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.
Which slope greater than -3?
answer: I , III and IV
which ....farthest from 0?
answer: I
which graph is steepest?
answer: III
hope it heps
Volume=hpir^2
d/2=r, 24/2=12=r
h=40
v=40pi12²
v=40pi144
v=5760pi cubic inches per section
Answer:
Step-by-step explanation:Simplifying
0 = 2.5y + -20
Reorder the terms:
0 = -20 + 2.5y
Solving
0 = -20 + 2.5y
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '-2.5y' to each side of the equation.
0 + -2.5y = -20 + 2.5y + -2.5y
Remove the zero:
-2.5y = -20 + 2.5y + -2.5y
Combine like terms: 2.5y + -2.5y = 0.0
-2.5y = -20 + 0.0
-2.5y = -20
Divide each side by '-2.5'.
y = 8
Simplifying
y = 8
SO the answer is y=8 I think srry if i get it wrong
