Answer:
16,242. 7 cm^3.
Step-by-step explanation:
We need to cut off a square piece at the 4 corners of the cardboard.
Let the length of their edges be x cm.
The volume of the box will be:
V = height * width * length
V = x(100-2x)(40-2x)
V = x(4000 - 200x - 80x + 4x^2)
V = x(4x^2 - 280x + 4000)
V = 4x^3 + - 280x^2 + 4000x
Finding the derivative:
dV / dx = 12x^2 - 560x + 4000 = 0 ( when V is a maxm or minm.)
4(3x^2 - 140x + 1000) = 0
x = 37.86, 8.80.
Looks like x = 8.80 is the right value but we can check this out be looking at the sign of the second derivative:
V" = 24x - 560, when x = 8.8 V" is negative so this is a Maximum for V.
So the maximum volume of the box is when x = 8.8 so we have
V = 8.8(100-2(8.8)(40 - 2(8.8)
= 16,242. 7 cm^3.
You have two of the same question man...
It is the third one because it equals the same as 8 times 54 . I hope this helped
Answer:
Marcus has 494 cards.
Jorge has 988 cards.
Ren has 518 cards.
Step-by-step explanation:
Let x represent Marcus's cards.
M + J + R
(x) + (2x) + (x+24) = 2000
x + 2x + x + 24 = 2000
4x +24 =2000
4x = 1976
x = 494
Answer:
"yes" or "no"
Step-by-step explanation:
