Question

ALGEBRA ONE!!!!!1 34 POINTS I WILLLLL GIVE TOOOO YOUUUUU!!

Answer 1

Answer:

±sqrt(T*L/m)=v

Step-by-step explanation:

T=mv^2/L

We want to solve the equation for v

Multiply each side by L

T*L=mv^2/L *L

T*L=mv^2

Divide each side by m

TL/m=mv^2/m

T*L/m=v^2

Take the square root of each side

±sqrt(T*L/m)=sqrt(v^2)

±sqrt(T*L/m)=v

Answer 2

Answer:

$\large\boxed{v=\pm\sqrt{\dfrac{LT}{m}}}$

Step-by-step explanation:

$\dfrac{mv^2}{L}=T\qquad\text{multiply both sides by}\ L\\\\L\!\!\!\!\diagup^1\cdot\dfrac{mv^2}{L\!\!\!\!\diagup_1}=LT\\\\mv^2=LT\qquad\text{divide both sides by}\ m\\\\\dfrac{m\!\!\!\!\diagup^1v^2}{m\!\!\!\!\diagup_1}=\dfrac{LT}{m}\\\\v^2=\dfrac{LT}{m}\qquad\text{square root of both sides}\\\\\sqrt{v^2}=\sqrt{\dfrac{LT}{m}}\qquad\text{use}\ \sqrt{a^2}=|a|\\\\|v|=\sqrt{\dfrac{LT}{m}}\Rightarrow v=\pm\sqrt{\dfrac{LT}{m}}$