If a planet was located approximately 24 thousand light-years from the center of a galaxy and orbits that center once every 194 million years, how fast is the planet traveling around the galaxy in km/hr? If needed, use 3.0 × 108 m/s for the speed of light.

84km/hr

Explanation:

To find one light yr

= 3E8m/s x 24x 365/1000

= 996980E7kms

So

Radius of orbit for 24000light years

=996980E7kms x 24000

Total orbit distance is = 2πr

= 2 *π x 996980E7kms x 24000

Total time will be

= 194E6 x 24x365 hrs

Finally speed = distance/ time

= 2 *π x 996980E7kms x 24000/194E6 x 24x365 hrs

= 84km/hr

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 .