W13 Regular

Due date: Sunday 4/12, 11:59pm

01

04

Parametric arclength

Find the arclength of the curve given parametrically by $x=2t^2$, $y=3t^2-1$ over the time interval $0\le t\le 4$.

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02 $★$

05

Minimum speed of a particle

Suppose a travelling particle has position modelled by the parametric curve:

$$c(t)=(t^3-4t,t^2+1)$$

What is the slowest speed of the particle?

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03

03

Convert points: Polar to Cartesian

Convert the polar coordinates for these points into Cartesian (rectangular) coordinates:

(a) $\left(3,\frac{\pi }{6}\right)$ (b) $\left(-6,\frac{3\pi }{4}\right)$ (c) $\left(0,\frac{\pi }{5}\right)$ (d) $\left(5,-\frac{\pi }{2}\right)$

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04 $★$

04

Convert equations: Cartesian to Polar

Convert the Cartesian equation to a polar equation. Be sure to simplify.

(a) $x^2+y^2=25$ (b) $x=5$ (c) $y=x^2$

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