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Help with Text book answer

  1. May 14, 2005 #1

    I am doing this problem in my text book and I am not sure what is happing in this one step.

    [tex]2y = 360 \sqrt{\pi} - \sqrt{\pi}y [/tex]

    Trying to solve for y and this is what they show as the next step

    [tex](2 + \sqrt{\pi})y = 360 \sqrt{\pi}[/tex]

    Where does this [tex](2 + \sqrt{\pi})[/tex] come from?? where did the other y go and the [tex]-\sqrt{\pi}[/tex]???
  2. jcsd
  3. May 14, 2005 #2
    The [tex](2 + \sqrt{\pi})y[/tex] came from adding [tex]\sqrt{\pi}y[/tex] to both sides and then factoring out a y from the left hand side. Have you not learnt about collecting terms??

    [tex]2y = 360 \sqrt{\pi} - \sqrt{\pi}y [/tex]

    [tex]2y + \sqrt{\pi}y = 360\sqrt{\pi} + \sqrt{\pi}y - \sqrt{\pi}y[/tex]

    [tex](2y + \sqrt{\pi})y = 360\sqrt{\pi}[/tex]
    Last edited: May 14, 2005
  4. May 14, 2005 #3
    They added [tex]\sqrt{\pi}y[/tex] to both sides.

    Now on the left side of the equation we get [tex]2y + \sqrt{\pi}y[/tex]

    and on the right we get [tex]360\sqrt{\pi}[/tex]

    Now on the left side, they factored out the y so you can solve for it.

    [tex]2y + \sqrt{\pi}y = y(2 + \sqrt{\pi})[/tex]

    Now putting all of this info together we get

    [tex](2 + \sqrt{\pi})y = 360 \sqrt{\pi}[/tex]

    and [tex] y = \frac{(360 \sqrt{\pi})}{(2 + \sqrt{\pi})}[/tex]

    Last edited: May 14, 2005
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