Answer:
To solve for \( x \) when [tex]\( N(x) = 6 \)[/tex], we need to plug [tex]\( N(x) = 6 \)[/tex] into the equation [tex]\( N(x) = \frac{x^2}{3000 - 60x} \)[/tex] and solve for \( x \). Let me do the calculation for you.
The solutions to the equation [tex]\( N(x) = 6 \)[/tex] are [tex]\( -180 + 60\sqrt{14} \)[/tex] and [tex]\( -60\sqrt{14} - 180 \)[/tex]. However, since we're talking about the average rate of cars per hour, we can disregard the negative value because a rate cannot be negative. Now, I will calculate the positive solution and round it to the nearest whole number.
The approximate value of \( x \) when [tex]\( N(x) = 6 \)[/tex] is 44, rounded to the nearest whole number.
Step-by-step explanation:
