At a carnival, a particular game requires the player to spin a wheel. When a child plays, the game operator allows them to conti
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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;
Where for the Broadway potion of the parade route, we have;
(x₁, y₁) = (12, 3)
(x₂, y₂) = (6, 0)
For the Central Avenue potion of the parade route, we have;
(x₁, y₁) = (6, 0)
(x₂, y₂) = (2, 4)
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;
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).
Answer:
The probability that no flaws occur in a certain portion of wire of length 5 millimeters = 1.1156 occur / millimeters
Step-by-step explanation:
<u>Step 1</u>:-
Given data A copper wire, it is known that, on the average, 1.5 flaws occur per millimeter.
by Poisson random variable given that λ = 1.5 flaws/millimeter
Poisson distribution
<u>Step 2:</u>-
The probability that no flaws occur in a certain portion of wire
On simplification we get
P(x=0) = 0.223 flaws occur / millimeters
<u>Conclusion</u>:-
The probability that no flaws occur in a certain portion of wire of length 5 millimeters = 5 X P(X=0) = 5X 0.223 = 1.1156 occur / millimeters
Step-by-step explanation:
We have given that,
The inner radius of a bicycle wheel is 12 inches.
It is required to find the expression to find the inside circumference of this wheel.
The outer surface of the wheel is equal to its circumference. It is given by :
r is radius of wheel
This is the required explanation.