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2 years ago

5

A park ranger would like to clear more than 10 miles of trail. So far, he has cleared 2 miles. From now on, he can clear 3/4 mil

e of trail each hour

1 answer:

Scilla [17]2 years ago

6 0

It would take 7:30 minutes to clear the rest of the 10 miles.

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find the Taylor Series for tan−1(x) based at 0. Give your answer using summation notation and give the largest open interval on

enyata [817]

Let $f(x)=\tan^{-1}x$ . Then $f'(x)=\frac1{1+x^2}$ . Note that $f(0)=0$ .

Recall that for $|x|$ , we have

$\displaystyle\frac1{1-x}=\sum_{n\ge0}x^n$

This means that for $|-x^2|=|x|^2$ , or $-1$ , we have

$\displaystyle f'(x)=\frac1{1+x^2}=\frac1{1-(-x^2)}=\sum_{n\ge0}(-x^2)^n=\sum_{n\ge0}(-1)^nx^{2n}$

Integrate the series to get

$f(x)=f(0)+\displaystyle\sum_{n\ge0}\frac{(-1)^n}{2n+1}x^{2n+1}$

$\implies\tan^{-1}x=\displaystyle\sum_{n\ge0}\frac{(-1)^n}{2n+1}x^{2n+1}$

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2 years ago

Give an example of two whole number factors with a product of 9

Monica [59]

3 and 3 or 1 and 9 not really sure of anything else

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2 years ago

There is 6 7/8 cups now i take 2 5/8 away how many is left ?

REY [17]

left means subtracting

6 7/8 - 2 5/8

Whole numbers subtract each other

Numerators subtract each other

The denominators stay the same.

6-2= 4

7-5=2

4 2/8

Reduce 2/8. Divide by 2. 2/2= 1, 8/2= 4

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Answer: 4 2/8 = 4 1/4 cups left

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3 years ago

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zheka24 [161]

Answer: Adjacent Angles

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