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You are not logged in. #151 20120919 21:46:25
Re: Objective TypeHi bobbym, Character is who you are when no one is looking. #152 20120920 00:11:03
Re: Objective TypeHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #153 20120920 18:18:36
Re: Objective TypeHi bobbym, 114. The curved surface area of a hollow cylinder is __________ (a) (b) (c) (d) 115. = _____________ (a) (b) (c) (d) Character is who you are when no one is looking. #154 20120920 20:16:52
Re: Objective TypeHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #155 20120921 14:41:30
Re: Objective TypeHi bobbym, The answer 115 is correct. Well done! 116. If f(x) = x + 5, g(x) = x^{2}, then f o g = ____________ (a) (x + 5)^{2} (b) x^{2} + 5 (c) x^{2} + x (d) x^{2}  5 117. The Greatest Common Divisor of is ____________ (a) (b) (c) (d) Character is who you are when no one is looking. #156 20120921 15:25:21
Re: Objective TypeHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #157 20120921 21:38:57
Re: Objective TypeHi bobbym, Character is who you are when no one is looking. #158 20120921 21:45:45
Re: Objective TypeHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #159 20120922 11:36:44
Re: Objective TypeHi bobbym, Character is who you are when no one is looking. #160 20120922 17:21:36
Re: Objective TypeHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #161 20120923 21:51:17
Re: Objective TypeHi bobbym, Character is who you are when no one is looking. #162 20120923 23:15:05
Re: Objective TypeHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #163 20120924 21:07:31
Re: Objective TypeHi bobbym, Character is who you are when no one is looking. #164 20120924 21:12:31
Re: Objective TypeHi ganesh; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #165 20120925 10:55:56
Re: Objective TypeHi! The theorem is simple to prove: Let the divisor be called D(x). Then P(x) R(x) ___ = Q(x) + ____ and multiplying through by D(x) gives D(x) D(x) P(x) = Q(x)D(x) + R(x) Therefore for the values of x that make D(x)=0 we have P(x)=Q(x)*0 + R(x); that is, P(x)=R(x). And this works for real and COMPLEX values of x. D(x) = (x3)(x+1) = x^22x3 divided into P(x) gives R(x)=2x+3 so P(3)=2(3)+3=3 and P(1)=2(1)+3=5. D(x) = (x+i)(xi) = x^2+1 divided into P(x) gives R(x)=5x8 so P(i)=5i8 and P(i)=5i8. Let D(x) = x^24x+13 which has roots 2+3i and 23i. Then P(x) divided by D(x) has remainder 3x8. so P(2+3i) = R(2+3i) = 3(2+3i)8 = 2+6i. We also have P(23i) = R(23i) = 3(23i)8 = 26i. So to evaluate P(x) at a+bi we form D(x) = (x(a+bi))(x(abi)) = x^22ax+(a^2+b^2). Then dividing P(x) by D(x) we get the corresponding remainder R(x). Since this is a linear expression P(a+bi) = R(a+bi) and P(abi) = R(abi) are complex conjugates. This gives us a way to evaluate polynomials at complex values WITHOUT having to work with complex values in the powers of x above the first power (which is involved in R(x)). It keeps it all real until the very end when evaluating R(x). Of course there is not much advantage to evaluating with real roots this way since we can just divide P(x) by xa and look at the remainder. But we could do just ONE division to obtain the evaluations for two (or more) real roots using this generalization. Also if R(x)=0 then D(x), each factor of D(x), and Q(x) are all factors of P(x), which is the factor theorem with higher degree divisors. Have a blessed day! Oops! It was number 124 than brought this to mind, not number 23. Last edited by noelevans (20120926 10:47:09) Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional). LaTex is like painting on many strips of paper and then stacking them to see what picture they make. #166 20120925 21:20:27
Re: Objective TypeHi bobbym and noelevans, Character is who you are when no one is looking. #167 20120925 21:39:20
Re: Objective TypeHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #168 20120926 18:09:35
Re: Objective TypeHi bobbym, 128. If a line is drawn parallel to one side of a triangle the other two sides are divided in __________ (a) same (b) the same ratio (c) parallel (d) perpendicular 129. The coordinate of the midpoint of the line segment joining the points A(3,2) and B(7,8) is ____________ (a) (5,5) (b) (5,5) (c) (2,5) (d) (2,5) Character is who you are when no one is looking. #169 20120926 19:18:36
Re: Objective TypeHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #170 20120927 15:23:13
Re: Objective TypeHi bobbym, Character is who you are when no one is looking. #171 20120927 18:16:53
Re: Objective TypeHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #172 20120928 15:05:17
Re: Objective TypeHi bobbym, (a) x^{6} (b) x^{10} (c) x^{7} (d) x^{23} Character is who you are when no one is looking. #173 20120928 16:25:53
Re: Objective TypeHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #174 20120929 18:37:43
Re: Objective TypeHi bobbym, Character is who you are when no one is looking. #175 20120929 19:48:31
Re: Objective TypeHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. 