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Math Help - Writing Equations

  1. #1
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    Writing Equations

    Write a single equation that describes the set of all points (x, y) that are 5 units from the origin or less that 10 units from the point (10, 0).
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  2. #2
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    Re: Writing Equations

    Quote Originally Posted by thamathkid1729 View Post
    Write a single equation that describes the set of all points (x, y) that are 5 units from the origin or less that 10 units from the point (10, 0).
    For starters...

    The set of points that are 5 units from the origin would be the circle of radius 5 centred at the origin. What would the equation of the circle be?

    The set of points that are less than 10 units from the point (10, 0) would be the region inside (but not including) the circle of radius 10 centred at (10, 0). What would the inequation of that region be?
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    Re: Writing Equations

    So, x^2 + y^2 = 25 and (x-10)^2 + y^2 < 100. But how would I write this as one equation???
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    Re: Writing Equations

    Quote Originally Posted by thamathkid1729 View Post
    So, x^2 + y^2 = 25 and (x-10)^2 + y^2 < 100. But how would I write this as one equation???
    \displaystyle \begin{align*} \left\{(x, y) | x^2 + y^2 = 25 \cup (x - 10)^2 + y^2 < 100\right\} \end{align*}
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  5. #5
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    Re: Writing Equations

    \{(x,y) | x^2+y^2=25 \, ; \, \frac{5}{4} < x \le 5\}
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    Re: Writing Equations

    Quote Originally Posted by skeeter View Post
    \{(x,y) | x^2+y^2=25 \, ; \, \frac{5}{4} < x \le 5\}
    The wording of the question implies that you can accept any point that is on EITHER region (i.e. the union) instead of only accepting the points that are on BOTH regions (i.e. the intersection).

    The OP needs to clarify this...
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    Re: Writing Equations

    Quote Originally Posted by Prove It View Post
    The wording of the question implies that you can accept any point that is on EITHER region (i.e. the union) instead of only accepting the points that are on BOTH regions (i.e. the intersection).

    The OP needs to clarify this...
    true ... I wrote it as the intersection, the set of all points 5 units from the origin and less than 10 units from (10,0).

    Oh well, both possibilities are covered.
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  8. #8
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    Re: Writing Equations

    I was looking for the union
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