Describe in words the region of R^{3} represented by the equation(s) or inequality. x = 5

Show that the equation represents a sphere, and find its center and radius.
$x^2+y^2+z^2+8x-6y+2z+17=0$

This question has to do with binary star systems, where i is the angle of inclination of the system.
Calculate the mean expectation value of the factor ${\displaystyle {\sin }^3}$ i, i.e., the mean value it would have among an ensemble of binaries with random inclinations. Find the masses of the two stars, if ${\displaystyle {\sin }^3}$ i has its mean value.
Hint: In spherical coordinates, ${\displaystyle (\theta ,\varphi )}$, integrate over the solid angle of a sphere where the observer is in the direction of the z-axis, with each solid angle element weighted by ${\displaystyle \sin \left\{3\right\}\left(\theta \right)}$.
${\displaystyle v_1=100k\frac{m}{s}}$
${\displaystyle v_2=200k\frac{m}{s}}$
Orbital period ${\displaystyle =2}$ days
${\displaystyle M_1=5.74e33g}$
${\displaystyle M_2=2.87e33g}$

Give a full answer for the given question: The covalent backbone of DNA and RNA consists of: ?

Convert the point from spherical coordinates to rectangular coordinates.
$(9,\pi ,\frac{\pi }{2})$
$(x,y,z)=?$

Let C be a circle, and let P be a point not on the circle. Prove that the maximum and minimum distances from P to a point X on C occur when the line X P goes through the center of C. [Hint: Choose coordinate systems so that C is defined by
$x2+y2=r2$ and P is a point (a,0)
on the x-axis with a $\ne \pm r,$ use calculus to find the maximum and minimum for the square of the distance. Don’t forget to pay attention to endpoints and places where a derivative might not exist.]

Describe in words the region of $R^3$ represented by the equation(s) or inequality.
$x^2+y^2=4$

Below are various vectors in cartesian, cylindrical and spherical coordinates. Express the given vectors in two other coordinate systems outside the coordinate system in which they are expressed
$a)\overrightarrow{A}(x,y,z)={\overrightarrow{e}}_x$
$d)\overrightarrow{A}(\rho ,\varphi ,z)={\overrightarrow{e}}_{\rho }$
$g)\overrightarrow{A}(r,\theta ,\varphi )={\overrightarrow{e}}_{\theta }$
$j)\overrightarrow{A}(x,y,z)=\frac{-y{\overrightarrow{e}}_x+x{\overrightarrow{e}}_y}{x^2+y^2}$