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This is the radius of a sphere around a black hole, at the surface of which, for any object to be be free of its gravitational pull its escape velocity be equal to the speed of light.

This is the maximum velocity that an object can reach when falling through a medium (like air). Note that it occurs when the drag on the object equals the pull of gravity.

In order to find the unknown variables x and y we need to simplify these equations in the way that will make it possible for us to get rid of either x or y variable, and make it easier to solve the remaining...

At first glance, this may seem quite complicated. However, it is simple once you make use of exponents. Let y=ln(x) . This can be written as: e y = e ln(x) e to the power of a natural log cancels out, which ...

To differentiate this, we use the quotient rule as we have 2 functions of x as a fraction. The quotient rule states that: where u is the numerator function and v is the denominator function. Therefore, u=ln ...