Answer:
$30
Step-by-step explanation:
$160-$130=$30
Refer to the diagram shown below.
The volume of the container is 10 m³, therefore
x*2x*h = 10
2x²h = 10
h = 5/x² (1)
The base area is 2x² m².
The cost is $10 per m², therefore the cost of the base is
(2x²)*($10) = 20x²
The area of the sides is
2hx + 2(2xh) = 6hx = 6x*(5/x²) = 30/x m²
The cost is $6 per m², therefore the cost of the sides is
(30/x)*($6) = 180/x
The total cost is
C = 20x² + 180/x
The minimum cost is determined by C' = 0.
That is,
40x - 180/x² = 0
x³ = 180/40 = 4.5
x = 1.651
The second derivative of C is
C'' = 40 + 360/x³
C''(1.651) = 120 >0, so x = 1.651 m yields the minimum cost.
The total cost is
C = 20(1.651)² + 180/1.651 = $163.54
Answer: $163.54
The average has to be at least 120 and at most 130
To calculate the average we need the sum of all values divided by the number of values, in this case, three (135, 145 and the third result).
120 ≤ (135 + 145 + n)/3 ≤ 130
In inequalities like this, what we change in one side, must be changed in the othe rside as well.
360 ≤ 280 + n ≤ 390
80 ≤ n ≤ 110
We try to factor by maybe grouping
experiment
(x²y³-11x²y)+(6y²-66)
factor
x²y(y²-11)+6(y²-11)
undistribute (y²-11) from each
(x²y+6)(y²-11)
we can force a factor out of the 2nd group in the form of a difference of 2 perfect squares
(x²y+6)(y-√11)(y+√11)
either of those 3 are factors
Answer:
a. 12 yd
Step-by-step explanation: