Question

What are the dimensions of V=2y^3+17y+8y

Answer 1

We decompose expression:



`\displaystyle\\ V=2y^3+17y^2+8y = y(2y^2+17y+8)\\\\ y_(12)= (-17 \pm √(17^2-4*2*8) )/(4)= (-17 \pm √(289-64) )/(4)= \\ \\ = (-17 \pm √(225) )/(4)=(-17 \pm 15)/(4)\\\\ y_1 = (-17 - 15)/(4)=(-32)/(4)=\boxed{-8}\\\\ y_2=(-17 +15)/(4)=(-2)/(4)=\boxed{-(1)/(2)}\\\\ \Longrightarrow~~V=y(2y^2+17y+8) = \boxed{y(y+8)(y+(1)/(2))}\\\\ \Longrightarrow~~ L = y+8,~~~l = y+(1)/(2) ~\text{ and }~ h = y`