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1) Let L = {

**r**in**R**| ra = 0}. a) If u and v are in L then (u+v)a...b) If**r**is in**R**and u is in L then (ru)a =**r**(ua) = 0, so ru is in L, which shows that L is...1 Answers · Science & Mathematics · 22/12/2010

**R**is not reflexive. For example, 1 is an integer, but it is not the case that 1**R**1, because 1 + 1 = 2 is not congruent to 0 mod 3. (So...**R**c, then a**R**c. Which shows that**R**is not transitive.)1 Answers · Science & Mathematics · 09/03/2014

-(

**r**+ 3) > 9 -(**r**) > 12**r**< -125 Answers · Science & Mathematics · 24/11/2010

Given: q(

**r**) =**r**^3+7r^2-24r+6 To find maximum/minimum, take the derivative: q'(**r**) = 3r^2 + 14r - 24 Find the roots: 0 = 3r^2 + 14r - 24**r**= (-14 +/- sqrt(14^2 - 4*3*(-24))) / (2*3)**r**= (-14 +/- sqrt(196 + 288)) / 6**r**= (-14...1 Answers · Science & Mathematics · 15/07/2008

∫9re^(

**r**/4) If we make the substitution u = e^(**r**/4), we get du = 4e^(**r**/4), or du/4 = e^(**r**/4), which we can write as: 9/4...u(ln(u) - 1) Replacing the u's with e^**r**/4: e^(**r**/4) * (ln(e^(**r**/4)) - 1), which is...1 Answers · Science & Mathematics · 13/03/2011

A = 2pi

**r**^2 + 2pi(**r**)(h) First, move the A to the right hand side. That means one side will be zero. 2pi**r**^2 + 2pi(**r**)(h) - A = 0 This is in the form of a quadratic, as...2 Answers · Science & Mathematics · 20/08/2008

**R**=A + C^2**R**-A= C^2 + or - sqrt(**R**-A) =C C=sqrt(**R**-A) or C=-sqrt(**R**-A)2 Answers · Science & Mathematics · 30/08/2007

**r**' = dr/d∂ = ∂ sqrt(cos∂) - (2∂ sin∂) / 2sqrt(cos∂) = = (2∂ cos∂ - 2∂ sin...3 Answers · Science & Mathematics · 13/10/2008

(7

**r**+ 10)/**r**(**r**+ 1)(**r**+ 2) = A/**r**+ B/(**r**+ 1) + C/(**r**+ 2) A(**r**+ 1...(**r**+ 1) = 7r + 10**r**= 0 --> 2A = 10 --> A = 5**r**= -1 --> -B = 3 --> B = -3**r**= -2 --> 2C = -4...1 Answers · Science & Mathematics · 03/01/2013

**r**^2 - 5r - 6r + 30 = 0**r**(**r**- 5) - 6(**r**- 5) = 0 (**r**- 6)(**r**- 5) = 0**r**- 6 = 0 or**r**- 5 = 0**r**= 6 or**r**= 53 Answers · Science & Mathematics · 06/02/2011