Ac3
  • Ac3
Simplify the following expression.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Ac3
  • Ac3
\[\sqrt{(7xcosx)^2+(-7xsinx+14cosx)^2}\]
Ac3
  • Ac3
the farthest i got to was\[\sqrt{49x^2-196sinxcosx+196\cos^2x}\]
Ac3
  • Ac3
We want the radical to go away if possible or get the least amount of terms under the radical at least.

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Ac3
  • Ac3
Any idea @Preetha ?
anonymous
  • anonymous
if you are lucky it is a prefect square
anonymous
  • anonymous
doesn't look like one though, maybe some other trick
Ac3
  • Ac3
I factored out a 49 and pulled it out of the radical. I was thinking maybe a trig identity for cos^2x not sure though.
freckles
  • freckles
was that thing really the initial problem?
Ac3
  • Ac3
Well if you want the initial problem I'll go ahead and give it to you.
anonymous
  • anonymous
the 49 comes out for sure not sure what else you can do here
anonymous
  • anonymous
graph if cool http://www.wolframalpha.com/input/?i=sqrt%28%287xcos%28x%29%29^2%2B%28-7xsin%28x%29%2B14cos%28x%29%29^2%29
anonymous
  • anonymous
*is
Ac3
  • Ac3
r(t)=(7tsint+7cost)i + 7j + (7tcost-7sint)k, Find the Tangential, Normal, Binormal, and the Torsion.
Ac3
  • Ac3
I think that's as far as it's going to go if I pull out the 49.
freckles
  • freckles
tangential is just ... \[|r'(t)| \text{ }\] \[r'(t)=[7 \sin(t)+7t \cos(t)-7\sin(t)]i+[0]j+[7 \cos(t)-7 t \sin(t)-7 \cos(t)]k \\ r'(t)=7 t \cos(t) i -7t \sin(t) k\]
freckles
  • freckles
\[|r'(t)|=\sqrt{(7 t \cos(t))^2+(-7 t \sin(t))^2}\]
freckles
  • freckles
this looks prettier
Ac3
  • Ac3
wait hold on let me check your derivative because I checked mine like 4 times.
freckles
  • freckles
it looks like your k component was different
freckles
  • freckles
yeah seems like you wrote 7cos(t)-7 cos(t) as 7 cos(t)+7 cos(t) instead
Ac3
  • Ac3
ahhhhhhhh i screwed up the last part!!!!!
Ac3
  • Ac3
thanks freckles.
freckles
  • freckles
np
Ac3
  • Ac3
derivative of -7sint = 7cost <--- lmfao i'm an idiot.
freckles
  • freckles
maybe for a sec you got antiderivative and derivative mixed up :p it happens to all of us especially on those crazy trig functions
Ac3
  • Ac3
It happens to me all the time.
Ac3
  • Ac3
I've been doing way too many integrals
freckles
  • freckles
anyways glad i can help
Ac3
  • Ac3
see ya man thx again!
freckles
  • freckles
peace

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