Sunrise Question
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The document provides information about sunrise times in Montreal throughout the year and asks questions to model this data with a sinusoidal function. It gives the latest sunrise of 9:15 AM on December 22nd and earliest of 3:15 AM on June 22nd. It asks to write cosine and sine equations using this data, sketch the graph, use one of the equations to predict the sunrise on September 7th, and find the average sunrise time.
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Judes Drafting Table The Sunrise Question
Part I has the student write two equations, one using cosine and one using sine, to model the sunrise times in Montreal over the year based on information given about the latest and earliest sunrise.
Part II has the student sketch the graph of the sinusoidal function, plotting the maximum, minimum and average sunrise times within one period or cycle based on the information.
Part III has the student use one of the equations from Part I to predict the sunrise time on a specific date by treating the number of days as the x-coordinate in the equation.
Part IV asks the student to determine the average sunrise time throughout the year by finding the parameter for the sinusoidal axis.
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Judes Drafting Table The Sunrise Question
Part I has the student write two equations, one using cosine and one using sine, to model the sunrise times in Montreal over the year based on information given about the latest and earliest sunrise.
Part II has the student sketch the graph of the sinusoidal function, plotting the maximum, minimum and average sunrise times within one period or cycle based on the information.
Part III has the student use one of the equations from Part I to predict the sunrise time on a specific date by treating the number of days as the x-coordinate in the equation.
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This document provides instructions for students to learn how to find the surface area of different 3D shapes. It outlines 7 stations where students will draw and label nets of shapes like rectangular prisms, cylinders, cones, and pyramids before calculating their surface areas using formulas like the area of a rectangle, circle, triangle or square. The document suggests simplifying the surface area process and assigns a cumulative review sheet as homework.
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Slide rules are analog calculating devices that use logarithmic scales to perform multiplications and divisions by lining up values on the different scales. The most common slide rule, the Pickett 120, contains multiple inner and outer scales labeled with letters that are used together to perform various calculations through alignment, such as using the C and D scales together for multiplication, or the A and B scales together for square roots. Proper use of the slide rule requires understanding of the mathematical concepts like exponents and logarithms that it is based on.
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Slide rules are analog computing devices that use logarithmic scales to perform multiplications, divisions, roots, and other calculations through alignment of the scales. The most common slide rule, the Pickett 120, contains multiple inner and outer scales labeled with letters to calculate operations like multiplication, reciprocals, square roots, trigonometric functions, and logarithms through simple alignment of the appropriate scales. Proper use of the slide rule requires understanding of the mathematical concepts like exponents and logarithms that it is based on.
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Similar to Sunrise Question
Graph Theory 117 © David Lippman Creative Commons BY-
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© David Lippman Creative Commons BY-SA
Graph Theory and Network Flows
In the modern world, planning efficient routes is essential for business and industry, with
applications as varied as product distribution, laying new fiber optic lines for broadband
internet, and suggesting new friends within social network websites like Facebook.
This field of mathematics started nearly 300 years ago as a look into a mathematical puzzle
(we’ll look at it in a bit). The field has exploded in importance in the last century, both
because of the growing complexity of business in a global economy and because of the
computational power that computers have provided us.
Graphs
Drawing Graphs
Example 1
Here is a portion of a housing development from Missoula, Montana1. As part of her job, the
development’s lawn inspector has to walk down every street in the development making sure
homeowners’ landscaping conforms to the community requirements.
1 Sam Beebe. http://www.flickr.com/photos/sbeebe/2850476641/, CC-BY
118
Naturally, she wants to minimize the amount of walking she has to do. Is it possible for her
to walk down every street in this development without having to do any backtracking?
While you might be able to answer that question just by looking at the picture for a while, it
would be ideal to be able to answer the question for any picture regardless of its complexity.
To do that, we first need to simplify the picture into a form that is easier to work with. We
can do that by drawing a simple line for each street. Where streets intersect, we will place a
dot.
This type of simplified picture is called a graph.
Graphs, Vertices, and Edges
A graph consists of a set of dots, called vertices, and a set of edges connecting pairs of
vertices.
While we drew our original graph to correspond with the picture we had, there is nothing
particularly important about the layout when we analyze a graph. Both of the graphs below
are equivalent to the one drawn above since they show the same edge connections between
the same vertices as the original graph.
You probably already noticed that we are using the term graph differently than you may have
used the term in the past to describe the graph of a mathematical function.
A
B
C
D
E
F
G
H
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Graph Theory 119
Example 2
Back in the 18th century in the Prussian city of
Königsberg, a river ran through the city and seven
bridges crossed the forks of the river. The river
and the bridges are highlighted in the picture to
the right2.
As a weekend amusement, townsfolk would see if
they could find a route that would take them
across every bridge once and return them to
where they started.
Leonard Euler (pronoun ...
Tipler volume 2 resolução 6 edição
1. This document contains conceptual problems and their solutions related to measurement and vectors in physics. It covers topics like SI base units, significant figures, dimensions of physical quantities, and vector operations.
2. Conceptual questions are answered by determining the relevant concepts, relationships between quantities, and applying definitions. Numerical problems are solved by substituting values into appropriate equations.
3. Estimation problems involve approximating quantities using given values and reasonable assumptions. Diagrams are used to illustrate vector concepts and solutions.
Tipler para cientistas e engenheiros resolução 6 edição
1) The document provides conceptual problems and their solutions related to measurement and vectors in physics. It covers topics like SI base units, significant figures, and vector operations.
2) Multiple choice questions test the understanding of concepts like unit conversions, vector directions, and approximations using dimensional analysis. Diagrammatic representations are provided for vector addition problems.
3) An example environmental debate question is included that involves estimating the number of disposable diapers used in the US annually based on population data, then calculating the resulting landfill volume and area requirements.
Graph Theory 117 © David Lippman Creative Commons BY-.docx
Graph Theory 117
© David Lippman Creative Commons BY-SA
Graph Theory and Network Flows
In the modern world, planning efficient routes is essential for business and industry, with
applications as varied as product distribution, laying new fiber optic lines for broadband
internet, and suggesting new friends within social network websites like Facebook.
This field of mathematics started nearly 300 years ago as a look into a mathematical puzzle
(we’ll look at it in a bit). The field has exploded in importance in the last century, both
because of the growing complexity of business in a global economy and because of the
computational power that computers have provided us.
Graphs
Drawing Graphs
Example 1
Here is a portion of a housing development from Missoula, Montana1. As part of her job, the
development’s lawn inspector has to walk down every street in the development making sure
homeowners’ landscaping conforms to the community requirements.
1 Sam Beebe. http://www.flickr.com/photos/sbeebe/2850476641/, CC-BY
118
Naturally, she wants to minimize the amount of walking she has to do. Is it possible for her
to walk down every street in this development without having to do any backtracking?
While you might be able to answer that question just by looking at the picture for a while, it
would be ideal to be able to answer the question for any picture regardless of its complexity.
To do that, we first need to simplify the picture into a form that is easier to work with. We
can do that by drawing a simple line for each street. Where streets intersect, we will place a
dot.
This type of simplified picture is called a graph.
Graphs, Vertices, and Edges
A graph consists of a set of dots, called vertices, and a set of edges connecting pairs of
vertices.
While we drew our original graph to correspond with the picture we had, there is nothing
particularly important about the layout when we analyze a graph. Both of the graphs below
are equivalent to the one drawn above since they show the same edge connections between
the same vertices as the original graph.
You probably already noticed that we are using the term graph differently than you may have
used the term in the past to describe the graph of a mathematical function.
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Graph Theory 119
Example 2
Back in the 18th century in the Prussian city of
Königsberg, a river ran through the city and seven
bridges crossed the forks of the river. The river
and the bridges are highlighted in the picture to
the right2.
As a weekend amusement, townsfolk would see if
they could find a route that would take them
across every bridge once and return them to
where they started.
Leonard Euler (pronoun.
Modelling handout
This document provides instructions for modeling average daily maximum temperature data from Cairo, Egypt and Melbourne, Australia using trigonometric functions. Students are asked to model the Cairo and Melbourne temperature data using sine and cosine functions by finding the period, amplitude, and translation parameters to best fit the data. They are also asked to determine which cities' data is better modeled by each function and discuss which data points are best and worst fitted. A second example is provided to model tide levels in a bay using trigonometric functions.
M112rev
This document provides a review of exercises for a Math 112 final exam. It contains 31 multi-part exercises covering topics like graphing, logarithms, trigonometry, and word problems. The review is intended to help students practice problems similar to what may appear on the exam. The exam will have two parts, one allowing a calculator and one not.
1. Assume that an algorithm to solve a problem takes f(n) microse.docx
1. Assume that an algorithm to solve a problem takes f(n) microseconds for some function f of the input size n. For each time t labeled across the top, determine the exact largest value of n which can be solved in time f(n) where f(n) ≤ t. Use a calculator! You will find it helpful to convert the t values to microseconds, and you may find it helpful to insert a row for n. Note that “lg n” is the log2 n. Note that the only row you can’t write out the values for fully is the “lg n” row—only there may you write 2x for the appropriate value of x. Use the Windows built-in scientific calculator (under Accessories menu) as necessary. A couple values are filled in to get you started. Important: “exact values” means precisely that. Check your answers with values above and below!
Time t =
f(n) =
1 second
1 hour
1 day
1 month
=30 days
n2
1,609,968
lg n
n3
2n
n lg n
2,755,147,513
2. Use loop counting to give a O( ) characterization of each of the following loops basing each upon the size of its input:
a. Algorithm Loop1(n):
s ← 0
for i ← 1 to n do
s ← s + i
b. Algorithm Loop2(p):
p ← 1
for i ← 1 to 2n do
p ← p * i
c. Algorithm Loop3(n):
p ← 1
for j ← 1 to n2 do
p ← p * i
d. Algorithm Loop4(n):
s ← 0
for j ← 1 to 2n do
for k ← 1 to j do
s ← s + j
e. Algorithm Loop5(n):
k ← 0
for r ← 1 to n2 do
for s ← 1 to r do
k ← k + r
3. Order the following functions from smallest to largest by their big-O notation—you can use the letters in your answer rather than copying each formula. Be clear which is smallest and which is largest, and which functions are asymptotically equivalent. For example, if g, h, and m are all O(n lg n), you would write g = h = m = O(n lg n).
a. 562 log3 108
b. n3
c. 2n lg n
d. lg nn
e. n3 lg n
f. (n3 lg n3)/2
g. nn
h. 56n
i. log5 (n!)
j. ncos n
k. n / lg n
l. lg* n
m.
4. a. Which of these equations is true, and why?
b. Which of these is smaller for very large n?
Trisecting the Circle: A Case for Euclidean Geometry
Author(s): Alfred S. Posamentier
Source: The Mathematics Teacher, Vol. 99, No. 6 (FEBRUARY 2006), pp. 414-418
Published by: National Council of Teachers of Mathematics
Stable URL: http://www.jstor.org/stable/27972006
Accessed: 09-02-2018 18:19 UTC
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide
range of content in a trusted digital archive. We use information technology and tools to increase productivity and
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Question 1 Solution
The document discusses tidal patterns over the month of September. It provides the maximum and minimum tide heights, dates of high and low tides, and uses this information to construct a trigonometric model of the tide levels over time. The model is then used to determine on what specific dates the tide height would reach 53 feet, allowing access to a cavern. The length of time the tide stays above 53 feet is also calculated.
Math426_Project3-1
This document describes a project to compute the volume of a section of the Atlantic Ocean off the coast of Florida using data obtained from a GeoMapApp. It includes mathematical derivations of interpolation formulas and integration methods to discretize the ocean area into rectangles and compute the volume. Computational details are provided on obtaining depth data from the app and implementing the volume calculation in MATLAB. A verification method using a rectangular prism approximation is also described and matches the computed volume result. Contributions of the four authors to various aspects of the project are outlined.
Graph theory02
This document provides an introduction to graph theory and network flows through examples and definitions. It discusses how graph theory can be used to model real-world networks and solve optimization problems. The key points are:
- Graph theory models relationships between discrete objects using vertices (nodes) and edges (connections). It has many applications in transportation, logistics, and social networks.
- Classical problems like the Königsberg bridges problem helped establish graph theory. Dijkstra's algorithm finds the shortest path between vertices in a graph by systematically exploring distances.
- Graphs can represent transportation networks with vertices as locations and edges as routes between them. Finding the optimal route is an important application of graph theory and network flows.
Calculus Assignment Help
I am Frank P. I am a SPSS Homework Solver at statisticshomeworksolver.com. I hold a Ph.D. in statistics, from Sunway University, Malaysia. I have been helping students with their homework for the past 6 years. I solve homework related to SPSS.
Visit statisticshomeworksolver.com or email support@statisticshomeworksolver.com. You can also call on +1 678 648 4277 for any assistance with SPSS Homework.
Recreational mathematics magazine number 3 march 2015
This document discusses early topological puzzles found in historical sources. It notes that a 1510 manuscript by Pacioli contains some of the earliest known appearances of puzzles like the Alliance Puzzle, Solomon's Seal, the Cherries Puzzle, the Chinese Wallet, and the Chinese Rings. The manuscript also includes problems related to paths between castles and wells, removing a ring from a loop, and constructing a support from knives. The document has added new information on topological patterns like the Star of David, Borromean Rings, and Möbius strip appearing earlier than previously known. It argues that Ozanam's 1723-1725 book provided more topological puzzles than any prior work, but important early examples are found in
Calculus_Early_Transcendentals,_second_Edition,_by_Sullivan_and.pdf
This document is the table of contents for Calculus, Early Transcendentals, Second Edition by Michael Sullivan. It lists 16 chapters that cover topics in calculus including limits, derivatives, integrals, vector calculus, and differential equations. The preface provides advice for students on how to effectively use the textbook to learn calculus, such as reading actively before class and using the examples and features to build understanding. The table of contents provides an overview of the scope and organization of content covered in the calculus textbook.
Pre-Cal 40S March 11, 2009
The document describes a trigonometric modeling problem about predicting sunrise times in Saskatchewan, Canada using a sinusoidal function. It states that the latest sunrise is December 21 at 9:15am and the earliest is June 21 at 3:15am. It then asks the reader to:
1) Sketch the sinusoidal graph and write two equations to model it, one using sine and one using cosine
2) Use one of the equations to predict the sunrise time on April 6
3) Calculate the average sunrise time throughout the year
4) Determine on what days the sun will rise at 7:00am
developing expert voice
This document discusses using trigonometric functions to model and predict weather data:
- The maximum temperature in Winnipeg on August 17, 2008 was 32.5°C and the minimum on January 13, 2009 was -32.6°C.
- A sinusoidal model is fit to the data with an amplitude of 32.55, period of 298 days, and horizontal shift of 229 days.
- Using the model, the predicted temperature for Christmas 2008 (December 25th) in Winnipeg is 10.82°C.
- About 226 days will have a predicted temperature below 0°C.
Darkonoid
- Darkonoid is a 3D version of the classic game Arkonoid where the player controls a base to bounce a ball and break blocks.
- The game contains classes for matrices, geometry objects, points and 3D polygons to represent the in-game objects.
- At each frame, the main algorithm checks for ball collisions with walls and items, updates the ball's movement and transforms, and checks if a life was lost. Reflection calculations and a modified base shape aid in gameplay.
Visualization of general defined space data
A new algorithm is presented which determines the dimensionality and signature of a measured space. The
algorithm generalizes the Map Maker’s algorithm
from 2D to n dimensions and works the same for 2D
measured spaces as the Map Maker’s algorithm but with better efficiency. The difficulty of generalizing the
geometric approach of the Map Maker’s algorithm from 2D to 3D and then to higher dimensions is
avo
ided by using this new approach. The new algorithm preserves all distances of the distance matrix and
also leads to a method for building the curved space as a subset of the N
-
1 dimensional embedding space.
This algorithm has direct application to Scientif
ic Visualization for data viewing and searching based on
Computational Geometry.
Unit 2
This document discusses brute force and divide-and-conquer algorithms. It covers various brute force algorithms like computing an, string matching, closest pair problem, convex hull problems, and exhaustive search algorithms like the traveling salesman problem and knapsack problem. It then discusses divide-and-conquer techniques like merge sort, quicksort, and multiplication of large integers. Examples and analysis of algorithms like selection sort, bubble sort, and mergesort are provided.
Ia 2 Modeling
The document discusses using mathematical modeling to analyze BMI data for females in the US from ages 2 to 20. The author fits the data to a sine function model with an equation of y=3.225sin.225x-12.5+18.425. This model provided a good fit to the original data set. However, when applying the model to a different BMI data set for girls in the UK from ages 0 to 15, the sine model did not fit the new data set well. A quadratic function provided a better fit for the UK data. Therefore, the author's sine function model is only applicable to the specific original US data set used to derive it and not other BMI data sets more generally.
PBL Implementation Mathematics
This document describes a problem-based learning (PBL) assignment for an Engineering Mathematics course at Bahrain Polytechnic that involves solving Archimedes' sphere and cylinder problem. The assignment aims to address various learning outcomes related to theoretical mathematics knowledge, practical skills, and problem-solving skills. Students are tasked with parameterizing the problem, calculating volumes using integration techniques, applying trigonometric identities and series expansions, and verifying the solution numerically and experimentally.
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Graph Theory 117 © David Lippman Creative Commons BY-
Graph Theory 117 © David Lippman Creative Commons BY-
Tipler para cientistas e engenheiros resolução 6 edição
Tipler para cientistas e engenheiros resolução 6 edição
Graph Theory 117 © David Lippman Creative Commons BY-.docx
Graph Theory 117 © David Lippman Creative Commons BY-.docx
1. Assume that an algorithm to solve a problem takes f(n) microse.docx
1. Assume that an algorithm to solve a problem takes f(n) microse.docx
Recreational mathematics magazine number 3 march 2015
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Calculus_Early_Transcendentals,_second_Edition,_by_Sullivan_and.pdf
Calculus_Early_Transcendentals,_second_Edition,_by_Sullivan_and.pdf
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みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
ここ3000字までしか入らないけどタイトルの方がたくさん文字入ると思います。
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みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
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Sunrise Question
- 9. THE GRAPH…