Question

A Water clock used in ancient Greek is designed as a closed vessel with a small orifice O.The time is determined according to the level of the water in the vessel. What should the shape of the vessel be for the time scale to be uniform. find mathematical equation governing curve AOB.

Answer 1

Answer:

Solution:-

f:N→Y

f(x)=4x2+12x+15

A function is invertible if the function is one-one and onto.

Let x1,x2∈N, such that

f(x1)=f(x2)

4x12+12x1+15=4x22+12x2+15

⇒(x12−x22)+3(x1−x2)=0

⇒(x1−x2)(x1+x2+3)=0

∵x1,x2∈N

⇒x1+x2+3