Final answer:
To evaluate dy/dx at x = 1 using the cost equation for Ectoplasm hair gel, we need to differentiate the equation with respect to x and solve for dy/dx.
Step-by-step explanation:
The cost equation for producing gallons of Ectoplasm hair gel is given as y^2 - 10xy = 200. To find the value of dy/dx at x = 1, we need to differentiate the equation with respect to x. Taking the derivative of y^2 - 10xy = 200 with respect to x, we get 2y(dy/dx) - 10y - 10x(dy/dx) = 0. To evaluate dy/dx at x = 1, we substitute x = 1 into the equation and solve for dy/dx.
By substituting x = 1 into 2y(dy/dx) - 10y - 10x(dy/dx) = 0, we get 2y(dy/dx) - 10y - 10(dy/dx) = 0. Simplifying this equation, we have (2y - 10)(dy/dx) = 10y. Dividing both sides by 2y - 10, we find that dy/dx = 10y / (2y - 10).
Since we don't have the specific value of y in the equation, we cannot calculate the exact value of dy/dx at x = 1 without additional information.