Question

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

Answer 1

\(s^2=\int_0^{48/360*2\pi}1+f'(x)^2dx\)
putting in the values:
\(16^2=\int_0^{48/360*2\pi}1dx+\int_0^{48/360*2\pi}f`(x)^2dx\)
continue

Answer 2

ok so that's the formula how to I cantinur to solve from there?

Answer 3

continue

Answer 4

Is this a trig class? are you using integrals, or the non-calculus arc length formula

\[\Large s=\alpha r\] (with \(\alpha\) in radians)??

Answer 5

its my pre calc class

Answer 6

just havinga a total brain fart on this one

Answer 7

these are my choices
sixty divided by pi cm

thirty divided by pi cm

one third cm

one hundred twenty divided by pi cm

Answer 8

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.

Answer 9

convert 48 degrees to radians then?

Answer 10

yes

Answer 11

Do it EXACTLY, don't reach for your calculator. ;)

Answer 12

if so that's \[\frac{ 4pie }{ 15 }\]

Answer 13

Yes, that's it.

Answer 14

\pi will give you \(\pi\) in the equation editor, btw. :)

Answer 15

so\[16=\frac{ 4pie }{ 15 } ?\]

Answer 16

don't forget r! that's what you're solving for!

Answer 17

so where does r go in that eqAUTION?

Answer 18

oops caps

Answer 19

\(\Large 16=\dfrac{ 4\pi }{ 15 }\cdot r\)

Answer 20

ok then uhmmm times r on both sides orrrr?

Answer 21

this is the general equation for arc length:
\(\Large s=\alpha r\) you're just plugging in the parts, and now solve for r.

Answer 22

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.

Answer 23

mmmmmmmm soooooo do I multiply reciperic or multiply bothtop and bottom by 15? sorry im trying I promise

Answer 24

so its \[\frac{ 60 }{ \pi }\] correct?

Answer 25

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).

Answer 26

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.

Answer 27

so the answer isn't 60 over pie?

Answer 28

lol.. yes, it is, that was my "yes" above. That's the correct answer. :)

But do YOU understand WHY?

Answer 29

yes I do now thank you so much !

Answer 30

You're welcome! :) happy to help.