1. A comet of mass m is in an elliptical orbit around a star of mass M. At the closest point of its orbit, point P, the comet is a distance D from the center of the star, and at the farthest point, point A, the distance is 3D. You may disregard the presence of all other celestial bodies. Derive an expression for the change in the comet’s kinetic energy as it moves from point P to point A, in terms of system parameters and constants. Does the comet have its greatest speed at point A or point P?

vapour or gas assuming atmospheriv pressure

a skateboard rolling across the street - apex

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 .

the aurora is formed when charged particles emitted from the sun during a solar flare penetrate the earth's magnetic shield and collide with atoms and molecules in our atmosphere. these collisions result in countless little bursts of light, called photons, which make up the aurora.

auroras are generated by charged solar particles hitting molecules in earth's atmosphere. this usually happens in high latitudes, because our planet’s magnetic field tends to funnel these particles toward the poles. that’s why it can be experienced in northern ohio.