SPECIAL PRODUCTS AND FACTORING STRATEGIES When you learn to factor quadratics‚ there are three other formulas that they usually introduce at the same time. The first is the "difference of squares" formula. Remember from your translation skills that "difference" means "subtraction". So a difference of squares is something that looks like x2 – 4. That’s because 4 = 22‚ so you really have x2 – 22‚ a difference of squares. To factor this‚ do your parentheses‚ same as usual: x2 – 4 = (x )(x
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Quantitative Methods: MAT540 Quiz 5 • Question 1 If we are solving a 0-1 integer programming problem‚ the constraint x1 ≤ x2 is a conditional constraint. Answer Selected Answer: True Correct Answer: True • Question 2 If we are solving a 0-1 integer programming problem with three decision variables‚ the constraint x1 + x2 + x3 ≤ 3 is a mutually exclusive constraint. Answer Selected Answer: False Correct Answer: False • Question 3 If we
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MATH 4321 Spring 2013 Assignment Solution 0-Sum Games 2 1. Reduce by dominance to 2x2 games and solve. 5 4 4 3 (a) 0 1 1 2 1 0 2 1 4 3 1 2 10 0 7 1 (b) 2 6 4 7 6 3 3 5 Solution: (a). Column 2 dominates column 1; then row 3 dominates row 4; then column 4 dominates column 3; then row 1 dominates row 2. The resulting submatrix consists of row 1 and 3 vs. columns 2 and 4. Solving this 2 by 2 game and moving back to the original game we find that value is
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Polynomials: Basic Operations and Factoring Mathematics 17 Institute of Mathematics Lecture 3 Math 17 (Inst. of Mathematics) Polynomials: Basic Operations and Factoring Lec 3 1 / 30 Outline 1 Algebraic Expressions and Polynomials Addition and Subtraction of Polynomials Multiplication of Polynomials Division of Polynomials 2 Factoring Sum and Difference of Two Cubes Factoring Trinomials Factoring By Grouping Completing the Square Math 17 (Inst. of Mathematics) Polynomials: Basic Operations
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X1 =the number of type 1 trucks produced X2 =the number of type 2 trucks produced The objective is to maximize the profit of producing the two truck types. The constraints are capacities of the paint and assembly shops. Max 300X1 + 500X2 subject to 7X1 + 8X2 ≤ 5600 (Paint Shop) 4X1 + 5X2 ≥ 6000 (Assembly Shop) X2 X1 ‚ X2 ≥ 0‚ integers (nonnegativity & integrality) 3.10 We want to minimize production and inventory costs while meeting demand. Only half of a week’s demand can be filled from that
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obtained from the appropriate terms of the original dividend (being careful that subtracting something having a minus sign is equivalent to adding something having a plus sign)‚ and write the result underneath ((x3 − 12x2) − (x3 − 3x2) = −12x2 + 3x2 = −9x2) Then‚ "bring down" the next term from the dividend. 4. Repeat the
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ence of two squares DIFFERENCE OF TWO SQUARESThis formula is used to factorise some algebraic expressions. Example 5Solution: | FACTORING THE SUM AND DIFFERENCE OF TWO CUBES The formula for factoring a sum of two cubes is: | x3+y3=(x+y)(x2−xy+y2) | | The formula for factoring a difference of two cubes is: | x3−y3=(x−y)(x2+xy+y2) | | When teaching these factorization methods‚ it may be a good idea to encourage students to know one method for these factorizations rather than have them
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increasing. 13. Find the local maximum & local minimum value of function x3– 12x2 + 36x – 4 14. For the curve y = 4x3 - 2x5‚ find all the points at which the tangent passes through the origin. 15. Find the interval in which the function f(x)= 2x3 -9x2 -24x-5 is Increasing or decreasing. 16. Find the equation of the tangents to the curve y = √3x-2 which is parallel to the line 4x-2y+5=0. 17. Find the interval in which the function f is given by f(x)=sin x – cos x ‚o ≤ x ≤ 2 π (i)
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Review problems 4 for 6.2‚ 6.3‚ 6.5‚ 6.6‚7.1 and 7.2 1. Add and subtract rational expressions. 2 3 x x 6 9 x2 4 x x 1 (2) 2 25 x x 5 9x 2 7 (3) 2 2 3x 2 x 8 3x x 4 3x 2 (4) 2 2 2x 9x 5 6x x 2 (1) 2 2. Simplify complex rational expressions. 3 2 (1) x 4 4 x 2 2 x 1 x4 2 6 (2) x 2 x 7 4 x 13 2 x 9 x 15 2 5 3 2 2 y xy x (3) 2 7 3 2 2 y xy x 1 xy 1 (4) 2 2 x y 1 3
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Attempt Score 34 out of 40 points Question 1 2 out of 2 points If exactly 3 projects are to be selected from a set of 5 projects‚ this would be written as 3 separate constraints in an integer program. Answer Selected Answer: False Correct Answer: False . Question 2 2 out of 2 points Rounding non-integer solution values up to the nearest integer value will result in an infeasible solution to an integer linear programming problem. Answer Selected
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