A is the center of the dilation because it is being delarged(is that even a word) by a factor of 2 downwards, and the only place possible to be the center of this "delargation" is A
Answer:
g(t) = 0
And
The differential equation 
is linear and homogeneous
Step-by-step explanation:
Given that,
The differential equation is -
![e^{t}y' + (9t - \frac{1}{t^{2} + 81 } )y = 0\\e^{t}y' + (\frac{9t(t^{2} + 81 ) - 1}{t^{2} + 81 } )y = 0\\e^{t}y' + (\frac{9t^{3} + 729t - 1}{t^{2} + 81 } )y = 0\\y' + [\frac{9t^{3} + 729t - 1}{e^{t}(t^{2} + 81) } ]y = 0](https://tex.z-dn.net/?f=e%5E%7Bt%7Dy%27%20%2B%20%289t%20-%20%5Cfrac%7B1%7D%7Bt%5E%7B2%7D%20%2B%2081%20%7D%20%29y%20%3D%200%5C%5Ce%5E%7Bt%7Dy%27%20%2B%20%28%5Cfrac%7B9t%28t%5E%7B2%7D%20%2B%2081%20%29%20-%201%7D%7Bt%5E%7B2%7D%20%2B%2081%20%7D%20%29y%20%3D%200%5C%5Ce%5E%7Bt%7Dy%27%20%2B%20%28%5Cfrac%7B9t%5E%7B3%7D%20%2B%20729t%20%20-%201%7D%7Bt%5E%7B2%7D%20%2B%2081%20%7D%20%29y%20%3D%200%5C%5Cy%27%20%2B%20%5B%5Cfrac%7B9t%5E%7B3%7D%20%2B%20729t%20%20-%201%7D%7Be%5E%7Bt%7D%28t%5E%7B2%7D%20%2B%2081%29%20%7D%20%5Dy%20%3D%200)
By comparing with y′+p(t)y=g(t), we get
g(t) = 0
And
The differential equation is linear and homogeneous.
It represented a vertical line that no matter what y is, x is always 6
<h3><u>
Answer:</u></h3>
Option: D
Horizontal stretching.
<h3><u>
Step-by-step explanation:</u></h3>
We have to find the effect on the graph of the function f(x)=2x when it is replaced by f(0.5 x).
We know that when a parent function f(x) is replaced by f(kx) then either the graph is stretched horizontally or shrinked horizontally.
if k>1 then the graph is shrinked horizontally.
if k<1 then the graph is stretched horizontally.
Hence here k=0.5<1 so the graph of the function is stretched horizontally.
