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Math Help - Simultaneous equations

  1. #1
    mathsdummy
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    Unhappy Simultaneous equations

    I'm having real grief with this problem





    Emma draws the graph of the circle x2 + y2 = 25.
    She is then told to draw the graph of the line x + y = 1 on the same set of axes.

    Find the coordinates of both points where the line intersects the circle
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  2. #2
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    Quote Originally Posted by mathsdummy View Post
    I'm having real grief with this problem





    Emma draws the graph of the circle x2 + y2 = 25.
    She is then told to draw the graph of the line x + y = –1 on the same set of axes.

    Find the coordinates of both points where the line intersects the circle
    Not to difficult, all we have to do is think about it.
    What info do we have?
    Well we know that x + y = -1
    now that means that y = -1 - x
    sub this in to out x^2 + y ^2 =25 formula and we get
    x^2 + (-1(x+1))^2 = 25
    x^2 + (-1)^2 . (x + 1)^2 = 25
    x^2 + (x + 1)^2 = 25
    x^2 + x^2 +2x +1 -25 = 0
    2x^2 + 2x -24 = 0
    x^2 + x -12 = 0
    By the cross method (x+4)(x-3) = 0
    x = -4 and x = 3
    Alternatively you can use quadratic fomula:
    x = (-b +- ((b^2 - 4ac)^1/2))/2a
    x = (-1 +- ( 1 + 48)^1/2)/2
    x = (-1 +- 7)/2
    x= -4 and 3
    Therefore subing in these x values into x + y = -1:
    -4 + y = -1
    y = 3
    Therefore one point is (-4,3)
    3 + y = -1
    y = -4
    Therefore one point is (3,-4)
    Therefore the 2 functions (actually i should say curves given that a circle isn't a function) meet at (-4,3) and (3, -4)

    Edit: Could someone please tell me where I can find the code to put in symbols and equations, such as square root signs instead of ^1/2 , integral signs and dy/dx etc. Much appreciated
    Last edited by behemoth100; May 27th 2007 at 11:53 PM. Reason: To put in smiley face :D
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by behemoth100 View Post

    Edit: Could someone please tell me where I can find the code to put in symbols and equations, such as square root signs instead of ^1/2 , integral signs and dy/dx etc. Much appreciated
    are you familiar with LaTex? well, its not that difficult even if you aren't, i just started learning it myself about 2 days ago. See the http://www.mathhelpforum.com/math-he...-tutorial.html
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by behemoth100 View Post
    Edit: Could someone please tell me where I can find the code to put in symbols and equations, such as square root signs instead of ^1/2 , integral signs and dy/dx etc. Much appreciated
    See the LaTeX tutorial here.

    RonL
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  5. #5
    Senior Member ecMathGeek's Avatar
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    How do you do this? (By "this" I am refering to the caption in place of a url.)

    Quote Originally Posted by CaptainBlack View Post
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by ecMathGeek View Post
    How do you do this? (By "this" I am refering to the caption in place of a url.)
    When creating a post, type the text you want (something like "here") select
    the text, then press the button on the format bar (blue globe with a chain
    link) this will give you a dialog box into which you can paste the link.

    RonL
    Last edited by CaptainBlack; May 28th 2007 at 01:39 PM.
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