A airplane crosses the Atlantic Ocean (3000 miles) with an airspeed of 600 miles per hour. The cost C (in dollars) per passenger is given by...

C(x)= 150 + x/20 + 36,000/x

Where x is the ground speed (airspeed plus or minus wind).

a. What is the cost per passenger for quiescent (no wind) conditions?

b. What is the cost per passenger with a head wind of 50 miles per hour?

c. What is the cost per passenger with a tail wind of 100 miles per hour?

d. What is the cost per passenger with a head wind of 100 miles per hour?

ground speed (x) = 600 +- wind speed

then use the formula, Tail wind add wind speed, headwind, subtract.

To answer these questions, we need to substitute the given values into the equation C(x) = 150 + x/20 + 36,000/x.

a. For quiescent (no wind) conditions, the ground speed (x) will be equal to the airspeed of the airplane, which is 600 mph. Substituting this value into the equation:
C(x) = 150 + 600/20 + 36,000/600
C(x) = 150 + 30 + 60
C(x) = 240 dollars

Therefore, the cost per passenger for quiescent conditions is $240.

b. With a headwind of 50 miles per hour, the ground speed (x) will be the airspeed (600 mph) minus the headwind (50 mph), which equals 550 mph. Substituting this value into the equation:
C(x) = 150 + 550/20 + 36,000/550
C(x) = 150 + 27.5 + 65.45
C(x) = 242.95 dollars

Therefore, the cost per passenger with a headwind of 50 mph is approximately $242.95.

c. With a tailwind of 100 miles per hour, the ground speed (x) will be the airspeed (600 mph) plus the tailwind (100 mph), which equals 700 mph. Substituting this value into the equation:
C(x) = 150 + 700/20 + 36,000/700
C(x) = 150 + 35 + 51.43
C(x) = 236.43 dollars

Therefore, the cost per passenger with a tailwind of 100 mph is approximately $236.43.

d. With a headwind of 100 miles per hour, the ground speed (x) will be the airspeed (600 mph) minus the headwind (100 mph), which equals 500 mph. Substituting this value into the equation:
C(x) = 150 + 500/20 + 36,000/500
C(x) = 150 + 25 + 72
C(x) = 247 dollars

Therefore, the cost per passenger with a headwind of 100 mph is $247.

To find the cost per passenger for different wind conditions, we need to substitute the values of ground speed into the given cost function C(x) and evaluate it. Let's solve each part step by step:

a. Quiescent (no wind) conditions mean that the ground speed (x) will be equal to the airspeed (600 miles per hour). So, substitute x = 600 into the cost function C(x):

C(600) = 150 + 600/20 + 36,000/600

Simplifying:

C(600) = 150 + 30 + 60

C(600) = 240

Therefore, the cost per passenger for quiescent conditions is $240.

b. With a headwind of 50 miles per hour, the ground speed would be airspeed (600 miles per hour) minus the headwind (50 miles per hour). So, x = 600 - 50 = 550.

Substitute x = 550 into the cost function C(x):

C(550) = 150 + 550/20 + 36,000/550

Simplifying:

C(550) = 150 + 27.5 + 65.45

C(550) ≈ 242.95

Therefore, the cost per passenger with a headwind of 50 miles per hour is approximately $242.95.

c. With a tailwind of 100 miles per hour, the ground speed would be airspeed (600 miles per hour) plus the tailwind (100 miles per hour). So, x = 600 + 100 = 700.

Substitute x = 700 into the cost function C(x):

C(700) = 150 + 700/20 + 36,000/700

Simplifying:

C(700) = 150 + 35 + 51.43

C(700) ≈ 236.43

Therefore, the cost per passenger with a tailwind of 100 miles per hour is approximately $236.43.

d. With a headwind of 100 miles per hour, the ground speed would be airspeed (600 miles per hour) minus the headwind (100 miles per hour). So, x = 600 - 100 = 500.

Substitute x = 500 into the cost function C(x):

C(500) = 150 + 500/20 + 36,000/500

Simplifying:

C(500) = 150 + 25 + 72

C(500) = 247

Therefore, the cost per passenger with a headwind of 100 miles per hour is $247.