18 Rearrange multi-variable equations

Question

WSJ
Solve for v in terms of s, t, and u.
s=
–
uvt
v=

Answer 1

To solve for \( v \) in terms of \( s \), \( t \), and \( u \) from the equation

\[ s = -uvt, \]

we need to isolate \( v \). Here's how to rearrange the equation step by step:

1. Start with the original equation: \[ s = -uvt. \]

2. To isolate \( uv \), multiply both sides by -1: \[ -s = uvt. \]

3. Now, divide both sides by \( ut \) (assuming \( u \) and \( t \) are not zero): \[ v = \frac{-s}{ut}. \]

So, the final expression for \( v \) in terms of \( s \), \( t \), and \( u \) is:

\[ v = \frac{-s}{ut}. \]