An airplane crosses the Atlantic Ocean ( 3000 miles) with an airspeed of 550 miles per hour. The cost \( C \) (in dollars) per passenger is given by \( C(x)=75+\frac{x}{10}+\frac{32,000}{x} \) where \( x \) is the ground speed (airspeed \( \pm \) wind). (a) What is the cost per passenger for quiescent (no wind) conditions? \( \$ \square \) (Round to the nearest cent as needed.)

To find the cost per passenger for quiescent (no wind) conditions, we need to determine the ground speed \( x \) when there is no wind. In this case, the ground speed \( x \) is equal to the airspeed of the airplane. Given: - Airspeed = 550 miles per hour - Cost function: \( C(x) = 75 + \frac{x}{10} + \frac{32,000}{x} \) Since there is no wind, we have: \[ x = 550 \] Now, we can substitute \( x \) into the cost function \( C(x) \) to find the cost per passenger. \[ C(550) = 75 + \frac{550}{10} + \frac{32,000}{550} \] Let's calculate each term step by step: 1. Calculate \( \frac{550}{10} \): \[ \frac{550}{10} = 55 \] 2. Calculate \( \frac{32,000}{550} \): \[ \frac{32,000}{550} \approx 58.18 \] Now, we can substitute these values back into the cost function: \[ C(550) = 75 + 55 + 58.18 \] Now, let's calculate the total: \[ C(550) = 75 + 55 + 58.18 = 188.18 \] Thus, the cost per passenger for quiescent conditions is approximately: \[ \boxed{188.18} \]