Question

Let xy=2 and dy/dt =5. Find dx/dt when x=3:
a) 2.5
b) 1.5
c) 5
d) 0.5

Answer 1

After differentiating xy=2 and substituting the given values, we find that dx/dt equals -22.5, which is not among the provided choices, indicating a possible error in the question.

Step-by-step explanation:

To find dx/dt when x=3, we will use the given information xy=2 and dy/dt=5. First, we differentiate both sides of the equation xy=2 with respect to t, using the product rule. This gives us:

x(dy/dt) + y(dx/dt) = 0
Substituting the known values, x=3 and dy/dt=5, into the equation yields:

3(5) + y(dx/dt) = 0

To find y, we use the initial equation xy=2, plug in x=3, and solve for y:
3y = 2 => y = 2/3

Now we have:

15 + (2/3)(dx/dt) = 0

Solving for dx/dt gives:

(dx/dt) = -15 * (3/2) = -45/2

Then, dx/dt = -22.5. However, this answer is not in the multiple choices provided by the student, suggesting there may have been a misunderstanding in the question's context or a typo. Usually, the question would be structured such that the answer matches one of the given choices.