13. Find the equations of the straight lines which passes
1 answer:
9514 1404 393
Answer:
- y = 1/2x +2
- y = -2x +7
Step-by-step explanation:
The slope of a line is the tangent of the angle it makes with the x-axis. The given line has a slope of -1/3, so the lines we want will have slopes of ...
m1 = tan(arctan(-1/3) +45°) = 0.5 . . . . . using a calculator
m2 = tan(arctan(-1/3) -45°) = -2
Of course, these two lines are perpendicular to each other, so their slopes will have a product of -1: (0.5)(-2) = -1.
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We can use the point-slope form of the equation for a line to write the desired equations:
y = m(x -h) +k . . . . . line with slope m through point (h, k)
<u>Line 1</u>:
y = 1/2(x -2) +3
y = 1/2x +2
<u>Line 2</u>:
y = -2(x -2) +3
y = -2x +7
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Answer:
Step-by-step explanation:
The expression to transform is:
Let's work first on the inside of the parenthesis.
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Therefore
Now let's replace with
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Now use the property that tells us how to proceed when we have "exponent of an exponent":
Therefore we get:
Finally remember that this expression was raised to the power 7, therefore:
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An use again the property for the exponent of a exponent:
Answer:
221.87 feet
Step-by-step explanation:
Given that,
A 525 ft cable runs from the top of an antenna to the ground.
The angle of elevation made by the ground to the top of an antena 25°
We need to find the height of the antenna.
Using trigonometry,
Hypotenuse, H = 525 ft
θ = 25°
So,
So, the height of the antenna is equal to 221.87 feet.