Calculus 2 Equations: Expert Solutions and More

$\sum _{x=1}^{\mathrm{\infty }}\frac{1}{8^n}$

Which of the following polar coordinate pairs does not represent the point with rectangular coordinates (-2,-2)?
(A)${\displaystyle (2\sqrt{2}.-135°)}$
(B)${\displaystyle (2\sqrt{2}.225°)}$
(C)${\displaystyle (-2\sqrt{2}.-315°)}$
(D)${\displaystyle (-2\sqrt{2}.45°)}$
(E)${\displaystyle (-2\sqrt{2}.135°)}$

Find a polar equation for the conic section. Assume one focus is at the origin.

Change from rectangular to spherical coordinates. (Let ${\displaystyle \rho \ge 0,0\le \theta \le 2\pi ,\text{ and }0\le \varphi \le \pi }$)
(a) $(0,-3,0)$
(b) ${\displaystyle (-1,1,-\sqrt{2})}$

The letters ${\displaystyle r\text{and}\theta }$ represent polar coordinates. Write each equation using rectangular coordinates $(x,y)$.

${\displaystyle r=\sin \theta -\cos \theta r=\sin \theta -\cos \theta }$

Help, please.

Write in Cartesian coordinates the parametric equations of the curve with polar equation ${\displaystyle r\left(t\right)=<\sqrt{t},\frac{\pi }{8}>}$.

Find a set of polar coordinates for the point for which the rectangular coordinates are given. Choose the polar coordinates where r is positive and ${\displaystyle 0\le \theta \le \pi (5\sqrt{3},5)}$

Parametric equations and a value for the parameter t are given ${\displaystyle x=7-4t,y=5+6t.t=1.}$
Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of t.

In polar coordinates ${\displaystyle r^2=-6r\sin \theta }$ equation in cartesian coordinates
Find the equation and plot it.

Convert the Cartesian coordinates $(-5,-12)$ into polar coordinates where $r>0$ and ${\displaystyle 0^o\le \theta \le {360}^o}$.
Hence, write the other two polar coordinates that represent the point.

Find the parameric equatins to represent the line segment from $(1,2)$ to $(3,5)$. Give the domain of the parameter

The equations of two functions are $y=-21x+9$ and $y=-24x+8$. Which function is changing more quickly? How do you know?

Simplify ${\displaystyle (\sec \theta -\tan \theta )(1+\sin \theta )}$

${\displaystyle (x-y)dx+xdy=0}$
Please, solve by using an appropriate substitution.

Find the point(s) of intersection of the graphs of the equations.

$x=73-y^2$

$y=x-1$

A point of intersection of the graphs of two equations is a point that satisfies both the equations. You can find the point(s) of intersection of the graphs of the given equations by solving their equations simultaneously.

Solve the first equation for $y^2$.

$x=73-y^2$

$=y^2$

Replace the polar equation with equivalent Cartesian equations. $x-y=3$

Given the points (2,6) and (6,10), find at least three equations from linear function that pass through these points

Convert the following coordinates between rectangular and polar form
${\displaystyle (4,-\frac{\pi }{4})}$

Sketch the parametric curve for the following set of parametric equations. Clearly indicate direction of motion
1)${\displaystyle x=5\cos t}$
2)${\displaystyle y=2\sin t}$
3)${\displaystyle 0\ge t\ge 2\pi }$

Find the tangent line(s) to the parametric curve given by
${\displaystyle x=t^5-4t^3}$
${\displaystyle y=t^2}$