Answer:
Step-by-step explanation:
![y = x + 4 \\ equating \: it \: with \\ y = mx + c \\ m = \boxed{1} \: \: c = \boxed{4}](https://tex.z-dn.net/?f=y%20%3D%20x%20%2B%204%20%5C%5C%20equating%20%5C%3A%20it%20%5C%3A%20with%20%5C%5C%20y%20%3D%20mx%20%2B%20c%20%5C%5C%20%20m%20%3D%20%20%5Cboxed%7B1%7D%20%5C%3A%20%20%5C%3A%20c%20%3D%20%20%5Cboxed%7B4%7D)
Compute the necessary values/derivatives of
at
:
![f(1)=3](https://tex.z-dn.net/?f=f%281%29%3D3)
![f'(1)=2](https://tex.z-dn.net/?f=f%27%281%29%3D2)
![f''(1)=-12](https://tex.z-dn.net/?f=f%27%27%281%29%3D-12)
![f'''(1)=-12](https://tex.z-dn.net/?f=f%27%27%27%281%29%3D-12)
![f^{(4)}(1)=48](https://tex.z-dn.net/?f=f%5E%7B%284%29%7D%281%29%3D48)
![f^{(5)}(1)=120](https://tex.z-dn.net/?f=f%5E%7B%285%29%7D%281%29%3D120)
Taylor's theorem then says we can "approximate" (in quotes because the Taylor polynomial for a polynomial is another, exact polynomial)
at
by
![T_5(x)=\dfrac3{0!}+\dfrac2{1!}(x-1)-\dfrac{12}{2!}(x-1)^2-\dfrac{12}{3!}(x-1)^3+\dfrac{48}{4!}(x-1)^4+\dfrac{120}{5!}(x-1)^5](https://tex.z-dn.net/?f=T_5%28x%29%3D%5Cdfrac3%7B0%21%7D%2B%5Cdfrac2%7B1%21%7D%28x-1%29-%5Cdfrac%7B12%7D%7B2%21%7D%28x-1%29%5E2-%5Cdfrac%7B12%7D%7B3%21%7D%28x-1%29%5E3%2B%5Cdfrac%7B48%7D%7B4%21%7D%28x-1%29%5E4%2B%5Cdfrac%7B120%7D%7B5%21%7D%28x-1%29%5E5)
![T_5(x)=3+2(x-1)-6(x-1)^2-2(x-1)^3+2(x-1)^4+(x-1)^5](https://tex.z-dn.net/?f=T_5%28x%29%3D3%2B2%28x-1%29-6%28x-1%29%5E2-2%28x-1%29%5E3%2B2%28x-1%29%5E4%2B%28x-1%29%5E5)
###
Another way of doing this would be to solve for the coefficients
in
![f(x)=a+b(x-1)+c(x-1)^2+d(x-1)^3+e(x-1)^4+g(x-1)^5](https://tex.z-dn.net/?f=f%28x%29%3Da%2Bb%28x-1%29%2Bc%28x-1%29%5E2%2Bd%28x-1%29%5E3%2Be%28x-1%29%5E4%2Bg%28x-1%29%5E5)
by expanding the right hand side and matching up terms with the same power of
.
You would earn $33.60 of interest
Explanation: To find the interest you would multiply 210 by .08 (the percent in its decimal form) by 2 to get 33.60
Well we know that:
1-4 stay on the floor,
5-9 it's round up time.
So with that in mind you would round the 9's up and they would round up th 4 to a 5. 5's round up so that would round up the first 4 to a 5.
SO your answer would be 5,000.
Answer:
1 black
Step-by-step explanation:
one more black to reach 3:2