Write an equations in indicated coordinate system. Also write a parametric equation and a vector equation for each of the following equations.1) frac{x-1}{2}=frac{y-5}{3}=frac{z-2}{4}

Use the given graph off over the interval (0, 6) to find the following.

a) The open intervals on whichfis increasing. (Enter your answer using interval notation.)
b) The open intervals on whichfis decreasing. (Enter your answer using interval notation.)
c) The open intervals on whichfis concave upward. (Enter your answer using interval notation.)
d) The open intervals on whichfis concave downward. (Enter your answer using interval notation.)
e) The coordinates of the point of inflection. $(x,y)=$

Replace the Cartesian equation with equivalent polar equations. xy = 2

What is the polar form of (-2, 10)?

Represent the plane curve by a vector-valued function. (There are many correct answers.)
${\displaystyle 3x+4y-12=0}$

Find sets of parametric equatons and symmetric equations of the line tha passes though the given point and is parallel to the given vector or line
$$\begin{array}{|cc|}\hline \text{Point}& \text{Parallel to}\\ (-1,0,8)& v=3i+4j-8k\\ \hline\end{array}$$
a) parametric equations
b) symmetric equations
${\displaystyle \frac{x+1}{3}=\frac{y}{4}=\frac{8-z}{8}}$

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

Vector-valued functions Find a function r(t) that describes the following curve.
Anellipse in te plane ${\displaystyle x=2}$ satisfying the equation
${\displaystyle \frac{y^2}{9}+\frac{z^2}{16}=1}$