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# A particle moves along the curve $y = 2 \sin (\pi x/2).$ As the particle passes through the point $(\frac {1}{3}, 1).$ its $x-$ coordinate increases at a rate of $\sqrt {10} cm/s.$ How fast is the distance from the particle to the origin changing at this instant?

## Distance of the particle from origin is increasing at the rate of 9.2 $\mathrm{cm} / \mathrm{s}$

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### Video Transcript

we know, given the fact that wise to sign of plaques over to we know he can write d y over DT as hi co sign Pi over six times word of 10 which simplifies to be pie squared of 30 over too. Which tells us then that d s over DT is gonna be one over too squared of 1/3 squared plus one squared times two times 1/3 snow. We're just putting in time squirt of 10 plus two times one times pi squirt of 30 over too, which we convince Simplify to D s over. DT is approximately 9.2 centimeters per seconds. The distance of the particle from the origin is increasing its positive 9.2 centimeters per second.

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