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anonymous

  • one year ago

A race pilot's average rate of speed over a 720-mile course is inversely proportional to the time in minutes t the pilot takes to fly a complete race course. The pilot's final score s is the average speed minus any penalty points p earned. 1. Write a function to model the pilot's score for a given t and p (Hint: d = rt) 2. Graph the function for a pilot who has two penalty points. 3. What is the maximum time a pilot with 2 penalty points can take to finish the course and still earn a score of at least 3?

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  1. anonymous
    • one year ago
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    i really don't understand this, please help

  2. ganeshie8
    • one year ago
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    For part 1, use the given hint. \[d=rt\] notice that we have \(d=720\) here, so \[720=rt \implies r = \dfrac{720}{t}\]

  3. ganeshie8
    • one year ago
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    `The pilot's final score s is the average speed minus any penalty points p earned.` \[s = r - p\] plugin the value of \(r\) above

  4. ganeshie8
    • one year ago
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    \[s=\dfrac{720}{t}-p\] thats the function for part1

  5. anonymous
    • one year ago
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    ok thank you, I actually already understood that part

  6. anonymous
    • one year ago
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    it's number 2 i need help with

  7. ganeshie8
    • one year ago
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    good, for part2, simply plugin \(p=2\) and graph the function

  8. anonymous
    • one year ago
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    oh, yeah of course

  9. anonymous
    • one year ago
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    so for part 3 do I just look for the maximum point on the graph?

  10. ganeshie8
    • one year ago
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    nope, for part3, simply plugin \(s=3\) in the function and solve \(t\)

  11. ganeshie8
    • one year ago
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    \[3=\dfrac{720}{t}-2\] solve \(t\)

  12. anonymous
    • one year ago
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    t=144

  13. anonymous
    • one year ago
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    so that's the maximum time

  14. ganeshie8
    • one year ago
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    Yes thats the maximum time acceptable anything greater than that will reduce the score

  15. anonymous
    • one year ago
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    ok, thanks again!

  16. ganeshie8
    • one year ago
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    yw

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