Find the length of MN by setting up a ratio:
Let MN = X
X/18 = 5/6
Cross Multiply:
6x = 90
Divide both sides by 6:
x = 15
Now you know MN add it to LM for the total length of LN:
15 + 5 = 20
Answer: y = (-3x/2) + 1
Step-by-step explanation:
From the standard equation y = mx + c, the slope of the equation is 2/3. Therefor slope of a line perpendicular to it will be -3/2.
Hence the equation will be
y = (-3x/2) + c
As this line passes through (-2,4), putting these values in this equation gives c = 1.
Hence the answer is y = (-3x/2) + 1
The center of the sun is approximately 46,800,000 degrees celsius.
Refer to the diagram shown below.
When x = 30 ft, the cable is at 15 ft, therefore y(30) = 15.
That is,
a(30 - h)² + k = 15 (1)
Also, because the distance between the supports is 90 ft, therefore
y(0) = 6 ft, and y(90) = 6 ft
That is,
a(-h)² + k = 6 (2)
a(90 - h)² + k = 6 (3)
From (2) and (3), obtain
a(90 - h)² = ah²
90² - 180h + h² = h²
180h = 90²
h = 45 ft.
From (1) and (2), obtain
225a + k = 15
2025a + k = 6
Therefore
1800a = -9
a = - 0.005
k = 15 - 225(-0.005) = 16.125 ft
Answer:
The equation for the cable is
y = - 0.005(x - 45)² + 16.125
A graph of the solution verifies that the solution is correct.