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Math Quiz: 9 is number one

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  • User profile image
    iStation

    when

    a = b

     

    multiply both sides by 8a

    8a^2 = 8ab

     

    add (a^2 - 9ab) to both sides

    8a^2 + (a^2 - 9ab) = 8ab + (a^2 - 9ab)

     

    simplify them to

    9(a^2 - ab) = (a^2 - ab)

     

    divide both sides by (a^2 - ab)

    9 = 1

     

    Smiley

  • User profile image
    bureX

    There's a a^2 - ab ≠ 0 missing somewhere, I think Wink

    (by the way, I suck at math)

  • User profile image
    algorith

    bureX said:

    There's a a^2 - ab ≠ 0 missing somewhere, I think Wink

    (by the way, I suck at math)

     That's right. 

    9(a^2 - ab) = (a^2 - ab)  → 0 = 0

     

  • User profile image
    iStation

    algorith said:
    bureX said:
    *snip*

     That's right. 

    9(a^2 - ab) = (a^2 - ab)  → 0 = 0

     

    OK!
    Another one,

     

    lim x->0 [{sin(9x)}/x] = ?

     

  • User profile image
    brianbec

    bureX said:

    There's a a^2 - ab ≠ 0 missing somewhere, I think Wink

    (by the way, I suck at math)

    if a == b, then a^2 == ab and a^2-ab==0. Division by zero is not permitted here Smiley  You can get any answer you want if you divide by zero, just as you can "prove" any proposition if you accept a contradiction, just as any statement about members of the empty set is logically true!

  • User profile image
    kettch

    brianbec said:
    bureX said:
    *snip*

    if a == b, then a^2 == ab and a^2-ab==0. Division by zero is not permitted here Smiley  You can get any answer you want if you divide by zero, just as you can "prove" any proposition if you accept a contradiction, just as any statement about members of the empty set is logically true!

    This statement is false.

  • User profile image
    brianbec

    iStation said:
    algorith said:
    *snip*

    OK!
    Another one,

     

    lim x->0 [{sin(9x)}/x] = ?

     

    Nice one. Here's another

     

    Find the first positive real value of t for which the following is zero

     

    256 cos^9(pi t / 162) - 576 cos^7(pi t / 162) + 432 cos^5(pi t / 162) -120 cos^3(pi t/162) + 9 cos(pi t / 162)

  • User profile image
    iStation

    brianbec said:
    iStation said:
    *snip*

    Nice one. Here's another

     

    Find the first positive real value of t for which the following is zero

     

    256 cos^9(pi t / 162) - 576 cos^7(pi t / 162) + 432 cos^5(pi t / 162) -120 cos^3(pi t/162) + 9 cos(pi t / 162)

    Wow!

     

    9! Right? [27, 45, 63, 81, 99....]

     

    How about this one?

     

    + ∞
    ∫ [{sin(9x)}/x]dx = ?
    − ∞

  • User profile image
    jkrishnaswa​my

    @iStation:

    You are dividing by 0!

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