Applications of Linear Systems Homework Days 3-5 (2)
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TRIGONOMET
Subject
Mathematics
Date
Jan 9, 2024
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Uploaded by ProfEmu2609
Applications
and
Problem
Solving
4.
Numbers
The
sum
of
two
numbers
is
255.
When
the
smaller
is
subtracted
from
the
larger,
the
result
is
39.
Find
the
numbers.
5.
Earning
interest
Isabel
invested
$8000,
part
at
9%
per
annum
and
the
remainder
at
4%
per
annum.
After
one
year,
the
total
interest
from
these
investments
was
$420.
How
much
did
she
invest
at
each
rate?
6.
Driving
Kareem
took
5
h
to
drive
470
km
from
Sudbury
to
Brantford.
For
part
of
the
trip,
he
drove
at
100
km/h.
For
the
rest
of
the
trip,
he
drove
at
90
km/h.
How
far
did
he
drive
at
each
speed?
7.
Patrol
boat
It
took
a
patrol
boat
5
h
to
travel
60
km
up
a
river
against
the
current,
and
3
h
for
the
return
trip
with
the
current.
Find
the
speed
of
the
boat
in
still
water
and
the
speed
of
the
current.
8.
Investments
Hakim
invested
$15
000.
He
put
part
of
it
in
a
term
deposit
that
paid
4%
per
annum,
and
the
remainder
in
a
treasury
bill
that
paid
5%
per
annum.
After
one
year,
the
total
interest
was
$690.
How
much
did
Hakim
invest
at
each
rate?
8.
Measurement
Find
the
values
of
x
and
9.
e
XN
/QX—}/)‘
(3x
+
2y)°
B
>
>
77
587
10.
Vinegar
solutions
White
vinegar
is
a
solution
of
acetic
acid
in
water.
There
are
two
strengths
of
white
vinegar—a
5%
solution
and
a
10%
solution.
How
many
millilitres
of
each
solution
must
be
mixed
to
make
50
mL
of
a
9%
vinegar
solution?
11.
Acid
solutions
What
volume,
in
millilitres,
of
a
60%
hydrochloric
acid
solution
must
be
added
to
100
mL
of
a
30%
hydrochloric
acid
solution
to
make
a
36%
hydrochloric
acid
solution?
12.
Measurement
Use
the
diagram
to
find
the
values
of
x
and
y.
.
\124°
B
(2x
+
3y)
Yx
-2y)
13.
Flying
speed
A
plane
took
4
h
to
fly
2200
km
from
Saskatoon
to
Toronto
with
a
tail
wind.
The
return
trip,
with
a
head
wind,
took
5
h.
Find
the
speed
of
the
plane
in
still
air
and
the
wind
speed.
14.
Pool
table
The
perimeter
of
a
pool
table
is
about
7.8
m.
Four
times
the
length
equals
nine
times
the
width.
What
are
the
dimensions
of
the
table,
in
metres?
15.
Fitness
Playing
tennis
burns
energy
at
a
rate
of
about
25
kJ/min.
Cycling
burns
energy
at
about
35
kJ/min.
Hans
exercised
by
playing
tennis
and
then
cycling.
He
exercised
for
50
min
altogether
and
used
a
total
of
1450
kJ
of
energy.
For
how
long
did
he
play
tennis?
3
16.
Measurement
The
rectangle
has
an
area
of
7
square
units
and
a
perimeter
of
27z
units.
-
What
is
the
value
of
«?
17.
Driving
distance
Erica
drove
from
Sarnia
at
80
km/h.
Aisha
left
Sarnia
one
hour
later
and
drove
along
the
same
road
at
100
km/h.
How
far
from
Sarnia
did
Aisha
overtake
Erica?
Answers
Applications
and
Problem
Solving
4.
147,
108
5.
$2000
at
6%,
$6000
at
4%
6.
200
km
at
100
km/h,
270
km
at
90
kim/h
7.
16
kin/h,
4
kin/h
8.
S6000
at
4%,
$9000
at
5%
9.a
=34,
y=10
10.
10
mL
of
the
5%
solution,
40
mL
of
the
10%
solution
11.25
mL
12,
v
=32,y
=20
13.495
km/h,
55
kin/h
14.
2.7
m
by
1.2
m
15.30
min
16.
2.5
17.
400
km
13.
Resort
costs
A
weekend
at
Bayview
Lodge
costs
$360
and
includes
two
nights’
accommodation
and
four
meals.
A
week
costs
$1200
and
includes
seven
nights’
accommodation
and
ten
meals.
If
7
represents
the
cost
of
one
night,
and
7
represents
the
cost
of
one
meal,
the
relationship
between
the
costs
can
be
modelled
by
the
following
system
of
equations.
2n
+
4m
=
360
7n
+
10m
=
1200
Determine
the
cost
of
one
night
and
the
cost
of
one
meal.
14.
Car
wash
The
Outdoors
Club
held
a
car
wash
to
raise
money.
They
washed
cars
for
$5
each
and
vans
for
$7
each.
They
washed
45
vehicles
and
earned
$243.
How
many
of
each
type
of
vehicle
did
they
wash?
15.
Buying
bonds
Li
bought
a
Canada
Savings
Bond
paying
5.5%
interest
and
a
provincial
government
bond
paying
6.5%
interest.
She
invested
a
total
of
$15
000
and
earned
$925
in
interest
in
the
first
year.
How
much
did
she
pay
for
each
bond?
16.
Lawn
fertilizer
One
lawn
fertilizer
is
24%
nitrogen,
and
another
is
12%
nitrogen.
How
much
of
each
fertilizer
should
be
mixed
to
obtain
100
kg
of
fertilizer
that
is
21%
nitrogen?
17.
Tail
wind
A
small
plane
took
3
h
to
fly
960
km
from
Ottawa
to
Halifax
with
a
tail
wind.
On
the
return
trip,
flying
into
the
wind,
the
plane
took
4
h.
Find
the
wind
speed
and
the
speed
of
the
plane
in
stll
air.
18.
Car
trip
Maria
drove
from
Owen
Sound
to
Ottawa,
a
distance
of
550
km.
The
trip
took
7
h.
Maria
drove
at
70
km/h
for
part
of
the
trip,
and
at
85
km/h
for
the
remainder
of
the
trip.
How
far
did
she
drive
at
70
km/h?
Answers
13.
one
night:
$150,
one
meal:
$15
14.
36
cars
and
9
vans
15.
$5000
Canada
Savingy
Bond,
$10
000
Provincial
Government
Bond
16.
75
kg
of
24%
nitrogen,
25
kg
of
12%
nitrogen
17.
40
kain/h;
280
km/h
18.
210
km
7.
Longest
rivers
The
Mackenzie,
the
longest
river
in
Canada,
is
1056
km
longer
than
the
Yukon,
the
second
longest
river.
The
total
length
of
the
two
rivers
is
7426
km.
Find
the
length
of
each
river.
8.
Granola
One
type
of
granola
is
30%
fruit,
and
another
type
is
15%
fruit.
What
mass
of
each
type
of
granola
should
be
mixed
to
make
600
g
of
granola
that
is
21%
fruit?
9.
Investments
Zach
invested
in
a
term
deposit
that
paid
4%
interest
per
annum
and
in
a
municipal
bond
that
paid
6%
interest
per
annum.
If
he
invested
a
total
of
$13
000 and
earned
$700
interest
in
a
year,
how
much
did
he
invest
at
each
rate?
10.
Flying
speeds
A
plane
flew
3000
km
from
Calgary
to
Montréal
with
the
wind
in
S
h.
The
return
flight
into
the
wind
took
6
h.
Find
the
wind
speed
and
the
speed
of
the
plane
in
still
air.
Answers
7.
Mackenzie
River:
4241
km.
Yukon
River:
3185
km
8.
240
g
of
30%
fruit,
3¢
=
of
15%
fruit
9.
term
deposit:
$4000,
municipal
fw=
$9000
10.
50
km/h,
550
km/h
-
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