QuestionAn airplane crosses the Atlantic Ocean (3000 miles) at 560 mph. Cost per passenger with a 100 mph tailwind is given by
$\theta(x)=150+\frac{x}{20}+\frac{32,000}{x}$
What is the cost per passenger? Round to the nearest cent.

Studdy Solution

STEP 1

Assumptions1. The cost per passenger is given by the function $\theta(x)=150+\frac{x}{20}+\frac{32,000}{x}$ , where $x$ is the ground speed in miles per hour. . The airspeed of the airplane is560 miles per hour.
3. The tail wind speed is100 miles per hour.

STEP 2

Firstly, we need to find the ground speed. Ground speed is the sum of the airspeed and the tail wind speed.
$Ground\, speed = Airspeed + Tail\, wind\, speed$

STEP 3

Now, plug in the given values for the airspeed and tail wind speed to calculate the ground speed.
$Ground\, speed =560\, mph +100\, mph$

STEP 4

Calculate the ground speed.
$Ground\, speed =560\, mph +100\, mph =660\, mph$

STEP 5

Now that we have the ground speed, we can find the cost per passenger. We do this by substituting the ground speed into the cost function.
$Cost\, per\, passenger = \theta(x) =150+\frac{x}{20}+\frac{32,000}{x}$

STEP 6

Plug in the value for the ground speed into the cost function.
$Cost\, per\, passenger =150+\frac{660}{20}+\frac{32,000}{660}$

STEP 7

Calculate the cost per passenger.
$Cost\, per\, passenger =150+\frac{660}{20}+\frac{32,000}{660} \approx \$608.48$ The cost per passenger with a tail wind of100 miles per hour is approximately $608.48.

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QuestionAn airplane crosses the Atlantic Ocean (3000 miles) at 560 mph. Cost per passenger with a 100 mph tailwind is given by
$\theta(x)=150+\frac{x}{20}+\frac{32,000}{x}$
What is the cost per passenger? Round to the nearest cent.

Studdy Solution

STEP 1

Assumptions1. The cost per passenger is given by the function $\theta(x)=150+\frac{x}{20}+\frac{32,000}{x}$ , where $x$ is the ground speed in miles per hour. . The airspeed of the airplane is560 miles per hour.
3. The tail wind speed is100 miles per hour.

STEP 2

Firstly, we need to find the ground speed. Ground speed is the sum of the airspeed and the tail wind speed.
$Ground\, speed = Airspeed + Tail\, wind\, speed$

STEP 3

Now, plug in the given values for the airspeed and tail wind speed to calculate the ground speed.
$Ground\, speed =560\, mph +100\, mph$

STEP 4

Calculate the ground speed.
$Ground\, speed =560\, mph +100\, mph =660\, mph$

STEP 5

Now that we have the ground speed, we can find the cost per passenger. We do this by substituting the ground speed into the cost function.
$Cost\, per\, passenger = \theta(x) =150+\frac{x}{20}+\frac{32,000}{x}$

STEP 6

Plug in the value for the ground speed into the cost function.
$Cost\, per\, passenger =150+\frac{660}{20}+\frac{32,000}{660}$

STEP 7

Calculate the cost per passenger.
$Cost\, per\, passenger =150+\frac{660}{20}+\frac{32,000}{660} \approx \$608.48$ The cost per passenger with a tail wind of100 miles per hour is approximately $608.48.

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QuestionAn airplane crosses the Atlantic Ocean (3000 miles) at 560 mph. Cost per passenger with a 100 mph tailwind is given by θ(x)=150+x20+32,000x \theta(x)=150+\frac{x}{20}+\frac{32,000}{x} θ(x)=150+20x​+x32,000​ What is the cost per passenger? Round to the nearest cent.

Studdy Solution

STEP 1

STEP 2

Firstly, we need to find the ground speed. Ground speed is the sum of the airspeed and the tail wind speed.Ground speed=Airspeed+Tail wind speedGround\, speed = Airspeed + Tail\, wind\, speedGroundspeed=Airspeed+Tailwindspeed

STEP 3

Now, plug in the given values for the airspeed and tail wind speed to calculate the ground speed.Ground speed=560 mph+100 mphGround\, speed =560\, mph +100\, mphGroundspeed=560mph+100mph

STEP 4

Calculate the ground speed.Ground speed=560 mph+100 mph=660 mphGround\, speed =560\, mph +100\, mph =660\, mphGroundspeed=560mph+100mph=660mph

STEP 5

Now that we have the ground speed, we can find the cost per passenger. We do this by substituting the ground speed into the cost function.Cost per passenger=θ(x)=150+x20+32,000xCost\, per\, passenger = \theta(x) =150+\frac{x}{20}+\frac{32,000}{x}Costperpassenger=θ(x)=150+20x​+x32,000​

STEP 6

Plug in the value for the ground speed into the cost function.Cost per passenger=150+66020+32,000660Cost\, per\, passenger =150+\frac{660}{20}+\frac{32,000}{660}Costperpassenger=150+20660​+66032,000​

STEP 7

Calculate the cost per passenger.Cost per passenger=150+66020+32,000660≈$608.48Cost\, per\, passenger =150+\frac{660}{20}+\frac{32,000}{660} \approx \$608.48Costperpassenger=150+20660​+66032,000​≈$608.48The cost per passenger with a tail wind of100 miles per hour is approximately $608.48.

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QuestionAn airplane crosses the Atlantic Ocean (3000 miles) at 560 mph. Cost per passenger with a 100 mph tailwind is given by
$\theta(x)=150+\frac{x}{20}+\frac{32,000}{x}$
What is the cost per passenger? Round to the nearest cent.

Firstly, we need to find the ground speed. Ground speed is the sum of the airspeed and the tail wind speed.
$Ground\, speed = Airspeed + Tail\, wind\, speed$

Now, plug in the given values for the airspeed and tail wind speed to calculate the ground speed.
$Ground\, speed =560\, mph +100\, mph$

Calculate the ground speed.
$Ground\, speed =560\, mph +100\, mph =660\, mph$

Now that we have the ground speed, we can find the cost per passenger. We do this by substituting the ground speed into the cost function.
$Cost\, per\, passenger = \theta(x) =150+\frac{x}{20}+\frac{32,000}{x}$

Plug in the value for the ground speed into the cost function.
$Cost\, per\, passenger =150+\frac{660}{20}+\frac{32,000}{660}$

Calculate the cost per passenger.
$Cost\, per\, passenger =150+\frac{660}{20}+\frac{32,000}{660} \approx \$608.48$ The cost per passenger with a tail wind of100 miles per hour is approximately $608.48.