Agas with constant temperature has a pressure of 4 atm this pressure changes to 0.2 atm causing the volume to increase to 500l what was the initial volume of the gas

Explanation:

The problem can be solved using Boyle's law for the volume and pressure of a gas at constant temperature:

Where the quantities with sub-index 1 are the initial conditions for the gas and the quantities with sub-index 2 are for the final conditions of the gas.

We want to know the initial volume, this is:

we also know from the problem that

Thus, the initial volume V1 is:

force is mass*acceleration.

we have a very small mass: 11.4*0.001 kg

if we want 0.035n of force, we need an acceleration:

0.035 = 11.4*0.001*a

a = 0.035/(11.4*0.001) m/s^2

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .