Question

Please help me i will really appreciate it!!!

Answer 1

`\displaystyle x=\sqrt{(2U)/(k)}`

The third option is the correct answer.

Explanation:

Equation Solving

We have the following equation:

`\displaystyle U=(1)/(2)kx^2`

And it's required to solve it for x.

To solve this equation we need to perform some operations to have the x isolated from any other variables, constants, or operations.

This will be done by conveniently operating on both sides as follows:

Eliminate the denominator by multiplying by 2:

`\displaystyle 2U=kx^2`

Move k to the other side by dividing by k:

`\displaystyle (2U)/(k)=x^2`

Swapping sides to have x at the left side:

`\displaystyle x^2=(2U)/(k)`

Taking the square root:

`\mathbf{\displaystyle x=\sqrt{(2U)/(k)}}`

The third option is the correct answer.