Answer:
irrational
Step-by-step explanation:
The formula to calculate the missing arc is,
![m\angle T=\frac{1}{2}\times m\angle arcTS](https://tex.z-dn.net/?f=m%5Cangle%20T%3D%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20m%5Cangle%20arcTS)
where,
![m\angle arcTS=146^0](https://tex.z-dn.net/?f=m%5Cangle%20arcTS%3D146%5E0)
Therefore,
![\begin{gathered} m\angle T=\frac{1}{2}\times146^0=73^0 \\ \therefore m\angle T=73^0 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20m%5Cangle%20T%3D%5Cfrac%7B1%7D%7B2%7D%5Ctimes146%5E0%3D73%5E0%20%5C%5C%20%5Ctherefore%20m%5Cangle%20T%3D73%5E0%20%5Cend%7Bgathered%7D)
Hence, the answer is
Answer:
8+2=10
Step-by-step explanation:
A negative minus a negative equals a positive. So 8-(-2) would go to 8+2
First, we need to solve the differential equation.
![\frac{d}{dt}\left(y\right)=2y\left(1-\frac{y}{8}\right)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%28y%5Cright%29%3D2y%5Cleft%281-%5Cfrac%7By%7D%7B8%7D%5Cright%29)
This a separable ODE. We can rewrite it like this:
![-\frac{4}{y^2-8y}{dy}=dt](https://tex.z-dn.net/?f=-%5Cfrac%7B4%7D%7By%5E2-8y%7D%7Bdy%7D%3Ddt)
Now we integrate both sides.
![\int \:-\frac{4}{y^2-8y}dy=\int \:dt](https://tex.z-dn.net/?f=%5Cint%20%5C%3A-%5Cfrac%7B4%7D%7By%5E2-8y%7Ddy%3D%5Cint%20%5C%3Adt)
We get:
![\frac{1}{2}\ln \left|\frac{y-4}{4}+1\right|-\frac{1}{2}\ln \left|\frac{y-4}{4}-1\right|=t+c_1](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5Cln%20%5Cleft%7C%5Cfrac%7By-4%7D%7B4%7D%2B1%5Cright%7C-%5Cfrac%7B1%7D%7B2%7D%5Cln%20%5Cleft%7C%5Cfrac%7By-4%7D%7B4%7D-1%5Cright%7C%3Dt%2Bc_1)
When we solve for y we get our solution:
![y=\frac{8e^{c_1+2t}}{e^{c_1+2t}-1}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B8e%5E%7Bc_1%2B2t%7D%7D%7Be%5E%7Bc_1%2B2t%7D-1%7D)
To find out if we have any horizontal asymptotes we must find the limits as x goes to infinity and minus infinity.
It is easy to see that when x goes to minus infinity our function goes to zero.
When x goes to plus infinity we have the following:
![$$\lim_{x\to\infty} f(x)$$=y=\frac{8e^{c_1+\infty}}{e^{c_1+\infty}-1} = 8](https://tex.z-dn.net/?f=%24%24%5Clim_%7Bx%5Cto%5Cinfty%7D%20f%28x%29%24%24%3Dy%3D%5Cfrac%7B8e%5E%7Bc_1%2B%5Cinfty%7D%7D%7Be%5E%7Bc_1%2B%5Cinfty%7D-1%7D%20%3D%208%20)
When you are calculating limits like this you always look at the fastest growing function in denominator and numerator and then act like they are constants.
So our asymptote is at y=8.
The answer is B because its where the two lines intersect or cross each other