**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

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

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

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

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

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

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

... (

**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 roots2 Answers · Science & Mathematics · 17/02/2011

S = (

**k**= 0 to 10), ∑(-2)^(-**k**) Here is one approach S = 1 - 1/2...li**k**e the clever telescoping approach above but it was (minus 2) ^ (minus**k**)2 Answers · Science & Mathematics · 23/07/2011

**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