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.
Answer:
7/16
Step-by-step explanation:
1. you have to have the same denominator
If n = $3 then plug it in
$10 + ($6-$3)
$6-$3 = $3
$10 + $3 = $13
Answer:
$40.4
Step-by-step explanation:
The regular price of the fishing rod is $97
There is a 60% discount from that price.
The discount is equal to 60% of $97 which is equal to .60 * $97 which is equal to $58.2
Discount is like a markdown, so subtract $58.2 from the price of the item before the change to get $97 - $58.2 = $38.8
This is the price of the item before tax is applied.
Now you apply the sales tax of 4%.
4% of $38.8 is equal to .04 * $38.8 which is equal to $1.552
Tax is like a markup, so add $1.552 to the price of the item before tax was applied to get a selling price of $38.8 + $1.552 which is equal to $40.352
Round it up and the answer is $40.4
