Relations between quantities

Prove that the product n geometric means between two quantities is equal to the nth power of a geometric mean of those two quantities.

In the following question two Quantities i.e., Quantity I and Quantity II are given. You have to determine the relation between Quantity I and Quantity II. ‘a’, ‘b’ and ‘c’ are positive integers. Quantity I: Value of a in ((a+b)^2 - (a-b)^2)/(8ab(a+b)^2) =1 Quantity II: Value of c in ((c+b)^3-(c-b)^3)/(b^2+3c^2)^2= 1/(8b)

In the following question two Quantities i.e., Quantity I and Quantity II are given. You have to determine the relation between Quantity I and Quantity II. Given, a, b, c and d are positive integers. I : a^(-b)/a^(-a)=a^b xx c II : (a^3xxb^3)/(axxb^2)=(b^3xxd^4)/(db) Quantity I: Value of ‘c’ Quantity II: Value of ‘d’

The velocity of water wave v may depend on their wavelength lambda , the density of water rho and the acceleration due to gravity g . The method of dimensions gives the relation between these quantities as

The velocity of water waves (v) may depend on their wavelength lamda , the density of water rho and the acceleration due to gravity g. The method of dimensions gives the relation between these quantities as v^(2)=kg^(x)lamda^(x)rho^(y) . The value of x is (Here k is a constant).

If n geometric means are inserted between two quantities; then the product of n geometric means is the nth power of the single geometric mean between two quantities.

Relation between torque and angular momentum is similar to the relation between