Answer:
25.133 units
Step-by-step explanation:
Since the density ρ = r, our mass is
m = ∫∫∫r³sinθdΦdrdθ. We integrate from θ = 0 to π (since it is a hemisphere), Φ = 0 to 2π and r = 0 to 2 and the maximum values of r = 2 in those directions. So
m =∫∫[∫r³sinθdΦ]drdθ
m = ∫[∫2πr³sinθdθ]dr ∫dФ = 2π
m = ∫2πr³∫sinθdθ]dr
m = 2π∫r³dr ∫sinθdθ = 1
m = 2π × 4 ∫r³dr = 4
m = 8π units
m = 25.133 units
Answer:

Step-by-step explanation:
Given



Required
Determine the coordinates of P
The coordinate of a point when divided into ratio is:

Where



This gives:




Step-by-step explanation:
I don't know if this helps but there is an app call symbols which is free which maybe it can help you to grapgh.
For a better understanding of the solution provided here please find the diagram attached.
Please note that in coordinate geometry, the coordinates of the midpoint of a line segment is always the average of the coordinates of the endpoints of that line segment.
Thus, if, for example, the end coordinates of a line segment are
and
then the coordinates of the midpoint of this line segment will be the average of the coordinates of the two endpoints and thus, it will be:

Thus for our question the endpoints are
and
and hence the midpoint will be:


Thus, Option C is the correct option.