Question

Consider the following parametric equations, $x = -1 - 2t$, $y = 3t - 3$; $-5 \le t \le 5$. Complete parts (a) through (d) below. a. Make a brief table of values of $t$, $x$, and $y$ \begin{tabular}{|c|c|c|c|c|c|} \hline t & -5 & -3 & 0 & 3 & 5 \\ \hline x(t) & 3 & 1 & -2 & -5 & -7 \\ \hline y(t) & 12 & 6 & -3 & -12 & -18 \\ \hline \end{tabular} (Type integers or decimals.) b. Plot the $(x, y)$ pairs in the table and the complete parametric curve, indicating the positive orientation (the direction of increasing c. Eliminate the parameter to obtain an equation in $x$ and $y$ d. Describe the curve. A. A line segment falls from right to left as $t$ increases. B. A line segment falls from left to right as $t$ increases. C. A line segment rises from left to right as $t$ increases. D. A line segment rises from right to left as $t$ increases.

          Consider the following parametric equations, $x = -1 - 2t$, $y = 3t - 3$; $-5 \le t \le 5$. Complete parts (a) through (d) below.
a. Make a brief table of values of $t$, $x$, and $y$
\begin{tabular}{|c|c|c|c|c|c|}
\hline
t & -5 & -3 & 0 & 3 & 5 \\
\hline
x(t) & 3 & 1 & -2 & -5 & -7 \\
\hline
y(t) & 12 & 6 & -3 & -12 & -18 \\
\hline
\end{tabular}
(Type integers or decimals.)
b. Plot the $(x, y)$ pairs in the table and the complete parametric curve, indicating the positive orientation (the direction of increasing
c. Eliminate the parameter to obtain an equation in $x$ and $y$
d. Describe the curve.
A. A line segment falls from right to left as $t$ increases.
B. A line segment falls from left to right as $t$ increases.
C. A line segment rises from left to right as $t$ increases.
D. A line segment rises from right to left as $t$ increases.

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Consider the following parametric equations, x = -1 - 2t, y = 3t - 3; -5 ≤ t ≤ 5. Complete parts (a) through (d) below.
a. Make a brief table of values of t, x, and y

t -5 -3 0 3 5

x(t) 3 1 -2 -5 -7

y(t) 12 6 -3 -12 -18

(Type integers or decimals.)
b. Plot the (x, y) pairs in the table and the complete parametric curve, indicating the positive orientation (the direction of increasing
c. Eliminate the parameter to obtain an equation in x and y
d. Describe the curve.
A. A line segment falls from right to left as t increases.
B. A line segment falls from left to right as t increases.
C. A line segment rises from left to right as t increases.
D. A line segment rises from right to left as t increases.

Added by Jennifer G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adnan Gill

05/27/2020

Step 1

t x(t) y(t) -5 3 12 -3 0 -2 0 -3 -3 3 -7 -48 6 -13 -363 12 -25 -4998 Show more…

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Texts: answer a-d please Consider the following parametric equations: x = -1 - 2t y = -3t - 3 - 5t^5 Complete parts a through d below: a. Make a brief table of values of t, x, and y: t x(t) y(t) -5 3 12 -3 0 -2 0 -3 -3 3 -7 -48 6 -13 -363 12 -25 -4998 b. Plot the (x, y) pairs in the table and the complete parametric curve, indicating the positive orientation (the direction of increasing t) from point O to point A and point B. c. Eliminate the parameter to obtain an equation in x and y. d. Describe the curve: O: A line segment falls from right to left as t increases. A: A line segment falls from left to right as t increases. B: A line segment rises from left to right as t increases. D: A line segment rises from right to left as t increases.

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Transcript

00:01 So we have a set of parametric equations.

00:04 X is equal to t to the power 3 minus 1.

00:08 Y is equal to 5t plus 1.

00:11 And the values of t go from negative 3 to positive 3.

00:17 So we're going to make a table first of all.

00:20 So we pick values for t.

00:22 Let's start with t is equal to negative 3, negative 1, 0, 1, and 3.

00:28 And for each t value we will calculate an x value.

00:32 So for t is equal to negative 3, that's equal to negative 28.

00:37 Negative 3 to the power 3 is negative 27 minus 1 is negative 28.

00:42 Similarly, for t is equal to negative 1, x is equal to negative 2, negative 1, and then 0, and then 26.

00:52 Similarly, we can calculate values for y.

00:55 So they come out to be equal to negative 14, negative 4, 1, 6, and 16.

01:03 So for part b, we need to graph these points on the coordinate plane.

01:11 So let's start with negative 28 minus 14.

01:15 So negative 28 minus 14 would be right here.

01:20 Then we got negative to my negative 4.

01:24 So negative 2, negative 4 is here.

01:28 And then we got negative 1 -1...

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