SECTION 3.5

Aug 03, 2012

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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

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1. SECTION 3.5 OPTIMIZATION PROBLEMS

2. 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? SOLUTION In order to get a feeling for what is happening in the problem, let�s experiment with some special cases.

3. P3 3.5 Example 1 SOLUTION Figure 1 shows three possible ways of laying out the 2400 ft of fencing.

Section 3.5 Implicit Differentiation

Section 3.5 Implicit Differentiation. Example. If f ( x ) = ( x 7 + 3 x 5 – 2 x 2 ) 10 , determine f ’ (x) . Answer: f ΄ ( x ) = 10( x 7 + 3 x 5 – 2 x 2 ) 9  (7 x 6 + 15 x 4 – 4 x ). Now write the answer above only in terms of y if y = ( x 7 + 3 x 5 – 2 x 2 ) .

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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 Examples

Section 3.5 Examples. Solving Equations by Adding or Subtracting Decimals pages 148 – 151. Solve each equation. x + 4.9 = 18.8 14.73 = -24.23 + b. Solve each equation. n – 5.85 = 15.25 -10 = c – 2.6. Homework. pages 150-151 #s 1-6 write problems, 8, 9-14 write problems, 16, 35-37

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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 3.5-3.6

CptS 401 Adam Carter. Section 3.5-3.6. Discuss Paper. Question 4. Anonymizer.com provides tools and services to obtain a new identity. send e-mail and surf the web anonymously. secretly spy on people visiting your Website. create an anonymous avatar. None of the above.

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SECTION 3.5 Translations

VOCABULARY Translation Image Transformation. SECTION 3.5 Translations. LEARNING TARGETS: Students will be able to table and draw translations. Students will be able to use algebraic notation to describe translations. Vocabulary:. TRANSFORMATION:

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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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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, 3.5a, 3.5b

Section 3.5, 3.5a, 3.5b. Overview For Storm-generated Mesoscale processes Local Effects Advective Effects. Storm Generated Mesoscale Process. Severe storms generate host of mesoscale effects Promote storm development, severity and longevity, or Weaken storms. Recall From Table 3.3.

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Section 3.5—Gas Behavior

Section 3.5—Gas Behavior. How does the behavior of gases affect airbags?. What is pressure?. Pressure – Force of gas particles running into a surface. Pressure and Number of Molecules. If pressure is molecular collisions with the container….

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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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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 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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Section 3.5 Transformations

Vertical Shifts (up or down). Graph, given f ( x ) = x 2. Section 3.5 Transformations. Every point shifts up 2 squares. Every point shifts down 4 squares. Horizontal Shifts (left or right). Graph, given f ( x ) = x 2. Section 3.5 Transformations. Every point shifts left 2 squares.

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Section 3.5: Temperature

Section 3.5: Temperature. Temperature. Temperature  Property of an object that determines the direction of heat energy ( Q ) transfer to or from other objects. Temperature Scales Three Common Scales are used to measure temperature: Fahrenheit Scale (°F)

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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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