Answer:
ok if u follow bwck and give me brainliest i need one more until next rank
Step-by-step explanation:
Your answer can be anything in the form y = mx+8 where you replace m with any real number.
You start with y = mx+b, and then replace the b with the y intercept 8.
The y intercept is where the polynomial crosses the y axis.
The value of m does not matter. So you could have y = 2x+8 or y = 3x+8 for instance. Replace m with whatever your favorite number is.
This is probably the hardest question I've ever had to answer. I'm going to take a wild guess and say 2?????
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Answer:
-10/3, 10/3
Step-by-step explanation:
<em>(In this answer I will use y' to denote the derivative of y with respect to t. You shouldn't normally do this because y' normally means the derivative of y with respect to x but I'll be a bit messy for this case)</em>
First calculate the derivatives:
.
Then plug the derivtes y'' and y into the equation:
![-9k^2\cos(kt) = -100\cos(kt)](https://tex.z-dn.net/?f=-9k%5E2%5Ccos%28kt%29%20%3D%20-100%5Ccos%28kt%29)
Solve the equation for k:
![100\cos(kt) - 9k^2\cos(kt) = 0 \\\\\Rightarrow \cos(kt)(100-9k^2) = 0](https://tex.z-dn.net/?f=100%5Ccos%28kt%29%20-%209k%5E2%5Ccos%28kt%29%20%3D%200%20%5C%5C%5C%5C%5CRightarrow%20%5Ccos%28kt%29%28100-9k%5E2%29%20%3D%200)
So then we have that
satisfies the differential equation when
or when
(or both). The solutions to these equations are:
![\left \{ {{\cos(kt)=0 \Rightarrow k=\frac{n\pi}{2t}} \atop {100-9k^2 = 0 \Rightarrow k= \pm \sqrt{\frac{100}{9}}=\pm \frac{10}{3}}} \right.](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7B%5Ccos%28kt%29%3D0%20%5CRightarrow%20k%3D%5Cfrac%7Bn%5Cpi%7D%7B2t%7D%7D%20%5Catop%20%7B100-9k%5E2%20%3D%200%20%5CRightarrow%20k%3D%20%5Cpm%20%5Csqrt%7B%5Cfrac%7B100%7D%7B9%7D%7D%3D%5Cpm%20%5Cfrac%7B10%7D%7B3%7D%7D%7D%20%5Cright.)
I understand that looks a bit complicated and I doubt you would have to give your answers in terms of t so if it asks for a separated list of answers I would go for:
k = -10/3, 10/3.