FS10_1825_006_Oct6_notes_5pages

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Unformatted text preview: MTH
1825
sec.
006
 
 Wednesday,
Oct.
6,
2010
 Section
3.4
–
Applications
of
Systems
of
Linear
Equations
in
Two
 Variables
 
 We
will
just
set
up
a
system
of
two
equations
for
each
problem.

Solve
these
on
your
own
 using
the
substitution
method
or
the
addition
method.
 
 Objective
1:

Applications
Involving
Cost
 
 Ex
1)


Kathleen
sells
two
sizes
of
a
handmade
craft
at
a
kiosk
in
a
mall.

The
small
size
costs
 $5
and
the
large
size
costs
$12.

If
Kathleen
sells
a
total
of
105
items
during
a
particular
 week
and
has
a
total
revenue
of
$826
for
that
week,
how
many
of
each
type
did
she
sell?
 
 
 
 
 
 
 
 
 
 
 
 Ex
2)


Ronald
bought
3
hamburgers
and
2
orders
of
fries
for
his
family
and
paid
$8.25.

 Leon
bought
5
hamburgers
and
4
orders
of
fries
for
his
family
and
paid
$14.61.

What
was
 the
cost
of
one
hamburger?

What
was
the
cost
of
one
order
of
fries?
 
 
 
 
 
 
 
 
 
 
 Ex
3)


Janice
has
3
less
dimes
than
nickels.

The
total
value
of
her
dimes
and
nickels
is
 $4.80.

How
many
dimes
does
she
have?

How
many
nickels
does
she
have?
 
 
 
 
 
 
 
 
 Page
1
of
5
 MTH
1825
sec.
006
 
 Wednesday,
Oct.
6,
2010
 Objective
2:

Applications
Involving
Mixtures
 
 Ex
4)


A
chemist
has
two
concentrations
of
solution:

40%
and
72%.

How
much
of
each
 concentration
should
be
mixed
to
produce
20
liters
of
a
52%
solution?
 
 
 
 
 
 
 
 
 
 
 
 Ex
5)


John
needs
to
make
102
gallons
of
a
60%
bleach
solution.

He
has
pure
bleach
and
a
 32%
bleach
solution.

How
much
of
each
should
be
combined?
 
 
 
 
 
 
 
 
 
 
 
 
 Objective
3:

Applications
Involving
Principal
and
Interest
 
 **Read
Example
3
on
p.
231
 
 Ex
6)


Helen
invested
$300
less
in
an
account
that
pays
4%
simple
interest
than
she
did
in
 an
account
that
pays
6.5%
interest.

If
the
total
amount
she
earned
after
1
year
was
$73.68,
 how
much
did
she
invest
in
each
account?
 
 
 
 Page
2
of
5
 MTH
1825
sec.
006
 
 Wednesday,
Oct.
6,
2010
 Ex
7)


George
invested
a
total
of
$4000
in
two
accounts:

one
that
pays
1.5%
simple
 interest
and
one
that
pays
2%
simple
interest.

At
the
end
of
8
years,
the
total
interest
 earned
was
$550.24.

How
much
was
invested
in
each
account?
 
 
 
 
 
 
 
 
 
 
 
 
 
 Objective
4:

Applications
Involving
Uniform
Motion
 
 Ex
8)


A
plane
can
travel
800
miles
in
4
hours
with
the
wind.

The
same
plane
takes
5
hours
 for
the
return
trip
against
the
wind.

Find
the
speed
of
the
plane
in
still
air
and
the
speed
of
 the
wind.
 
 
 
 
 
 
 
 
 
 
 
 
 Ex
9)


A
boat
travels
upstream
(against
the
current)
for
40
miles
in
2.5
hours.

The
boat
 then
turns
around
and
travels
60
miles
going
downstream
(with
the
current)
for
2
hours.

 What
is
the
speed
of
the
boat
in
still
water?

What
is
the
speed
of
the
current?
 
 
 
 
 Page
3
of
5
 MTH
1825
sec.
006
 
 Wednesday,
Oct.
6,
2010
 Objective
5:

Applications
Involving
Geometry
 
 Ex
10)

One
angle
measures
9
degrees
less
than
twice
the
other.

If
the
two
angles
are
 supplementary,
find
the
measure
of
each
angle.
 
 
 
 
 
 
 
 
 
 
 
 
 Section
4.1:

Addition
and
Subtraction
of
Polynomials
 
 A
polynomial
in
x
is
defined
as
a
finite
sum
of
terms
of
the
forms
 ax n ,
where
a
is
real
and
n
 is
a
whole
number
(0,
1,
2,
3,
etc.)
 
 For
each
term,
a
is
called
the
__________________________
and
n
is
the
_________________
of
the
term.
 € 
 
 An
example
of
a
polynomial
in
x
is:
 
 
 If
a
polynomial
has
exactly
one
term,
it
is
called
a
____________________________.
 
 If
a
polynomial
has
exactly
two
terms,
it
is
called
a
_____________________________.
 
 If
a
polynomial
has
exactly
three
terms,
it
is
called
a
_____________________________.
 
 
 In
a
polynomial,
the
term
with
the
highest
degree
is
called
the
______________________________
 (because
it
is
the
most
important)
and
we
usually
write
it
as
the
first
term.

The
coefficient
 of
the
leading
term
is
called
the
______________________________________________.
 
 
 The
degree
of
a
polynomial
is
______________________________________________________________________
 
 ________________________________________________________________________________________________________.
 
 
 Page
4
of
5
 MTH
1825
sec.
006
 
 Wednesday,
Oct.
6,
2010
 Examples
of
polynomials
in
x:
 Polynomial
 Type
 4 x 3 + 7x 5 − 2x 
 −8 x + 3 
 Degree
 
 
 
 
 Leading
Coefficient
 
 
 
 
 
 
 
 
 € € −53
 4 3 x5
 € € 
 
 Polynomials
can
have
more
than
one
variable.

The
degree
of
each
term
is
the
sum
of
the
 exponents
on
the
variables
within
the
term.

The
degree
of
the
polynomial
is
the
largest
of
 those
degrees.
 
 4 x 6 y 3 z − 9 xyz + 12 xy2 − y2 z 5 
 
 
 
 
 
 
 
 
 
 Adding
and
Subtracting
Polynomials
 
 To
add
polynomials,
just
add
like
terms.
 
 To
subtract
polynomials,
distribute
the
negative
sign
first
then
add
like
terms.
 
 Note:

Polynomials
are
not
equations,
so
you
cannot
clear
fractions!
 
 2 4 4 2 312 x + 5 x − 7 x + 3 − 2 x − 3 x − x + 5 
 3 4 
 
 
 € 
 
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