Math · Physics

One way of solving an equation with 2 variables

When trying to solve a problem, you may run into a situation with 2 variables. At first you may feel stumped. But just take a breath and ask yourself: “Is this a situation where one of the variables may be redefined by some factor of the other variable?”

What does this mean?

a situation with 2 variables

Well consider the following problem.

24 vehicles pass by a traffic monitor. Some of the vehicles are motorcycles and some of them are 4 wheeled vehicles.
There were 80 wheels in all.

 

How many 4 wheeled vehicles went by?

When first thinking this through one realizes that there are 2 variables to this problem.

X is for motorcycle with 2 wheels and Y is for a vehicle with 4 wheels.

2X + 4Y = 80

But are there really 2 variables? In terms of wheels you could say that Y is equal 2x.

y = 2X
2X + 4(2X) = 80

Then solve for X.

2X + 4(2X) = 80
2x + 8x = 80
10X = 80
X = 8

Now since you know Y = 2X, solving for Y is easy.

y = 2X
y = 2(8)
y = 16

By this you cans see that 16 vehicles with 4 wheels  went by.

When faced with multiple variables, see if it is possible to redefine variables in terms of another variable.

 

 

 

 

 

Physics

Physics: change

The notes found here will reflect my fascination with unlocking the secrets of fundamental physical constants. Locked within these constants are secrets to the connection between classical physics and what has been described as the “weird” and even nonsensical world of the Quantum mechanics.

This first note under the main category of physics in this blog, will be a mention of “change”. In the world of math and physics, change is usually denoted by upper-case letter Δ or

 

Delta, Δ, is the first letter of the Greek word for “difference”,  διαφορά diaphorá. The lower case “d”, ∂,  is also used to describe change by notation of derivatives and differentials.

Describing change is of absolute importance if one is to understand the truth of what is actually happening in a physical system.