Error Anslysis: Brenna solved an equation for m. Do you agree with her? Explain your answer.
Her problem; mv^1 = (m+M)v^2
mv^2+Mv^2
___________
m = v^1
To determine if Brenna's solution for the equation is correct or not, let's go through the error analysis step by step.
Given equation: mv^1 = (m+M)v^2
Brenna's solution:
mv^2 + Mv^2
_______________
m = v^1
Now, to analyze her steps:
1. Adding the terms on the right-hand side: Brenna correctly combines the terms mv^2 and Mv^2 to get (mv^2 + Mv^2).
2. Dividing both sides by the common factor: Here is where Brenna makes the error. In her solution, she divides both the numerator and denominator by v^1, which is not mathematically valid. The exponents in the original equation are v^1 and v^2, and we cannot divide both sides by v^1 because the equation does not satisfy the condition v^1 = v^2.
Therefore, Brenna's solution is not correct due to the error in step 2. The equation cannot be simplified to the form m = v^1 using the steps she presented.