The variables x, v, and a have the dimensions of [l], [l]/[t], and [l]/[t]2, respectively. these variables are related by an equation that has the form vn = 2ax, where n is an integer constant (1, 2, 3, etc.) without dimensions. what must be the value of n, so that both sides of the equation have the same dimensions?

The value of n must be 2, so that both sides of the equation have the same dimensions.

Explanation

The variables and have the dimensions of and respectively.

These variables are related by an equation that has the form

So, the dimension of the left side ⇒   ⇒

and the dimension of the right side ⇒ ⇒

If both sides of the equation have the same dimensions, so...

So, the value of must be 2.

step-by-step explanation: yes

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)