Answer:
The star is at a distance of 100 parsecs.
Explanation:
The distance can be determined by means of the distance modulus:
(1)
Where M is the absolute magnitude, m is the apparent magnitude and d is the distance in units of parsec.
Therefore, d can be isolated from equation 1

Then, Applying logarithmic properties it is gotten:
(2)
The absolute magnitude is the intrinsic brightness of a star, while the apparent magnitude is the apparent brightness that a star will appear to have as is seen from the Earth.
Since both have the same spectral type is absolute magnitude will be the same.
Finally, equation 2 can be used:
Hence, the star is at a distance of 100 parsecs.
Key term:
Parsec: Parallax of arc seconds
There are many different types of precipitation —rain, snow, hail, and sleet for example—yet they all have a few things in common. They all come from clouds. They are all forms of water that fall from the sky.
Answer:

Explanation:
Given




Required
Determine the linear equation for P in terms of h
First, we calculate the slope/rate (m);
The following formula is used:

Substitute values for P's and h's



Multiply by 1000/1000


The equation is then calculated using:

Substitute values for m, h1 and P1



Make P the subject

<em>The above is the required linear equation</em>
Since Astronaut and wrench system is isolated in the space and there is no external force on it
So here momentum of the system will remain conserved
so here we can say

initially both are at rest
so here plug in all values


so here the astronaut will move in opposite direction and its speed will be equal to 0.20 m/s