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3 years ago

Determine the holes, vertical asymptotes, and horizontal asymptotes of the rational function y=3x^2+10x-8/x^2+7x+12

1 answer:

8 0

There would be a hole when x = -4.

If you factor both the top and the bottom, you will see that the factor (x + 4) is in both the numerator and denominator. Therefore, the would be a hole when x = -4 because that would also make the denominator 0.

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<img src="https://tex.z-dn.net/?f=cos%20%5B%20arctan%28%5Cfrac%7B12%7D%7B5%7D%29%20-%20arcsin%20%28%5Cfrac%7B-3%7D%7B5%7D%29%5D"

qwelly [4]

Answer: -16/65

Step-by-step explanation:

Drawing the right triangle (as attached) gives us that $\arctan \left(\frac{12}{5} \right)=\arcsin \left(\frac{12}{13} \right)$

Also, $-\arcsin \left(-\frac{3}{5} \right)=\arcsin \left(\frac{3}{5} \right)$

This means our original expression is equal to:

$\cos \left[\arcsin \left(\frac{12}{13} \right)+\arcsin \left(\frac{3}{5} \right) \right]$

Using the cosine addition formula, which states $\cos(a+b)=\cos a \cos b-\sin a \sin b$ , we get this itself is equal to:

$\cos \left(\arcsin \left(\frac{12}{13} \right) \right)\cos \left(\arcsin \left(\frac{3}{5} \right)\right)-\sin \left(\arcsin \left(\frac{12}{13} \right) \right)\sin \left(\arcsin \left(\frac{3}{5} \right)\right)$

Since $\sin^{2} \theta+\cos^{2} \theta=1$ , we know that:

$\sin^{2} \left(\arcsin \left(\frac{12}{13} \right)\right)+\cos^{2} \left(\arcsin \left(\frac{12}{13} \right)\right)=1\\\\\frac{144}{169} +\cos^{2} \left(\arcsin \left(\frac{12}{13} \right)\right)=1\\\\cos^{2} \left(\arcsin \left(\frac{12}{13} \right)\right)=\frac{25}{169}\\\\cos \left(\arcsin \left(\frac{12}{13} \right)\right)=\frac{5}{13}$

Similarly, cos(arcsin(3/5))=4/5.

This means the given expression is equal to:

$\left(\frac{5}{13} \right) \left(\frac{4}{5} \right)-\left(\frac{12}{13} \right) \left(\frac{3}{5} \right)\\\\\frac{20}{65}-\frac{36}{65}=\boxed{-\frac{16}{65}}$

3 0

2 years ago

Lila bought a green poster that measured 36 inches by 24 inches and a red poster that measured 12 inches by 18 inches. If the po

kramer

36 × 24 = 864 square inches. 864 sq in × $0.05 = $43.20. The green poster cost $43.20

12 × 18 = 216 square inches. 216 sq in × $0.05 = $10.80. The red poster cost $10.80

Please mark brainliest

5 0

3 years ago

Subtract the following. Write your answer in standard notation.*<br> 18-92 X 10+

charle [14.2K]

Answer:

-740

Step-by-step explanation:

18-72 equals -74

now -74 *10 equals-740

6 0

3 years ago

amanda has $40 to spend on flowers. she bought a vase for $18. at most how much can she spend on flowers

masha68 [24]

Answer:

at most she can spend $22 on flowers

Step-by-step explanation:

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5 0

4 years ago

A particular prism has ten faces. How many edges does it have?

vova2212 [387]

Answer:

I think the answer is .........

Step-by-step explanation:

24 edges,

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3 years ago