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Section 3.5 Solving Systems using Determinants

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Why Study Determinants?. Determinants offer a quick, number-crunching way to solve Systems of EquationsNo GraphingNo Elimination MethodNo Substitution MethodPut your equations in standard formCreate a few determinantsEvaluate them according to formulas. Concept: A Determinant is a Square Matrix.

Section 3.5 Solving Systems using Determinants

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SECTION 3.5

P2. 3.5. Example 1. A farmer has 2400 ft of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along the river. What are the dimensions of the field that has the largest area? SOLUTIONIn order to get a feeling for what is happening in the problem,

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Section 3.5

Math in Our World. Section 3.5. Euler Circles. Learning Objectives. Define syllogism . Use Euler circles to determine the validity of an argument. Euler Circles. Euler circles are diagrams similar to Venn diagrams. We will use them to study arguments using four types of statements.

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Section 3.5: Equation Solving and Modeling

Section 3.5: Equation Solving and Modeling. March 5, 2014. Solving Algebraically. Solve for x. More Solving. Solve for x. Round to the nearest hundredth. Solving Graph ically. Solve for x. Write answers as fractions or integers. More Solving.

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Section 3.5

Section 3.5. Applications of Logarithims. One-to-One Nature of Exponential and Logarithmic Functions. Examples:. Logs are used to express values that would become impractically large or small. Large distances… from earth to sun, from earth to moon, “width” of Milky Way

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Section 3.5

Section 3.5. Velocities. Linear Velocity. Angular Velocity. Angular Velocity. Greek Letter Omega (lowercase). Angular Velocity . #1: A CD player turns a CD at about 13680˚ in 5 seconds. What is the angular speed of the cd in radians per second?. Linear Velocity and Angular Velocity .

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Section 3.5/3.5

Section 3.5/3.5. Using Measures of Position to Describe Spread?. Percentile. The p th percentile is a value such that p percent of the observations fall below or at that value. Finding Quartiles . Splits the data into four parts Arrange the data in order

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Section 3.5

Section 3.5. Solving Inequalities with Variables on Both Sides. California Standards. 4.0 Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2 x – 5) + 4( x – 2) = 12 .

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Section 3.5

Section 3.5. Compound Interest Formula. Is there an easier way of computing compound interest?. Calculating compound interest using the simple interest formula is tedious when there are numerous periods. What variables do you think would appear in a compound interest formula?

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3.5 Solving Linear Systems in Three Variables

3.5 Solving Linear Systems in Three Variables. 10/4/13. Intersection of 3 planes. We’ve been solving system of equations in 2 variables. The solution is a point where the lines intersect. For systems of equations with 3 variables, the solution is a point where all 3 planes intersect. Solve:.

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Section 3.5

Empirical and Molecular Formulas. Section 3.5. Empirical Formulas. Tells us relative number of atoms of each element it contains Example: H 2 O: 2 atoms of H per 1 atom of O ALSO: H 2 O: 2 mol of H per 1 mol of O Mole concept allows us to calculate the empirical formula. Example.

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Section 3.5

Section 3.5. Applications and Problem Solving. Topics Covered. Translating Verbal Statements Into Equations . Applications of Linear Equations. Translation Review. Addition a+b : the sum of a and b a plus b a increased by b the total of a and b b added to a* b more than a*.

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Section 3.5

Section 3.5. Exponential and Logarithmic Models. Important Vocabulary. Bell-shaped curve The graph of a Gaussian model. Logistic curve A model for describing populations initially having rapid growth followed by a declining rate of growth.

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SECTION 3.5

SECTION 3.5. REAL ZEROS OF A POLYNOMIAL FUNCTION. THE REAL ZEROS OF A POLYNOMIAL FUNCTION. When we divide one polynomial by another, we obtain a quotient and a remainder. Thus the dividend can be written as: (Divisor)(Quotient) + Remainder. Dividend divisor quotient remainder.

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Section 3.5

Section 3.5. Slope-Intercept Form. Page 205. Slope-Intercept Form. The line with slope m and y- intercept b is given by y = mx + b, the slope–intercept form of a line. Example. Page 205. For the graph write the slope-intercept form of the line. Solution

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3.5 Solution by Determinants

3.5 Solution by Determinants. The Determinant of a Matrix. The determinant of a matrix A is denoted by |A|. Determinants exist only for square matrices. The Determinant for a 2x2 matrix. If A = Then This one is easy. Coefficient Matrix.

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Section 3.5

Section 3.5. Distributive Property. You must use the Distributive Property first. Then use the rules from Section 3.4 to solve. 3.5 Using the Distributive Property. Key Skills. Solve the equation:. 3( x – 4) = 48. 4( x + 1) = 16. 3 x – 12 = 48. 4 x + 4 = 16.

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Section 7 – 3 Solving Systems Using Elimination

Section 7 – 3 Solving Systems Using Elimination. Objectives: To solve systems by adding or subtracting To multiply first when solving systems. Elimination Method :. Add or subtract equations to eliminate a variable. REMEMBER: Opposites Cancel! - 5 + 5 = 0 5x + -5x = 0.

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Section 3.5

Section 3.5. The Five Number Summary and Boxplots. Exploratory data analysis = the process of using statistical tools (such as graphs, measures of center, and measures of variation) to investigate data sets in order to understand their important characteristics. Five Number Summary.

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3.5 Solving Equations

3.5 Solving Equations. With Fractions!!!. Opposites . Same Exact Procedure! Determine what must be moved to the opposite side of the equation to isolate the variable Use the rule of opposites to get rid of those numbers Write your answer upside down.

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Section 3.5

Section 3.5. Recursive Algorithms. Recursive Algorithms. Sometimes we can reduce solution of problem to solution of same problem with set of smaller input values

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Section 3.5 Systems of Equations

Section 3.5 Systems of Equations. What is a system of equations?. Two or more equations in the same variables. To solve a system. Find all ordered pairs (x, y) that make both equations true. Methods to Solve. Graphing method Substitution method Linear combination/Elimination method.

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