(a)
or, via symmetry
____________
(b)
By the chain rule:
For polar coordinates, x = rcosθ and y = rsinθ. Since
<span>r = 3 + 2cosθ, it follows that
Differentiating with respect to theta
2/3 is the slope
____________
(c)
"</span><span>distance between the particle and the origin increases at a constant rate of 3 units per second" implies dr/dt = 3
A</span>ngle θ and r are related via <span>r = 3 + 2cosθ, so implicitly differentiating with respect to time
</span><span />
or, via symmetry
____________
(b)
By the chain rule:
For polar coordinates, x = rcosθ and y = rsinθ. Since
<span>r = 3 + 2cosθ, it follows that
Differentiating with respect to theta
2/3 is the slope
____________
(c)
"</span><span>distance between the particle and the origin increases at a constant rate of 3 units per second" implies dr/dt = 3
A</span>ngle θ and r are related via <span>r = 3 + 2cosθ, so implicitly differentiating with respect to time
</span><span />