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30 2 37 - - K K 30 2 37 - - K K � EMBED Equation.3 ���-5 � EMBED Equation.3 ���5 Sum=b 0 Product=a x c 1x (-25) x2+0x-25=0 substitute the value of bx to facilitate factorization The denominator is a constant term (x2+5x)(-5x-25)=0 x (x+5)-5(x+5)=0 (x+5)(x-5) are the factors for the domain All values of x in the expression are included as dividing by the domain will yield a solution Thus D=� EMBED Equation.3 ��� � EMBED Equation.3 ���The Domain is Integer 2 which divides any factor in the numerator. We factorize the Numerator to obtain the factors. � EMBED Equation.3 ���-6 � EMBED Equation.3 ���5 Sum=b -1 Product=a x c 1x (-30) k2+5k-6k-30=0 substitute the value of bx to facilitate factorization (k2+5k)(-6k-30)=0 k (k+5)-6(k+5)=0 (k+5)(k-6) are the factors for the domain k=-5 and k=6 are the excluded values in the expression since they will equal 0 in any range of values. Thus D={K:K� EMBED Equation.3 ���� EMBED Equation.3 ���,K� EMBED Equation.3 ���(-5) ,k� EMBED Equation.3 ���6} L � EMBED Equation.3 ���Factorizing the domain in the form we find factors:  2 25 2 - x 30 2 37 - - K K 30 2 37 - - K K Î Â ¹ ¹ 30 2 37 - - K K _1071350467.unknown _1071351244.unknown _1071350591.unknown _1071350663.unknown _1071348848.unknown INSTRUCTOR GUIDANCE EXAMPLE: Week One Discussion Domains of Rational Expressions Students, you are perfectly welcome to format your math work just as I have done in these examples. However, the written parts of the assignment MUST be done about your own thoughts and in your own words. You are NOT to simply copy this wording into your posts! Here are my given rational expressions oh which to base my work. 25x2 – 4 67 5 – 9w 9w2 – 4 The domain of a rational expression is the set of all numbers which are allowed to substitute for the variable in the expression. It is possible that some numbers will not be allowed depending on what the denominator has in it. In our Real Number System division by zero cannot be done. There is no number (or any other object) which can be the answer to division by zero so we must simply call the attempt “undefined.” A denominator cannot be zero because in a rational number or expression the denominator divides the numerator. In my first expression, the denominator is a constant term, meaning there is no variable present. Since it is impossible for 67 to equal zero, there are no excluded values for the domain. We can say the domain (D) is the set of all Real Numbers, written in set notation that would look like this: D = {x| x ∈ ℜ} or even more simply as D = ℜ. For my second expression, I need to set the denominator equal to zero to find my excluded values for w. 9w2 – 4 = 0 I notice this is a difference of squares which I can factor. (3w – 2)(3w + 2) = 0 Set each factor equal to zero. 3w – 2 = 0 or 3w + 2 = 0 Add or subtract 2 from both sides.
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Ece141u29 32online
1.
Math & Science
for Young Children ECE 141 / 111F winter quarter 2011 Emily McMason Units 29 - 32
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Sir Cumference &
the Dragon of Pi a math adventure Cindy Neuschwander
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Unit 31 geometry,
data collection & algebraic thinking
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