Respuesta :
If there is no wind, then s = 0. Substituting into the equation:
[tex]\begin{gathered} p=25-0.01\cdot0^2 \\ p=25 \end{gathered}[/tex]The amount of particulate pollution when there is no wind is 25 ounces per cubic yard.
If there is no particulate pollution, then p = 0. Substituting into the equation:
[tex]0=25-0.01s^2[/tex]The expression on the right is a difference of squares. Taking the square root of each term:
[tex]\begin{gathered} \sqrt[]{25}=5 \\ \sqrt[]{0.01s^2}=\sqrt[]{0.01}\sqrt[]{s^2}=0.1s \end{gathered}[/tex]Recalling the equation:
[tex]0=(5-0.1s)(5+0.1s)[/tex]This equation has two solutions:
[tex]\begin{gathered} 5-0.1s=0 \\ 5-0.1s+0.1s=0+0.1s \\ 5=0.1s \\ \frac{5}{0.1}=\frac{0.1s}{0.1} \\ 50=s \end{gathered}[/tex]Or:
[tex]\begin{gathered} 5+0.1s=0 \\ 5=-0.1s \\ \frac{5}{-0.1}=s \\ -50=s \end{gathered}[/tex]Wind speed cannot be negative, then the last solution is discarded.
The wind speed has to be 50 miles per hour to have no particulate pollution.
