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anonymous

  • 5 years ago

Find the exact positive value of c if the area between the graph of y=x^2-c^2 and the x -axis is 36. Does that mean x=36? but then how do i solve for c?

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  1. amistre64
    • 5 years ago
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    the area under the curve is equal to 36

  2. amistre64
    • 5 years ago
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    c is a constant here that you are trying to determine

  3. amistre64
    • 5 years ago
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    in other words; what is the integral of y = x^2 + C such that it equals 36

  4. amistre64
    • 5 years ago
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    youd need to find the solution for: 108 = x (x+sqrt(3C)) (x-sqrt(3C))

  5. amistre64
    • 5 years ago
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    or simply put..... since C = c^2 108 = x (x - csqrt(3))(x + csqrt(c))

  6. amistre64
    • 5 years ago
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    if you can read thru the typos... i hope its helpful

  7. amistre64
    • 5 years ago
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    something like this

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  8. anonymous
    • 5 years ago
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    i came out with the answer of 3 by\[\int\limits_{c}^{-c}x^2-c^2\]

  9. anonymous
    • 5 years ago
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    taking the antiderivative and getting x^3/3-c^2x

  10. amistre64
    • 5 years ago
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    make sure you integrate half of that area then multiply it by 2 to check yourself

  11. anonymous
    • 5 years ago
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    then substituting c for x

  12. anonymous
    • 5 years ago
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    why would you have to take half

  13. amistre64
    • 5 years ago
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    do we want the interval and the value of "c" in the equation to be the same?

  14. amistre64
    • 5 years ago
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    because the graph of y = x^2 -C is centered on the y axis; and if you take the area of that, you get "zero' regardless of where you put it :)

  15. amistre64
    • 5 years ago
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    both sides cancel each other out.... just a hazard of the trade really

  16. anonymous
    • 5 years ago
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    oh I got it Thanks for the help!

  17. amistre64
    • 5 years ago
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    youre welcome

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