I think you want me to solve for k
expanding, you get
24k-9=-42+24k
which is clearly no solution
I don't know the exact question but heres the best i got
the surface area would be 294 inches
one face would be 49 inches
and the volume would be 343
Answer: First Question: True
Second Question: False
Third Question: False
Step-by-step explanation:
Based on the equations in the image, I used the substitution method.
Let x represent the side length of the square end, and let d represent the dimension that is the sum of length and girth. Then the volume V is given by
V = x²(d -4x)
Volume will be maximized when the derivative of V is zero.
dV/dx = 0 = -12x² +2dx
0 = -2x(6x -d)
This has solutions
x = 0, x = d/6
a) The largest possible volume is
(d/6)²(d -4d/6) = 2(d/6)³
= 2(108 in/6)³ = 11,664 in³
b) The dimensions of the package with largest volume are
d/6 = 18 inches square by
d -4d/6 = d/3 = 36 inches long