Studdy AI Logo
Math

QuestionAn airplane flies 3000 miles at 500 mph. Cost per passenger is C(x)=75+x25+31,000xC(x)=75+\frac{x}{25}+\frac{31,000}{x}. Find cost with no wind. $□\$ \square (Round to the nearest cent.)

Studdy Solution

STEP 1

Assumptions1. The airplane crosses the Atlantic Ocean which is3000 miles. The airspeed of the airplane is500 miles per hour3. The cost C (in dollars) per passenger is given by the equationC(x)=75+x25+31,000xC(x)=75+\frac{x}{25}+\frac{31,000}{x} 4. The variable xx represents the ground speed, which is the airspeed +/- wind speed5. In quiescent conditions, there is no wind, so the ground speed is equal to the airspeed

STEP 2

In quiescent conditions, the ground speed xx is equal to the airspeed. So, we can substitute the airspeed into the cost equation.
C(x)=75+x25+31,000xC(x)=75+\frac{x}{25}+\frac{31,000}{x} becomesC(500)=75+50025+31,000500C(500)=75+\frac{500}{25}+\frac{31,000}{500}

STEP 3

Now, we can simplify the equation by performing the operations.
First, divide500 by2550025=20\frac{500}{25} =20Then, divide31,000 by50031,000500=62\frac{31,000}{500} =62So, the equation becomesC(500)=75+20+62C(500)=75+20+62

STEP 4

Finally, add the numbers together to find the cost per passenger for quiescent conditions.
C(500)=75+20+62=$157C(500)=75+20+62 = \$157So, the cost per passenger for quiescent conditions is $157.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord