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3 years ago

In a circle of radius 1, what is the length of an arc cut off by a central angle of 2 radians?

Mathematics

1 answer:

slamgirl [31]3 years ago

8 0

Answer:

What is the length of an arc cut off?

If θ (in radians) is a central angle in a circle with radius r, then the length of the arc cut off by θ is given by s = r θ (θ is in radians).

Step-by-step explanation:

Length of an Arc = θ × r, where θ is in radian.

Length of an Arc = θ × (π/180) × r, where θ is in degree.

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Find the sum of the first 8 terms of the series. 1/2 + 1 + 2 + 4

Roman55 [17]

$\bf \cfrac{1}{2}~~,~~\stackrel{2\cdot \frac{1}{2}}{1}~~,~~\stackrel{2\cdot 1}{2}~~,~~\stackrel{2\cdot 2}{4}~~,...$

so as you can see the common ratio is 2, and the first term is 1/2,

$\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ r=2\\ a_1=\frac{1}{2}\\ n=8 \end{cases} \\\\\\ S_8=\cfrac{1}{2}\left( \cfrac{1-2^8}{1-2} \right)\implies S_8=\cfrac{1}{2}\left( \cfrac{-255}{-1} \right)\implies S_8=\cfrac{255}{2}$

4 0

4 years ago

Read 2 more answers

Coffee with sugar and milk added to it can contain up to calories. To consume a maximum of 600 mg if caffeine per day, how many

Marina CMI [18]

We know there is 330 mg of caffeine per 16-ounce serving. So if we want 8-ounce servings:
330 mg : 2 = 165 mg
Also we have to consume a maximum of 600 mg.
165 mg * 3 = 495 mg < 600 mg
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Answer: Someone could drink 3 full 8-ounce servings in a day and still stay below the limit.

8 0

3 years ago

Read 2 more answers

I forgot how to do this, can someone help me-

Artyom0805 [142]

Step-by-step explanation:

1) x/20 = -9

By cross multiplication,

x = -180

2) -168 = -14k

k = -168/-14

k = 12

3) -5m = -50

m = 10

4) -320 = -20n

n = 16

5) -4 = x - 5

x = 1

6) -6(-8 + n) = -54

42 - 6n = -54

-6n = -54 -52

6n = 106

n = 17.6

7) 3(x - 9) = -3

3x - 27 = -3

3x = 24

x = 8

8) 9k + 3 = -78

9k = -81

k = -9

9)4 + (n/4) = 8

By taking LCM,

16 + n/4 = 8

16 + n = 32

n = 16

10) -5r + 7 = -73

-5r = -80

r = 16

Hope it helps.

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2 years ago

Given f(x) =3x+7 find f(5)

ra1l [238]

Answer:

Step-by-step explanation:

f (5)=3 (5)+7

f (5)=15+7

f (5)=22

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3 years ago

Help me quickly 1/2 -1/2 2 -2

Pavlova-9 [17]

Answer:

$\frac{-1}{2}$

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3 years ago