Provide an appropriate response.
-A point is moving on the graph of xy = 24. When the point is at (4, 6), its x coordinate is increasing at the rate of 9 units per second. How fast is the y coordinate changing at that moment?
A) decreasing at 9 units per second
B) increasing at 9 units per second
C) units per second
D) units per second

Question

Provide an appropriate response.
-A point is moving on the graph of xy = 24. When the point is at (4, 6), its x coordinate is increasing at the rate of 9 units per second. How fast is the y coordinate changing at that moment?
A) decreasing at 9 units per second 
B) increasing at 9 units per second 
C) units per second 
D) units per second

Quizplus · Accepted Answer

We have xy = 24, and we want to find how fast y is changing when x = 4 and dx/dt = 9.

To do this, we can take the derivative of both sides of xy = 24 with respect to time:

d/dt (xy) = d/dt (24)

Using the product rule, we get:

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

We can plug in x = 4 and dx/dt = 9:

(4)(dy/dt) + (6)(9) = 0

Solving for dy/dt, we get:

dy/dt = -54/4 = -13.5

So the y coordinate is changing at a rate of -13.5 units per second, which means it is decreasing at 13.5 units per second.

Provide an Appropriate Response