How do you solve 3b(9b-27)=0
2 answers:
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Answer:
$4800
Step-by-step explanation:
The cost is minimized when any pair of opposite faces of the box costs the same as any other pair. Since the top+bottom total $25 per square foot and the sides (left+right or front+back) total $20 per square foot, the area of a side must be 25/20 = 5/4 times the area of the top or bottom.
If we let x represent the length of one side of the square bottom, then 5/4x will be the height of the box. Its volume will be ...
(5/4x)(x²) = 640 ft³
x³ = (4/5)(640 ft³) = 512 ft³ . . . . . . multiply by 4/5
x = 8 ft . . . . . . . . . . . . . . . . . . . . . . . take the cube root
The base area is then (8 ft)² = 64 ft², and the cost of the top+bottom is ...
64 ft² × $25/ft² = $1600
The three pairs of opposite sides will cost 3×$1600 = $4800.
The minimum cost of the constructed box is $4800.
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You can also write an equation for the total cost in terms of x, the side length of the base. That cost function will be ...
c(x) = 15x² + 10x² + 10·4x(640/x²)
This simplifies to ...
c(x) = 25x² +25600/x
A graph shows the minimum is c(8) = 4800 (as above).
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Algebraically, you can set the derivative to zero to find the value of x.
dc/dx = 0 = 50x -25600/x²
512 = x³ . . . . multiply by x²/50 and add 512
8 = x . . . . . . . take the square root. Same solution as above. <em>Cost is minimized when the side length of the base is 8 ft</em>.
1. Geometric Sequence
2.
3.
Step-by-step explanation:
Given sequence is:
6, 18, 54, 162,....
Here
(a) Is this an arithmetic or geometric sequence?
We can see that the difference between the terms is not same so it cannot be an arithmetic sequence.
We have to check for common ratio (ratio between consecutive terms of a sequence) denoted by r
As the common ratio is same, the given sequence is a geometric sequence.
(b) How can you find the next number in the sequence?
Recursive formulas are used to find the next number in sequence using previous term
Recursive formula for a geometric sequence is given by:
In case of given sequence,
So to find the 5th term
(c) Give the rule you would use to find the 20th week.
In order to find the pushups for 20th week, explicit formul for sequence will be used.
The general form of explicit formula is given by:
Putting the values of a_1 and r
Hence,
1. Geometric Sequence
2.
3.
Keywords: Geometric sequence, common ratio
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