where x is the height of the box or the side of the equal squares from each corner and turning up the sides

V = (60-2x) (10-2x) (x)
V = (60 - 2x) (10x - 2x^2)
V = 600x - 120x^2 -20x^2 + 4x^3
V = 4x^3 - 100x^2 + 600x

To maximize the volume, we differentiate the expression of the volume and equate it to zero.

V = 4x^3 - 100x^2 + 600x
dV/dx = 12x^2 - 200x + 600
12x^2 - 200x + 600 = 0

x^2 - 50/3x + 50 = 0

Solving for x,
x1 = 12.74 ; Volume = -315.56 (cannot be negative)
x2 = 3.92 ; Volume = 1056.31

So, the answer would be that the maximum volume would be 1056.31 cm^3.

6 0

3 years ago

Triangle X Y Z is shown. The length of side X Y is (9 n + 12) feet and the length of side X Z is (15 n minus 6) feet. Angles X Y

posledela

*the figure is shown in the attachment

Answer/Step-by-step explanation:

Since <XYZ and <YZX are said to be congruent, therefore, the side opposite to each of the angle are also equal. Therefore, ∆XYZ is an isosceles ∆.

Find the value of n by creating an equation to solve for n:

XY = (9n + 12) ft

XZ = (15n - 6) ft

XY = XZ (2 equal lengths of isosceles ∆)

9n + 12 = 15n - 6 (substitution)

Combine like terms

9n - 15n = - 12 - 6

-6n = -18

Divide both sides by -6

-6n/-6 = -18/-6

n = 3

Find the length of leg XY by substituting n = 3 into XY = (9n + 12) ft.

XY = (9(3) + 12) ft

XY = (27 + 12) ft

XY = 39 ft

Find the length of leg XZ by substituting n = 3 into XZ = (15n - 6) ft.

XZ = (15(3) - 6) ft

XZ = (45 - 6) ft

XZ = 39 ft

7 0

3 years ago