Answer:
Yes
Step-by-step explanation:
First, we need to put them in the same terms.
30/60... 30 is half of 60 so it can be simplified to be written as 1/2, 2/4, 4/8, or 5/10.
5/10 is smaller than 9/10
9/10 is bigger than 5/10
9/10 is bigger than 30/60
The formula for the general sin function is
![y=Asin(bx+c)](https://tex.z-dn.net/?f=y%3DAsin%28bx%2Bc%29)
where b is the period and c is the phase shift. We are given a period of
![\frac{ \pi }{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Cpi%20%7D%7B4%7D%20)
and the formula to solve for b is
![period= \frac{2 \pi }{b}](https://tex.z-dn.net/?f=period%3D%20%5Cfrac%7B2%20%5Cpi%20%7D%7Bb%7D%20)
. We set up to solve for b:
![\frac{ \pi }{4} = \frac{2 \pi }{b}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Cpi%20%7D%7B4%7D%20%3D%20%5Cfrac%7B2%20%5Cpi%20%7D%7Bb%7D%20)
. Cross multiply to get
![b \pi =8 \pi](https://tex.z-dn.net/?f=b%20%5Cpi%20%3D8%20%5Cpi%20)
and b = 8. Now for the phase shift. The formula for that is -c/b, and since we already know b, and we have a phase shift value of pi/2, we solve for c:
![\frac{ \pi }{2}= \frac{-c}{8}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Cpi%20%7D%7B2%7D%3D%20%5Cfrac%7B-c%7D%7B8%7D%20%20)
and
![8 \pi =-2c](https://tex.z-dn.net/?f=8%20%5Cpi%20%3D-2c)
. Therefore,
![c=-4 \pi](https://tex.z-dn.net/?f=c%3D-4%20%5Cpi%20)
. Putting all that together into the equation with the A value of 6, we have
![y=6sin(8x-4\pi)](https://tex.z-dn.net/?f=y%3D6sin%288x-4%5Cpi%29)
. Factoring out the 8 then, the final equation is
![y=6sin(8(x- \frac{\pi}{2} ))](https://tex.z-dn.net/?f=y%3D6sin%288%28x-%20%5Cfrac%7B%5Cpi%7D%7B2%7D%20%29%29)
, third choice down.
The rule for a reflection across the x-axis is (x,y)-->(x,-y). Apply this to (-4,3) and you get (-4,-3).
Answer:
320
Step-by-step explanation:
64 by 5 equals 320