make t the subject of the formula
p divided by 2 square root t+r divided by g.
To make t the subject of the formula p/(2√(t+r)/g), we need to isolate t on one side of the equation. Here's the step-by-step process:
1. Start with the equation: p/(2√(t+r)/g).
2. Multiply both sides of the equation by 2√(t+r)/g to cancel out the denominator:
p = 2√(t+r)/g * t.
3. Multiply both sides of the equation by g to further cancel out the denominator:
pg = 2√(t+r) * t.
4. Square both sides of the equation to eliminate the square root:
(pg)^2 = (2√(t+r) * t)^2.
5. Simplify both sides of the equation:
p^2g^2 = 4(t+r) * t.
6. Distribute the squared term on the right side:
p^2g^2 = 4t^3 + 4rt.
7. Rearrange the equation by subtracting 4t^3 and 4rt from both sides:
p^2g^2 - 4t^3 - 4rt = 0.
8. Factor out t from the left side of the equation:
t(4t^2 + 4r) - p^2g^2 = 0.
9. Finally, divide both sides of the equation by (4t^2 + 4r):
t = p^2g^2 / (4t^2 + 4r).
So, the value of t can be calculated using the formula t = p^2g^2 / (4t^2 + 4r).