Chapter 9, Problem 12CT

a.

To determine

To find:Set of parametric equations.

Answer to Problem 12CT

  $\begin{array}{l}x=t\\ y=-3t+5\end{array}$

Explanation of Solution

Given information:

  $y=-3x+5$

  $t=x$

  $y=-3x+5$

Substitute $x=t$ in above equation

We get

  $\begin{array}{l}y=-3x+5\\ \Rightarrow y=-3\left(t\right)+5\\ \Rightarrow y=-3t+5\end{array}$

The set $x=t$ and $y=-3t+5$ represents the set of parametric equations of given the Rectangular equation $y=-3x+5$

b.

To determine

To find:Set of parametric equations.

Answer to Problem 12CT

  $\begin{array}{l}x=2-t\\ y=3t-1\end{array}$

Explanation of Solution

Given information:

  $y=-3x+5$

  $t=2-x$

  $y=-3x+5$

  $\begin{array}{l}t=2-x\\ \Rightarrow x=2-t\end{array}$

Substitute $x=2-t$ in the equation $y=-3x+5$

We get

  $\begin{array}{l}y=-3\left(2-t\right)+5\\ \Rightarrow y=-3\left(2\right)-3\left(-t\right)+5\\ \Rightarrow y=-6+3t+5\\ \Rightarrow y=3t-1\end{array}$

Therefore, the set $x=2-t$ and $y=3t-1$ also represents the set of parametric equations of the given Rectangular equation $y=-3x+5$

a.

To determine

To find: Variables and inequalities and graph of given situation.

Answer to Problem 12CT

Variables are

‘ $w$ ’ be the weight.

‘ $h$ ’ be the height

Inequalities are

  $\begin{array}{l}h<79\\ w<295\end{array}$

Explanation of Solution

Given information:

Height must be under = 6 ft 7 inches.

Weight must be under =295 lb.

We know

1feet =12 inches

Therefore

6 feet 7 inches = 6 feet + 7 inches

= $6\left(12\right)+7$

= $72+7$

=79 inches

Let ‘ $w$ ’ be the weight.

Let ‘ $h$ ’ be the height.

From the given information

Height must be less than 79 inches

Therefore

  $h<79$ -----------(1)

Weight must be less than 295 lb.

Therefore

  $w<295$ ----------(2)

Equations-(1) and (2) represents the inequalities of above situation.

  

Here

Blue colour represents the region of $w<295$

Red colour represents the region of $h<79$ .

Common region of Red colour and Blue colour represent the solution of above inequalities.

b.

To determine

To find: One possible solution.

Answer to Problem 12CT

  $\left(65,200\right)$

Height = 65 inches.

Weight = 200 lb.

Explanation of Solution

Given information:

Height must be under = 6 ft 7 inches.

Weight must be under =295 lb.

Inequalities are

  $\begin{array}{l}h<79\\ w<295\end{array}$

Graph of given inequalities is

  

Blue colour represents the region of $w<295$

Red colour represents the region of $h<79$ .

Common region of Red colour and Blue colour represent the solution of above inequalities.

As $\left(65,200\right)$ is present in the common region of both inequalities.

  $\left(65,200\right)$ is one possible solution.

c.

To determine

To find: Is $\left(50,180\right)$ a solution.

Answer to Problem 12CT

Yes.

Explanation of Solution

Given information:

Height must be under = 6 ft 7 inches.

Weight must be under =295 lb.

Graph of given inequalities is

  

Blue colour represents the region of $w<295$

Red colour represents the region of $h<79$

Common region of Red colour and Blue colour represent the solution of above inequalities.

As $\left(50,180\right)$ is present in the common region of both inequalities. So $\left(50,180\right)$ is a solution.