QuestionAn airplane crosses 3000 miles at 550 mph. Find cost per passenger $C(x)$ with a 100 mph headwind. Round to nearest cent.

Studdy Solution

STEP 1

Assumptions1. The airplane's airspeed is550 miles per hour. The cost per passenger is given by the function $C(x)=150+\frac{x}{25}+\frac{32,000}{x}$
3. The ground speed $x$ is the airspeed plus or minus the wind speed4. There is a head wind of100 miles per hour

STEP 2

First, we need to find the ground speed. Since it's a head wind, it will slow the airplane down, so we subtract 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.
$x =550\, mph -100\, mph$

STEP 4

Calculate the ground speed.
$x =550\, mph -100\, mph =450\, mph$

STEP 5

Now that we have the ground speed, we can plug this 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.
$C(450)=150+\frac{450}{25}+\frac{32,000}{450}$

STEP 7

implify the cost function.
$C(450)=150+18+\frac{32,000}{450}$

STEP 8

Calculate the cost per passenger.
$C(450)=150+18+\frac{32,000}{450} = \$187.11$ The cost per passenger with a head wind of100 miles per hour is $187.11.

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QuestionAn airplane crosses 3000 miles at 550 mph. Find cost per passenger $C(x)$ with a 100 mph headwind. Round to nearest cent.

Studdy Solution

STEP 1

Assumptions1. The airplane's airspeed is550 miles per hour. The cost per passenger is given by the function $C(x)=150+\frac{x}{25}+\frac{32,000}{x}$
3. The ground speed $x$ is the airspeed plus or minus the wind speed4. There is a head wind of100 miles per hour

STEP 2

First, we need to find the ground speed. Since it's a head wind, it will slow the airplane down, so we subtract 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.
$x =550\, mph -100\, mph$

STEP 4

Calculate the ground speed.
$x =550\, mph -100\, mph =450\, mph$

STEP 5

Now that we have the ground speed, we can plug this 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.
$C(450)=150+\frac{450}{25}+\frac{32,000}{450}$

STEP 7

implify the cost function.
$C(450)=150+18+\frac{32,000}{450}$

STEP 8

Calculate the cost per passenger.
$C(450)=150+18+\frac{32,000}{450} = \$187.11$ The cost per passenger with a head wind of100 miles per hour is $187.11.

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QuestionAn airplane crosses 3000 miles at 550 mph. Find cost per passenger C(x)C(x)C(x) with a 100 mph headwind. Round to nearest cent.

Studdy Solution

STEP 1

STEP 2

First, we need to find the ground speed. Since it's a head wind, it will slow the airplane down, so we subtract 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 mph−100 mphx =550\, mph -100\, mphx=550mph−100mph

STEP 4

Calculate the ground speed.x=550 mph−100 mph=450 mphx =550\, mph -100\, mph =450\, mphx=550mph−100mph=450mph

STEP 5

Now that we have the ground speed, we can plug this 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(450)=150+45025+32,000450C(450)=150+\frac{450}{25}+\frac{32,000}{450}C(450)=150+25450​+45032,000​

STEP 7

implify the cost function.C(450)=150+18+32,000450C(450)=150+18+\frac{32,000}{450}C(450)=150+18+45032,000​

STEP 8

Calculate the cost per passenger.C(450)=150+18+32,000450=$187.11C(450)=150+18+\frac{32,000}{450} = \$187.11C(450)=150+18+45032,000​=$187.11The cost per passenger with a head wind of100 miles per hour is $187.11.

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QuestionAn airplane crosses 3000 miles at 550 mph. Find cost per passenger $C(x)$ with a 100 mph headwind. Round to nearest cent.

First, we need to find the ground speed. Since it's a head wind, it will slow the airplane down, so we subtract 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.
$x =550\, mph -100\, mph$

Calculate the ground speed.
$x =550\, mph -100\, mph =450\, mph$

Now that we have the ground speed, we can plug this 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.
$C(450)=150+\frac{450}{25}+\frac{32,000}{450}$

implify the cost function.
$C(450)=150+18+\frac{32,000}{450}$

Calculate the cost per passenger.
$C(450)=150+18+\frac{32,000}{450} = \$187.11$ The cost per passenger with a head wind of100 miles per hour is $187.11.