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.