the y-intercept). Use your slope (m) from task three and one of the identified endpoints of that line (x, y).
- After solving for b, write each red line’s equation using only the value for slope and the y-intercept value, leaving x and y as variables!
Help Center to Water Slide #1
Solve for B:
Y = _____ X + _____ |
Toddler Area to Concessions
Solve for B:
Y = _____ X + _____
|
Gift Shop to Restrooms
Solve for B:
Y = _____ X + _____ |
Security Desk to Water Slide #2
Solve for B:
Y = _____ X + _____
|
Lazy River to Large Whirlpool
Solve for B:
Y = _____ X + _____
|
Help Center to Gift Shop
Solve for B:
Y = _____ X + _____
|
Restrooms to Water Slide #3
Solve for B:
Y = _____ X + _____
|
Concessions to Lazy River
Solve for B:
Y = _____ X + ______ |
Water Slide #1 to Water Slide #2
Solve for B:
Y = _____ X + _____
|
Water Slide #2 to Water Slide #3
Solve for B:
Y = _____ X + _____
|
Task 8: Solving for Systems of Linear Equations: Determining “intersection” point.
By successfully writing equations to define each red line, you are now to solve for where those lines might meet on your coordinate grid.
- Select two lines, preferably two that cross on your blueprint, and use the substitution method to solve for their intersection point.
- Mark each intersection point using a YELLOW POINT on your blueprint.
- Repeat this for a total of three intersecting lines.
Example problem:
Y = -2X + 14 and Y = 3X – 7 -2X + 14 = 3X – 7 Y = -2(4.2) + 14
-2X = 3X – 21 Y = -8.4 + 14
-5X = -21 Y = 5.6
X = 4.2
Intersection point = ( 4.2, 5.6 )
A.
Equations: ________________________ and ________________________
Solve for X: Substitute for Y:
Intersection point = ( _________ , _________ )
B.
Equations: ________________________ and ________________________
Solve for X: Substitute for Y:
Intersection point = ( _________ , _________ )
C.
Equations: ________________________ and ________________________
Solve for X: Substitute for Y:
Intersection point = ( _________ , _________ )
Your Name
Subject and Section
Professor’s Name
Date of Submission
TASK 5: Calculating the Distance
A team of surveyors is trying to determine how large a space they will need to design your park. You have been asked to determine, using the distance formula, how far away certain attractions are from one another. This will provide them with the information they need to expand the park from your scaled blueprint to actual dimensions. Calculate the distance in unit dimensions by applying your selected attraction points (Task 2) and the distance formula, D= (x2-x1)2+ (y2-y1)2
Show your work in the space provided!
Help Center (0,0) to Water Slide #1 (10,20)
D= (x2-x1)2+ (y2-y1)2
D= (10-0)2+ (20-0)2
D= 500
D= 22.36 units
Toddler Area (6, 13) to Concessions (14, 4)
D= (x2-x1)2+ (y2-y1)2
D= (14-6)2+ (4-13)2
D= 145
D= 12.04 units
Gift Shop (-16, -24) to Restrooms (7, 27)
D= (x2-x1)2+ (y2-y1)2
D= [7--16]2+ [27--24]2
D= (7+16)2+ (27+24)2
D= 3130
D= 55.95 units
Security Desk (12, -25) to Water Slide #2 (-14, -5)
D= (x2-x1)2+ (y2-y1)2
D= (-14-12)2+ [-5--25]2
D= (-14-12)2+ (-5+25)2
D= 1076
D= 32.80 units
Lazy River (-17, 29) to Large Whirlpool (0, -16)
D= (x2-x1)2+ (y2-y1)2
D= [0--17]2+ (-16-29)2
D= (0+17)2+ (-16-29)2
D= 2314
D= 48.10 units
Help Center (0, 0) to Gift Shop -16, -24)
D= (x2-x1)2+ (y2-y1)2
D= (-24-0)2+ (-16-0)2
D= 832
D= 28.84 units
Restrooms (7, 27) to Water Slide #3 (10, -7)
D= (x2-x1)2+ (y2-y1)2
D= (10-7)2+ (-7-27)2
D= 1165
D= 34.13 units
Concessions (14, 4) to Lazy River (-17, 29)
D= (x2-x1)2+ (y2-y1)2
D= (-17-14)2+ (29-4)2
D= 1586
D= 39.82 units
Water Slide #1 (-10, 20) to Water Slide #2 (-14, -5)
D= (x2-x1)2+ (y2-y1)2
D= [-14--10]2+ (-5-20)2
D= (-14+10)2+ (-5-20)2
D= 641
D= 25.32 units
Water Slide #2 (-14, -5) to Water Slide #3 (10, -7)
D= (x2-x1)2+ (y2-y1)2
D= [10--14]2+ [-7--5]2
D= (10+14)2+ (-7+5)2
D= 580
D= 24.08 units
Task 6: Converting to Actual Dimensions
Your water park design has been drawn as a blueprint, but to build it, you will need actual dimensions in lieu of the unit dimensions. A large rectangular plot of land has been selected for development, and the city has given approval for construction. Knowing that the actual dimensions for the land is 301m x 196 m in size, determine the scale of your coordinate system.
1st: count the number of spaces along the length of your paper: ____67_____ spaces.
2nd: set a ratio equal to ____67____ spaces per 301m.
Now, use this ratio to solve for the actual unknown distances by setting up a proportion and calculating. Show your work!
Show your work in the space provided!
Help Center to Water Slide #1
D= x2+ y2
D= (10)2+ (20)2
D= 500
D= 22.36 units
67301 m= 22.36x
67 x67= 6730.56 m67
x=100.46 m
Toddler Area to Concessions
D= x2+ y2
D= (9)2+ (8)2
D= 145
D= 12.04 units
67301 m= 12.04x
67 x67= 3624.04 m67
x=54.09 m
Gift Shop to Restrooms
D= x2+ y2
D= (23)2+ (51)2
D= 3130
D= 55.95 units
67301 m= 55.95x
67 x67= 16840.35 m67
x=251.34 m
Security Desk to Water Slide #2
D= x2+ y2
D= (26)2+ (20)2
D= 1076
D= 32.80 units
67301 m= 32.80x
67 x67= 9872.8 m67
x=147.36 m
Lazy River to Large Whirlpool
D= x2+ y2
D= (17)2+ (45)2
D= 2314
D= 48.10 units
67301 m= 48.10x
67 x67= 14478.1 m67
x=216.09 m
Help Center to Gift Shop
D= x2+ y2
D= (16)2+ (24)2
D= 832
D= 28.84 units
67301 m= 28.84x
67 x67= 8680.84 m67
x=129.56 m
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