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Natasha2012 [34]
3 years ago
12

Which proportion can be used to determine the number that is 15% of 30?

Mathematics
1 answer:
Nata [24]3 years ago
7 0
X/30=15/100. Cross multiply to find x.
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Given: cos θ=-4/5, sin x = -12/13, θ is in the third quadrant, 
USPshnik [31]

By definition of tangent,

tan(2<em>θ</em>) = sin(2<em>θ</em>) / cos(2<em>θ</em>)

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sin(2<em>θ</em>) = 2 sin(<em>θ</em>) cos(<em>θ</em>)

cos(2<em>θ</em>) = cos²(<em>θ</em>) - sin²(<em>θ</em>) = 2 cos²(<em>θ</em>) - 1

where the latter equality follows from the Pythagorean identity, cos²(<em>θ</em>) + sin²(<em>θ</em>) = 1. From this identity we can solve for the unknown value of sin(<em>θ</em>):

sin(<em>θ</em>) = ± √(1 - cos²(<em>θ</em>))

and the sign of sin(<em>θ</em>) is determined by the quadrant in which the angle terminates.

<em />

We're given that <em>θ</em> belongs to the third quadrant, for which both sin(<em>θ</em>) and cos(<em>θ</em>) are negative. So if cos(<em>θ</em>) = -4/5, we get

sin(<em>θ</em>) = - √(1 - (-4/5)²) = -3/5

Then

tan(2<em>θ</em>) = sin(2<em>θ</em>) / cos(2<em>θ</em>)

tan(2<em>θ</em>) = (2 sin(<em>θ</em>) cos(<em>θ</em>)) / (2 cos²(<em>θ</em>) - 1)

tan(2<em>θ</em>) = (2 (-3/5) (-4/5)) / (2 (-4/5)² - 1)

tan(2<em>θ</em>) = 24/7

4 0
3 years ago
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madreJ [45]

Answer:

20,000

Step-by-step explanation:

you just take one zero off

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