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3 years ago

Solve for r 0.5(r+2.76)=3

Mathematics

1 answer:

11111nata11111 [884]3 years ago

8 0

Answer:

r=1.43147648, −4.19147648

Step-by-step explanation:

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3 years ago

If sin theta = 8/17 and cot theta < 0, what is sec theta?

klasskru [66]

Answer:

$-\frac{17}{15}$

Step-by-step explanation:

By definition, $\cot \theta=\frac{1}{\tan \theta}$ and $\sec \theta=\frac{1}{\cos \theta}$ . Since since $\cot \theta$ is negative, $\tan \theta$ must also be negative, and since $\sin \theta$ is positive, we must be in Quadrant II.

In a right triangle, the sine of an angle is equal to its opposite side divided by the hypotenuse. The cosine of an angle in a right triangle is equal to its adjacent side divided by the hypotenuse. Therefore, we can draw a right triangle in Quadrant II, where the opposite side to angle theta is 8 and the hypotenuse of the triangle is 17.

To find the remaining leg, use to the Pythagorean Theorem, where $a^2+b^2=c^2$ , where $c$ is the hypotenuse, or longest side, of the right triangle and $a$ and $b$ are the two legs of the right triangle.

Solving, we get:

$8^2+b^2=17^2,\\b^2=17^2-8^2,\\b^2=\sqrt{17^2-8^2}=\sqrt{225}=15$

Since all values of cosine theta are negative in Quadrant II, all values of secant theta must also be negative in Quadrant II.

Thus, we have:

$\sec\theta=\frac{1}{\cos \theta}=-\frac{1}{\frac{15}{17}}=\boxed{-\frac{17}{15}}$

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3 years ago