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anonymous

  • 4 years ago

Earthquakes release seismic waves that occur in concentric circles from the epicenter of the earthquake. Suppose a seismograph station determines the epicenter of an earthquake is located 9 kilometers from the station. If the epicenter is located at the origin, write the equation for the circular wave that passes through the station. A. x2 + y2 = 81 B. x2 + y2 = 9 C. (x - 9)2 + (y - 9)2 = 0 D. (x + 9)2 + (y + 9)2 = 0

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  1. JamesJ
    • 4 years ago
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    Which of these equations is the equation of circle of radius 9 centered at the origin?

  2. JamesJ
    • 4 years ago
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    Hint: the equation of a circle centered at \( (a,b) \) and of radius \( r \) is \[ (x-a)^2 + (y-b)^2 = r^2 \]

  3. anonymous
    • 4 years ago
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    James <3 can you help me after by any chance?

  4. JamesJ
    • 4 years ago
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    To make this as explicit as I can for you without giving the answer: if the circle is centered at the origin, then \[ (a,b) = (0,0) \] If the radius is 9 km, then \( r = 9 \). Now, using those values of the variables and the general form of the circle I wrote above, what is the equation of a circle, centered at the origin and of radius 9?

  5. JamesJ
    • 4 years ago
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    \[ (x-a)^2 - (y-b)^2 = r^2 \] Now fill in the values of the variables, \(a, b\) and \( r \).

  6. JamesJ
    • 4 years ago
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    **correction + \[ (x-a)^2 + (y-b)^2 = r^2 \]

  7. anonymous
    • 4 years ago
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    Okay so, Take the epicentre as the centre point of the circle (Since earthquake waves are circular.) Then, since the epicentre is 9 km away, let the station be any point on the circle. So, radius= 9^2 = 81 So, equation of the circle: x^2 + y^2 = 81 is your answer.|dw:1328818229713:dw|

  8. JamesJ
    • 4 years ago
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    @vengance, why did you just give the answer? Wasn't it entirely obvious that I was helping the questioner get to the answer?

  9. anonymous
    • 4 years ago
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    I think it's A. because it would be (x-o)^2 + (y-o)^2 = 9^2 , which equals 81.

  10. JamesJ
    • 4 years ago
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    yes, that's right.

  11. anonymous
    • 4 years ago
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    @JamesJ= Why not? Some people understand via concepts as you are helping them, while others can learn better with examples which maybe used as reference questions.

  12. anonymous
    • 4 years ago
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    It's okay James , i understand. Thank you for trying to help me without just giving me the answer. Although I do appreciate your answer too, vengeance921! Thank you both!! (:

  13. anonymous
    • 4 years ago
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    Not a problem xD

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