How do you turn a proportionality between variables into an equation?

Answer. By adding the proportionality constant .

Explanation:

suppose 'x' a  is directly proportional to the 'y' , where x and y are variables:

x ∝ y

with an input of constant value 'K' proportionality relation gets converted into  an equation:

x = K y

For example : Gravitational force is directly proportional to the product of two masses and inversely proportional to the square of the distance between the two masses.

F ∝

To convert this proportionality relation constant 'G'  was introduced known as gravitational constant whose value remains constant under every conditions.

samuel de champlain. in 1608, king henry iv sponsored pierre dugua, sieur de mons and samuel de champlain as founders of the city of quebec with 28 men. this was the second permanent french settlement in the colony of canada.

first let us lay out the formula for potential

and kinetic energy:

pe = mgh

ke = (mv^2)/2

where: m=mass, v=velocity, g=gravitational

acceleration, h=height

calculating for mass using the known values of

pe:

340j = m (9.81 m/s^2) (50ft) (1m/3.28ft)

m = 2.27 kg

the law of conservation of energy states that

energy is neither created nor destroyed. therefore, the change in kinetic

energy from 50 ft to 35 ft would be equal to the change in potential energy

from 50 ft to 35 ft. however it would be opposite in signs since one is losing

while other is gaining.

ke(35ft) – ke(50ft) = - [ pe(35ft) – pe(50ft]

ke(50ft) = 0 since the brick is initially at rest

ke(35ft) = 340j - 2.27kg (9.81 m/s^2) (35ft)

(1m/3.28 ft)

ke(35ft)

= 102.38 j