Combine the like terms X + x + y + y - y + x -2 =
1 answer:
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Answer:
For least material to be used lengths of square base and sides = 10 units.
Step-by-step explanation:
Let the lengths of the square base and the sides = x feet, x feet and y feet
Area of the square base = x² feet
Volume of the rectangular prism = Area of the square base × Height
= x²y cubic feet
1000 = x²y
y = -------(1)
Material used in the prism = Surface area of the rectangular prism
= 2(lb + bh + hl)
Here, h = height of the prism
l = length of the base
w = Width of the base
Material to be used (S) = 2(xy + x² + xy) - Area of lid
S = 2(x² + 2xy) - x²
S = x² + 2xy
Now by substituting the value of y from equation (1),
S = x² +
= x² +
For least amount of material used,
We will find the derivative of the given function and equate it to zero.
S' = 2x -
2x - = 0
2x³ = 2000
x³ = 1000
x = 10 feet
From equation (1),
y =
y = 10 feet
Therefore, for least amount of the material used lengths of square base and sides will be 10 feet.
Answer:
4 2/7
Step-by-step explanation:
It is convenient to let a spreadsheet or graphing calculator do the tedious math for you. (See the attachment.)
_____
The sum of the numbers is 56, so their average is 56/7 = 8. Then the absolute deviations from average are ...
... 8, 5, 2, 1, 3, 5, 6
and the total of these is 30. The mean absolute deviation is this sum divided by the number of numbers, 7, so is ...
... 30/7 = 4 2/7
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<em>More about Absolute Deviation from Average</em>
"Absolute" here refers to the absolute value function, which drops the sign of a negative number. The absolute deviation of the data value 0 is ...
... |0 - 8| = |-8| = 8
For 3, it is ...
... |3 - 8| = |-5| = 5
