Lecture 7.3 bt
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The document outlines an agenda for a class that includes attendance, questions from a previous class, sections 7.3, and exam schedules. It then provides information on applications of linear programming including assigning variables, using tables to organize information, writing constraints as inequalities, finding the objective function, and optimizing over the feasible region. Several examples of constraints and an objective function for a word problem about goats and pigs are given. The classwork/homework assignment is problems 1-11 odd on page 409.
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Lecture 7.3 bt
The document outlines the agenda for today's class, which includes turning in a take home quiz, discussing questions from Friday, and covering sections 7.3. It also lists the exam schedule. The rest of the document provides instructions on applying linear programming, including assigning variables, writing constraints as inequalities, finding the objective function, and optimizing over the feasible region. Examples are given to translate a word problem into the constraints and objective function of a linear programming problem.
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This document discusses key concepts in geometry related to ratios, proportions, and similarity. It introduces ratios and proportions, covering verifying proportions using cross multiplication and solving proportions. It then discusses similar shapes, geometric means, and the extreme and mean ratio property. Several constructions are presented for the extreme and mean ratio, including using squares, triangles, and the golden ratio. Homework problems are assigned.
Geo 6.1 bt
This document discusses various topics in modern geometry including:
- Ratios and proportions, and methods for verifying and solving proportions.
- Geometric mean and finding the geometric mean of two numbers.
- The extreme and mean ratio, and constructions for drawing a point B given the ratio of AB to AC.
- Fibonacci numbers and the ratio of successive numbers.
- The golden ratio φ and its relationship to dividing a line segment in the golden ratio.
- Applications of the golden ratio including the golden rectangle and golden spiral.
Lecture 4.2 bt
The document outlines an agenda that includes:
1) Attendance and announcements
2) Covering sections 4.2 of the textbook
3) A quiz on Chapter 4
4) The Chapter 4 exam on Wednesday March 18th
Lecture 4.1 bt
The document outlines an agenda for today which includes attendance, submitting projects, covering a section, homework due on Sunday, and a quiz on Monday. It then provides three pay rate plans - Plan A pays $200,000 per day, Plan B starts at $50,000 and increases by $10,000 each day, and Plan C starts at 2 cents and doubles each day. Finally, it discusses exponential functions, including basic graphs, functions with initial values, and examples of finding exponential functions from data points.
Geo 5.1 bt
This document contains notes from a geometry class covering modern geometry, logic, parallel lines, and non-Euclidean geometry. It introduces key concepts like proof by direct reasoning, conditional statements, the law of detachment and syllogism. It also covers parallel lines cut by a transversal and the parallel postulate. Finally, it discusses what would happen if Euclid's parallel postulate was incorrect, introducing elliptic and hyperbolic geometry as alternatives.
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Lecture 7.3 bt
- 1. Today’s Agenda Attendance / Announcements Questions from Friday Sections 7.3
- 2. Exam Schedule Exam 4 (Ch 6,7) Fri 11/15 Exam 5 (Ch 10) Thur 12/5 Final Exam (All) Thur 12/12
- 3. Applications of Linear Programming • Assign Variables • Can use a table to organize given information • Write constraints as a system of inequalities • Find Objective function • Optimize over the feasible region
- 4. Linear Programming The Objective Function is what we need to maximize or minimize. For us, this will be a function of 2 variables, f(x, y)
- 5. Linear Programming The Constraints are the inequalities that provide us with the Feasible Region.
- 6. Applications of Linear Programming The only thing we need to do today is to translate the word problem into the constraints and objective function.
- 8. let goats x let pigs y
- 10. Constraints: x y 16 x 10
- 11. Constraints: x y 16 25x 75 y 900 x 10 25x 75 y 900 25 x 3y 36
- 12. Constraints: x y 16 x 10 x 3y 36 x 0 y 0 Are there other “natural” or assumed constraints?
- 13. Constraints: x y 16 x 10 x 3y 36 Objective: x 0 y 0 P( x, y) 14x 40 y
- 17. Cost less than $560 40x 80 y 560 Floor space less than 72 feet 6 x 8 y 72 And can’t have negative cabinets x 0, y 0
- 18. We want the greatest storage capacity S ( x, y) 8x 12 y
- 26. Classwork / Homework • Page 409 • 1 – 11 odd