A.) Let the length of the sides of the bottom of the box be y and z, and let the length of the sides of the square cut-outs be x, then
V = xyz . . . (1)
2x + y = 24 => y = 24 - 2x . . . (2)
2x + z = 24 => z = 24 - 2x . . . (3)
Putting (2) and (3) into (1), gives:
V = x(24 - 2x)(24 - 2x) = x(24 - 2x)^2 = x(576 - 96x + 4x^2)
V = 4x^3 - 96x^2 + 576x
b.) For maximum volume, dV/dx = 0
dV/dx = 12x^2 - 192x + 576 = 0
x^2 - 16x + 48 = 0
(x - 4)(x - 12) = 0
x = 4 or x = 12
but x = 12 is unrearistice
Therefore, x = 4.
y = z = 24 - 2(4) = 24 - 8 = 16
Therefore, the dimensions of the box that enclose the largest possible volume is 16 inches by 16 inches by 4 inches.
c.) Maximum volume = 16 x 16 x 4 = 1024 cubic inches.
Answer:
2 column proof is a logical argument consisting of statements and the reasons to show why those statememts are true.
Step-by-step explanation:
Answer:
9/14 cm
Step-by-step explanation:
godysjbfsjxyskxhdoxydiydoy
<span>1/root(5-x) = 1/(root5 * root 1- x/5)
1/root5 * (1-x/5)^-1/2
Using the 1st 2 terms of the binomial expansion 1 +nx:
1/root5 ( 1 + x/10)
= X/10root5 + 1/root5</span>
Answer:
the answer is 19.5
Step-by-step explanation:
im smart
