To determine which formula is correct based on the relationship [tex]\( v = c \lambda \)[/tex], let's analyze each option.
1. [tex]\( v = c \lambda \)[/tex]:
- This is the original equation provided. Clearly, this should be correct.
2. [tex]\( v \div \lambda = c \)[/tex]:
- We can rearrange the original equation [tex]\( v = c \lambda \)[/tex] to solve for [tex]\( c \)[/tex]:
[tex]\[
v = c \lambda \implies \frac{v}{\lambda} = c
\][/tex]
- This indicates that this formula is also correct.
3. [tex]\( v + \lambda = c \)[/tex]:
- According to the original equation [tex]\( v = c \lambda \)[/tex], if we add [tex]\( \lambda \)[/tex] to [tex]\( v \)[/tex], it doesn't directly relate to [tex]\( c \)[/tex]. Therefore, this formula is incorrect.
4. [tex]\( v \lambda = c \)[/tex]:
- If we multiply [tex]\( v \)[/tex] by [tex]\( \lambda \)[/tex], we obtain a term that does not match the original equation [tex]\( v = c \lambda \)[/tex]. Therefore, this formula is incorrect.
5. [tex]\( \lambda = c v \)[/tex]:
- Rearranging the original equation [tex]\( v = c \lambda \)[/tex] to solve for [tex]\( \lambda \)[/tex] gives:
[tex]\[
\lambda = \frac{v}{c}
\][/tex]
- The formula [tex]\( \lambda = c v \)[/tex] does not match this rearrangement, so it is incorrect.
So, the correct formulas based on the equation [tex]\( v = c \lambda \)[/tex] are:
1. [tex]\( v = c \lambda \)[/tex]
2. [tex]\( v \div \lambda = c \)[/tex]
Thus, the correct formulas are the first and the second ones as they are the only ones consistent with [tex]\( v = c \lambda \)[/tex]. The others are incorrect.
