QuestionAn airplane flies 3000 miles at 550 mph. Cost per passenger is $C(x)=150+\frac{x}{25}+\frac{32,000}{x}$ . Find cost with 50 mph headwind.

Studdy Solution

STEP 1

Assumptions1. The airspeed of the airplane is550 miles per hour. . The cost function is given by $C(x)=150+\frac{x}{25}+\frac{32,000}{x}$ , where $x$ is the ground speed (airspeed ± wind).
3. The wind is acting as a headwind, which means it is opposing the airplane's motion, so it will decrease the ground speed.
4. The speed of the headwind is50 miles per hour.

STEP 2

We need to find the ground speed first. Since the wind is a headwind, it will decrease the ground speed. We can calculate the ground speed by subtracting the wind speed from the airspeed.
$x = Airspeed - Wind\, speed$

STEP 3

Now, plug in the given values for the airspeed and wind speed to calculate the ground speed.
$x =550 -50$

STEP 4

Calculate the ground speed.
$x =550 -50 =500$

STEP 5

Now that we have the ground speed, we can substitute this value into the cost function to find the cost per passenger.
$C(x)=150+\frac{x}{25}+\frac{32,000}{x}$

STEP 6

Plug in the value for the ground speed into the cost function.
$C(500)=150+\frac{500}{25}+\frac{32,000}{500}$

STEP 7

Calculate the cost per passenger.
$C(500)=150+20+\frac{32,000}{500}$

STEP 8

Continue to calculate the cost per passenger.
$C(500)=170+\frac{32,000}{500}$

STEP 9

Continue to calculate the cost per passenger.
$C(500)=170+64$

STEP 10

Calculate the final cost per passenger.
$C(500)=170+64 = \$234$ The cost per passenger with a head wind of50 miles per hour is $234.

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QuestionAn airplane flies 3000 miles at 550 mph. Cost per passenger is $C(x)=150+\frac{x}{25}+\frac{32,000}{x}$ . Find cost with 50 mph headwind.

Studdy Solution

STEP 1

STEP 2

We need to find the ground speed first. Since the wind is a headwind, it will decrease the ground speed. We can calculate the ground speed by subtracting the wind speed from the airspeed.
$x = Airspeed - Wind\, speed$

STEP 3

Now, plug in the given values for the airspeed and wind speed to calculate the ground speed.
$x =550 -50$

STEP 4

Calculate the ground speed.
$x =550 -50 =500$

STEP 5

Now that we have the ground speed, we can substitute this value into the cost function to find the cost per passenger.
$C(x)=150+\frac{x}{25}+\frac{32,000}{x}$

STEP 6

Plug in the value for the ground speed into the cost function.
$C(500)=150+\frac{500}{25}+\frac{32,000}{500}$

STEP 7

Calculate the cost per passenger.
$C(500)=150+20+\frac{32,000}{500}$

STEP 8

Continue to calculate the cost per passenger.
$C(500)=170+\frac{32,000}{500}$

STEP 9

Continue to calculate the cost per passenger.
$C(500)=170+64$

STEP 10

Calculate the final cost per passenger.
$C(500)=170+64 = \$234$ The cost per passenger with a head wind of50 miles per hour is $234.

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QuestionAn airplane flies 3000 miles at 550 mph. Cost per passenger is C(x)=150+x25+32,000xC(x)=150+\frac{x}{25}+\frac{32,000}{x}C(x)=150+25x​+x32,000​. Find cost with 50 mph headwind.

Studdy Solution

STEP 1

STEP 2

We need to find the ground speed first. Since the wind is a headwind, it will decrease the ground speed. We can calculate the ground speed by subtracting the wind speed from the airspeed.x=Airspeed−Wind speedx = Airspeed - Wind\, speedx=Airspeed−Windspeed

STEP 3

Now, plug in the given values for the airspeed and wind speed to calculate the ground speed.x=550−50x =550 -50x=550−50

STEP 4

Calculate the ground speed.x=550−50=500x =550 -50 =500x=550−50=500

STEP 5

Now that we have the ground speed, we can substitute this value into the cost function to find the cost per passenger.C(x)=150+x25+32,000xC(x)=150+\frac{x}{25}+\frac{32,000}{x}C(x)=150+25x​+x32,000​

STEP 6

Plug in the value for the ground speed into the cost function.C(500)=150+50025+32,000500C(500)=150+\frac{500}{25}+\frac{32,000}{500}C(500)=150+25500​+50032,000​

STEP 7

Calculate the cost per passenger.C(500)=150+20+32,000500C(500)=150+20+\frac{32,000}{500}C(500)=150+20+50032,000​

STEP 8

Continue to calculate the cost per passenger.C(500)=170+32,000500C(500)=170+\frac{32,000}{500}C(500)=170+50032,000​

STEP 9

Continue to calculate the cost per passenger.C(500)=170+64C(500)=170+64C(500)=170+64

STEP 10

Calculate the final cost per passenger.C(500)=170+64=$234C(500)=170+64 = \$234C(500)=170+64=$234The cost per passenger with a head wind of50 miles per hour is $234.

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QuestionAn airplane flies 3000 miles at 550 mph. Cost per passenger is $C(x)=150+\frac{x}{25}+\frac{32,000}{x}$ . Find cost with 50 mph headwind.

We need to find the ground speed first. Since the wind is a headwind, it will decrease the ground speed. We can calculate the ground speed by subtracting the wind speed from the airspeed.
$x = Airspeed - Wind\, speed$

Now, plug in the given values for the airspeed and wind speed to calculate the ground speed.
$x =550 -50$

Calculate the ground speed.
$x =550 -50 =500$

Now that we have the ground speed, we can substitute this value into the cost function to find the cost per passenger.
$C(x)=150+\frac{x}{25}+\frac{32,000}{x}$

Plug in the value for the ground speed into the cost function.
$C(500)=150+\frac{500}{25}+\frac{32,000}{500}$

Calculate the cost per passenger.
$C(500)=150+20+\frac{32,000}{500}$

Continue to calculate the cost per passenger.
$C(500)=170+\frac{32,000}{500}$

Continue to calculate the cost per passenger.
$C(500)=170+64$

Calculate the final cost per passenger.
$C(500)=170+64 = \$234$ The cost per passenger with a head wind of50 miles per hour is $234.