The radius of the event horizon of a black hole (the point at which it is impossible to escape the black hole because the escape velocity would exceed the speed of light) is given by the formula r = 2Gm/c^2, where G is the gravitational constant, c is the speed of light, and m is the mass of the black hole.
Rearrange this formula to isolate c.
r= 2Gm/c^2
rc^2=2Gm
c^2=(2Gm)/r
c=+or- sqrt[(2Gm)/r]
c= sqrt[(2Gm)/r] (the speed of light is positive)
r = 2Gm/c^2
c^2 = 2Gm/r
now just take the square root.
To isolate c in the formula r = 2Gm/c^2, we can follow these steps:
1. Start with the given formula: r = 2Gm/c^2
2. Multiply both sides of the equation by c^2: r * c^2 = 2Gm
3. Divide both sides of the equation by r: c^2 = 2Gm/r
4. Take the square root of both sides to solve for c: √(c^2) = √(2Gm/r)
5. Simplify the left side of the equation: c = √(2Gm/r)
Therefore, the rearranged formula to isolate c is: c = √(2Gm/r).
To rearrange the formula r = 2Gm/c^2 to isolate c, we can follow these steps:
Step 1: Multiply both sides of the equation by c^2 to eliminate the denominator on the right side:
r * c^2 = 2Gm
Step 2: Divide both sides of the equation by r to isolate c^2:
c^2 = (2Gm) / r
Step 3: Take the square root of both sides to solve for c:
c = √[(2Gm) / r]
Thus, the formula to isolate c is c = √[(2Gm) / r].