A particle is moving along the curve y=2 SQRT(4x+4) . As the particle passes through the point (3,8), its x-coordinate increases at a rate of 3 units per second. Find the rate of change of the distance from the particle to the origin at this instant.

Question

anonymous · Answer

1.take the implicit derivative wrt to time. you will end up with 4 variables:
$$x, y, \frac{dx}{dt},\frac{dy}{dt}$$

you are given 3 of these and can thus solve the fourth.

2. The distance from the origin is given as:
   $$r = \sqrt{x^2+y^2}$$

you then have to solve for dr/dt, which can be found by taking implicit derivative and subing in the previous values you solved earlier

lin.ivory · Answer

how do i identify which is which though? Can i simply substitute (x,y) as (3,8)? or does y becomes 2 sqrt(4x+4)?

anonymous · Answer

You'll find that if you sub x=3 into the original equation you will get y= 8 out of it.  By giving you the y value of the point they've given you more info than you needed