The coordinates of a particle in the metric xy-plane are differentiable functions of time t with:

dx/dt= -2m/sec and dy/dt = -8m/sec

how fast is the particle's distance from the origin changing as it passes through the point (9,12)? give answer in m/sec

The rate of change of the distance when x = 9 and y = 12 is .

Step-by-step explanation:

This is an example of a related rate problem. A related rate problem is a problem in which we know one of the rates of change at a given instant and we want to find the other rate at that instant.

We know the rate of change of x-coordinate and y-coordinate:

We want to find the rate of change of the distance when x = 9 and y = 12.

The distance of a point (x, y) and the origin is calculated by:

We need to use the concept of implicit differentiation, we differentiate each side of an equation with two variables by treating one of the variables as a function of the other.

If we apply implicit differentiation in the formula of the distance we get

Substituting the values we know into the above formula

The rate of change of the distance when x = 9 and y = 12 is

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step-by-step explanation:

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