anonymous
  • anonymous
please help :) Use the arc length formula and the given information to find r. s = 16 cm, θ = 48°; r = ? sixty divided by pi cm thirty divided by pi cm one third cm one hundred twenty divided by pi cm
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\(s^2=\int_0^{48/360*2\pi}1+f'(x)^2dx\) putting in the values: \(16^2=\int_0^{48/360*2\pi}1dx+\int_0^{48/360*2\pi}f`(x)^2dx\) continue
anonymous
  • anonymous
ok so that's the formula how to I cantinur to solve from there?
anonymous
  • anonymous
continue

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More answers

DebbieG
  • DebbieG
Is this a trig class? are you using integrals, or the non-calculus arc length formula \[\Large s=\alpha r\] (with \(\alpha\) in radians)??
anonymous
  • anonymous
its my pre calc class
anonymous
  • anonymous
just havinga a total brain fart on this one
anonymous
  • anonymous
these are my choices sixty divided by pi cm thirty divided by pi cm one third cm one hundred twenty divided by pi cm
DebbieG
  • DebbieG
Well, if it's pre-calc, then I doubt you're doing integrals yet. The formula \(\Large s=\alpha r\) should look familiar though. But you have to convert to radians. \[\Large \alpha \cdot\frac{ \pi }{ 180 }\] will convert from degrees to radians. Then set up the equation with the formula, and solve it for r.
anonymous
  • anonymous
convert 48 degrees to radians then?
DebbieG
  • DebbieG
yes
DebbieG
  • DebbieG
Do it EXACTLY, don't reach for your calculator. ;)
anonymous
  • anonymous
if so that's \[\frac{ 4pie }{ 15 }\]
DebbieG
  • DebbieG
Yes, that's it.
DebbieG
  • DebbieG
\pi will give you \(\pi\) in the equation editor, btw. :)
anonymous
  • anonymous
so\[16=\frac{ 4pie }{ 15 } ?\]
DebbieG
  • DebbieG
don't forget r! that's what you're solving for!
anonymous
  • anonymous
so where does r go in that eqAUTION?
anonymous
  • anonymous
oops caps
DebbieG
  • DebbieG
\(\Large 16=\dfrac{ 4\pi }{ 15 }\cdot r\)
anonymous
  • anonymous
ok then uhmmm times r on both sides orrrr?
DebbieG
  • DebbieG
this is the general equation for arc length: \(\Large s=\alpha r\) you're just plugging in the parts, and now solve for r.
DebbieG
  • DebbieG
If you multiply by r on both sides, you'll have \(r^2\) on the right, and and r on the left. That is not useful, you want to ISOLATE r, so you need to deal with the \(\Large \dfrac{ 4\pi }{ 15 }\) coefficient. NOT the r.
anonymous
  • anonymous
mmmmmmmm soooooo do I multiply reciperic or multiply bothtop and bottom by 15? sorry im trying I promise
anonymous
  • anonymous
so its \[\frac{ 60 }{ \pi }\] correct?
DebbieG
  • DebbieG
yes, the most direct way is just to multiply both sides by the reciprocal (since you have a rational coefficient and need to get it to the other side).
DebbieG
  • DebbieG
multiplying "top and bottom" by 15 would not be useful. :) But, you could also do it in "2 steps", multiplying both SIDES by 15, and then dividing both sides by 4... that would work as well.
anonymous
  • anonymous
so the answer isn't 60 over pie?
DebbieG
  • DebbieG
lol.. yes, it is, that was my "yes" above. That's the correct answer. :) But do YOU understand WHY?
anonymous
  • anonymous
yes I do now thank you so much !
DebbieG
  • DebbieG
You're welcome! :) happy to help.

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