0.
Notes for
Engineering
Mathematics A
...
;.~\-
\;:;?\
'\SJ
~;;
:\
}.·\
.
.
··~· .
·.. ..: .. ,,
.
'
'
...
Acknowledgements
Project Manager:
Max Gregory
Writers:
Jon Phillips
Mel Williams
~
ijiJ
Section 1 Arithmetic
1.1
1.2
1.3
(' ·:
Rational numbers and surds
S.I. units and scientific/ engineering notation
Approximations, errors and significant digits
Review
Answers to activities
ta
Section 2 Algebra
2.1
2.2
2.3
2.4
25
Basic Algebra
Indices and linear equations
Factors and simple trinomials
Factors of harder terms
Transposition and evaluation
Review
...j
Answers to activities
Section 3 Geometry
3.1
3.2
3.3
3.4
Angles
Triangles
Quadrilaterals
Trigonometry
Review
Answers to activities
Section 4 Coordinate Geometry
4.1
The number plane
4.4 The equation of a straight line
4.3
4.4
D
.
'\
Function notation
Simultaneous equations
Review
Answers to activities
Section Contents
.~'.:
-
1.1
1.11
1.12
1.13
1.14
1.2
124
1.25
1.26
(
.
(jllJ
Rational & Irrational Numbers
Surds
Manipulation of Surds
Activity 1
S.I. Units and scientific/engineering notation
1.21
1.22
1.23
,;'
3
Rational Numbers and Surds
6
Indices Base 10
Scientific and engineering notation
Activity 2
S.I. units & basic conversions
Harder conversions
Activity 3
4
; r::-
1.3
Approximations, errors· and significant digits
1.31
1.32
1.33
1.34.
13
Approximations
Errors in measurement
Significant figures
Activity 4
Review
17
Answers
18
1- 1
.
.
Arithmetic
A
\(!:)
At the completion of this section you should be able to:
f
-:..-
-::
D
simplify expressions involving square roots and cube
roots of rational numbers
D
evaluate expressions involving square roots and tube
roots
D
convert numbers using laws of indices in base 10
D
convert values between decimal notation, scientific
notation and engineering notation
D
convert units pf physical quantities expressed in SI units
D
show awareness of errors in measurement and calculate
maximum probable error of a measurement
D
give results in appropriate number of significant digits
D
use estimation and approximations to check the
reasonableness of results
:
,>,
t ..
€).
Cc).
().
I
1-2
Arithmetic
1.11 Definition
Any number that can be expressed in the form a , where a and b are
b
integers and b:;t: 0, is said to be rational. For example, the numbers
·na1.
-128
- - are ratio
4'5'25
Any number that cannot be expressed in the form a , ·is said to be
.
b
irrational Examples of irrational numbers include tr (the ratio of the
diameter of a circle to its circumference),
}i, V4.
..fi,
1.12 Surds
.J4 = 2 is a rational number since 2 can be written as 21 .
Consider the term ./3 (..[j = 1. 7320508... ), which cannot be expressed in
Note. that
!: . This term is irrational and is called a surd. Any number
the form
b
written -with a radical (.[) si~ that is also irrational, is called a surd.
Other examples include:
.Js, 3..fi, 1 + ../2, ..ff - .Js.
Example 1: Determine ~hether tl:le following numbers are ratio~ pr
. irrational. _·.
...
.
.
. .• •. . ... . 9
'
. (a).
0.9
(b)
·. Vf6··
(c)
Js
(d)
1
<i
. -10
. ..
...
........ .
.
· O9- · · rationalii · .
· .Jl6 = 4
rational ...
../5 = 2.236 ... irrational •-·
..
Ji
(e).
;{ii.
(f)
Vs .
1
../3 -
1
---irrational
1.732.~ ..
V27 = 3
ratio~
. (note 3j(3x!3=27)
VS =2· · ·. r~ti~nctl
. .: ·• •·
·(note 2x2x2=8) ·.
1-3
Apthmeµc
1.13 Manipulating Surds
There are some basic rules that must followed when working with surds:
..jab =
.Ja Jb
X
Ji= 7,,
c:·
'.
®
::
'
-:
j
:•:.· .. : ·.:.·:
...::::\:\.·'.'···:·.····
. ;... ::·:~: :-·, ;'" ..
(e):J:ii~f
~i
·
· ·..·. ·.· . . .r. •.
~..
.:..:...
·.
:"
. :..-··. ~;
·.::.·:·· . . . . . -: ·.....
:...: ::_~·:·· ·.-i:. _:~}'.: ::·/:::{:.;-: ~.. :. .
;
··.•:·:·.. ~
;/8:ti :: :....Jili.: ..· ·... · ·
:==Jix~•.
·.·.=3 ,'
t~1~!l ·. · ·.
0
. ·. =2
Pih
~
1-4
· Arithmetic
....
1.14 Activity 1
Use a calculator to evaluate the following (to two decimal places)
{a)
../63-../5.i
(b)
(c)
345
0.123x0.0412
(d}
(e)
('.;..
..
'
Vw
../Io-.fi
(f)
2.99 + ~./7 .63
3.14 X .Js.g
30-J3o
3 V-1s + s.Jii
Simplify the following, leaving your answer as a surd where
applicable.
'
(b)
2,.J6 X '3-,J5
(c)
../s 8/i. -
(d)
.Jio +Ji.
(e)
10./3 + 5./3
(f)
16./8 + .Js
X
Simplify, leaving your answer as a surd where applicable. ·
.,fil
(b)
4/&
(c) .fii-..fi
(d)
Flo X Jg
"./4o
{a)
(.. ...
~
'
(e)
®
3l
49
{f)
,4
16
2../6 X 3./5
~
1-5
A1
\;_:)
.. ···-~·-··.·:-s:.···\~:: --:·: i-'- :.: . · .. . •....
:- ·: ·-~-- . ~: :_ ·= :-:· ....; ·.,·:· - ::··
...
.
.....
~
;- : .-.:.=-= ··-:
•
. •.
··:::.:-:::·_;:}?( .~:rr.f,.:i:·::: .·.-:-:·....
1.21 Indices: base 10
Numbers such as 10, 100, 1000 or 1, 0.1, 0.01 etc, can be expressed in
index form by noting the following relationship:
10 1 = 10
10 2 = 100
3
10 = 1000
10n
1 followed by one zero.
1 followed by two zeros.
1 followed by three zeros.
=10000 .....
1 followed by n zeros.
We could state further that
10° = 1
10-1 = 0.1
10-2 = 0.01
10-3 = 0.001
1 followed by no zeros.
1 preceded by one zero.
1 preceded by two zeros.
1 preceded by three zeros.
~
~
When multiplying or dividing numbers expressed with indices some
basic rules apply.
Rulel
10a x }Ob = 1oa+b
Rule 2
IO a + IOb = 10a-b
>{c}IO~/:?<:'fO.:; i~:;ilo~i ·
·. ·. ::)~~:::t'::;;(:;;i;~ifr~
2~: ' ·. ' > .. ·•
.
:-:·.:-. . .
=:0.01 .·
iii'. J;1&:);{1 o:: ·. • . . •
1
(~)
.. , 10 , ~ 10
.· .. ·.;:,,...
·;·;·:·;
JO .
L:lrli
V
.
A
Arithmetic
1.22 Scientific and Engineering Notation
'tt;I
1.
Scientific Notation
Scientific notation (sometimes called standard form) requires numbers to
be expressed in the form a x 1on where I 5 a < l O. ( a must be bigger
than or equal to 1, but less than 10).
.
.
?(ci} 446- = 4l46 x010
l·· :
V
2
: .•-
The decimal point is placed, generally between the first two digits, to
create a number between 1 and 10, and adjustments made to the index of
10. Compare the index with the number of places the decimal point has
moved.
·_- Examples:~:fuefcillo~ginscte.rt¥c.:rtotation. · •
::., ·<:·· -~ ..
. .. ·.: ... : .::;~::,:-:;.:,:··.-:..~:·· ..
~
Jd) 0~046 ~k6xHf
2 _.- ••. - •• _ ·:
:
: .
.
.: ··.
.
:
.
:
::._.
··kfo.oo&~ .~ 8~9 x~~~j: · ·
In the examples:
large numbers have positive indices,
small numbers have negative indices.
2.
Engineering Notation
Engineering notation also requires numbers to be written in the form
ax ion, but where 15 a <1000 and the index of 10 is a multiple of three
3
3
6
(10- ' 10°' 10 ' 10 etc).
Bxa.mple6:
Write the following in engineering.notation..
_ (a) 446000 ~ 446x 103 ·
(c) 12500 = 12.5 X 103
·-··). -·-··-..-· .... .: .: ·• .•. -_· ·. -_-
.
(b) 1138,6
:.~. -..
.•· ·
{d) 72~0000000 = 720; ~0 9
__ .
. . '3. _- .
{e) 0~046..= 46.0xlO-
· ·- (f}0.386 ~386.0 x16~~ .. ;.:.:.
.
{g):~~000000890 ·= 890 x 10-
9
®..
= l.1386x 103
. •
..
.
~--··
·.
.
...
·
..
(h) -0~00072~ = 721 x10~.•
1-7
Arithmepc
1.23 Activity 2
.
.
CB•
I
1 Use the index laws to simplify, leaving answers in index form.
10 4
(b) 10 4 + 10-2
10-S X 10 3
(c)
104
10-2
(d) 10-3 X 10-6
10-3 X 10-s
(e) 10-2 X 10-4
. 10-S X 10 7
(/) 10-2 + 103
(a) 10 6
X
2 Complete the table below
Decimal
notation
Scientific
notation
Engineering
notation
24700
84000000
0.00123
,...
i6
X
10-l
155 X 10 6
3.52 X 10 5
32.1 X 10-3
3 Write the following as decimals
r··
'·
(a) 1.35 X 10-2
(b) 75.9 X 10-6
(c) 354.5 X 10 3
(d) 1.345 X 10 4
~.
V
/!Pit-.
~
1-8
Arithmetic
ft
1.24 S. I. Units
~
The number system based on multiples of 10 is called the System
Internationale or SI system of counting. All units in this system differ by
3
factors of 10 and, in particular, by factors of 1000 or 10 •
For example, 1 kilometre is equivalent to 1 x 10 3 metres or 1000m.
Each quantity in the system has a base unit The table below lists some of
the more common quantities used in engineering, with the appropriate
base unit
Quantity
/,
.. -.:
~
lensrth
time
mass
velocity
acceleration
area
volume
potential
difference
current
resistance
force
power
work
Base unit
metres
seconds
kilograms
metres per
second
_ metres per
second squared
square metres
cubic metres
volts
amperes
ohms
newton
watt
joules
Units
m
s
kg
ml s or ms-1
ml s 2 or ms-2
m2
m3
V
...
A
n
N
w
J
There are many other units used to express quantities, each one differing
by 1000 from the previous one.
Quantity
pico
nano
micro
milli
base unit
kilo
mega
giga
Order
base unitx 10-12
base unit X 10-9
base unit x IO~
base unit X 10-3
base unit x 10°
base unit x 10 3
base unit x 10 6
base unit X }0 9
Prefix
p
T/
µ
m
quantity
k
M
G
t.:t'".\
0
1-9
.
Arithmetic
...
One quantity that is not included. on page 9, but which is commonly
used, is centi (base unit x 10-2 ), as in centimetre (cm). Strictly speaking
only multiples of 1000 should be used in the SI system.
1.25 Harder Conversions
1
Areas and Volume
Consider fue two squares below. They are the same size but each is
measured in different units.
1m
1000 mm
D1m
Area= Im
D10d0mm
Area
2
= 1000 x 1000 mm 2
= 10 6 mm 2
Both of the squares above are exactly the same. The relationship between
units when squaring (area) or cubing (volume) can be shown as:
Area lm 2 = 10 6 mm 2
Volume
:·Example 8: "Nofofhe
1m 3
followfu.Kconvemons..,.·. · · •· · · .
.:::.: :../:· ·(-.:f: :.. :.. ·>- . .--~~::.:··; /·:::: .· ·: .<{·:-.~·.:::_.:.:,_:.-.::~ .·· . :: .·.. :::
··:·.(g}1·~~;
= 109 mm 3
.+.:~kjiQ~:ni2··•.··
.
~-:·
··~::·:· :. :·:
..... ~-..: ... ;.:·:·.<>/:. > .
.. =:::·:..t.::::·:.; <:-.:~~· ..... :.. -~ ·,_ ~ ~
..... :•. ,..,:: ... ;·:·.···;-
..
:;: :·.·:.>:_ ....
;·:\•(iIJJ.:mf;;g;··:f.~[ijf-'.f&n-,•:•;
. ..
1-10
-.~··: ·. •.
··.
\;:. ~-;,.:.
:.··,.·
@
...
Arithmetic
2
Related Rates
Velocity is measured in base units as metres/ second, acceleration as
metres/ second squared. These are examples of related rates and when
converting units, both quantities must be changed.
JL ..
;~
3
Liquid Measure
The litre ( Z), used to describe fluid capacity, relates to volume in the
following manner:
IZ = 1ooom1
1m1 = 10-3 z
4
lm 3 = 100oz
IZ = 10-3 m 3
1ml = 1000mm 3
if(_.
~-
-
1 mm 3 = 10-3 ml
Example 10: .Convert the following~ ·. · •·
.(d}i~j~.~~ i. . . .
3
:
.
. . ..
~
.
.
.
.
..-..
. ..
3
.· (b)0~58m tp{ :·:
1-11
..·. '-······~'··:;;
Alj.thmetjc
1.26 Activity 3
1
Convert the following
=
=
=
(a)2.8km
(e)l0 6 g
'···
s
mm
=
ms
µm
=
17s
=
=
V
mV
GV
=
A
=
µA
=
.MA
(d}300kV
=
(f)3mA
(&).
Convert the following
(a)0.27m 2 =
km.2
mm2
~-=
(c) 250 m 3
=
cm2
=
=
mm 3
(e) 30km/h
(
cm3
l
=
. 1-12
(b)53.lµs
=
kg
mg
Mg
=
=
=
(:i
3
m
= n
= kn
= an
(c)6.MQ
2
G)
=
=
=
m/s
mm/s
mm/min
(b)4 X 10 6 mm 2 =
(d) 12 X 10 6 ml
m2
=
km2
=
cm2
=
=.
l
=
mm3
m3
(/) sooz I day = m 3 /h
=
=
ml/s
ml/day
Express
(a) 204g in kg
(b) 0.74A in mA
{c) 0.94N in kN
(d) 12km2 in m 2
(e) 3000ml in mm3
(f) 4 x 10 6 Ml/ day in m 3 / s
()
'
...
Arithmetic
1.31 Approximations
· When working with a calculator to derive answers to any mathematical
problem, it is important to have an approximate idea of what the answer
should be. This approximation is not meant to be accurate, but is
designed to stop wildly inaccurate calculations from giving false results .
.:~~~~1~:,1.-~:~i>~f9~tfo!15~the~y()~~:·~!1aticins;>•-· ._.·
•t1rz,:1tht1ji40,:tc: ~~~~r¥:i1:::j;t_·titt,jr\2
·:.:: ..::=t:\:);:\\i.
.
·-·:.::.::.
!;!!~:~:;~;:;
>IF;6•:•.••
·+-0.5.
?i·"t;t~r~r;_[_ii:"
·'.• ..::: .·:_:··:':";--:·i :::.· :
The answers above are not accurate. They reflect the order of the correct
answer. If a calculator produced an answer of 23267 for example lO(a),
then the approximation allows you to doubt the result-and check the
calculations. Also note the use of the ~ symbol to indicate
"approximately equal to".
1.32 Errors in Measurement
Any quantity measured has a certain error in the measurement. This
error may occur for any number of reasons, including:
inappropriate measuring instrument;
temperature changes;
human fallibility.
Maximum Possible Error (MPE)
When stating an answer for any measurement, the number of decimal
places used is often an indicator of the level of perceived accuracy. The
Jv.lPE is derived from this accuracy. As an example:
a distance measured as 10.3m indicates accuracy to one decimal
place or O.lm. The actual distance is between 10.25 and 10.35m
and the 1v.lPE =0.05 (one half of O.lm above or below 10.3m).
1-13
Arithmetic
...
'
a rustance measured as 10.30m indicates accuracy to two decimal
places (O.Olm). The actual distance is between 10295 and 10.305m
and the :MPE=0.005 (one half of 0.01 above or below 10.30m).
The :MPE could be found by taking one half of the next decimal place in
the answer and indicates the range of the answer. The :MPE can a1so be
expressed as a percentage of the original measurement.
.. . . •..•
::: :;:;: ... •,•.'.,::·; .., ·. ···:,....:~-.;:?:·.~:/:)::··:.:::; ........ ·. :-·-···.: ..... .
..
.::: ·:::::·. · : ·:·: ~:·.:. :. : : : : ~: :·
. .:-~~-·- ::}~<:::::}::~:.:?
'•. ·.. ·:; :;_ ·:;-..::j::::: :/:/>·~=_:\· .: ~~ ·: · : :_._. : ·. 5' ·::.· : =-·:~:..,:.:; :.
.
·.·.
_;:.·:
;::·:·: ·-··:<:=~=-·
..;;_::.::::·:·\::;.-:::··
.··=:-•--.>X-. ·•
... 6005:•··· •./.a:: :
~-0.00833% .
Percentage Error
An error of SmA in a reading of 40mA suggests an actual reading
somewhere between 35mA and 45m.A. The absolute error is SmA.
An error of SmA in a reading of 40A also gives an absolute error of Sm.A.
Obviously there is a difference in the accuracy of the two measurements
and this can be found by converting the errors to a percentage.
C.,.
'Example 12: Convert to a percentage erro! .. ·
. .
.·
.. :·.:·:::·:! . ::-: ...
... :·.
-~: .
.......... •.;
··:·(af1?.~r.:¥:··•·~•n:0-_iit40Trl4.:·i.::
5 100 .. .
··.•,·'<•
..........
=40X.T'''
. :~ ...·.!.
1-14
01
\..;F
...
Arithmetic
1.33 Significant Figures
The accuracy of an answer can also be expressed in significant figures.
ForexampIB,
_
a measure of 10.3m is stated to 3 sig. fig. and suggests an actual
measure between 10.25 and 10.35.
a measure of 10.30m is stated to 4 sig. fig. and suggests an actual
measure between 10295 and 10.305.
There are some basic rules that must be obeyed when working with
significant figures. These are:
The first significant figure is the first non-zero digit, moving from
left to right.
All non -zero digits are significant
Zeros between other digits are significant.
Zeros written after a decimal place are significant.
Zeros at the start of a number are not significant.
Zeros at the end of a whole number may be significant. If they are
some indication should be included with the number.
:•••·Number
.··1206
...
:0.3010
•,
... i:210
··· .. 0.301
·.
<> .i•~~'030.
...
:.-: ..
:... fa·:-: :·: .;
:. :.~.· ······ ·-:-:-...·.:·: <;.... .:}t··.:;·:-:·:·::
. > >iiooo:);/·::<:j-):
. •. : .::it(3_• .
.
:··3a4
1.81
. . .
.
4 .
4
..
:
•
•:
.
,:
E4lx10
. L.405xl0 •..·.
0.00003450 ·
R0000345
·.: ,6800.
./:68QO.
3~14159 .... ·:•·. / . . .
.· ·: 1.805
In generaL when calculating any practical measurement, cµ15Wers should
be given to the least number of significant figures in the information.
In practical terms, to minimise error, measurements are written accurate
to the least number of significant figures in the data. For example,
98.61 x 51.3 x 0.46 = 2300. The answer is stated to two sig. figures (the
data has scores of 4, 3 and 2 sig. figures).
1-15
Review questions
These questions will help you revise what you have learnt in Section 1.
1.
Name the two measuring systems commonly used in Australia.
·----------------------------·-----------------------------
2.
-------
3.
Match the symbols to the units by writing the symbol in the brackets beside the
unit.
millimetre
(
)
in
metre
(
)
mm
kilometre
(
)
ft
inch
(
)
t
foot
(
)
g
yard
(
)
op
Celsius
(
)
yd
Fahrenheit
(
)
lb
gram
(
)
t
kilogram
(
)
km
tonne
(
)
kg
ounce
(
)
oc
pound
(
)
oz
ton
(
)
m
- - - - - - --···-
Use a calculator to convert 3.750" into mm.
EPC87 Introduction - Measurement
Student Workbook
January 1999
.......... ~,
.... O : O U C A ' T I - ~
19
il1~1
12.
Use a calculator to convert 127 .6 lb into kilograms.
1~.
Use the Kilograms, Pounds Equivalents chart to find the equivalent kilograms for
57 pounds.
14.
Use the Kilograms, Pounds Equivalents chart to find the equivalent pounds for
98 kilograms.
15.
Comparative measurement uses a master component as a standard to compare
other components against. True or false? (Circle the right answer)
16.
Dirty measuring instruments won't affect the accuracy of measurements taken.
True or False? (Circle the right answer)
EPC87 Introduction - Measurement
Student Workbook
January 1999
Ii,,~
.
···--··-a
:::::;.:
,.,.o ..""'"""•,;t:
21
'•\
,•
=I
.
Arithmetic
...
1.34 Activity 4
1 Find approximations to the following and then use a calculator
to·find an accurate answer to three sig. figures.
(a) 9.8 X 19.5 X 11.8
(b) 199x48+5.l
20.2 X 10.3 X 9.8
5.4 X 14.8
(d) ~51.4 + ../fo34
~19.2-(13) 3
(c) .Jl03.4 X 3.4
10.6 X .J321
(e} 8.87 X 10 3
+ ../38.5 X 10 4
(f) 1.405 X 103 - 23.4 X }06
.Js.32 x 101
2 Find the percentage :MPE of the following. State also the range
of each measurement
(. ,; ::
(a) 6.38m
(b) 6.380m
(c) 6m
(d) 0.006km
,..
(e) 6.38 X 106 µm
(/) 638mm
3 Find the percentage error of the following.
(a) 4mA in 50mA
(b) 0.5V in lkV
(c) 2mH in 25H
(d) Imm in 15m
(e) 120µ.A in 4mA
(f) 6Hz in 200MHz
4 Copy and complete the table of significant figures
Sionifirant Figures
Number
3
2
1
30200m
1.004.A
7.015N
0.003251m
0.03456kg
43000
1-16
\
¥thme1:ic
Answers
Activityl
1
(a) 029
2
(a)
J6
3
(a)
if2
®
(b) 5.75
(b)
(b)3
Activity2
(a) 1010
1
2
(:..
fr/3o
(b) 106
(c)
(d) ~
MO
(d) 5.fi.
(c) 5../i
(c) 10....s
(d) 10 7
(e) 526
(f) 11.97
(e) 2
(f) 16
(e) 9.fi.
(f) 6,./2
7
(e) 10-2
{f) 107
24700
2.47x 10 4
84000000
8.4 x 10 7
1.23 X 10-3
7.6 X 10-l
24.7 X 10 3
84 X 10 6
1.23 X 10-3
760x 10-3
1.55 X 10 8
155 X 10 6
· 3.52 X 10 5
3.21 X 10-2
352x 103
32.1 X 10-3
0.00123
0.76
155000000
352000
~.0.0321
3
(c) 68079.56 (d) 0.38
(b) 0.0000759
(a) 0.0135
(c)_ 354500
-
(d) 13450
Activity 3
1
2.8 X 10 3
53.1 X 10-6
(a) 2.8 X 10 6
{b) 53.1 X 10-3
2.8 X 10 9
~.·
53.1 X 10 3
0
X
10 6
(c) 6 X 10 3
6 X 10-3
@
{~\
.
300 X 10
3
(d) 300 X 10 6
10
3
3 X 10-3
(e) 10 9
(f) 3 X 10 3
300 X 10-6
1
3 X 10-9
0.27x10-6
4
250xl0 9
2
(b) 4 X 10-6
(c) 250x10 6
2.7x 10 3
40 X 10 3
250xl0 3
12 X 10 3
8.3
0.02
(a) 0-27x10 6
(e) 8.3xl0 3
(d) 12
12 X 10 9
3
1-18
(a) 0204
(b) 740
500xl0 3
(c) 0.00094
(f) 5.79
500xl0 3
(d) 12 X 10 6 (e) 3 X 10 6 {!) 462%
e
Arithmetic
....
A
u
Activity4
1
(a) 282
2
(b) 0.919
(c) 0.182
(5.5-6.5)
(e) 0.078 % (6.375-6.385)
3
. (f) 594
(b) 7.84x 10-3 % (6.3795-6.3805)
(a) 0.078% (6.375-6.385)
(c) 8.3 %
(e) 9490
(d) 1.79
X
10 6
(d) 8.3 %
(0.0055-0.0065)
(f) 0.078%
(6.375-6.385)
(a) 8 %
(b) 0.05 %
(c) 8 X 10-3 %
(d) 6.67 X 10-3 %
(e) 3 %
(f) 3 X 10-o %
4
30200m
1.004A
7.015N
0.003251m
0.03456kg
43000
( ·.
V
Review
1
30.2
1.00
7.02
0.00325
0.0346
43000
30
1.0
7.0
0.0033
0.035
43000
Estimates first then calculator answers.
(a) 6-14 ~ -8
(b) _2_.., 3
2.5
(c)
170 X 2 :,; 170
2
(e) 2 X 10 2
(f} lx 60.., I
(a)-7.05
(d) 4820
(b) 4.37
(e) 214
(c) 197
(f) 1.15
(a) (i) 5.608xl0 7
(ii) 56.08 X 10 6
{b) (i) 9.78 X 10(ii) 97 .8 X 10-9
(c) 0.0000983
(d) 68300
(a) 0.5816kg
(d) 15000m 2
(b) 3.567 X 10-3
(e) 12.96km/h
(c) 95.2A
(a) :MPE=0.005
(b) PE=0.0366%
(a) 18
(d) .2.
(b) .Jio
(e)-3
(d)
L
30
1
7
0.003
0.03
40000
4400.., 4400
1
60
2
8
3
4
5
.fi.
(c) 2
(f) 10-2.../5
@
1-19