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expeople1 [14]
3 years ago
5

Use the properties of exponents to enter an equivalent expression with a single exponent.

Mathematics
1 answer:
Gelneren [198K]3 years ago
5 0

({10}^{2} ) {}^{4}  =  {10}^{2 \times 4}  =  {10}^{8}

I hope this can help you ^_^

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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>)

Recall the double angle identities:

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
Fifty-five percent of what number is 27.5?
adelina 88 [10]

Answer:

50

Step-by-step explanation:

7 0
2 years ago
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Misha Larkins [42]
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Sally has 2 cats and each cat eats 1/4 of a tin of cat food each day.
Mashutka [201]

If one cat eats 1/4 of a tin per day then two cats eat 1/2 of a tin per day.

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Hope this helps.

5 0
3 years ago
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Steve needs to take at least 24 milligrams of calcium, 15 milligrams of iron, and 16 milligrams of vitamins. Which ordered pairs
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