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anonymous
 one year ago
I'm not fully understanding this and need help.
Points A and B lie on a circle centered at point O. If length of own AB/radius=π/10, what is the ratio of the area of sector AOB to the area of the circle?
A.) 1/10
B.) π/10
C.) 1/20
D.) π/20
I already know B isn't the answer. I'm thinking A is.
anonymous
 one year ago
I'm not fully understanding this and need help. Points A and B lie on a circle centered at point O. If length of own AB/radius=π/10, what is the ratio of the area of sector AOB to the area of the circle? A.) 1/10 B.) π/10 C.) 1/20 D.) π/20 I already know B isn't the answer. I'm thinking A is.

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phi
 one year ago
Best ResponseYou've already chosen the best response.1when you say "own AB" do you mean "arc AB" ?

phi
 one year ago
Best ResponseYou've already chosen the best response.1there is an expression \[ r \theta = s\] which means radius times the angle (in radians) = the length of the arc

phi
 one year ago
Best ResponseYou've already chosen the best response.1for your problem, where we use arc AB instead of "s" \[ r \theta = arc AB \] if we divide both sides by r we get \[ \theta = \frac{arc\ AB}{r} \] the question says that is pi/10 \[ \theta = \frac{arc\ AB}{r} = \frac{\pi}{10}\]

phi
 one year ago
Best ResponseYou've already chosen the best response.1I think you want the ratio of theta (the angle of the sector) divided by 2pi (the angle of the whole circle)

phi
 one year ago
Best ResponseYou've already chosen the best response.1or instead of dividing theta by 2pi, multiply by 1/(2pi)

phi
 one year ago
Best ResponseYou've already chosen the best response.1the idea is the angle of sector / 2pi is the fraction of the whole circle we want to know \[ \frac{\pi}{10} \cdot \frac{1}{2 \pi} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So I would solve that?

phi
 one year ago
Best ResponseYou've already chosen the best response.1strictly speaking you only solve equations (which have = signs) in this case, you simplify. notice you have a pi "up top" and "down below" which means pi/pi = 1 (i.e. it cancels) to multiply the fraction, you multiply top time top and bottom times bottom (and of course simplify pi/pi to 1)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So replace both pi with 1 (I'm trying to fully understand ^^;)

phi
 one year ago
Best ResponseYou've already chosen the best response.1it works the same way as with numbers. for example if you had 6/3 (which we know is 2) but we write it as \[ \frac{3\cdot 2}{3} = \frac{3}{3} \cdot 2 = 1 \cdot 2 = 2\]

phi
 one year ago
Best ResponseYou've already chosen the best response.1think of the pi as the "3" in that example \[ \frac{\pi}{10} \cdot \frac{1}{2 \pi} = \frac{\pi}{\pi} \cdot \frac{1}{10 \cdot 2} \]

phi
 one year ago
Best ResponseYou've already chosen the best response.12pi means 2 * pi so the top is 1*pi the bottom is 2*10*pi and the pi's cancel

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh I understand it now. The pi would cancel out and then the answer would pretty much be right in front of you. (As you just said)

phi
 one year ago
Best ResponseYou've already chosen the best response.1the top simplifies to 1 the bottom to 2*10 which (I assume) you know is 20
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