Mathematics

Problem

A particle moves so that its coordinates

(x,y)

satisfy

4x^{2}+y^{2}=20

. (i) When

x=2

y=4

and

x

is decreasing at

2\,\text{cm s}^{-1}

, find

\dfrac{dy}{dt}

. (ii) Using the value from (i), determine the rate at which the particle’s distance

r

from the origin is changing at that same instant.