a point is moving on the graph of xy=30. when the point is at (6,5), its x-coordinate is increasing by 6 units per second. how fast is the y-coordinate changing at the moment

see other post.

To find out how fast the y-coordinate is changing at the moment, we need to take the derivative of the equation xy = 30 with respect to time and then substitute the given values.

Let's start by differentiating the given equation with respect to time:

d(xy)/dt = d(30)/dt

Using the product rule of differentiation, we can write this as:

x(dy/dt) + y(dx/dt) = 0

Now we can substitute the given values. At the given moment, x = 6 and dx/dt = 6 (since the x-coordinate is increasing by 6 units per second).

Plugging in these values, we get:

6(dy/dt) + 5(6) = 0

Simplifying, we have:

6(dy/dt) = -30

Now we can solve for dy/dt:

dy/dt = -30/6

Simplifying further, we get:

dy/dt = -5

Therefore, the y-coordinate is changing at a rate of -5 units per second at the given moment.