Question

A particle moves on the hyperbola xy = 18 for time t > 0 seconds. At a certain instant, y = 6, and dy/dt = 8. Which of the following is true about x at this instant?

Options:
a. x = 3
b. x = 2
c. x = 4
d. x = 6

Answer 1

The correct option is a.

When y=6 and dy/dt=8 for a particle moving on the hyperbola xy=18, the value of x can be determined by rearranging the equation to x = 18/y, yielding x = 3.

Step-by-step explanation:

To find the value of x when y = 6 and dy/dt = 8 for a particle moving on the hyperbola defined by the equation xy = 18, you can simply rearrange the equation to solve for x.

Multiply both sides of the equation by y, then divide both sides by y:

xy = 18 → x = 18/y

Substitute y = 6 into the equation:

x = 18/6

x = 3

Therefore, the correct answer is a. x = 3.