Answer:
length of path illuminated = 17.615 m
Step-by-step explanation:
To solve the problem graphically,
1. draw two lines at 30 degrees to each other.
2. place lights at 0, 5, 10 from the intersection (assuming there is a light at the intersection.
3. draw circles of 6m at each light.
4. The furthest intersection of the circles with the other path is the end of the illuminated path.
5. See diagram attached, which is (6.658,5.766) from the illuminated path.
6. The distance of the un-illuminated path is obtained by Pythagoras theorem,
distance, d = sqrt(6.658^2+5.766^2) = 8.808m
Since the path is illuminated on each side of the intersection, the total length of illuminated path = 2d = 17.615m
d
Given:
A triangle has side lengths of (7.8v+2.6) centimeters, (5.3v+4.5) centimeters, and (2.4w-6.7) centimeters.
To find:
The expression which represents the perimeter, in centimeters, of the triangle.
Solution:
We know that
Perimeter of a triangle = Sum of length of all sides of the triangle
Now, combine like terms.
Therefore, the expression for perimeter, in centimeters, of the triangle is .
Answer:
y = cos(3/2x)
Step-by-step explanation:
A general sine or cosine function will have parameters of amplitude, vertical and horizontal offset, and period. The values of these parameters can be determined from the given graph.
y = A·cos(2π(x -B)/P) +C
where A is the amplitude, B and C are the horizontal and vertical offsets, and P is the period.
<h3>Amplitude</h3>For sine and cosine functions, the amplitude of the function is half the difference between the maximum and minimum:
A = (3 -1)/2 = 1
<h3>Horizontal offset</h3>A sine function has its first rising zero-crossing at x=0. A cosine has its first peak at x=0. The given graph has its first peak at x=0, so it is a cosine function with no horizontal offset.
B = 0
<h3>Vertical offset</h3>For sine and cosine functions, the vertical offset is the average of the maximum and minimum values:
C = (3 +1)/2 = 2
<h3>Period</h3>The period is the difference in x-values between points where the function starts to repeat itself. Here, we can use the peaks to identify the period as 4π/3.
P = 4π/3
<h3>Function equation</h3>Using the parameter values we determined, the function can be written as ...
y = cos(3/2x) +2
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<em>Additional comment</em>
The argument of the cosine function is ...