Question

A particle moves on the hyperbola xy=15 for time t≥0 seconds. At a certain instant, x=3 and dx/dt=6. Which of the following is true about y at this instant?

Answer 1

Answer:

y is decreasing by 10units per second

Step-by-step explanation:

Given xy = 15

If x = 3

y = 15/3

y = 5

dx/dt= 6

Differentiating xy = 15 implicitly with respect to t using product rule

x

xdy/dt + ydx/dt = 0

Substitute the given value into the expression and solve for dy/dt as shown:

3dy/dt + 5(6) = 0

3dy/dt + 30 = 0

3dy/dt = -30

Divide both sides by 3

(3dy/dt )/3 = -30/3

dy/dt = -10

This means that y is decreasing by 10units per second (it is decreasing because of the negative sign)