Problem 7-07
F'rntjlem 7709
F Ellillem 741
F'r'nljlem 7
Pmblem 7707
The followlng duesrlons rererto a capital budgetlng problem with SlX ijects represented pv U71 varlaples m. xz, x3. X4. x5, and X5
Frinl \tern
Chapter 5 Homework
Pmblem 6-06
Krern chemrcars. rnc., produces a soecrar orrnbased matenal that rs currentrv m short suoorv. Four orKrern's customers have already oraced orders that toge
9x-2y=-6
7x+8=y
Please explain the steps
solve for x on the first equation 2x+2y=2, result x=1-y
then use the x value found and plug it into the second equation 3(1-y)-y=1, results y=1/2
later use the
What is Discrete Mathematics ?
Discrete mathematics is mathematics that deals with discrete objects.
Discrete objects are those which are separated from (not connected to/distinct
from) each other. In
Contents
Often we want to discuss properties/relations common to all propositions. In such a case rather
than stating them for each individual proposition we use variables representing an arbitrary
pr
proposition
Contents
Sentences considered in propositional logic are not arbitrary sentences but are the ones that are
either true or false, but not both. This kind of sentences are called propositio
Once we have it in this compact form, it is fairly easy to compute S for different values of A, R
and n, though one still has to compute (1 + R)n + 1 . This simple formula represents infinitely
many c
Logic is a language for reasoning. It is a collection of rules we use when
doing logical reasoning. Human reasoning has been observed over centuries
from at least the times of Greeks, and patterns app
Introduction
Everyone must have felt at least once in his or her life how wonderful it would be if we could
solve a problem at hand preferably without much difficulty or even with some difficulties.
U
One of the most important thing, if not the most important, in the university education is the
cultivation of the ability to extrapolate. Obviously we can not anticipate all the problems you are
going
Example 5
This is a find type problem and "working backward" technique is used.
Problem: Given a 4 quart pail and a 9 quart pail, obtain 6 quarts of water in the 9 quart pail
using these two pails. Yo
Example 1
This is an example in which you can find a solution once you analyze and understand the
unknowns and data.
Problem: A survey of TV viewers shows the following results:
To the question "Do yo
As an example, let us consider a simple problem of investment. Suppose that we invest $1,000
every year with expected return of 10% a year. How much are we going to have after 3 years, 5
years, or 10
Let us define the meaning of the five connectives by showing the relationship between the truth
value (i.e. true or false) of composite propositions and those of their component propositions.
They are
You've already seen glimpses of matrices - determinants (for Cramer's
Rule) and Gaussian elimination. Now, we'll see what else we can do
with them.
A matrix is just a rectangular grid of numbers. Kean
Remember that a trinomial has three terms.
Like this guy:
Right now, we're really interested in a certain type of trinomial.
Remember FOIL?
We can multiply
and get
Hey - that's our trinomial from abov
This is a pretty easy method. But, it only works when you can factor
something. As I told you before, except for in math books, things
usually don't factor.
But, this is a good method to help you unde
Let's start with an easy one:
Solve
x = 10
We can just look at it and see that
.
But, what if we didn't see that? What would we do?
Here's the Algebra trick:
We'll add
3 to both sides!
*Remember the s
Square Roots:
Here are a few square roots:
The first two popped cleanly (because they had perfect squares inside.)
But, the last guy didn't. He's an irrational number. His decimal part
goes on forever
So far, we've learned how to add and subtract matrices (the sizes had to
be the same) and how to multiply a matrix by a scalar. These were really
easy.
Multiplying two matrices is a bit tricky, but, o
Now, we're going to learn how to factor guys with a number in front of
the
.
I'm not going to lie to you - these can be pretty tricky. Some students
don't like these because there is no way to just me
Remember from your arithmetic days (or is that daze?) what this
means?
That's three 2's all multiplied together:
As you know by now, in algebra, we work with that unknown guy. Mr. X!
The thing to reme