Proportional Reasoning

As a directly proportional variable increases the answer will increase by same factor.

As an indirectly proportional variable increases the answer will decrease by the same factor.

If a variable is squared the answer will increase by factor squared.

If a variable is inversely proportional to the square of a variable the answer will decrease by square of factor.

If F is doubled a will double

If F is tripled a will triple

If m is doubled, a will be halved.

if m is halved, a will be doubled

?a = 4F/m ?=4

?a = 3F/m ?=3

?a = F/2m ? = 1/2

?a = F/4m ? = 1/4

?a = F/(1/2m) ? = 2

? a = F/(1/4m) ? = 4

?a = 4F/2m ?=4/2 ?=2

?F = 2mv²/r ? = 2

?F = m(2v)²/r ? = 4

?F = m(3v)²/r ? = 9

?F = 2m(2v)²/r ? = 8

?F = 2m(3v)²/r ? = 18

?G = m/(2r)² ?=1/4

?G = m/(3r)² ?= 9

?G = m/(4r)² ?=16

?G = m/(1/2r)² ? = 1/4

?G = m/(1/3r)^{2 ?} = 1/9

?G = 2m/(1/2r)² ?=8

?G = 2m/(5r)² ? =4/25