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anonymous

  • 4 years ago

Express the ratio of the area of the larger circle to the area of the smaller circle in simplest radical form. Larger circle: radius of 2 + √3 and smaller circle's radius: 2-√3.

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  1. anonymous
    • 4 years ago
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    |dw:1328379356570:dw|

  2. dumbcow
    • 4 years ago
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    is this a repost? what was unclear on explainations in prev post?

  3. anonymous
    • 4 years ago
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    Why is it 7 + 4√3?

  4. anonymous
    • 4 years ago
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    I tried pi (2)^2 + √3^2

  5. dumbcow
    • 4 years ago
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    oh you forgot the middle term (2+sqrt3)^2 = 4 + 2sqrt3 +2sqrt3 + 3

  6. dumbcow
    • 4 years ago
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    (a+b)^2 does Not equal (a^2 +b^2)

  7. anonymous
    • 4 years ago
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    middle term? what? D:

  8. dumbcow
    • 4 years ago
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    FOIL ? (2+sqrt3)(2+sqrt3) = 4+4sqrt3 +3

  9. anonymous
    • 4 years ago
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    ohhh.

  10. anonymous
    • 4 years ago
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    thank you!

  11. dumbcow
    • 4 years ago
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    :)

  12. anonymous
    • 4 years ago
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    Okay so I have now: \[\pi \times 7 + 4\sqrt{3} \div \pi \times 7-4\sqrt{3} \times \pi \times 7+4\sqrt{3} \div \pi \times 7+4\sqrt{3}\]

  13. dumbcow
    • 4 years ago
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    yes except the pi cancels out...pi/pi = 1 so you can get rid of it

  14. anonymous
    • 4 years ago
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    ohh..

  15. anonymous
    • 4 years ago
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    Is that the same for 7/7?

  16. dumbcow
    • 4 years ago
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    no because its not a multiplicative constant...or its part of the addition so it can't cancel it helps to put parenthesis around them, (7+4sqrt3) is like 1 term so only if (7+4sqrt3) is on bottom can it cancel sorry if that was confusing

  17. anonymous
    • 4 years ago
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    Okay so: = \[(7 + 4\sqrt{3})(7 + 4\sqrt{3}) \div (7 - 4\sqrt{3})(7 + 4\sqrt{3})\] = \[49 + 28\sqrt{3} + 28\sqrt{3} + 16\sqrt{9} \div 49 + 28\sqrt{3} - 28\sqrt{3} - 16\sqrt{9}\] = \[121\sqrt{15} \div \]

  18. anonymous
    • 4 years ago
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    \[33\sqrt{15}\]

  19. anonymous
    • 4 years ago
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    The answer is supposed to be: 97 + 56√3

  20. dumbcow
    • 4 years ago
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    correct until last line...where did 121 come from?

  21. dumbcow
    • 4 years ago
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    also the numbers inside the radicals doNOt change when adding

  22. dumbcow
    • 4 years ago
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    oh i see what you did ... 2sqrt3 + 3sqrt2 does NOT equal 5sqrt5 keep the terms with radicals separate you can only combine sqrt2 with other sqrt2 's

  23. dumbcow
    • 4 years ago
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    Top: 16sqrt9 = 16*3 = 48 28sqrt3 + 28sqrt3 = 56sqrt3 49 + 48 = 97 --> 97 + 56sqrt3 Bottom: 49 - 48 = 1 28sqrt3 - 28sqrt3 = 0 --> 1

  24. anonymous
    • 4 years ago
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    ohhhh. Thank you!

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