Expert: Sherman D. - 8/3/2007

Question
I just have a few quick questions. I tried to figure these out on my own and I couldn't understand them:

1.)A marching band has 52 members and there are 24 in the pom-pom squad.  They wish to form several hexagons and squares like those diagrammed below.  Can it be done with no people left over?

   B     B              P     P
B      P      B             B
   B     B              P     P

2.)The points of intersection of the graphs of xy = 20 and x 2  + y 2  = 41 are joined to form a rectangle.  Find the area of the rectangle.

3.)Explain how to determine (in the solving process) if a system is inconsistent or consistent?

Thank you so much for your help.  

Answer
7(7) = 49, leaves 3 Bs
5(4) = 20, leaves 4 Ps

assuming that the ones left over get together then they can form another Hexagon.

So it really depends if you are planning on keeping that exact form or if you are allowed to mix up the left overs so that they form the correct shape.

My answer is Yes, but only with exceptions. If your not allowed exceptions, then i'm not certain. There is probably a mathematical way of doing this, but i'm not going to try and figure it out.

if you already have a yahoo account, try your luck at answers.yahoo.com

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2.)
xy = 20
x^2 + y^2 = 41

y = 20/x

x^2 + (20/x)^2 = 41
x^2 + (400/(x^2)) = 41
x^4 + 400 = 41x^2
x^4 - 41x^2 + 400 = 0

x^2 = (-(-41) ± sqrt((-41)^2 - 4(1)(400)))/(2(1))
x^2 = (41 ± sqrt(1681 - 1600))/2
x^2 = (41 ± sqrt(81))/2
x^2 = (41 ± 9)/2
x^2 = (32/2) or (50/2)
x^2 = 16 or 25
x = ±4 or ±5

since we can't have negative length

x = 4 or 5

xy = 20
(4 or 5)y = 20
y = 5 or 4

(4,5) and (5,4)

the answer i believe is 20.

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3.)
the easiest way to tell. put both graphs in y = form and if they both have the same slope but different y-intercepts, then they are inconsistent. If they have opposite reciprocal slopes then they are consistent. if they have the same slope and y-intercept then they have infinite consistencies.