A particle is moving along the curve below.
y=sqrt_{x}
As the particle passes through the point (4,2), its x-coordinate increases at a rate of 5 cm/s. How fast is the distance from the particle to the origin changing at this instant?

Question

A particle is moving along the curve below.
y=sqrt_{x}
As the particle passes through the point (4,2), its x-coordinate increases at a rate of 5 cm/s. How fast is the distance from the particle to the origin changing at this instant?

anonymous · Answer

$$y= \sqrt{x} $$

anonymous · Answer

first take the derivative of the function

y' = .5/x^.5

Plug in the x coordinate, 4

.5/(4^.5)= its instantaneous rate of change

anonymous · Answer

isn't that just that just the rate of change of y with respect to x? They asked asked for the rate of change of distance right?

anonymous · Answer

ps it didn't work.

anonymous · Answer

oh glad i could help do

anonymous · Answer

what? i just said it didn't work.