The mean proportional of 4a^2 and x is 1/(5a), where a is a positive number. Find the value of x.

Question

Accepted Answer

The mean proportional between two numbers a and b is given by the square root of their product, i.e., sqrt(a * b).

Given the mean proportional of 4a^2 and x is 1/(5a).

So, sqrt(4a^2 * x) = 1/(5a)

Squaring both sides:  
4a^2 * x = (1/(5a))^2    
4a^2 * x = 1/(25a^2)

Divide both sides by 4a^2:  
x = 1/(25a^2 * 4a^2) = 1/(100a^4)

Therefore, the value of x is 1/(100a^4).

Answer

Answer

Answer