Why variables in directly proportinality are multipiled Why variables (RHS) in directly proportionality are always multiplied.
Suppose the Newton's 2nd law
$$F \propto m$$
$$F \propto a$$
$$F \propto m*a$$
Please don't give a rigorous proof. I just want to understand it intuitively.
 A: Suppose you first increase mass $m$ by twice, that is $m\rightarrow2m$ thaen $F∝m$ implies that the force should also increase twice $F \rightarrow 2F$. After this let's increase the $a$ twice- this  implies that the force shoudl again become twice, that is $2F\rightarrow 4F$.
If we simultaneously increase mass and acceleration to double then the force should increase 4 times. Symbolically this can be written as:
$$F∝m \ \ and\ \ \  F∝a \implies F∝m∗a$$
A: The first proportionality indicates that $F=m \cdot C$ for some value of $C$. Let $C=a$ and you get $F=ma$.
In the same way, the second proportionality gives you $F = a \cdot D$ for some value of $D$, then let $D=m$ and you again get $F = ma$.
A: pro·por·tion·al  (prə-pôr′shə-nəl, -pōr′-)
adj.


*

*Forming a relationship with other parts or quantities; being in proportion.

*Properly related in size, degree, or other measurable characteristics; corresponding: Punishment ought to be proportional to the crime.

*Mathematics Having the same or a constant ratio.


The number of eggs that I break is directly proportional to the number of houses that don't give me candy. I don't necessarily need to throw just one egg at every house, I could throw 3 if I wanted to, in that case I would break 3 eggs for every cheap house. $$eggs = 3 \times houses$$
