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anonymous

  • one year ago

Use geometry to evaluate https://i.gyazo.com/82a9844552783f2bbc8a49003e361671.png

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  1. anonymous
    • one year ago
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    I know how to solve it but what do they mean "use geometry"

  2. anonymous
    • one year ago
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    @zzr0ck3r Can you give me a hand?

  3. anonymous
    • one year ago
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    @dan815 Maybe you could help?

  4. mathmate
    • one year ago
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    Hint: see drawing below: |dw:1441330734684:dw|

  5. anonymous
    • one year ago
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    I don't get it @mathmate :/

  6. anonymous
    • one year ago
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    @peachpi

  7. anonymous
    • one year ago
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    You don't have to evaluate an integral. \(y=\sqrt{4-x^2}\) is the equation for the top half of a circle with radius 2, centered at the origin. That's what @mathmate drew. They only want the integral from 0 to 2, so they want the area of ¼ of the circle.|dw:1441403513050:dw|

  8. anonymous
    • one year ago
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    Oh ok, that makes sense but how would I find that area?

  9. anonymous
    • one year ago
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    A=πr²

  10. anonymous
    • one year ago
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    Can you by any chance set it up for me? I'm more of a visual person, so I tend to retrace what someone has done to learn it.

  11. anonymous
    • one year ago
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    there's nothing to set up here. You just plug in 2 into the formula for area of a circle

  12. anonymous
    • one year ago
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    Why? I don't get it :/ Even if I plug in 2 for the area I'd get the radius no?

  13. anonymous
    • one year ago
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    Sorry, I'm really not sure what's confusing you. This is a straight up geometry problem. If the RADIUS of a circle is 2, what's the AREA of a quarter of the circle? \[A = \pi r^2\] Plug in 2 for r to get the area of the whole circle. Then divide the area by 4 to get the area of a quarter of the circle. That's literally all there is to it. Nothing to set up or integrate. No calculus involved here other than knowing that a definite integral gives the area under a curve.

  14. mathmate
    • one year ago
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    "I know how to solve it but what do they mean "use geometry" If you are not sure, you can also check your answer using geometry with your answer by integration.

  15. anonymous
    • one year ago
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    You see I'm very bad with geometry, so if I solve using calculus, I'd get the same answer correct?

  16. anonymous
    • one year ago
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    yes. same result either way

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