2 years ago

a circle with a circumference of 6 has an arc with a 20 degree central angle.What is the length of the arc

Mathematics

1 answer:

alex41 [277]2 years ago

7 0

Answer:

2.094395 ft

Step-by-step explanation:

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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

X:y=5:3 and x+y=56 work out he value of x-y

Alex

Answer:14

Step-by-step explanation:

x+y=56

x:y=5:3

Sum of ratio=5+3

Sum of ratio=8

x=5/8x56

x=(5x56) ➗ 8

x=280 ➗ 8

x=35

y=3/8x56

y=(3x56) ➗ 8

y=168 ➗ 8

y=21

x-y

35-21=14

x-y=14

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