Find the value of x or y so that the line passing through the given points has the given slope. (-9,y),(0,-3),m=frac{-7}{9}

a) What coordinate system is suggested to be used when seeing the integrand ${\displaystyle {(x^2+y^2)}^{\frac{5}{2}}}$, cylindrical or Cartesian?
b) List the conversion factors for rectangular to cylindrical coordinate systems.

Consider the elliptical-cylindrical coordinate system (eta, psi, z), defined by $x=a\cos h\eta \cos \psi ,y=a\sin h\eta \sin \psi ;z=z,\eta GE0,0LE\psi LE2\pi ,zR.InPS6$
it was shown that this is an orthogonal coordinate system with scale factors ${\displaystyle h_1=h_2=a{({\text{cosh}}^2\eta -{\cos }^2\psi )}^{\frac{1}{2}}.}$
Determine the dual bases ${\displaystyle (E1,E2,E3),(\eta ,\eta \psi ,z).Showt\widehat{:}f=a\frac{1}{a}\frac{{({\text{cosh}}^{2}eat-{\cos }^s\psi )}^1}{2}[\frac{f}{\eta }e1+\frac{f}{\psi }e2+\frac{f}{z}e3,\frac{f}{w}here(e1,e2,e3)}$ denotes the unit coordinate basis.

The equivalent polar equation for the given rectangular - coordinate equation.
${\displaystyle y=-3}$

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 ${\sin }^3\theta$.
${\displaystyle v_1=100k\frac{m}{s}}$
${\displaystyle v_2=200k\frac{m}{s}}$
Orbital period ${\displaystyle =2}$ days
${\displaystyle M_1=5.74e^{33}g}$
${\displaystyle M_2=2.87e^{33}g}$

What are polar coordinates? What equations relate polar coordi-nates to Cartesian coordinates? Why might you want to change from one coordinate system to the other?

To solve:
the system of equation ${\displaystyle 2x+3y=5\text{and}6x+9y=15}$.

Let A and C be the following ordered bases of P3(t): ${\displaystyle A=(1,1+t,1+t+t^2,1+t+t^2+t^3)}$
${\displaystyle C=(1,-t,t^2-t^3)}$ Find tha change of coordinate matrix ${\displaystyle I_{CA}}$