Make n the subject of the formulae
m=3√ax²-n/w-n
To make n the subject of the formula, we need to isolate it on one side of the equation.
Given equation: m = 3√(ax² - n/w - n)
Step 1: Square both sides of the equation to remove the cube root.
m² = 9(ax² - n/w - n)
Step 2: Expand the equation.
m² = 9ax² - 9n/w - 9n
Step 3: Move the terms containing n to one side of the equation.
9n/w + 9n = 9ax² - m²
Step 4: Combine like terms.
(9 + 9/w)n = 9ax² - m²
Step 5: Divide both sides of the equation by (9 + 9/w) to isolate n.
n = (9ax² - m²)/(9 + 9/w)
Therefore, n is the subject of the given equation when rearranged.
To make "n" the subject of the formula, we need to isolate it on one side of the equation. Let's go through the steps:
1. Start with the given formula: m = 3√(ax² - n)/(w - n)
2. Multiply both sides of the equation by (w - n) to remove the denominator:
m(w - n) = 3√(ax² - n)
3. Cube both sides of the equation to eliminate the cube root:
(m(w - n))^3 = (3√(ax² - n))^3
4. Simplify both sides:
(m(w - n))^3 = (ax² - n)
5. Expand the left side of the equation:
m³(w - n)³ = ax² - n
6. Expand the left side further by cubing (w - n):
m³(w³ - 3w²n + 3wn² - n³) = ax² - n
7. Distribute m³ to every term inside the parentheses:
m³w³ - 3m³w²n + 3m³wn² - m³n³ = ax² - n
8. Rearrange the terms to group all n terms on one side of the equation:
m³w³ - ax² = 3m³w²n - 3m³wn² + m³n³ + n
9. Combine like terms on both sides, specifically on the right side of the equation:
m³w³ - ax² = 3m³w²n - 3m³wn² + (m³n³ + n)
10. Factor out "n" from the terms on the right side:
m³w³ - ax² = n(3m³w² - 3m³wn + m³n² + 1)
11. Divide both sides of the equation by (3m³w² - 3m³wn + m³n² + 1):
n = (m³w³ - ax²)/(3m³w² - 3m³wn + m³n² + 1)
Therefore, the formula for "n" as the subject is n = (m³w³ - ax²)/(3m³w² - 3m³wn + m³n² + 1).