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3 years ago

Find the values of x and y.

Mathematics

1 answer:

3241004551 [841]3 years ago

8 0

Answer:

x = 11, y = 17

Step-by-step explanation:

Note that

9x - 4 = 8x + 7 ( vertical angles )

Subtract 8x from both sides

x - 4 = 7 ( add 4 to both sides )

x = 11

and

7y - 34 = 5y ( vertical angles )

Subtract 5y from both sides )

2y - 34 = 0 ( add 34 to both sides )

2y = 34 ( divide both sides by 2 )

y = 17

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The angle θ 1 is located in Quadrant IV, and cos ⁡ ( θ 1 ) = 9/ 19 , theta, start subscript, 1, end subscript, right parenthesis

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$sin\theta_1 = - \frac{2\sqrt{70}}{19}$

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We are given that $\theta_1$ is in fourth quadrant.

$cos\theta_1$ is always positive in 4th quadrant and

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Also, we know the following identity about $sin\theta$ and $cos\theta$ :

$sin^2\theta + cos^2\theta = 1$

Using \theta_1 in place of \theta:

$sin^2\theta_1 + cos^2\theta_1 = 1$

We are given that $cos\theta_1 = \frac{9}{19}$

$\Rightarrow sin^2\theta_1 + \dfrac{9^2}{19^2} = 1\\\Rightarrow sin^2\theta_1 = 1 - \dfrac{81}{361}\\\Rightarrow sin^2\theta_1 = \dfrac{361-81}{361}\\\Rightarrow sin^2\theta_1 = \dfrac{280}{361}\\\Rightarrow sin\theta_1 = \sqrt{\dfrac{280}{361}}\\\Rightarrow sin\theta_1 = +\dfrac{2\sqrt{70}}{19}, -\dfrac{2\sqrt{70}}{19}$

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