a) sketch a graph of C.

b) find the vector-valued function f(t) associated with this parameterization of the curve C.

c) find the velocity vector and the speed of f(t) at t=1.

prelimaf1
2021-12-04
Answered

Let C be the curve described by the parametric equations $x\left(t\right)=t,y\left(t\right)={t}^{3}$ .

a) sketch a graph of C.

b) find the vector-valued function f(t) associated with this parameterization of the curve C.

c) find the velocity vector and the speed of f(t) at t=1.

a) sketch a graph of C.

b) find the vector-valued function f(t) associated with this parameterization of the curve C.

c) find the velocity vector and the speed of f(t) at t=1.

You can still ask an expert for help

kayleeveez7

Answered 2021-12-05
Author has **10** answers

Step 1

Given equation is

Step2

To sketch the curve let convert it into Cartesian form

Step3

Graph of curve Cis as shown

Step4

b)

vector-valued function f(t) associated with this parameterization of the curve C.

Step5

c) the velocity vector and the speed of f(t) at t=1.

asked 2021-05-14

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.$(x,\text{}y)=$

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.

asked 2021-11-26

Find sets of parametric equations and symmetric equations of the line that passes through the given point and is parallel to the given vector or line.

$$\begin{array}{|cc|}\hline \text{Point}& \text{Parallel to}v=\\ (0,\text{}0,\text{}0)& 8,\text{}1,\text{}4\\ \hline\end{array}$$

(a) parametric equations

(b) symmetric equations

$8x=y=4z$

$4x=y=8z$

$\frac{x}{8}=y=\frac{z}{4}$

$\frac{x}{4}=y=\frac{z}{8}$

(a) parametric equations

(b) symmetric equations

asked 2021-12-06

Determine whether the graphs of the polar equation are symmetric with respect to the x-axis, the y -axis, or the origin.

$r=1+\mathrm{cos}0$

asked 2021-11-16

Data points $(x,\text{}y)$

$$\begin{array}{|cccccccccc|}\hline x& & 2& 4& 6& 8& 10& 12& 14& 16\\ y& 0.08& 0.12& 0.18& 0.25& 0.36& 0.52& 0.73& 1.06\\ \hline\end{array}$$

Draw scatter plots of$(x,\text{}\mathrm{ln}y)$ and $(\mathrm{ln}x,\text{}\mathrm{ln}y)$

Draw scatter plots of

asked 2022-02-01

What is the polar form of (5, -3)?

asked 2021-11-26

Find a set of parametric equations of the line with the given characteristics. The line passes through the point $(-4,\text{}5,\text{}2)$ and is parallel to the xy-plane and the yz-plane

asked 2021-11-23

Represent the plane curve by a vector-valued function. ${x}^{2}+{y}^{2}=25$