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Math Help - pre-calculus questions

  1. #1
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    Exclamation pre-calculus questions

    I have an online quiz, that I am currently taking and should submit pretty soon.
    The answer in bold is the one I chose. If I am wrong, please explain why
    Thanks for any input, I appreciate it.
    ---

    1) Let R be the region between the curves y=x^2
    and y=2x-(x^2).

    To find the area of R, we need to

    A) integrate [(x^2)-(2x-x^2)] from 0 to 1
    B) integrate [(2x-x^2)-(x^2)] from 0 to 1
    C) integrate [(x^2)-(2x-x^2)] from 0 to 2
    D) integrate [(2x-x^2)-(x^2)] from 0 to 2


    2)Let R be the region bounded by the curves y=(x^2)+3 and y=x, for x in [-1,1].


    The area of R is equal to

    A) 2
    B) 17/3
    C) 20/3


    3) Let R be the region bounded by the curves x=(y^2) and y=x+5, for y in [-1,2].

    Sketch the region, then answer the following question.

    The most convenient way to find the area of R is to slice the region...

    A) horizontally
    B) vertically
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by daneeyah View Post
    I have an online quiz, that I am currently taking and should submit pretty soon.
    The answer in bold is the one I chose. If I am wrong, please explain why
    Thanks for any input, I appreciate it.
    ---

    1) Let R be the region between the curves y=x^2
    and y=2x-(x^2).

    To find the area of R, we need to

    A) integrate [(x^2)-(2x-x^2)] from 0 to 1
    B) integrate [(2x-x^2)-(x^2)] from 0 to 1
    C) integrate [(x^2)-(2x-x^2)] from 0 to 2
    D) integrate [(2x-x^2)-(x^2)] from 0 to 2
    correct
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  3. #3
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    Exclamation

    Thank you I appreciate it

    What about the other two?
    I am pretty sure #2 is correct, but #3 I am a bit unsure about.
    Thanks again for your time, I appreciate it.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by daneeyah View Post
    2)Let R be the region bounded by the curves y=(x^2)+3 and y=x, for x in [-1,1].


    The area of R is equal to

    A) 2
    B) 17/3
    C) 20/3
    yes
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by daneeyah View Post
    3) Let R be the region bounded by the curves x=(y^2) and y=x+5, for y in [-1,2].

    Sketch the region, then answer the following question.

    The most convenient way to find the area of R is to slice the region...

    A) horizontally
    B) vertically
    no. did you graph it?

    it is almost obvious from the graph that the best way to find the area here is to write both functions in terms of y and do the required integral. in that case, we need rectangles whose lengths are parallel to the x-axis (you need to know how we define the integral based on Riemann sums to know what rectangles we are talking about here)
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  6. #6
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    Smile

    Quote Originally Posted by Jhevon View Post
    no. did you graph it?

    it is almost obvious from the graph that the best way to find the area here is to write both functions in terms of y and do the required integral. in that case, we need rectangles whose lengths are parallel to the x-axis (you need to know how we define the integral based on Riemann sums to know what rectangles we are talking about here)
    I just graphed it again.. I see how horizontal would be better.
    Thanks again.. I just submitted my quiz and got a 100.
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  7. #7
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    Quote Originally Posted by daneeyah View Post
    I have an online quiz, that I am currently taking and should submit pretty soon.
    The answer in bold is the one I chose. If I am wrong, please explain why
    Thanks for any input, I appreciate it.
    ---

    1) Let R be the region between the curves y=x^2
    and y=2x-(x^2).

    To find the area of R, we need to

    A) integrate [(x^2)-(2x-x^2)] from 0 to 1
    B) integrate [(2x-x^2)-(x^2)] from 0 to 1 Mr F says: Correct.
    C) integrate [(x^2)-(2x-x^2)] from 0 to 2
    D) integrate [(2x-x^2)-(x^2)] from 0 to 2


    2)Let R be the region bounded by the curves y=(x^2)+3 and y=x, for x in [-1,1].


    The area of R is equal to

    A) 2
    B) 17/3
    C) 20/3 Mr F says: Correct.


    3) Let R be the region bounded by the curves x=(y^2) and y=x+5, for y in [-1,2].

    Sketch the region, then answer the following question.

    The most convenient way to find the area of R is to slice the region...

    A) horizontally
    B) vertically Mr F says: Horizontal is most convenient for me. But you know what they say .... one man's meat is another man's poison ..... I think the question is quite stupid, actually.
    ..
    Last edited by mr fantastic; January 26th 2008 at 09:06 PM. Reason: Well, that's what happens when you answer the phone ....
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  8. #8
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by daneeyah View Post
    I just graphed it again.. I see how horizontal would be better.
    Thanks again..
    you're welcome

    I just submitted my quiz and got a 100.
    very nice!
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  9. #9
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    Quote Originally Posted by Jhevon View Post
    you're welcome

    very nice!
    Yes, well done Jhevon!
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