1. Z=4 10-6
2 y= 6 48/8
3. Q= 13 12+1
6 m=15 11+4
7. 21 19+2
8. S=2 3-1
9. C=6 24/4
Answer:
8 < x < 16
Step-by-step explanation:
Consider an angle slightly less than 180 between the 4 and 12 ft sides. The measure between the 2 end points is slightly less than the total of the two sides. So the greatest length is 16.
Consider an angle slightly more than 0 between the 4 and 12 ft sides. The measure between the 2 end points is slightly more than the difference between the two sides. So the lowest length is 8.
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.
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