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# A thin wire has the shape of the first-quadrant part of the circle with center the origin and radius $a$. If the density function is $\rho (x, y) = kxy$, find the mass and center of mass of the wire.

## $$\left(\frac{2 a}{3}, \frac{2 a}{3}\right)$$

Vector Calculus

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##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

first hard from part of the circle was radius a So X. It is a co scientist. Why's a sign t and ah to you from zero to pie over too. Grow if who's k X y So what is mass masses in the crate road? Yes, we have the fill out. Yes, but yes, it's nothing but a TT by similar computer your city and your identity and square some take the square root zero two pi over to row is K X Y ex wise K square Scientific Cose I Inti the A the party s is It's okay from zero to pirate to scientific society we do a u substitution will be easy because ah, antiterror activist thiss probably empire over it too. Okay, two times one over two. So that should be the That should be the mass for center of mass. We have to do a few more in the group. So this computer Ah, it's a crow Hack through Yes, Access Eko Society bro is okay X y So it's still okay. Score scientific society. Okay. A square co signed his society uh, the vt So we actually have a to the fourth power Katie Integral. Otis. So we get we should connective coast on Cuba over three. It is entitled Riveted ve We probably pie over too. Um, we should get zero, and we probably zero. We get one. So we minus negative one over three. So it's okay for over three. I would make another computation. Why? Wrote? Yes. Still from zero to a pirate, too. Why's a scientist e roes que x y scientific co sign t. And we still have. Ah, yes, it is. Okay. Fourth science Quartey Cose I Inti, this is U substitution parents. So you have scientist who issue. So I have news for you, Q over three. Prime power two year one. So we, uh, and promising. Oh, yeah. Zero. So he had won over three. Okay, fourth, so the same as this one. So when we do the division one over three K force if I buy the math, Okay, one over to K Q. She gives us to a over three. And that's the same for X and Y Sosa center off meth. So this is a mass and the scent off math. Thus we computed in the next two pages R hsueh over Siri for Post X and y coordinate

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#### Topics

Vector Calculus

##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp