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Math Refresh
• Evaluating Equations
– We have 4 basic relatiojnships
•
•
•
•
Y= k X
Y=k/X
Y=k Xn
Y=k/ Xn
Direct Proportion
Inverse proportion
Direct Exponential
Inverse Exponential
Direct Proportion
• Y=kX
• This equation of a straight line with slope k
• As X increases, Y increases by same proportion
– If you increase X by 10%, Y will increase 10%
– If you double X, you will double Y
8
6
4
– Very straight forward
2
0
-10
-5
-2
-4
-6
-8
0
5
10
Inverse proportion
• Y= k / X
– If you increase X by 10%, Y will decrease by 10%
– If you double X, Y will decline by factor of 2
– Y and X move in opposite direction, one increases,
the other decreases
1.20
1.00
0.80
0.60
0.40
0.20
0.00
0
5
10
15
Direct Exponential
• Y=kXn
The Exponent n is very powerful
If n=2 and you double X, then Y increases
by factor of 4
If n= 3 and you double X, Y increases by
factor of 9
120
100
80
60
Series1
40
20
0
0
5
10
15
Inverse Exponential
• Inverse Exponential
–
Y=k/ Xn
– Again, n is very powerful, but now it increases
the effect of X in the denominator
1.20
1.00
0.80
Y
0.60
Series1
0.40
0.20
0.00
0
5
10
X
15
Math Refresher
• Inverse Relationship
• Y= 5/X Y declines in proportion to X increasing
• Y =5/X2 Y declines much faster with X increasing
( Inverse Squared relation)
• For example when x=1, then Y=5
• But when x=2, then Y = 1.25 or one fourth what is
was when x =1
• What is Y when x=3?
Powers of 10
• There are 31,557,600 seconds per year
• Light travels at 300,000,000 meters per
second
• Distance traveled in one year
9.47 x 1015 meters
3.15576x 107 x 3.00 x 108 = 9.47 x 1015 meters
Powers of 10
• Scale of Universe
1.5 x 1026 meters
Scale of Hydrogen Nucleus
1x 10-15 meters
The range of Powers of 10 from atomic scale to
Scale of Universe
Is captured by 41 powers of 10
Powers of 10 Rules
• Multiplication
– ADD the exponents
Division
Move the Exponent terms from denominator to
numerator and change the sign of exponent
Then proceed as with Multiplication, ie, add the
exponents
Example
• E= MC2
• Solve for Mass of an electron if its mass energy is
8.19 x 10-14 joules and C = 3.0 x 108 m/s
• M=E/C2 = 8.19 x 10-14 / (3.0 x 108)2
= 8.19 x 10-14 / (9.0 X 1016 )
= .91 x 10-14 x 10-16
= .91 x 10-30
= 9.1 x 10-31 kg
Math Refresher
• Evaluate in Powers of 10 notation
• (30x 80,000,000,000)/.0004
= 3.0 x 101 x 8 x 1010 / (4 x 10-4 )
= 6 x 101 x 1010 x 104 = 6 x 1015
• 0.0001/(60,000 x 200)
= 1 x 10-4 / (6 x 104 x 2 x 102 )
= .08 x 10-4 x 10-4 x 10-2 = .08 x 10-10 = 8 x 1012
Algebra
• a/b = c/d
Must be able to solve for any one of the
four if you know the other three
So: a = bc/d
b = ad/c
c = ad/b
Math Refresher
• For further review, in appendix A of Text