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Slope of a Parametric Curve

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The position of a particle moving in the xyxy-plane for time t≥0t \geq 0 is given by the parametric equations x=ln⁡(t+1)x = \ln(t + 1) and y=kt2y = kt^2, where kk is a positive constant. The slope of the line tangent to the particle’s path at t=3t = 3 is 88. What is the value of kk?

A

163\displaystyle \frac{16}{3}

B

43\displaystyle \frac{4}{3}

C

1192\displaystyle \frac{1}{192}

D

13\displaystyle \frac{1}{3}

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