Aparticle is moving along the parabola x^2=4(y+6). as the particle passes through the point (8,10), the rate of change of its y-coordinate is 5 units per second. how fast, in units per second, is the x-coordinate changing at this instant?

The instantaneous rate of change is the rate of change at a particular instant.

The rate of change per second in the x-coordinate is 1.25 units per second

The parabola is given as:

The rate of change of y is given as:

Start by differentiating both sides, implicitly

Divide both sides by 2x

From the question, we have:

Substitute 8 for x in

Substitute

Hence, the rate of change per second in the x-coordinate is 1.25 units per second

Read more about rates of change at:

link

idkit the do u know da way and ligma consumed ninja

step-by-step explanation: