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dybincka [34]
2 years ago
12

Angles α and β are the two acute angles in a right triangle. Use the relationship between sine and cosine to find the value of β

if β > α.
sin(x/2+20)=cos(2x-25/2)


A) 25°
B) 33°
C) 36.5°
D) 53.5°

HINT: Sine and cosine of complementary angles are related
Mathematics
1 answer:
igomit [66]2 years ago
5 0

Answer:

D) 53.5°

Step-by-step explanation:

Sine and cosine of complementary angles are equal:

sin θ = cos(90 − θ)

sin(x/2 + 20) = cos(2x − 25/2)

cos(90 − (x/2 + 20)) = cos(2x − 25/2)

90 − (x/2 + 20) = 2x − 25/2

90 − x/2 − 20 = 2x − 25/2

165/2 = 5x/2

5x = 165

x = 33

x/2 + 20 = 36.5

2x − 25/2 = 53.5

Since β > α, β = 53.5°.

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Answer:

300%

Step-by-step explanation:

Given

y\ \alpha\ \frac{1}{x^2}

Required

Find the percentage change in y when x decreased by 50%

First, convert to equation

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Y = \frac{k}{(x - 0.5x)^2}

Y = \frac{k}{(0.5x)^2}

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Expand

Y = \frac{1}{0.25} * \frac{k}{x^2}

Substitute \frac{k}{x^2} for y

Y = \frac{1}{0.25} * y

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The percentage change is then calculated as:

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