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anonymous

  • 5 years ago

An architect is designing a public storage building with two different sized storage units. The ceilings will be 8 feet high for each storage unit. A) All small storage units will have square floors the volume of each small unit will be 1,800 cubic feet. What will be the dimensions of each of these storage units? B) The ration of the dimensions in the architect’s drawing to the dimension of the actual small storage unit is 1 inch to 72 inches. How many inches of the architects drawing would represent the actual width of each small storage unit in Part A?

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  1. anonymous
    • 5 years ago
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    So a room's volume is its height*its width*its length. We are given the height and the volume, as well as the fact that its width=its length. We can construct an algebraic equation with this information that will let us solve for the length and width.

  2. anonymous
    • 5 years ago
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    Ok

  3. anonymous
    • 5 years ago
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    The tricky part is trying to represent this algebraically.

  4. anonymous
    • 5 years ago
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    We have height*width*length=volume. What do you get when you plug in the known values?

  5. anonymous
    • 5 years ago
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    What are the values.

  6. anonymous
    • 5 years ago
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    Sorry i fail at math so bad.

  7. anonymous
    • 5 years ago
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    That's ok, it just takes practice. So you know the rooms height and volume - its given to you in the question! Those are height=8ft and volume=1800ft^3.

  8. anonymous
    • 5 years ago
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    Ok

  9. anonymous
    • 5 years ago
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    Lets give these dimensions variable names so that we can better work with them. Lets call x width, y length, and w height. If x (height) = 8, then we have 8*x*y=1800 for our equation. Do you follow?

  10. anonymous
    • 5 years ago
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    Yeah i understand

  11. anonymous
    • 5 years ago
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    Now we have two unknown variables to solve for, which would be impossible usually except that in this case we have an extra bit of information that will help us. We are dealing with a square room.

  12. anonymous
    • 5 years ago
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    Ok Yeah im following

  13. anonymous
    • 5 years ago
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    A square room implies width=length! Fabulous, this actually means we are only dealing with one unknown variable now instead of two!

  14. anonymous
    • 5 years ago
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    8*x*x=1800 -> 8*x^2=1800!

  15. anonymous
    • 5 years ago
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    Whats that?

  16. anonymous
    • 5 years ago
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    So since width=length, we have x=y. They are always going to be the same in a square room, so we can choose to use just one or the other.

  17. anonymous
    • 5 years ago
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    so instead of 8*x*y, we can write 8*x*x or 8*y*y. I doesn't really matter, because since x=y they are all equal

  18. anonymous
    • 5 years ago
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    Ok yeah

  19. anonymous
    • 5 years ago
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    So the rest is algebra. You can divide both sides by 8, and take the square root of the left hand side to find your width and length.

  20. anonymous
    • 5 years ago
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    The answer is 15 ft ?

  21. anonymous
    • 5 years ago
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    Yep

  22. anonymous
    • 5 years ago
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    Oh ok. Can you help me on part 2. im not sure if its correct.

  23. anonymous
    • 5 years ago
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    And in your second part, the scale implies you divide everything by 72 to bring it into the representative scale.

  24. anonymous
    • 5 years ago
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    so 15/72

  25. anonymous
    • 5 years ago
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    i got 2.5 inches.

  26. anonymous
    • 5 years ago
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    sorry...got mixed up between inches and feet

  27. anonymous
    • 5 years ago
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    Oh

  28. anonymous
    • 5 years ago
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    rather (12*15)/72

  29. anonymous
    • 5 years ago
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    Yeah so i was correct.

  30. anonymous
    • 5 years ago
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    Yep

  31. anonymous
    • 5 years ago
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    I have Part c and Part D if your not busy can you take a look it it please?

  32. anonymous
    • 5 years ago
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    Mm - wish I could but I've got to get back to studying for 3 math finals!

  33. anonymous
    • 5 years ago
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    Oh thanks for your help.

  34. anonymous
    • 5 years ago
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    Your in college?

  35. anonymous
    • 5 years ago
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    Yeah...we call it University here in Canada ;)

  36. anonymous
    • 5 years ago
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    Oh wow. Your one smart guy, well goodluck on your finals.

  37. anonymous
    • 5 years ago
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    thanks

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