Greenwood press

24
EQUATIONS

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EQUATIONS
25
of the fraction’s denominators, or 
15T
c
, the equation can be rewritten as 
5T
c
+3T
c
= 15. After combining like terms and dividing both sides of the equation 
by 8, the solution will be 
T
c
=
15
8
, which translates to 1 hour, 52 minutes, and 30 
seconds. Reciprocal equations exist in other applications as well. The image 
formed by a converging or diverging lens can be located with the equation 
1
D
i
+
1
D
o
=
1
F
, where 
D
i
is the distance from the lens to the image, 
D
o
is the distance 
from the object to the lens, and 
F is the focal distance of the lens. 
Sports statistics involve unusual equations. The NFL quarterback rating is a
computation that measures the effectiveness of a player based on his number of
touchdowns (t), interceptions (i), attempts (a), completions (c), and passing
yards (p). The equation that determines the quarterback rating, r, is
r = (500c + 25p + 2000t + 12.5a − 2500i)/(6a).
Notice that interceptions are weighted so that the rating decreases by more than
the value of a touchdown, and that touchdown passes are weighted four times as
much as a completion. This equation is proportioned so that the average quarter-
back will have a rating near 100, according to historical performances in the
league. This equation is based on NFL statistics and needs to be adjusted for
other football leagues, since the fields and rules are slightly different. For exam-
ple, scoring in the Arena Football League occurs more often, since the field is
only 50 yards long, compared to 100 yards in the NFL. 
online sources for further exploration
Arena Football League quarterback rating

Robert Boyle and his data

Boyle’s Law and absolute zero and Cartesian diver and Model of Lung 

Burning rate of stars

Calculate the escape velocity

Euler’s formula and topology

Ideal gases

Image forming by a lens


Orbit simulation

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Quarterback rating system


Seventeen proofs of Euler’s formula

Universal law of gravitation

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