anonymous
  • anonymous
If the length of an arc is 12 inches and the radius of the circle is 10 inches, what is the measure of the arc? 216 degrees 270 degrees 288 degrees
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
@campbell_st whered that answer go?
wampominater
  • wampominater
do you still need help?
anonymous
  • anonymous
yes please...

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wampominater
  • wampominater
ok
wampominater
  • wampominater
so, the first thing you need is the formula for arc length, which is \[arclength = 2piR(\frac{ \theta }{ 360 })\]
wampominater
  • wampominater
now, look at the values you are given
wampominater
  • wampominater
you have the arc length and the radius, so plug those in.
wampominater
  • wampominater
and what do you get when you do that?
anonymous
  • anonymous
where am i plugging the arc length into?
wampominater
  • wampominater
look at the formula, see where it says arc length? you plug the value you have for arc length right there.
anonymous
  • anonymous
yeah and i can plug in the radius too. but what am i solving for?|dw:1438157454848:dw|
wampominater
  • wampominater
yep! now you want to solve for theta.
anonymous
  • anonymous
theta?
wampominater
  • wampominater
so to make it easier, replace theta with x. it is the symbol in the numerator of the fraction: \[\theta\]
anonymous
  • anonymous
oh okay.
wampominater
  • wampominater
so the first step is to isolate x, the best way to do that is to first deal with everything outside the parenthesis
wampominater
  • wampominater
you know all the values for those, just solve 2πr
wampominater
  • wampominater
and then, what you want to do is divide both sides by the value that you get for 2πr, which will isolate the fraction and let you solve that next
anonymous
  • anonymous
62.8?
wampominater
  • wampominater
yep!
wampominater
  • wampominater
now divide both sides by 62.8
wampominater
  • wampominater
what do you get?
anonymous
  • anonymous
okay |dw:1438157770787:dw| now divide by it?
wampominater
  • wampominater
mhm, so it would be 12 over 62.8
wampominater
  • wampominater
that leaves you with \[\frac{ 12 }{ 62.8 } = \frac{ x }{ 360 }\]
wampominater
  • wampominater
now, go ahead and divide 12 by 62.8, what does that get you?
anonymous
  • anonymous
couldnt you do that as a proportion?
wampominater
  • wampominater
yes, you could if you like
anonymous
  • anonymous
seems easier
anonymous
  • anonymous
|dw:1438157995138:dw|
wampominater
  • wampominater
yep! so that would be the answer i believe.
anonymous
  • anonymous
isnt right
wampominater
  • wampominater
hmm, let me see if i did something wrong
anonymous
  • anonymous
yeah man
wampominater
  • wampominater
hmm, im not sure what I did Wrong, sorry :(
anonymous
  • anonymous
|dw:1438158390561:dw|
anonymous
  • anonymous
@aric200
UsukiDoll
  • UsukiDoll
actually there is a dupe question and that also led to a dead end http://openstudy.com/study#/updates/52eafc6ae4b0d95ca6b32d90
wampominater
  • wampominater
hmm, could be the question then? idk if you looked at the work usuki, is it right?
anonymous
  • anonymous
its supposed to be 12 pi and copy paste takes out the pi part
UsukiDoll
  • UsukiDoll
I think the question is a bit screwed up... yes ! 12 pi that's what we need
wampominater
  • wampominater
there we go! lol
wampominater
  • wampominater
ok so then, it is 12π and not 12?
UsukiDoll
  • UsukiDoll
anonymous
  • anonymous
yep
wampominater
  • wampominater
alright, do you need help still then or are you good?
anonymous
  • anonymous
so its 216?
UsukiDoll
  • UsukiDoll
I don't know if I should touch on this.. if there's a duplicate question. why not look at the past and learn in the future?
wampominater
  • wampominater
good point, i didnt look :p
wampominater
  • wampominater
yes it is 216
UsukiDoll
  • UsukiDoll
I could go over it for verification purposes so given radius at 10 ( r = 10) Arc length is 12pi (s=12pi) we need theta \[s = \theta r \rightarrow \frac{s}{r} = \theta \] \[\frac{12 \pi}{10} = \theta \] that bad boy is in radians and we need degrees so multiply that 12pi/10 with 180/pi so the pi's cancel \[\frac{12 \pi}{10} \cdot \frac{180}{\pi} = \theta \] \[\frac{12 }{10} \cdot \frac{180}{1} = \theta \] \[\frac{2160}{10} = \theta \] \[216 = \theta \]
anonymous
  • anonymous
what would be the symbol/variable for arc length?
UsukiDoll
  • UsukiDoll
arc length is s radius is r angle is the theta
wampominater
  • wampominater
Alright, well thanks for the Help @UsukiDoll , ill be more careful in the future. goodnight!

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