Which of these equations is dimensionally correct? I. mv/ t= F
II. xv^2= Fx^3/ x^2
III. xt= vt^2+at^3

first and third.

Explanation:

An equation is dimensionally correct if the units are the same in both sides of the equation.

first, let's define the units used:

{m} = kg

{v} = m/s

{F} = kg*m/s^2

{x} = m

{t} = s

{a} = m/s^2

Now, let's analyze each option:

1) m*v/t = F

in the left side the units are:

{m}*{v}/{t} =  kg*(m/s)*(1/s) = kg*m/s^2

And as is written above, these are the units of F, so this is correct.

2) x*v^2 = F*(x^3/x^2)

This is more trivial, in the right side we can see an F, that has mass units (kg)  and in the left side we have x and v, and we know that none of these have mass units, so this expression is not correct.

3) xt= vt^2+at^3

the units in the right side are:

{x}*{t] = m*s

in the right side are:

{v}*{t}^2 + {a}*{t}^2 = (m/s)*s^2 + (m/s^2)*s^3 = m*s + m*s

So in both sides of the equation we have the same units, then this equation is dimensionally correct.

the largest known star in the universe is uy scuti, a hypergiant with a radius around 1,700 times larger than the sun.jul 26, 2018

explanation:

the working equation for the angular size is the product of the physical size and 360 degrees divided by the product of two pi and distance from earth. the minimum size would be 0.559 degrees while the maximum size would be 0.49 degrees.