Estimate. 24.12 dived by 8.1 A. 2 B. 2.9 C. 3 D. 3.9
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>.
Answer:
14
Step-by-step explanation:
starting at -18 you must add 5.4 until you reach 60
-18 + 5.4 = -12.6 once (1)
-12.6 + 5.4 = -7.2 twice (2)
-7.2 + 5.4 = -1.8 thrice (3)
-1.8 + 5.4 = 3.6 fourth (4)
3.6 + 5.4 = 9 fifth (5)
9 + 5.4 = 14.4 sixth (6)
14.4 + 5.4 = 19.8 seventh (7)
19.8 + 5.4 = 25.2 eighth (8)
25.2 + 5.4 = 30.6 ninth (9)
30.6 + 5.4 = 36 tenth (10)
36 + 5.4 = 41.4 eleventh (11)
41.4 + 5.4 = 46.8 twelth (12)
46.8 + 5.4 = 52.2 thirteenth (13)
52.2 + 5.4 = 57.6 fourteenth (14)
since 57.6 + 5.4 is over 60, we need to find the difference in how much we need
57.6 - 60 = -2.4
we need 2.4 so subtract by 5.4
5.4 - 2.4 = 3
therefore we should divide
= 14.444...
which means it goes into 60 (starting at -18) 14.444... repeating times
another way to find the answer is
add 18 + 60
18 + 60 = 78
78/5.4 = 14.444... repeating or 14
hope this helps:)