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anonymous

  • 5 years ago

just checking over solution for question: A tract of land bordered by a highway along the y-axis, a dirt road along the x-axis, and a river whose path is given by the equation y=4-0.2x^2, where x and y are in hindreds of meters. The tract is 300m deep along the dirt road The value of the land is constant in any strip parallel to the highway and increases as you move way from the highway, with the value given by v=1000+50x dollars per 10,000 m^2 at the sample point (x,y). Find dW, the worth of a strip. Write an integral that equals the worth of the entire tract.

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  1. anonymous
    • 5 years ago
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    here is my solution. we have integral dw, where dw is a strip of the "worth" of the land. The dw is like Area(x)*value(x) at x as you go along , but Area(x) is y(x)*dx

  2. anonymous
    • 5 years ago
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    so integral (4 - .2x^2) ( 1000 + 50x) dx from 0 to 3

  3. bahrom7893
    • 5 years ago
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    why 0 to 3?

  4. anonymous
    • 5 years ago
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    oh, because 300 m deep along dirt road

  5. bahrom7893
    • 5 years ago
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    Oh okay

  6. anonymous
    • 5 years ago
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    do you think this needs a double integral?

  7. bahrom7893
    • 5 years ago
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    i honestly have no idea, did you try both ways? One with a double integral one with a regular one and solve them on the calculator and check the answer?

  8. anonymous
    • 5 years ago
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    dont know how to set up double integral for this one

  9. anonymous
    • 5 years ago
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    if the value was constant, we would have k integral y(x)* dx , where y(x)*dx is a strip of area (or a infinitely thin rectangle). but its changing so we have to put it inside the integral

  10. anonymous
    • 5 years ago
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    since total area = integral y(x)*dx

  11. anonymous
    • 5 years ago
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    so i look at integration as summing the infinitely thin rectangles

  12. bahrom7893
    • 5 years ago
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    what is the answer?

  13. anonymous
    • 5 years ago
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    oh i dont really care about the answer. i just want to set it up correctly , lol

  14. anonymous
    • 5 years ago
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    math people just prove a solution exists, they leave the calculations for another day, i suppose

  15. anonymous
    • 5 years ago
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    well the ancient greeks let the slaves approximate. but i think archimedes was the first to sit down and approximate pi to many digits

  16. bahrom7893
    • 5 years ago
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    i mean if u knew the answer, we could see if ur setup was correct. I tried it on the calculator and got 0.009561, etc

  17. bahrom7893
    • 5 years ago
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    and math is hard, im regretting my math majorin decision

  18. anonymous
    • 5 years ago
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    oh are you undergrad?

  19. bahrom7893
    • 5 years ago
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    yeah, im a freshman

  20. anonymous
    • 5 years ago
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    what country?

  21. bahrom7893
    • 5 years ago
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    US

  22. anonymous
    • 5 years ago
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    youre doing great if youre freshman, and solved that integral problem the e^x

  23. anonymous
    • 5 years ago
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    of course math takes effort . but i hit a wall in math personally. in the advanced math stuff,

  24. bahrom7893
    • 5 years ago
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    i took calc 1 and 2 in hs, it was okay, calc 3 knocked me down in college

  25. anonymous
    • 5 years ago
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    you can do math for engineering , and that will allow you avoid the advanced formal stuff like topology, for example

  26. anonymous
    • 5 years ago
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    calc 3 is hard. lol. you have to go over it more than once. i have my own gaps in knowledge. have you tried khanacademy.org

  27. bahrom7893
    • 5 years ago
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    yeah

  28. bahrom7893
    • 5 years ago
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    okay just finished half of my own hw, sorry gtg ttyl, bye

  29. anonymous
    • 5 years ago
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    oh there is units issue

  30. bahrom7893
    • 5 years ago
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    100 meters?

  31. anonymous
    • 5 years ago
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    no its fine well the y dx is 100 meters * 100 meters, so 10000 m^2, but the value is per 10,000 m^2 , so they cancel. i got 10897.5 as the answer

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