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anonymous

  • one year ago

Water coming out from a fountain is modeled by the function f(x) = -x2 + 5x + 4 where f(x) represents the height, in feet, of the water from the fountain at different times x, in seconds. What does the average rate of change of f(x) from x = 3 to x = 5 represent? The water falls down with an average speed of 3 feet per second from 3 seconds to 5 seconds. The water falls down with an average speed of 5 feet per second from 3 seconds to 5 seconds. The water travels an average distance of 3 feet from 3 seconds to 5 seconds. The water travels an average distance of 5 feet from 3 seconds

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  1. freckles
    • one year ago
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    average rate of change is given by the change of y over the change of x. \[\frac{ f(5)-f(3)}{5-3} \]

  2. freckles
    • one year ago
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    you are dividing a change of height by a change in time

  3. anonymous
    • one year ago
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    So x = 2?

  4. dumbcow
    • one year ago
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    also "rate of change" = speed

  5. anonymous
    • one year ago
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    So, I know its either A or B, right?

  6. dumbcow
    • one year ago
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    yes

  7. anonymous
    • one year ago
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    So its either 5 or 3 feet per 3-5 seconds?

  8. freckles
    • one year ago
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    just used the formula I gave above to figure out between A and B

  9. anonymous
    • one year ago
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    I dont understand the formula you gave me.

  10. anonymous
    • one year ago
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    f(5) - f(3) = f(2) ----- 2 ??????????????

  11. freckles
    • one year ago
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    ...how did you get f(5)-f(3)=f(2)?

  12. freckles
    • one year ago
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    f(5)=-5^2+5(5)+4 and f(3)=-3^2+5(3)+4

  13. anonymous
    • one year ago
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    So f(5) = 3154 And f(3) = 110

  14. freckles
    • one year ago
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    -5^2+5(5)+4 ------ first we know 5^2=5(5)=25 so -5^2+5(5)+4 can be written as -25+25+4

  15. freckles
    • one year ago
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    -25+25 is 0 though so you have -5^2+5(5)+4 can be written as 0+4 which is just 4

  16. freckles
    • one year ago
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    can you try doing f(3)

  17. anonymous
    • one year ago
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    f(3) = 25?

  18. freckles
    • one year ago
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    are you guessing?

  19. anonymous
    • one year ago
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    No

  20. freckles
    • one year ago
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    f(x)=-x^2+5x+4 just plug in 3 where x is

  21. anonymous
    • one year ago
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    OH there is a negative, my bad

  22. freckles
    • one year ago
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    f(3)=-3^2+5(3)+4 3^2 means 3(3) which is 9 5(3) is 15 f(3)=-9+15+4

  23. anonymous
    • one year ago
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    so 10?

  24. freckles
    • one year ago
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    \[\frac{f(5)-f(3)}{5-3}=\frac{4-10}{5-3}\]

  25. anonymous
    • one year ago
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    so its 3

  26. anonymous
    • one year ago
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    So the answer is a?

  27. freckles
    • one year ago
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    well -3 where the units is distance/time which is a speed unit which just means going down at a speed of 3ft/sec

  28. freckles
    • one year ago
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    and yes a sounds great

  29. anonymous
    • one year ago
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    Thx for the help! Ima submit my test now, lets see :D

  30. anonymous
    • one year ago
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    Oh no! I got a %62 on my test :(. 5 questions wrong out of 13. But the one you helped me with was right, ty so much!

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