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anonymous
 one year ago
I need help figuring out the wording to this Calc 2 problem
anonymous
 one year ago
I need help figuring out the wording to this Calc 2 problem

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Consider the parametric equation \[x = 16(\cos \theta + \theta \sin \theta)\] \[y = 16( \sin \theta  \theta \cos \theta)\] What is the length of the curve for \[0 \le \theta \le \frac{ 11 }{ 8 }\pi\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I understand what the arc length means, but the equations have two separate arcs over the interval

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@mathstudent55 you seem like the most qualified person answering right now, I just need to understand what it's asking for, I can do the math myself

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2\[\int_{a}^{b} ds\] given that ds is \[ds=\sqrt{(x')^2+(y')^2}dt\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Where does this equation come from? Just so I have a base of understanding. I don't remember seeing anything like that in lecture

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2its just the result of takeing the segment of an arc ... and comparing it to a right triangle

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2dw:1439771344418:dw

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2as we work our way to infinitesimals we get: dw:1439771398544:dw and the pythag takes care of the rest

thomas5267
 one year ago
Best ResponseYou've already chosen the best response.0Wikipedia is your friend. https://en.wikipedia.org/wiki/Arc_length#Finding_arc_lengths_by_integrating

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2x=16(cos(t) +t sin(t)) x' = 16(cos(t)+sin(t) +t cos(t)) dt y=16(sin(t) t cos(t)) y'=16(cos(t) cos(t) +t sin(t)) dt

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2if we can eliminate the parameter, and make y a function of x, then x'=1 ... but thats not always a simple case is it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So that equation accounts for the two arcs?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2yes, whether it makes life simpler or not ... thats to be seen :)

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2\[\int~ds\implies\int_{a}^{b}\sqrt{(\frac{dx}{dt})^2+(\frac{dy}{dt})^2}~dt\]

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2http://tutorial.math.lamar.edu/Classes/CalcII/ParaArcLength.aspx

thomas5267
 one year ago
Best ResponseYou've already chosen the best response.0\[ \begin{align*} x^\phantom{'}&=16\left(\cos(\theta)+\theta\sin(\theta)\right)\\ x'&=16\left(\sin(\theta)+\sin(\theta)+\theta\cos(\theta)\right)\\ y^\phantom{'}&=16\left(\sin(\theta)\theta\cos(\theta)\right)\\ y'&=16\left(\cos(\theta)\cos(\theta)+\theta\sin(\theta)\right)\\ \end{align*} \]

thomas5267
 one year ago
Best ResponseYou've already chosen the best response.0The integral is much easier to evaluate once I got rid of my error lol.

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2heheh .. my x' got befuddled as well

thomas5267
 one year ago
Best ResponseYou've already chosen the best response.0I got \(x'=\sin(\theta)+\sin(\theta)+\theta\cos(\theta)\) and got a mess when evaluating the integral.

amistre64
 one year ago
Best ResponseYou've already chosen the best response.216t dt from a to b ...

amistre64
 one year ago
Best ResponseYou've already chosen the best response.2maybe ... trying to do it in my head bites at my age

thomas5267
 one year ago
Best ResponseYou've already chosen the best response.0Just use the answer box as scrap paper lol.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thomas, dumb question but could you walk me through the derivation of x real quick? I know the 16 can just get pulled out first

thomas5267
 one year ago
Best ResponseYou've already chosen the best response.0\[ \frac{d}{dx}\cos(x)=\sin(x) \] And product rule.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, thank you so much guys, got the answer right finally!
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