Answer:
Angle bisector
Step-by-step explanation:
Bisector means that the two angles have the same measure and it is an angle bisector because it is separating angles.
Like terms" are terms whose variables (and their exponents such as the 2 in x2) are the same. In other words, terms that are "like" each other. Note: the coefficients (the numbers you multiply by, such as "5" in 5x) can be different.
![f(x)=\begin{cases}x^2&\text{for }x\le2\\mx+b&\text{for }x>2\end{cases}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cbegin%7Bcases%7Dx%5E2%26%5Ctext%7Bfor%20%7Dx%5Cle2%5C%5Cmx%2Bb%26%5Ctext%7Bfor%20%7Dx%3E2%5Cend%7Bcases%7D)
In order to be differentiable everywhere,
must first be continuous everywhere, which means the limits from either side as
must be the same and equal to
. By definition,
, and
![\displaystyle\lim_{x\to2^-}f(x)=\lim_{x\to2}x^2=4](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bx%5Cto2%5E-%7Df%28x%29%3D%5Clim_%7Bx%5Cto2%7Dx%5E2%3D4)
![\displaystyle\lim_{x\to2^+}f(x)=\lim_{x\to2}(mx+b)=2m+b](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bx%5Cto2%5E%2B%7Df%28x%29%3D%5Clim_%7Bx%5Cto2%7D%28mx%2Bb%29%3D2m%2Bb)
so we need to have
.
For
to be differentiable at
, the derivative needs to be continuous at
, i.e.
![\displaystyle\lim_{x\to2^-}f'(x)=\lim_{x\to2^+}f'(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bx%5Cto2%5E-%7Df%27%28x%29%3D%5Clim_%7Bx%5Cto2%5E%2B%7Df%27%28x%29)
We then need to have
![\displaystyle\lim_{x\to2}2x=\lim_{x\to2}m\implies\boxed{m=4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bx%5Cto2%7D2x%3D%5Clim_%7Bx%5Cto2%7Dm%5Cimplies%5Cboxed%7Bm%3D4%7D)
Then
![2m+b=4\implies\boxed{b=-4}](https://tex.z-dn.net/?f=2m%2Bb%3D4%5Cimplies%5Cboxed%7Bb%3D-4%7D)
Answer:
If Hank shoots from inside the three-point line we can say that he has to shoot 246 inches to make the ball into the hoop.