The evil team of ms. moonstruck and mr. luny intend to deflect the moon from its orbit around earth by pulling it with a force of 7870 n . they plan to accomplish this by placing a mini black hole 5.23 × 10 6 m from the center of the moon and letting gravitation do what gravitation does. what must the mass of the mini black hole be for the evil duo's evil scheme to succeed? the mass of the moon is 7.36 × 10 22 kg .

43850.49112 kg

Explanation:

M = Mass of moon =

r = Distance from Moon's center =

G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

m = Mass of black hole

F = Force = 7870 N

From the universal force of gravity we have

The mass of the mini black hole is 43850.49112 kg

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .