4.2 Equations

$f=32a$ .
The equation expresses the relationship between the variables $f$ and $a$ . It states that the value of $f$ is always 32 times that of $a$ .

$y=6x+8$ .
The equation expresses the relationship between the variables $x$ and $y$ . It states that the value of $y$ is always 8 more than 6 times the value of $x$ .

$\begin{array}{llll}f\hfill & =\hfill & 32a.\hfill & \text{Determine}\text{the}\text{value}\text{of}f\text{if}a=2.\hfill \\ f\hfill & =\hfill & 32(2)\hfill & \text{Replace}a\text{by}2.\hfill \\ \hfill & =\hfill & 64\hfill & \hfill \end{array}$

$p=\frac{10,000}{v}$ .

This chemistry equation expresses the relationship between the pressure $p$ of a gas and the volume $v$ of the gas. Determine the value of $p$ if $v=500$ .

$\begin{array}{llll}p\hfill & =\hfill & \frac{10,000}{500}\hfill & \text{Replace}v\text{by}500.\hfill \\ \hfill & =\hfill & 20\hfill & \hfill \end{array}$

On the Calculator
$\begin{array}{ll}\hfill & \hfill \\ \text{Type}\hfill & 10000\hfill \\ \text{Press}\hfill & \begin{array}{||}\hline ÷\\ \hline\end{array}\hfill \\ \text{Type}\hfill & 500\hfill \\ \text{Press}\hfill & \begin{array}{||}\hline =\\ \hline\end{array}\hfill \\ \text{Display}\text{reads:}\hfill & 20\hfill \end{array}$

$z=\frac{x-u}{s}$ .

This statistics equation expresses the relationship between the variables $z,x,u\text{and}s$ . Determine the value of $z\text{if}x=41,u=45,\text{and}s=1.3$ . Round to two decimal places.

$\begin{array}{lll}z\hfill & =\hfill & \frac{41-45}{1.3}\hfill \\ \hfill & =\hfill & \frac{-4}{1.3}\hfill \\ \hfill & =\hfill & -3.08\hfill \end{array}$

On the Calculator
$\begin{array}{ll}\hfill & \hfill \\ \text{Type}\hfill & 41\hfill \\ \text{Press}\hfill & \begin{array}{||}\hline -\\ \hline\end{array}\hfill \\ \text{Type}\hfill & 45\hfill \\ \text{Press}\hfill & \begin{array}{||}\hline =\\ \hline\end{array}\hfill \\ \text{Press}\hfill & \begin{array}{||}\hline ÷\\ \hline\end{array}\hfill \\ \text{Type}\hfill & 1.3\hfill \\ \text{Press}\hfill & \begin{array}{||}\hline =\\ \hline\end{array}\hfill \\ \text{Display}\text{reads:}\hfill & -3.076923\hfill \\ \text{We'll}\text{round}\text{to}-3.08\hfill & \hfill \end{array}$

$p=5w^3+w^2-w-1$ .

This equation expresses the relationship between $p$ and $w$ . Determine the value of $p$ if $w=5$ .

$\begin{array}{lll}p\hfill & =\hfill & 5{(5)}^3+{(5)}^2-(5)-1\hfill \\ \hfill & =\hfill & 5(125)+25-(5)-1\hfill \\ \hfill & =\hfill & 625+25-5-1\hfill \\ \hfill & =\hfill & 644\hfill \end{array}$

On the Calculator
$\begin{array}{ll}\hfill & \hfill \\ \text{Type}\hfill & 5\hfill \\ \text{Press}\hfill & \begin{array}{||}\hline y^x\\ \hline\end{array}\hfill \\ \text{Type}\hfill & 3\hfill \\ \text{Press}\hfill & \begin{array}{||}\hline =\\ \hline\end{array}\hfill \\ \text{Press}\hfill & \begin{array}{||}\hline \times \\ \hline\end{array}\hfill \\ \text{Type}\hfill & 5\hfill \\ \text{Press}\hfill & \begin{array}{||}\hline =\\ \hline\end{array}\hfill \\ \text{Press}\hfill & \begin{array}{||}\hline +\\ \hline\end{array}\hfill \\ \text{Type}\hfill & 5\hfill \\ \text{Press}\hfill & \begin{array}{||}\hline x^2\\ \hline\end{array}\hfill \\ \text{Press}\hfill & \begin{array}{||}\hline -\\ \hline\end{array}\hfill \\ \text{Type}\hfill & 5\hfill \\ \text{Press}\hfill & \begin{array}{||}\hline -\\ \hline\end{array}\hfill \\ \text{Type}\hfill & 1\hfill \\ \text{Press}\hfill & \begin{array}{||}\hline =\\ \hline\end{array}\hfill \\ \text{Display}\text{reads:}\hfill & 644\hfill \end{array}$