Suppose xy=−2 and dy/dt=−4. Find dx/dt when x=−1.

  -2

Step-by-step explanation:

Dividing the given equation by x, we find y to be ...

  y = -2/x

Then ...

  dy/dx = 2/x^2

and ...

  dy/dt = (2/x^2)dx/dt

  dx/dt = (x^2/2)dy/dt

When dy/dt = -4 and x=-1, this is ...

  dx/dt = (-1)^2/2(-4) = (1/2)(-4)

  dx/dt = -2

2(2x + 3) = -4 + 2(2x + 5)

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 6

4x - 6 + 6 = 4x - 6 + 6

4x = 4x

x = x

unlimited solutions.

twenty-six miles over two gallons because the proportion for the original 13 miles to one gallon would be written 13/1 and, doing the same thing to the top and bottom, i multiplied by 2 and got 26/2