Question
Make Q the subject of the formula:T=P√Q²/Q²-1
Answers
GPT 3.5
To make Q the subject of the formula, we can follow these steps:
1. Start with the given formula: T = P√(Q² / (Q² - 1))
2. Square both sides of the equation to eliminate the square root: T² = P²(Q² / (Q² - 1))
3. Multiply both sides by (Q² - 1) to eliminate the fraction: T²(Q² - 1) = P²Q²
4. Expand the equation: T²Q² - T² = P²Q²
5. Move all the terms involving Q to one side of the equation: T²Q² - P²Q² = T²
6. Factor out the common factor of Q²: Q²(T² - P²) = T²
7. Divide both sides by (T² - P²): Q² = T² / (T² - P²)
8. Take the square root of both sides: Q = √(T² / (T² - P²))
Therefore, Q is the subject of the formula: Q = √(T² / (T² - P²))
1. Start with the given formula: T = P√(Q² / (Q² - 1))
2. Square both sides of the equation to eliminate the square root: T² = P²(Q² / (Q² - 1))
3. Multiply both sides by (Q² - 1) to eliminate the fraction: T²(Q² - 1) = P²Q²
4. Expand the equation: T²Q² - T² = P²Q²
5. Move all the terms involving Q to one side of the equation: T²Q² - P²Q² = T²
6. Factor out the common factor of Q²: Q²(T² - P²) = T²
7. Divide both sides by (T² - P²): Q² = T² / (T² - P²)
8. Take the square root of both sides: Q = √(T² / (T² - P²))
Therefore, Q is the subject of the formula: Q = √(T² / (T² - P²))