For number 2 the correct answer is 3, number 3 the correct answer is 1/8, for number 7 the correct answer is 8/63, for number 4 the correct answer is 2/15, and the correct answer for number 8 is 25/78. If you want to see the steps done you can download Photomath. It is very helpful. Glad I could help!
Answer:
![\frac{x}{\sqrt{x^2+9}}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B%5Csqrt%7Bx%5E2%2B9%7D%7D)
Step-by-step explanation:
Let
.
Then
.
Construct a right triangle.
Make one of the non-right angles
.
Recall
is equal to the ratio of the side that is opposite to
to the side that is adjacent to
.
This means opposite side
while adjacent side
since
.
We can find the hypotenuse by using the Pythagorean Theorem.
![(x)^2+(3)^2=(\text{hyp})^2](https://tex.z-dn.net/?f=%28x%29%5E2%2B%283%29%5E2%3D%28%5Ctext%7Bhyp%7D%29%5E2)
![x^2+9=(\text{hyp})^2](https://tex.z-dn.net/?f=x%5E2%2B9%3D%28%5Ctext%7Bhyp%7D%29%5E2)
Take the square root of both sides:
.
Recall
is equal to the ratio of the side that is opposite to
to the hypotenuse.
![\sin(\arctan(\frac{x}{3}))](https://tex.z-dn.net/?f=%5Csin%28%5Carctan%28%5Cfrac%7Bx%7D%7B3%7D%29%29)
-->Because we let the inside equal
.
-->Because ![\sin(u)=\frac{\text{opp}}{\text{hyp}}](https://tex.z-dn.net/?f=%5Csin%28u%29%3D%5Cfrac%7B%5Ctext%7Bopp%7D%7D%7B%5Ctext%7Bhyp%7D%7D)
Answer:
A
Step-by-step explanation:
Answer:
664.94
Step-by-step explanation:
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