the process for rationalizing a denominator in a variable expression is the same as in a numeric expression…

the process for rationalizing a denominator in a variable expression is the same as in a numeric expression. heres a real - world example. the kinetic energy of the car of a rollercoaster is given by the formula $k = \\frac{1}{2}mv^{2}$, where k is kinetic energy, m is the mass of the car, and v is the velocity of the car. solving this formula for v, we get $v=sqrt{\\frac{2k}{m}}$. which formula gives the velocity of the car in simplest form? $v = \\frac{sqrt{2km}}{2m}$ $v = \\frac{sqrt{2km}}{m}$ $v = \\frac{sqrt{2k}}{m}$ done

the process for rationalizing a denominator in a variable expression is the same as in a numeric expression. heres a real - world example. the kinetic energy of the car of a rollercoaster is given by the formula $k = \\frac{1}{2}mv^{2}$, where k is kinetic energy, m is the mass of the car, and v is the velocity of the car. solving this formula for v, we get $v=sqrt{\\frac{2k}{m}}$. which formula gives the velocity of the car in simplest form? $v = \\frac{sqrt{2km}}{2m}$ $v = \\frac{sqrt{2km}}{m}$ $v = \\frac{sqrt{2k}}{m}$ done

Answer

Explanation:

Step1: Start with kinetic - energy formula

Given $k=\frac{1}{2}mv^{2}$.

Step2: Isolate $v^{2}$

Multiply both sides by $2$ to get $2k = mv^{2}$, then $v^{2}=\frac{2k}{m}$.

Step3: Solve for $v$

Take the square - root of both sides, $v=\sqrt{\frac{2k}{m}}=\frac{\sqrt{2k}}{\sqrt{m}}$. Rationalizing the denominator (if needed, but in the given options it's not further rationalized in this form), we have the formula for $v$.

Answer:

$v = \frac{\sqrt{2k}}{m}$ (assuming the correct option is the one with this formula among the given choices in the image)