y varies directly with x find each constant of variation the

y varies directly with x. find each constant of variation. then find the value of y when x=-3, y=4 when x is =- x3

Solution

The expression is not clear. The last term appears to be -x³. The solution is, therefore ,on best effort basis.

Let y = x where is the constant of variation. When x = -x³, we have x+x³ = 0 or, x(1+x²) = 0. Then either x = 0 or x² +1 = 0. When x² +1 = 0, we havet x = ±-1 = ± i.

Now, if x = 0, we have 4 = y = x = 0 which is not correct. Hence x 0.Further, if x =± i, we have 4 = y = ± i so that = ± 4/i = ± 4i. Then, when x = -3, we have y = (-3) = -3 = -3*(±4i ) = ±12i.