1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
svlad2 [7]
3 years ago
13

Performance task: A parade route must start And and at the intersections shown on the map. The city requires that the total dist

ance of the route cannot exceed 3 miles. A propos route is shown.
Part A: Why does the proposed route not meet the requirement?

Part B: Assuming that the roads used for the
route are the same and the end point is the same,
at what intersection could the parade start so the
total distance is as close to 3 miles as possible?

Part C: The city wants to station video cameras halfway down each road in the parade. Using your answer to Part B, what are the coordinates of locations for the cameras?

Mathematics
1 answer:
GaryK [48]3 years ago
5 0

Answer:

Part A: The proposed route does not meet requirement because it is longer than the maximum required length of 3 miles

Part B: For the total distance is as close to 3 miles as possible, the start point of the parade should be at the point on Broadway with coordinates (9.941, 4.970)

Part C: The coordinates of the cameras stationed half way down each road are;

For central avenue; (4, 2)

For Broadway; (7.97, 2.49)

Step-by-step explanation:

Part A: The length of the given route can be found using the equation for the distance, l, between coordinate points as follows;

l = \sqrt{\left (y_{2}-y_{1}  \right )^{2}+\left (x_{2}-x_{1}  \right )^{2}}

Where for the Broadway potion of the parade route, we have;

(x₁, y₁) = (12, 3)

(x₂, y₂) = (6, 0)

l_1 = \sqrt{\left (0 -3\right )^{2}+\left (6-12 \right )^{2}} = 3 \cdot \sqrt{5}

For the Central Avenue potion of the parade route, we have;

(x₁, y₁) = (6, 0)

(x₂, y₂) = (2, 4)

l_2 = \sqrt{\left (4 -0\right )^{2}+\left (2-6 \right )^{2}} = 4 \cdot \sqrt{2}

Therefore, the total length of the parade route =-3·√5 + 4·√2 = 12.265 unit

The scale of the drawing is 1 unit = 0.25 miles

Therefore;

The actual length of the initial parade =0.25×12.265 unit = 3.09 miles

The proposed route does not meet requirement because it is longer than the maximum required length of 3 miles

Part B:

For an actual length of 3 miles, the length on the scale drawing should be given as follows;

1 unit = 0.25 miles

0.25 miles = 1 unit

1 mile =  1 unit/(0.25) = 4 units

3 miles = 3 × 4 units = 12 units

With the same end point and route, we have;

l_1 = \sqrt{\left (0 -y\right )^{2}+\left (6-x \right )^{2}} = 12 - 4 \cdot \sqrt{2}

y² + (6 - x)² = 176 - 96·√2

y² = 176 - 96·√2 - (6 - x)²............(1)

Also, the gradient of l₁ = (3 - 0)/(12 - 6) = 1/2

Which gives;

y/x = 1/2

y = x/2 ..............................(2)

Equating equation (1) to (2) gives;

176 - 96·√2 - (6 - x)² = (x/2)²

176 - 96·√2 - (6 - x)² - (x/2)²= 0

176 - 96·√2 - (1.25·x²- 12·x+36) = 0

Solving using a graphing calculator, gives;

(x - 9.941)(x + 0.341) = 0

Therefore;

x ≈ 9.941 or x = -0.341

Since l₁ is required to be 12 - 4·√2, we have and positive, we have;

x ≈ 9.941 and y = x/2 ≈ 9.941/2 = 4.97

Therefore, the start point of the parade should be the point (9.941, 4.970) on Broadway so that the total distance is as close to 3 miles as possible

Part C: The coordinates of the cameras stationed half way down each road are;

For central avenue;

Camera location = ((6 + 2)/2, (4 + 0)/2) = (4, 2)

For Broadway;

Camera location = ((6 + 9.941)/2, (0 + 4.970)/2) = (7.97, 2.49).

You might be interested in
Which combinations of transformations will always produce congruent figures? check all that apply
Vinvika [58]
You didnt provide the selections, but some answers would most likely be rotations, translations, and reflections.
4 0
3 years ago
Read 2 more answers
Which equation represents a line perpendicular to the line shown on the graph?
Vadim26 [7]

Answer:

See description below.

Step-by-step explanation:

To choose the correct equation, find the slope of the line on the graph. Identify two points on the line. Then subtract to find their rate of change using the slope formula.

m=\frac{y_2-y_1}{x_2-x_1}

When you know the slope, find the negative reciprocal. For example, if the slope is 2/1 then the negative reciprocal is -1/2. This is the slope of a perpendicular line to a line with slope 2. Choose the equation which has this same slope.

Example:

y = 2x -1

y= -1/2 +5

4 0
3 years ago
If you can buy one pineapple for $4, then<br> how many can you buy with $12?
larisa86 [58]

Answer:

you can buy 3 pineapples

Step-by-step explanation:

$4(3)= $12 total

8 0
2 years ago
A farmer packs 26 apples into trays for market. Each tray holds 6 apples. How many apples are in the partly filled tray? 32 chil
Tom [10]
2 apples in the partly filled tray, 11 tents are needed for all the children
3 0
2 years ago
The isosceles triangle has two sides with the same length. The base is one-half the length of a side. The expression which repre
gavmur [86]

Answer:

20 units

Step-by-step explanation:

s = 8

Perimeter = s + s + \frac{1}{2}*s

                = 8 + 8 + \frac{1}{2}*8

                = 8 + 8 + 4

               = 20 units

8 0
3 years ago
Read 2 more answers
Other questions:
  • Jules kicks a soccer ball off the ground and into the air with an initial velocity of 25 feet per second. Assume the starting he
    14·1 answer
  • Trevor’s total employment compensation is $33,500. If Trevor has no job expenses and his gross pay is $28,600, then his total em
    10·2 answers
  • In parallelogram ABCD , diagonals AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E, BE=2x2−x , and DE=x2+6 . What is BD ?
    13·2 answers
  • A bag contains 1 blue, 2 green, and 3 red marbles, as shown. What is the probability of drawing a green marble out of the bag wi
    10·2 answers
  • Hannah read 5 books in 15 months.What was her rate of reading I’m books per month ?
    7·2 answers
  • What is the average rate of change of the function f(x)=5(2)^x from x = 1 to x = 5?
    9·1 answer
  • Multiply 5 yards 18 inches by 3? please show work
    13·1 answer
  • Courtney drives 279 miles in 6 hours. What is her unit rate (miles per hour)? Show your written steps to earn full credit.
    8·2 answers
  • Solve the following quadratic equation for all values of x in simplest form.
    6·1 answer
  • Four 1 1/6 inch wood strips are used to form
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!