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saveliy_v [14]
3 years ago
15

Find the exact value of cos theta​, given that sin thetaequalsStartFraction 15 Over 17 EndFraction and theta is in quadrant II.

Rationalize denominators when applicable.
Mathematics
1 answer:
vova2212 [387]3 years ago
5 0

Answer:

cos \theta = -\frac{8}{17}

Step-by-step explanation:

For this case we know that:

sin \theta = \frac{15}{17}

And we want to find the value for cos \theta, so then we can use the following basic identity:

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

And if we solve for cos \theta we got:

cos^2 \theta = 1- sin^2 \theta

cos \theta =\pm \sqrt{1-sin^2 \theta}

And if we replace the value given we got:

cos \theta =\pm \sqrt{1- (\frac{15}{17})^2}=\sqrt{\frac{64}{289}}=\frac{\sqrt{64}}{\sqrt{289}}=\frac{8}{17}

For our case we know that the angle is on the II quadrant, and on this quadrant we know that the sine is positive but the cosine is negative so then the correct answer for this case would be:

cos \theta = -\frac{8}{17}

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Hypothesis:

Null hypothesis:H₀:μ=13

Alternative hypothesis:Hₐ:μ>13

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n=30,

Degree of freedom n-1=30-1=29

\bar{x}=13.8 and s=3.1

To test the null hypothesis H₀, the value of test static would be calculated as follows:

\begin{aligned}t&=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}\\ t_{29}&=\frac{13.8- 13}{\frac{3.1}{\sqrt{30}}}\\ &=\frac{0.8}{0.566}\\ &=1.413\end

Hence, the value of the test static for the hypothesis with the mean weight loss of these participants as 13.8 pounds with a standard deviation of 3.1 pounds is 1.413.

Learn more about hypothesis from here brainly.com/question/14783359

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<em>y</em> = 2<em>x</em> + 2  ==>  -2<em>x</em> + <em>y</em> = 2

<em>y</em> = 2<em>x</em> + 5  ==>  -2<em>x</em> + <em>y</em> = 5

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Compute the Jacobian determinant for this change of coordinates:

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