Transcript Onestep

One Step Equations
• An equation is a mathematical statement,
in symbols, that two things are exactly the
same (or equivalent). (LS=RS)
is exactly
the same
as….
is exactly
the same
as….
• An equation is a mathematical statement,
in symbols, that two things are exactly the
same (or equivalent).
2+2
2+2
is exactly
the same
as….
=4
4
What do we use equations for?
• Equations are more
than just a pile of
numbers and letters…
Equations describe
What does the word “relationship”
mean to you?
In math, we strive to
understand the mechanics
of various relationship
All major advances in
technology (and society) have
arisen from the study of how
things relate….for example
and
Understanding the mechanics of a
relationship, which is where we will
start today, is only the start of any
mathematical analysis.
Communicating the results so others
can understand is also a key aspect to
the study of relationships. (next
chapter)
Mechanics….
Some are quite simple:
x+3=4
Some are quite complex:
x=-b +
2
b
2a
- 4ac
The most famous equation in
history only contains 3 variables,
yet it dramatically changed the
way we understand the world
around us….
These kinds of
relationships make up
the back-bone of
mathematical study
We shall begin with some
simple operations
To solve an equation:
Find the value of the unknown
that makes the equation true.
x + 7 = 10
x= 3
Some equations can be solved by
inspection….
For other equations, a procedure is
needed to ensure accuracy
Over the next few days we will
develop and practice this procedure.
To solve an equation,
remember the following:
1. Add / Sub and Multiply / Divide
are opposite operations.
2. The same operation must be
done on both sides of the
equation to keep the equation
true (or balanced).
Demonstrate with pick a number
zero
To isolate x,
eliminate the +7
You must
therefore impose
this operation to
both sides of the
equation
x + 7 = 10
-7 -7
x= 3
1
To isolate m,
eliminate the 3
You must
therefore impose
this operation to
both sides of the
equation
The opposite of
add 7, is subtract 7
1
3m = 12
3
3
m= 4
The opposite of
times by 3, is
divide by 3
1
5X C
5
1
=
-2 X 5
C = - 10
-2 + y = -5
+2
+2
y= -3
See sheets
STOP HERE
E=
2
mc
E = energy (J)
m = mass (Kg)
8
c = speed of light 3.0 X 10 m / s
Consider a 1 liter bottle of water
2
mc
E=
8
2
= 1kg X (3.0 X 10 )
16
= 9 X 10 Joules
= 90 000 000 000 000 000 J
= (ninety million billion)
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What is a Joule?
Flea: 7 – 10 J
Free throw: 15 J
Fastball pitch: 120J
Bowl a strike: 230J
Water: 9 X 1016 J
H bomb: 2.4 X 1017 J (10 bottles)
Hurricane: 3.8 X 1019 J (1000 bottles)
Supernova: 1044 J
1 watt = 1 joule expended
continuously for 1 second
• 1 liter of water converted directly
to energy could light a square filled
every 10 cm with 100 W light
bulbs for 2.5 hours.
• The square would be …
31km X 31km