Question
Upstudy AI Solution
Tutor-Verified Answer
Answer
The HCF of \( \frac{m v^{2}}{t} \) and \( \frac{m^{2} v}{t} \) is \( \frac{mv}{t} \).
Solution
To find the highest common factor (HCF) of the expressions \( \frac{m v^{2}}{t} \) and \( \frac{m^{2} v}{t} \), we can follow these steps:
1. **Identify the expressions:**
- Let \( A = \frac{m v^{2}}{t} \)
- Let \( B = \frac{m^{2} v}{t} \)
2. **Factor out the common terms:**
- Both expressions have a common denominator \( t \).
- The numerators are \( m v^{2} \) and \( m^{2} v \).
3. **Find the HCF of the numerators:**
- The HCF of \( m v^{2} \) and \( m^{2} v \) can be found by taking the lowest power of each variable:
- For \( m \): The lowest power is \( m^{1} \).
- For \( v \): The lowest power is \( v^{1} \).
Therefore, the HCF of the numerators is \( m^{1} v^{1} = mv \).
4. **Combine with the common denominator:**
- The HCF of the two expressions is then:
\[
\text{HCF} = \frac{mv}{t}
\]
Thus, the HCF of \( \frac{m v^{2}}{t} \) and \( \frac{m^{2} v}{t} \) is \( \frac{mv}{t} \).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Mind Expander
To find the Highest Common Factor (HCF) of the two given expressions, \( \frac{m v^{2}}{t} \) and \( \frac{m^{2} v}{t} \), we first factor each expression. The first expression can be rewritten as \( \frac{mv^2}{t} \), and the second as \( \frac{m^2v}{t} \). Next, we will look for common factors: - The common factor in the numerators \( mv^2 \) and \( m^2v \) is \( mv \). - The denominator \( t \) remains constant in both expressions. Therefore, the HCF is: \[ \text{HCF} = \frac{mv}{t} \] This means no matter how crazy the calculations get, ensure you're always on the lookout for those common terms!
