Answer:
Step-by-step explanation:
tan42=32/w and tan48=39/w
w=32/tan42 and w=39/tan48
w=35.54 and w=35.12
35yd is the closest to either of the above widths.
Answer:
y=-21/2x+5
Step-by-step explanation:
slope from two points
Answer:
![P(x) = x - x^2 + x^3 - x^4+x^5](https://tex.z-dn.net/?f=P%28x%29%20%3D%20x%20-%20x%5E2%20%2B%20x%5E3%20-%20x%5E4%2Bx%5E5)
Step-by-step explanation:
Let us first remember how a Taylor polynomial looks like:
Given a differentiable function
then we can find its Taylor series to the
degree as follows:
![P(x) = f(x_{0}) + f'(x_{0}).(x-x_{0}) + \frac{f''(x_{0})}{2!}.(x-x_{0})^2+.....+\frac{f^n(x_{0})}{n!}.(x-x_{0})^n + R_{n}(x).(x-x_{0})^n](https://tex.z-dn.net/?f=P%28x%29%20%3D%20f%28x_%7B0%7D%29%20%2B%20f%27%28x_%7B0%7D%29.%28x-x_%7B0%7D%29%20%2B%20%5Cfrac%7Bf%27%27%28x_%7B0%7D%29%7D%7B2%21%7D.%28x-x_%7B0%7D%29%5E2%2B.....%2B%5Cfrac%7Bf%5En%28x_%7B0%7D%29%7D%7Bn%21%7D.%28x-x_%7B0%7D%29%5En%20%2B%20R_%7Bn%7D%28x%29.%28x-x_%7B0%7D%29%5En)
Where
represents the <em>Remainder </em>and
is the
derivative of
.
So let us find those derivatives.
![f(x) = \frac{x}{1+x}\\f'(x) = \frac{1}{(1+x)^2}\\f''(x) = \frac{-2}{(1+x)^3}\\f'''(x) = \frac{6}{(1+x)^4}\\f''''(x) = \frac{-24}{(1+x)^5}\\f'''''(x) = \frac{120}{(1+x)^6}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7Bx%7D%7B1%2Bx%7D%5C%5Cf%27%28x%29%20%3D%20%5Cfrac%7B1%7D%7B%281%2Bx%29%5E2%7D%5C%5Cf%27%27%28x%29%20%3D%20%5Cfrac%7B-2%7D%7B%281%2Bx%29%5E3%7D%5C%5Cf%27%27%27%28x%29%20%3D%20%5Cfrac%7B6%7D%7B%281%2Bx%29%5E4%7D%5C%5Cf%27%27%27%27%28x%29%20%3D%20%5Cfrac%7B-24%7D%7B%281%2Bx%29%5E5%7D%5C%5Cf%27%27%27%27%27%28x%29%20%3D%20%5Cfrac%7B120%7D%7B%281%2Bx%29%5E6%7D)
The only trick for this derivatives is for the very first one:
![f'(x) = \frac{1}{1+x} - \frac{x}{(1+x)^2}\\f'(x) = \frac{(1+x) - x}{(1+x)^2} = \frac{1}{(1+x)^2}\\](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20%5Cfrac%7B1%7D%7B1%2Bx%7D%20-%20%5Cfrac%7Bx%7D%7B%281%2Bx%29%5E2%7D%5C%5Cf%27%28x%29%20%3D%20%5Cfrac%7B%281%2Bx%29%20-%20x%7D%7B%281%2Bx%29%5E2%7D%20%3D%20%5Cfrac%7B1%7D%7B%281%2Bx%29%5E2%7D%5C%5C)
Then it's only matter of replacing on the Taylor Series and replacing ![x_{0}=0](https://tex.z-dn.net/?f=x_%7B0%7D%3D0)
Answer:
♡(> ਊ <)♡ ʕ ꈍᴥꈍʔ
Step-by-step explanation:
(〃゚3゚〃)
Answer:
1) 3*0.7 = 2.1 pounds
2) 3.7*3.9 = 14.43 miles long
3) 20.64/2 = $10.32 each
4) (2*13.75)/(5+6) = $2.50 each