SOLUTION: How do I isolate {{{v}}} from {{{L=i * sqrt(1-v^2/c^2) }}} ?

Algebra ->  Radicals -> SOLUTION: How do I isolate {{{v}}} from {{{L=i * sqrt(1-v^2/c^2) }}} ?      Log On


   

Question 1086951: How do I isolate v from L=i+%2A+sqrt%281-v%5E2%2Fc%5E2%29+ ?
Found 2 solutions by jim_thompson5910, MathTherapy:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
L=i+%2A+sqrt%281-v%5E2%2Fc%5E2%29+

L%2Fi=%28i+%2A+sqrt%281-v%5E2%2Fc%5E2%29%29%2Fi+ Divide both sides by 'i'

L%2Fi=sqrt%281-v%5E2%2Fc%5E2%29+

%28L%2Fi%29%5E2=%28sqrt%281-v%5E2%2Fc%5E2%29%29%5E2+ Square both sides

%28L%2Fi%29%5E2=1-v%5E2%2Fc%5E2+

%28L%2Fi%29%5E2-1=1-v%5E2%2Fc%5E2-1+ Subtract 1 from both sides

%28L%2Fi%29%5E2-1=-v%5E2%2Fc%5E2+

-c%5E2%28%28L%2Fi%29%5E2-1%29=-c%5E2%28-v%5E2%2Fc%5E2%29+ Multiply both sides by -c^2

-c%5E2%28%28L%2Fi%29%5E2-1%29=v%5E2+

v%5E2+=+-c%5E2%28%28L%2Fi%29%5E2-1%29

v+=+%22%22%2B-sqrt%28-c%5E2%28%28L%2Fi%29%5E2-1%29%29 Apply the square root to both sides

v+=+sqrt%28-c%5E2%28%28L%2Fi%29%5E2-1%29%29 You can drop the plus minus sign assuming +v+%3E=+0


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

How do I isolate v from L=i+%2A+sqrt%281-v%5E2%2Fc%5E2%29+ ?
L%2Fi+=+sqrt%281+-+v%5E2%2Fc%5E2%29 ------- Dividing both sides by i
%28L%2Fi%29%5E2+=+%28sqrt%281+-+v%5E2%2Fc%5E2%29%29%5E2 ------- Squaring both sides
L%5E2%2Fi%5E2+=+1+-+v%5E2%2Fc%5E2
v%5E2%2Fc%5E2+=+1+-+L%5E2%2Fi%5E2 -------- Adding v%5E2%2Fc%5E2 and subtracting L%5E2%2Fi%5E2 from both sides
sqrt%28v%5E2%2Fc%5E2%29+=+sqrt%281+-+L%5E2%2Fi%5E2%29 ------- Taking square root of both sides
v%2Fc+=+sqrt%281+-+L%5E2%2Fi%5E2%29 =======> highlight_green%28matrix%281%2C3%2C+v%2C+%22=%22%2C++c+%2A+sqrt%281+-+L%5E2%2Fi%5E2%29%29%29