Can you find the blue area? |

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  • เผยแพร่เมื่อ 12 พ.ย. 2024

ความคิดเห็น • 5

  • @pentaglion3918
    @pentaglion3918 2 หลายเดือนก่อน

    Gracias por estos videos, me hacen pensar y aprender. Thanks for these videos, they make me think and learn.

    • @mrtalbotmaths
      @mrtalbotmaths  2 หลายเดือนก่อน

      Thanks for your comment, glad you enjoy 😀

  • @slytherinbrian
    @slytherinbrian 2 หลายเดือนก่อน

    Wow, that was pretty breezy! I solved it a bit differently. I rotated the whole figure 45 degrees, and put it on an x-y plane centered at the center of the figure. I then found a formula for the blue circle and for the quarter circle centered at the bottom of the (now) diamond. Those are:
    y = sqrt(25 - x^2) and y = sqrt(100 - x^2) - sqrt(50)
    I solved that system of equations to figure out where they cross (on the right), at x=5 sqrt(14)/4.
    Then I set up the integral to find the area between those two graphs over the range x=0 to x=5 sqrt(14)/4, which gives a quarter of the total blue area. Multiply by 4 to get 29.276.
    Sure, I plugged the integral into Wolfram Alpha, but if we're just looking for a numerical answer, that's good enough, right?

    • @mrtalbotmaths
      @mrtalbotmaths  2 หลายเดือนก่อน

      Nice solution!! I’ll talk a bit slower next video 😀

    • @slytherinbrian
      @slytherinbrian 2 หลายเดือนก่อน +1

      @@mrtalbotmaths Haha awesome!