your answer will be
answer: 1/4 in.
Answer:
y = 1/2x - 7
Step-by-step explanation:
y = mx + b
m (slope) = 1/2
x = 4
y = -5
<em>substitute</em>
-5 = 1/2 * 4 + b
-5 = 2 + b
-5 -2 = b
-7 = b
y = mx + b
y = 1/2x -7
We can use the fact that, for
,

Notice that
![\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1{1-x}\right]=\dfrac1{(1-x)^2}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5B%5Cdfrac1%7B1-x%7D%5Cright%5D%3D%5Cdfrac1%7B%281-x%29%5E2%7D)
so that
![f(x)=\displaystyle\frac5{(1-x)^2}=5\frac{\mathrm d}{\mathrm dx}\left[\sum_{n=0}^\infty x^n\right]](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdisplaystyle%5Cfrac5%7B%281-x%29%5E2%7D%3D5%5Cfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5B%5Csum_%7Bn%3D0%7D%5E%5Cinfty%20x%5En%5Cright%5D)



By the ratio test, this series converges if

so the series has radius of convergence
.
Answer:
x-2y=0 is a direct variation
Step-by-step explanation:
Direct variation is of the form
y= kx
Can we get the equation in that form
x-2y =0
Add 2y to each side
x-2y+2y =0_2y
x=2y
Divide each side by 2
x/2 = 2y/2
1/2x =y
Flip the sides
y = 1/2x
This is of the form y= kx where k = 1/2
x-2y=0 is a direct variation