Algebra.Com's Answer #370682 by bucky(2189)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
It appears as if no tutor has commented to this problem yet. So before it drops
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document.write( " down the line so far that it disappears from the list, I'll offer you some input
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document.write( "that might be useful to you. However, before that, I'm really impressed with the visual
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document.write( "that you provided with your problem. That was quite spectacular and made your statement
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document.write( "of the problem considerably easier to understand. Good job!!!
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document.write( "Now to your problem. My first comment is, \"Are you sure that the equation:
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document.write( "describes the parabolic shape of the building?\" The reason I ask this comes from
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document.write( "the following analysis:
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document.write( "Suppose y equals zero. That should cause the equation to represent the two places
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document.write( "where the graph intersects the horizontal axis on which the bottom of the building
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document.write( "rests. But if you set y equal to zero, the equation becomes:
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document.write( "Solve this by factoring the right side of the equation as below:
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document.write( "Notice that the right side of the equation will equal zero also if either of the factors
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document.write( "are zero. So either:
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document.write( " or 
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document.write( "To solve for the value of x that will make the second factor equal to zero, let's first
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document.write( "multiply both sides (all terms) by 36 to get rid of the denominator. This multiplication
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document.write( "results in:
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document.write( " which becomes: 
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document.write( "When you solve this you get the second answer for the intercept as being 
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document.write( "So the equation you gave for the parabolic arch should intercept the horizontal axis at 0,
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document.write( "as it does, and also at +108, but it doesn't. Instead of 108 it appears to show the right
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document.write( "hand intercept at 150. Is the equation in error or the drawing? Or perhaps I'm do not
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document.write( "understand the problem as well as I should before I comment to it.
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document.write( "Regardless of that, here's an idea of how you might determine the lengths that you need.
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document.write( "Look at the drawing you provided of just the single first layer. You need to get the
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document.write( "length of the top horizontal line. Note that it intersects with the parabolic graph on
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document.write( "both ends. Therefore, the endpoints of the line must satisfy the equation for the parabola.
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document.write( "In other words, the endpoints can be solved for x if the value of y is known in the equation
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document.write( "for the parabola. For this first level, what is the value of y for the top horizontal
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document.write( "line? It is 2.5, is it not? So for the given equation you could write the equation as:
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document.write( "This equation can be solved by first multiplying both sides (all terms) by 36 to get rid
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document.write( "of the denominator. As a result of this multiplication the equation becomes:
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document.write( "Add x^2 - 108x to both sides and the equation then becomes:
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document.write( "This is in the standard quadratic form of:
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document.write( "and therefore it can be solved for the two values of x at the endpoints by applying the
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document.write( "quadratic formula:
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document.write( "In which you substitute 1 for a, -108 for b, and 90 for c to get:
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document.write( "This simplifies to:
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document.write( "and the terms in the radical combine to give:
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document.write( "Taking the square root results in the two answers of:
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document.write( " and 
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document.write( "and this leads to the two answers for x of 0.839865 and 107.160135.
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document.write( "(This is correct for the given equation results in the ground level intercepts are
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document.write( "at 0 and 108, not 0 and 150.)
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document.write( "For each following set of x values, all you have to do is increase the value of y by 2.5.
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document.write( "So for the next level up, you would solve the equation:
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document.write( "This would lead to the quadratic form:
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document.write( "And in general, you could say that the quadratic solution is:
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document.write( "which by multiplying out the third term becomes:
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document.write( "where n is 1, 2, 3, 4, ... up to the ceiling level for the top floor.
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document.write( "by applying the quadratic formula you get:
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document.write( "and by multiplying out the terms you get:
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document.write( "And then you can divide by 2 to get:
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document.write( "Now to get the values of x for the multiple levels of the building, just substitute
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document.write( "for n the values of 1, 2, 3, 4, 5, and so on and calculate the pairs of x at each ceiling
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document.write( "level for the entire building. That should enable you to find the triangles of unused space
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document.write( "at each level.
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document.write( "I hope this helps you with your problem. Check my math and logic to see if I made some
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document.write( "dumb mistake in doing this analysis rather quickly. If my interpretation of the problem
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document.write( "doesn't help you, please post your problem again and some other tutor may be able to
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document.write( "solve it in a better way than I did.
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