Solve for the indicated variable.
[tex]L=\frac{1}{4} m v^5 \quad \text { for } m[/tex]
Answer (2)
To solve for m in the equation L = 4 1 m v 5 , first multiply both sides by 4 to get 4 L = m v 5 . Then, divide both sides by v 5 to isolate m , resulting in m = v 5 4 L .
;
Multiply both sides of the equation by 4: 4 L = m v 5 .
Divide both sides of the equation by v 5 : f r a c 4 L v 5 = m .
The solution is m = f r a c 4 L v 5 .
The final answer is f r a c 4 L v 5 .
Explanation
Understanding the Problem We are given the equation L = f r a c 1 4 m v 5 and asked to solve for m . This means we want to isolate m on one side of the equation.
Isolating m To isolate m , we need to get rid of the f r a c 1 4 and the v 5 that are multiplied by m . We can do this by performing inverse operations on both sides of the equation.
Multiply by 4 First, we multiply both sides of the equation by 4 to get rid of the f r a c 1 4 :
4 t im es L = 4 t im es f r a c 1 4 m v 5
4 L = m v 5
Divide by v^5 Next, we divide both sides of the equation by v 5 to isolate m :
v 5 4 L = f r a c m v 5 v 5
v 5 4 L = m
Final Answer Therefore, we have solved for m :
m = f r a c 4 L v 5
Examples
In physics, this formula could relate to angular momentum, where L represents angular momentum, m is mass, and v is velocity. If you know the angular momentum and velocity of an object, you can find its mass using this formula. For example, if a spinning object has an angular momentum of 10 k g c d o t m 2 / s and a velocity of 2 m/s, and given the equation L = f r a c 1 4 m v 5 , we can find the object's mass by solving for m.
