anonymous
  • anonymous
A rectangular storage container with an open top is to have a volume of 10 m3. The length of this base is twice the width. Material for the base costs $20 per square meter. Material for the sides costs $12 per square meter. Find the cost of materials for the cheapest such container. (Round your answer to the nearest cent.) I got $236.15 Im not sure if its right, could someone check my answer please!
Mathematics
chestercat
  • chestercat
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misty1212
  • misty1212
HI!
triciaal
  • triciaal
|dw:1436037958423:dw|
misty1212
  • misty1212
i got $206 not $236 but i could have made a mistake

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misty1212
  • misty1212
if you call the length of the base x and the height h, then via \[2x^2h=10\] you get \[h=\frac{5}{x^2}\]
misty1212
  • misty1212
i got for the total cost \[40x^2+36xh\] which when substuting gives \[40x^2+\frac{180}{x}\]
misty1212
  • misty1212
but like i said, i did it rather quickly so i might have made an error
anonymous
  • anonymous
Someone just showed me all of the work and got $327.08 but thank you!
misty1212
  • misty1212
you sure it is right?
triciaal
  • triciaal
base area = 2w^2 height = like Misty1212 = 5/w^2
anonymous
  • anonymous
yeah it was right, I typed it in and it is 327.08
triciaal
  • triciaal
area of the sides = perimeter * height = 2(l + w) *h 6w*5/w^2 = 30/w

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