Question

equations in one variable as a reasoning process - item 9446 in jerome’s physics class, he had to solve the equation ( 40 = \frac{1}{2}mv^2 ) for ( m ). each step of his work is shown below. use the drop - down menus to explain each step. given equation ( 40 = \frac{1}{2}mv^2 ) step 1 ( \frac{40}{v^2} = \frac{1}{2}m ) on both sides of the equation. step 2 ( \frac{80}{v^2} = m ) on both sides of the equation.

Explanation:

Step 1: Divide by \( v^2 \)

To isolate terms with \( m \), divide both sides of \( 40 = \frac{1}{2}mv^2 \) by \( v^2 \).
\( \frac{40}{v^2} = \frac{1}{2}m \)

Step 2: Multiply by 2

To solve for \( m \), multiply both sides of \( \frac{40}{v^2} = \frac{1}{2}m \) by 2.
\( \frac{80}{v^2} = m \)

Answer:

Step 1: Divide by \( v^2 \); Step 2: Multiply by 2. Final solution for \( m \) is \( \boldsymbol{\frac{80}{v^2}} \)