Mathematics: An open box is to be made from a ft by ft rectangular piece of sheet metal by cutting out squares of equal size from the four corners and bending up the sides. Find the maximum volume that the box can have.

Answer is belowStep-by-step explanation:Rewrite equationsSolve 2x+3y=−1 for x(Add -3y to both sides)SubstituteNo solutions...

An open box is to be made from a ft by ft rectangular

mel2001love

06.02.2022

432 cm $^{3}$

Step-by-step explanation:

The volume of the box can be determine by using derivative function:

V = (18 - 2x) (18 - 2x) x

dV/dx = 4x^3 + 324 + 144x

equating to zero;

(x - 9) (x - 3) = 0

x = 9 , 3

putting the values in the equation;

V = (18 - 2 [3]) (18 - 2[3]) 3

volume = 432.

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golderhadashaowtatz

23.03.2023

Answer is below

Step-by-step explanation:

Rewrite equations

2x+3y=-1;-2x-3y+1=1

Solve 2x+3y=−1 for x

$2x+3y=-1\\2x+3y+-3y=-1+-3y$

(Add -3y to both sides)

$2x=-3y-1\\\frac{2x}{2}=\frac{-3y-1}{2}$

$x=\frac{-3}{2}y+\frac{-1}{2}$

Substitute

$-2x-3y+1=1\\-2(\frac{-3}{2}y+\frac{-1}{2})-3y+1=1\\2=1\\2+-2=1+-2\\0=-1\\$

No solutions

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