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  1. K = 1/2 a b sin(c) The mathematics for this go back to the Greeks...to Hero (or Heron) of Alexandria (c. 10–70 AD). K is just an arbitrary letter, possibly simply chosen to not be confused...

    1 Answers · Education & Reference · 07/05/2010

  2. 2x² + ( k + 3)x = -10 2x² + ( k + 3)x + 10 = 0 α + β = -( k + 3)/2 αβ = 10/2 = 5 α² + β² = (α + β)² - 2αβ 4 = [-( k + 3)/2]² - 2(5) 4 = ( k + 3)²/4 - 10 56 = ( k + 3)² ...

    2 Answers · Science & Mathematics · 14/10/2012

  3. 1) Show that (- k ) is a root of x^3 + (1 - k ^2)x + k . x^3 + (1 - k ^2)x + k = 0 x^3 + x - k ^2x + k = 0 -( k + x)(kx - x^2 - 1) = 0 => k + x = 0 x = 0 - k x = - k (first solution) => kx - x^2 - 1 = 0 kx - x^2...

    3 Answers · Science & Mathematics · 02/04/2013

  4. y - 9x = k => y = 9x + k where m = slope of normal line = 9 => slope of tangent line = -1/9...9 = -1/(x - 2)^2 => 9 = (x - 2)^2 => x - 2 = +/- 3 => x = 5, 1 So k actually takes on multiple values: When x = 5: y - 1/3...

    1 Answers · Science & Mathematics · 08/09/2013

  5. Since k divides n, we have k = qk for some integer q. Then, x^n - 1 = x^(qk) - 1 = (x^ k )^q - 1^q = (x^ k - 1) * (x^ k + (x^ k )^2 + (x^ k )^3 + ... + (x^ k )^(q-1)), via finite geometric series or otherwise...

    1 Answers · Science & Mathematics · 23/02/2013

  6. dp/dt = (r/ k ) * (pk - p^2) dp / (pk - p^2) = (r/ k ) * dt k * dp / (pk - p^2) = r * dt k * dp / (p * ( k - p)) = r * dt A/p + B/( k - p) = k /(p * ( k - p)) ...

    2 Answers · Science & Mathematics · 13/04/2013

  7. 45 = 12 k Divide both sides by 12. 45/12 = k 55 = 12k 55/12 = k 50 = 12k 50/12 = k 25/6 = k

    2 Answers · Science & Mathematics · 19/01/2016

  8. ... ( k -3)^2 - 36 > 0 or ( k -3)^2 - 6^2 > 0 or ( k -3-6)( k -3+6) > 0 or ( k -9)( k +3) > 0...39;ll see that the only time that the curve is positive is: k < -3 and k > 9 ← your roots

    2 Answers · Science & Mathematics · 17/02/2011

  9. S = ( k = 0 to 10), ∑(-2)^(- k ) Here is one approach S = 1 - 1/2...like the clever telescoping approach above but it was (minus 2) ^ (minus k )

    2 Answers · Science & Mathematics · 23/07/2011

  10. k =log(2) 3, then: log(2) 48 = = log(2) (6*8) = = log(2) (2* 3 *2^3) = = log(2) (2^4 * 3) = = log(2) 2^4 + log(2) 3 = = 4 * log(2) 2 + log(2) 3 = = 4*1 + k -----> Therefore: k + 4.

    4 Answers · Science & Mathematics · 09/01/2017

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