Math Help

Discussion in 'Community' started by applemacdude, Jul 15, 2003.

  1. applemacdude macrumors 68040

    applemacdude

    Joined:
    Mar 26, 2001
    Location:
    Over The Rainbow
    #1
    I need some help with a math problem. Somehow I don't remember how to do this and I can't find my notes.I'm probaly missing some thing. Please help.

    Thanks in advance!



    Riding on a pyramid


    Five Flaggs (not a typo) has designed a new rollercoaster ride; the ride is in the shape of a rentagualar pyramid. The base of the ride covers an area os 4,800 sq ft, and the length of the base is 20 feet longer than the width of the base.

    The entrance to the ride is in the middle of the south side of the structure. The car travels to the east along the edge of the structure to the southwest corner. There the car turns 90 degrees and continues north to the northeast corner of the base of the pyramid. At the northeast corner the car makes a sharp turn and goes southwest directly to the center of the base of the pyramid.

    When the car reaches the center it starts to rise vertically until it reaches the apex of teh pyramid, a distance of 120 ft. When the car reaches the top, it drops along the southwest edge of the pyramid until it reaches the southwest corner. This is the end of teh ride and all passengers exit the car.

    What is the length of the ride?
     
  2. King Cobra macrumors 603

    Joined:
    Mar 2, 2002
    #2
    Re: Math Help

    I'm finally not late for one of these. :)

    >Five Flaggs (not a typo) has designed a new rollercoaster ride; the ride is in the shape of a rentagualar pyramid. The base of the ride covers an area os 4,800 sq ft, and the length of the base is 20 feet longer than the width of the base.

    Width = W = x
    Length = L = 20 + x

    Area of base = A = WL
    A = 4800 = x (20 + x)
    x = 60

    W = 60
    L = 80

    >The entrance to the ride is in the middle of the south side of the structure. The car travels to the east along the edge of the structure to the southwest corner. There the car turns 90 degrees and continues north to the northeast corner of the base of the pyramid.

    Very confusing wording. I don't understand and cannot make calculations.

    >At the northeast corner the car makes a sharp turn and goes southwest directly to the center of the base of the pyramid.

    Base = rectangle : Pythagorian's theorm is needed to solve...selected triangle has hypothenuse "c" of half the base diagonal.

    : right triangle sides are also half the base.

    Preferred triangle. has sides 30 by 40.

    Using PTheorm, "c" = 50.

    Added distance: 50

    >When the car reaches the center it starts to rise vertically until it reaches the apex of teh pyramid, a distance of 120 ft.

    Added distance: 120

    >When the car reaches the top, it drops along the southwest edge of the pyramid until it reaches the southwest corner.

    Preferred triangle uses height (h = 120) and base (b = half base diagonal = 50)

    Use PTheorm to solve for slant height, l.
    l = 130

    Added distance: 130
     
  3. applemacdude thread starter macrumors 68040

    applemacdude

    Joined:
    Mar 26, 2001
    Location:
    Over The Rainbow
    #3
    Im so damn confused right now. Damn Oakland school district...
     
  4. mactastic macrumors 68040

    mactastic

    Joined:
    Apr 24, 2003
    Location:
    Colly-fornia
    #4
    That ride sux man, sounds like a painful rollercoaster!:p
     
  5. King Cobra macrumors 603

    Joined:
    Mar 2, 2002
    #5
    One step at a time

    The base of the pyramid is rectangular. It's dimensions are:
    Width: "x"
    Length: "20 + x". (i.e. 20 feet longer than the width)

    Area = 4800 (given)
    Area = WL (formula)

    4800 = WL
    4800 = x (20 + x)

    Solve. x = 60

    Recall:
    Width: "x" x = 60
    W = 60
    Length: "20 + x" x = 60
    L = 80

    >At the northeast corner the car makes a sharp turn and goes southwest directly to the center of the base of the pyramid.

    You are going from one corner of the base (rectangular) to the center. That distance is one half of the diagonal of the rectangle. (If you are confused, draw it.)

    To find the distance, use Pythagorian's Theorm.

    a^2 + b^2 = c^2

    You want "c".

    Use the triangle for the corner of the base to the center of the rectangle and to either side.

    Visual assistance:
    Grab a pencil and paper. Draw a rectangle. Draw a segment from any corner to the center of the rectangle. Draw a segment from that center to the center of either side of the rectangle close to the corner of the line you just drew. This is your triangle.

    One dimension, "a", is one side. The other is "b". Using geometry, you can find out that "a" and "b" are half "W" and "L".
    "a" = 60/2 = 30
    "b" = 80/2 = 40

    Solve: a^2 + b^2 = c^2
    30^2 + 40^2 = c^2
    c = 50

    >When the car reaches the top, it drops along the southwest edge of the pyramid until it reaches the southwest corner.

    Your triangle is as follows:

    The diagonal slant from the very top of the pyramid to a corner base, to the center of the base, to the very top of the pyramid again.

    Your height = 120 as given. --> "a"
    Your base is 50, as previously calculated. --> "b"

    Solve using Pythagorian's theorm.

    c = 130
     
  6. applemacdude thread starter macrumors 68040

    applemacdude

    Joined:
    Mar 26, 2001
    Location:
    Over The Rainbow
  7. rainman::|:| macrumors 603

    rainman::|:|

    Joined:
    Feb 2, 2002
    Location:
    iowa
    #7
    that is one cluster**** of a word problem... we didn't have crap like that back when i was in school (a few years ago ;)), the student would get confused halfway through and start drinking... no one wanted to encourage that...

    ;)

    pnw
     
  8. Doctor Q Administrator

    Doctor Q

    Staff Member

    Joined:
    Sep 19, 2002
    Location:
    Los Angeles
    #8
    It's good to understand not only King Cobra's solution, but the way you might go about solving any problem of this type in a systematic way. Here's the general approach:

    1. Draw a picture. Hey, if you have the right software, you can even create a wireframe model of the pyramid and print it out! But a crude hand-drawn version is fine because you don't have to get the scale and proportions right, just the shape.

    2. Draw a line to show the path of interest, in this case the path that the car takes during the ride.

    3. Label what you know, i.e., write in the numbers you are given: the lengths of edges, the areas of sides, or the volume if that's part of the problem.

    4. Label what you want to find out, i.e., assign variables (x,y,z) to unknown measurements that you need to know.

    5. Find the formulas about pyramids, e.g., formulas for the area of the base or a side, the lengths of the sides, the height, the volume. You may not need all of these formulas, but you'll need some of them.

    6. Pick the appropriate formulas (step 5) to compute the quantities you need (step 4) from the quantities you know (step 3).

    If these steps make sense to you, then you have the means to solve lots of 3D geometric problems.
     
  9. eyelikeart Moderator emeritus

    eyelikeart

    Joined:
    Jan 2, 2001
    Location:
    Metairie, LA
    #9
    hmm...I'm an artist...

    I failed algebra in high school...have not one math credit from college...

    but I can write & draw... ;)
     
  10. King Cobra macrumors 603

    Joined:
    Mar 2, 2002
    #10
    Q, step processes are always nice.

    I like to draw every visual to perfect proportions, even if it's a 20 x 8000 rect. (I'm that much of a visual-perfectionist.)

    eye, glad to you can still draw, as well as wear the same doll face every day. :p

    (grabs pencil and paper and begins to draw hypercubes)
     

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