This document contains notes from a math class on solving and graphing two variable equations. The notes include examples of determining if equations represent functions, solving various two variable equations, finding solutions for specific values, graphing linear equations, and determining if a graphed equation is a function. The students are assigned homework problems from their textbook on these concepts.
Mathematical Induction
CMSC 56 | Discrete Mathematical Structure for Computer Science
October 18, 2018
Instructor: Allyn Joy D. Calcaben
College of Arts & Sciences
University of the Philippines Visayas
CYCLIC RESOLVING NUMBER OF GRID AND AUGMENTED GRID GRAPHSijcoa
For an ordered set W = {w1, w2 … wk} V (G) of vertices, we refer to the ordered k-tuple r(v W) = (d(v, w1), d(v, w2) … d(v, wk)) as the (metric) representation of v with respect to W. A set W of a connected graph G is called a resolving set of G if distinct vertices of G have distinct representations with respect to W. A resolving set with minimum cardinality is called a minimum resolving set or a basis. The dimension, dim(G), is the number of vertices in a basis for G. By imposing additional constraints on the resolving set, many resolving parameters are formed. In this paper, we introduce cyclic resolving set and find the cyclic resolving number for a grid graph and augmented grid graph.
The answer to the question whether there are any odd perfect numbers is one of the unsolved problems in mathematics. In this paper, we will show that there aren't.
Presentation given by Amit Prasad, Director of Smart Grid, New Delhi Municipal Council on August 3rd, 2011 at eWorld Forum (www.eworldforum.net) in the session Urban Governance and Infrastructure
Mathematical Induction
CMSC 56 | Discrete Mathematical Structure for Computer Science
October 18, 2018
Instructor: Allyn Joy D. Calcaben
College of Arts & Sciences
University of the Philippines Visayas
CYCLIC RESOLVING NUMBER OF GRID AND AUGMENTED GRID GRAPHSijcoa
For an ordered set W = {w1, w2 … wk} V (G) of vertices, we refer to the ordered k-tuple r(v W) = (d(v, w1), d(v, w2) … d(v, wk)) as the (metric) representation of v with respect to W. A set W of a connected graph G is called a resolving set of G if distinct vertices of G have distinct representations with respect to W. A resolving set with minimum cardinality is called a minimum resolving set or a basis. The dimension, dim(G), is the number of vertices in a basis for G. By imposing additional constraints on the resolving set, many resolving parameters are formed. In this paper, we introduce cyclic resolving set and find the cyclic resolving number for a grid graph and augmented grid graph.
The answer to the question whether there are any odd perfect numbers is one of the unsolved problems in mathematics. In this paper, we will show that there aren't.
Presentation given by Amit Prasad, Director of Smart Grid, New Delhi Municipal Council on August 3rd, 2011 at eWorld Forum (www.eworldforum.net) in the session Urban Governance and Infrastructure
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Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
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We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
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8.2 notes
1. 8.2 solve and graph two variable February 29, 2012
Solve for y.
1. 2 + y = 3y 1
2. 8y 13 = 11
3. y + 2 = 6
4
4. 7(y + 3) = 24
Bellwork
Objective: solve and graph two variable equations
HW pg. 408 #325 odds 1
2. 8.2 solve and graph two variable February 29, 2012
1. Function, there is one range value for each domain value.
2. Not a Function, 4 and 3 each go to two range values.
3. Not a Function, 6 goes to two values.
4. Not a Function, 3 goes to two values
5. Function, each domain goes to one range value
11. Function
12. Function
13. Not a Function
14. Not a Function
15. Function
16. Not a Function
17. Not a Function
18. Not a Function
19. Function
20. Function
21. Not a Function
22. Function
Page 403 # 1 5, 11 22 all
HW pg. 408 #325 odds 2
5. 8.2 solve and graph two variable February 29, 2012
The equation t = 21 0.01n models the normal low July temperature in
degrees Celsius at Mount Rushmore, South Dakota. In the equation, t is
the temperature at n meters above the base of the mountain. Find the
normal low July temperature at 300m above the base.
HW pg. 408 #325 odds 5
6. 8.2 solve and graph two variable February 29, 2012
An equation with two variables can have many solutions.
A linear equation is any equation whose graph is a line.
Graph y = (1/2)x + 3
HW pg. 408 #325 odds 6
