Answer:
7x-13y=-117
Step-by-step explanation:
I don't know how this question wants me to solve it, but I just used the slope intercept form. So first, start off with y = mx+b. Plug in the slope for m, so 7/13. Then plug in your points for x,y which is 0,9. You'll get 9 = b. So then you have y = 7/13x+9. So now you need to change into standard form. So, multiply by the denominator (13) and you'll get 13y = 7x+117. Then move the variable over and you'll get 13y - 7x = 117. But it doesn't fit any, so then just multiply by -1 and you'll get -13y + 7x = -117.
Answer:
Midpoint = (4,4.5) or written as fraction (4,
)
Step-by-step explanation:
![MP= (\frac{x_1+x_2}{2}),(\frac{y_1+y_2}{2} ) \\MP= (\frac{8+0}{2}),(\frac{6+3}{2} ) \\MP= (\frac{8}{2}),(\frac{9}{2} ) \\MP= (4,4.5)](https://tex.z-dn.net/?f=MP%3D%20%28%5Cfrac%7Bx_1%2Bx_2%7D%7B2%7D%29%2C%28%5Cfrac%7By_1%2By_2%7D%7B2%7D%20%29%20%5C%5CMP%3D%20%28%5Cfrac%7B8%2B0%7D%7B2%7D%29%2C%28%5Cfrac%7B6%2B3%7D%7B2%7D%20%29%20%5C%5CMP%3D%20%28%5Cfrac%7B8%7D%7B2%7D%29%2C%28%5Cfrac%7B9%7D%7B2%7D%20%29%20%5C%5CMP%3D%20%284%2C4.5%29)
![f(x) = a \cos(bx + c) + d](https://tex.z-dn.net/?f=f%28x%29%20%3D%20a%20%5Ccos%28bx%20%2B%20c%29%20%20%2B%20d)
Where a is the amplitude
b is used to find the period
![\frac{2\pi}{b}](https://tex.z-dn.net/?f=%20%5Cfrac%7B2%5Cpi%7D%7Bb%7D%20%20)
The phase shift can be fined by doing
![bx + c = 0](https://tex.z-dn.net/?f=bx%20%2B%20c%20%3D%200)
then the midline is y=d.
Finding A: The amplitude is the half of the distance between the. y values of the max and the min.
![\frac{2 - ( - 3)}{2} = 2.5](https://tex.z-dn.net/?f=%20%5Cfrac%7B2%20-%20%28%20-%203%29%7D%7B2%7D%20%20%3D%202.5)
So a=2.5
Note: A is Positve never negative so if you get a negative a, take the absolute value.
Period:
Find the distance between x values,
![- 1 - ( - 4) = 3](https://tex.z-dn.net/?f=%20-%201%20-%20%28%20-%204%29%20%3D%203)
The distance between the x values of the max and min x values is half the distance of the period. So the period is 6.
![\frac{2\pi}{b} = 6](https://tex.z-dn.net/?f=%20%5Cfrac%7B2%5Cpi%7D%7Bb%7D%20%20%3D%206)
![b = \frac{\pi}{3}](https://tex.z-dn.net/?f=b%20%3D%20%20%5Cfrac%7B%5Cpi%7D%7B3%7D%20)
Note : If b is negative, take the absolute value.
Finding the midline.
To find the midline find the midpoint of the max and min y values.
![\frac{2 + ( - 3)}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B2%20%2B%20%28%20-%203%29%7D%7B2%7D%20)
![\frac{ - 1}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%20%20-%20%201%7D%7B2%7D%20)
So our midline is
![- 0.5](https://tex.z-dn.net/?f=%20-%200.5)
So as of right now, our trig formula is
![2.5 \cos( \frac{\pi}{3}x ) - 0.5](https://tex.z-dn.net/?f=2.5%20%5Ccos%28%20%5Cfrac%7B%5Cpi%7D%7B3%7Dx%20%29%20%20-%200.5)
Plug in any x or y value,
![2.5 \cos( \frac{\pi}{3} ( - 4)) - 0.5 = 2](https://tex.z-dn.net/?f=2.5%20%5Ccos%28%20%5Cfrac%7B%5Cpi%7D%7B3%7D%20%28%20-%204%29%29%20%20-%200.5%20%3D%202)
![2.5 \cos( \frac{ - 4\pi}{3} ) = 2.5](https://tex.z-dn.net/?f=2.5%20%5Ccos%28%20%5Cfrac%7B%20-%204%5Cpi%7D%7B3%7D%20%29%20%20%3D%202.5)
![\cos( \frac{ - 4\pi}{3} ) = 1](https://tex.z-dn.net/?f=%20%5Ccos%28%20%5Cfrac%7B%20-%204%5Cpi%7D%7B3%7D%20%29%20%20%3D%201)
This is not right so we need to shift this to the nearest value that is right
If we subtract,
![\frac{ - 2\pi}{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20-%202%5Cpi%7D%7B3%7D%20)
We will have a cosine value of 1.
So our phase shift is
![2.5\cos( \frac{\pi}{3} x - \frac{2\pi}{3} ) - 0.5](https://tex.z-dn.net/?f=%202.5%5Ccos%28%20%5Cfrac%7B%5Cpi%7D%7B3%7D%20x%20-%20%20%5Cfrac%7B2%5Cpi%7D%7B3%7D%20%29%20%20-%200.5)
Our phase shift would be 2 units to the right.
![2.5 \cos( \frac{\pi}{3} (x - 2)) - 0.5](https://tex.z-dn.net/?f=2.5%20%5Ccos%28%20%5Cfrac%7B%5Cpi%7D%7B3%7D%20%28x%20-%202%29%29%20%20-%200.5)
How to rationalize the denominator with square roots?
So, in order to rationalize the denominator, we need to get rid of all radicals that are in the denominator.
Step 1: Multiply numerator and denominator by a radical that will get rid of the radical in the denominator. ...
Step 2: Make sure all radicals are simplified. ...
Step 3: Simplify the fraction if needed.
hope this helps!