What is a point-Slope equation of the line with slope -10 that goes thought the point (1,4)?
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This is a geometric progression problem. We can the general formula that can tell us how many flowers would be planted each month.
Let's write the terms that we know and see if we can find the pattern:
The patern here is obvious. Let's write it down:
This formula gives us a number of flowers planted in the n-th month.
Let's write the terms that we know and see if we can find the pattern:
The patern here is obvious. Let's write it down:
This formula gives us a number of flowers planted in the n-th month.
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 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