V = Length x Width x Height = 288
If we call the width w
then length = 3w
And height = 288/(3w x w)
Assuming none of the material used overlaps the box will need 6 faces ( top, bottom, 2 ends and 2 sides)
Area of material = 2 x LW + 2 x HW + 2 x HL
= 2(3w x w + 288/(3w x w) x w + 288/(3w x w) x 3w)
= 2(3w^2 + 288/3w + 288/w)
= 2(3w^2 + 96/w + 288/w)
= 2(3w^2 + 384/w)
= 6w^2 + 768/w
Taking the derivative in terms of w
A’ = 12w - 768/w^2
A’ is zero when 12w = 768/w^2
w^3 = 768/12 = 64
w = cube root of 64 = 4
This makes the box with the minimum materials 12 x 4 x 6
So the length that uses the minimum material is 12 inches
To find out whether the expressions equal 9, plug the values of x and y into each problem. For example, the first expression would be 4 to the power of 2 + 6×1/3, which would simplify to 16+2 which is 18, not 9. The expressions that do equal 9 are B, D, and E.
Length = 3 breadth
which means 256 = 8 breadth
breadth = 32
length = 96
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Answer:
h(x) ≥ |x - 5| +1
Step-by-step explanation:
Given graph represents an absolute function (parent function)
f(x) = |x|
Since, graph of the function 'f' has been shifted 5 units to the right new function will be,
g(x) = f(x - 5)
g(x) = |x - 5|
Again function 'g' is shifted 1 unit upwards along the y-axis then the new function will be,
h(x) = g(x) + 1
h(x) = |x - 5| + 1
There is a shaded region representing the solution area lying above the intersecting dark lines,
Therefore, solution region will be re[presented by the inequality,
h(x) ≥ |x - 5| + 1