Unit 4 Exponential and Logarithmic
Functions
Lesson 4.1 Integer Exponents
Lesson 4.2 Rational Exponents
Lesson 4.3 Exponential Function Basics
Lesson 4.4 Finding Equations of Exponentials
Lesson 4.5 The Method of Common Bases
Lesson 4.6 Exponential
Unit 6 Quadratic Functions and Their Algebra
Lesson 6.1 Quadratic Function Review
Lesson 6.2 Factoring
Lesson 6.3 Factoring Trinomials
Lesson 6.4 Complete Factoring
Lesson 6.5 Factoring by Grouping
Lesson 6.6 The Zero Product Law
Unit 5 Sequences and Series
Lesson 5.1 Sequences
Lesson 5.2 Arithmetic and Geometric Sequences
Lesson 5.3 Summation Notation
Lesson 5.4 Arithmetic Series
Lesson 5.5 Geometric Series
Lesson 5.6 Mortgage Payments
An angle is the figure formed by two rays,
called the sides of the angle, sharing a
common endpoint, called the vertex of the
angle.
The Angle
portfolio
Angle Consruction
Jasdev Singh
Step 1. Mark a point
the new line.
Line
Segment
R that will be one end
SUMMARY OUTPUT
Part
Regression Statistics
Multiple R 0.552766
R Square
0.30555
Adjusted R 0.276615
Standard E 392862.2
Observatio
26
10000
5000
Residuals
5000
10000
ANOVA
df
Regression
Residual
Total
SS
MS
F Significance F
1 1.6E+012 1.6E+012 10.55973 0
Country 1930 Per c 1950 Deaths per million men
Australia
480
180
Canada
500
150
Denmark
380
170
Finland
1100
350
Great Brita
1100
460
Iceland
230
60
The Nether
490
240
Norway
250
90
Sweden
300
110
Switzerlan
510
250
United Stat
1300
200
cigarette c 0.7373
NEW YORK CITY COLLEGE OF TECHNOLOGY
The City University of New York
DEPARTMENT:
Mathematics
COURSE:
MAT 2580
TITLE:
Introduction to Linear Algebra
DESCRIPTION:
An introductory course in Linear Algebra.
Topics include vectors, vector spaces, systems
of lin
Weathaering Erosion and Deposition
1. Which property of water makes frost action a common and
effective form of weathering?
1) Water dissolves many earth materials.
2) Water expands when it freezes.
3) Water cools the surroundings when it evaporates.
4) W
Homework Pack 3  Rocks
1. The profile below shows the average diameter of sediment that was sorted and deposited in specific areas A, B, C, and D by a stream
entering an ocean.
As compaction and cementation of these sediments eventually occur, which area

title: "Buffon Needle Experiment"
output: html_document

This is an R Markdown document. Markdown is a simple formatting syntax for authoring HTML, PDF, and MS Word documents. For more details on using R Markdown see <http:/rmarkdown.rstudio.com>.
When

title: "Untitled"
output: html_document

This is an R Markdown document. Markdown is a simple formatting syntax for authoring HTML, PDF, and MS Word documents. For more details on using R Markdown see <http:/rmarkdown.rstudio.com>.
When you click the *
MAT 3772 Stochastic Models: SpadeHomeworks
by Eric Lewis
CityTech CUNY  Semester: Fall 2015
Introduction to MonteCarlo Methods
1. If X and Y are drawn uniformly at random from the interval (5, 3), use 1 million computer simulations to estimate the prob
Markov Chain: Homework
Eric Lewis
December 9, 2015
Invariant Distribution
P = matrix(c(0.3,0.2,0.5,0.4,0.3,0.3,0.3,0.4,0.3),nrow=3,ncol=3,byrow=TRUE)
dimnames(P) = list(c("up","same","down"),c("up","same","down")
P
#
up same down
# up
0.3 0.2 0.5
# same 0
Curvature
In this section we want to briefly discuss the curvature of a smooth curve (recall that for a
smooth curve we require
is continuous and
). The curvature measures how fast a curve is changing direction at a given point.
There are several formulas
CalculuswithVectorFunctions
In this section we need to talk briefly about limits, derivatives and integrals of vector functions.
As you will see, these behave in a fairly predictable manner. We will be doing all of the work in
but we can naturally extend
ArcLengthwithVectorFunctions
In this section well recast an old formula into terms of vector functions. We want to determine
the length of a vector function,
on the interval
.
We actually already know how to do this. Recall that we can write the vector fu
Tangent,NormalandBinormalVectors
In this section we want to look at an application of derivatives for vector functions. Actually,
there are a couple of applications, but they all come back to needing the first one.
In the past weve used the fact that the
VectorFunctions
We first saw vector functions back when we were looking at the Equation of Lines. In that
section we talked about them because we wrote down the equation of a line in
in
terms of a vector function (sometimes called a vectorvalued function
QuadricSurfaces
In the previous two sections weve looked at lines and planes in three dimensions (or
) and while these are used quite heavily at times in a Calculus class there are many other
surfaces that are also used fairly regularly and so we need to
EquationsofPlanes
In the first section of this chapter we saw a couple of equations of planes. However, none of
those equations had three variables in them and were really extensions of graphs that we could
look at in two dimensions. We would like a more
FunctionsofSeveralVariables
In this section we want to go over some of the basic ideas about functions of more than one
variable.
First, remember that graphs of functions of two variables,
are surfaces in three dimensional space. For example here is the g
EquationsofLines
In this section we need to take a look at the equation of a line in
. As we saw in the
previous section the equation
does not describe a
line in
, instead it describes a plane. This doesnt mean however that we cant write
down an equation
The3DCoordinateSystem
Well start the chapter off with a fairly short discussion introducing the 3D coordinate system
and the conventions that well be using. We will also take a brief look at how the different
coordinate systems can change the graph of an