anonymous
  • anonymous
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.
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
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dumbcow
  • dumbcow
is this a repost? what was unclear on explainations in prev post?
anonymous
  • anonymous
Why is it 7 + 4√3?

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anonymous
  • anonymous
I tried pi (2)^2 + √3^2
dumbcow
  • dumbcow
oh you forgot the middle term (2+sqrt3)^2 = 4 + 2sqrt3 +2sqrt3 + 3
dumbcow
  • dumbcow
(a+b)^2 does Not equal (a^2 +b^2)
anonymous
  • anonymous
middle term? what? D:
dumbcow
  • dumbcow
FOIL ? (2+sqrt3)(2+sqrt3) = 4+4sqrt3 +3
anonymous
  • anonymous
ohhh.
anonymous
  • anonymous
thank you!
dumbcow
  • dumbcow
:)
anonymous
  • anonymous
Okay so I have now: \[\pi \times 7 + 4\sqrt{3} \div \pi \times 7-4\sqrt{3} \times \pi \times 7+4\sqrt{3} \div \pi \times 7+4\sqrt{3}\]
dumbcow
  • dumbcow
yes except the pi cancels out...pi/pi = 1 so you can get rid of it
anonymous
  • anonymous
ohh..
anonymous
  • anonymous
Is that the same for 7/7?
dumbcow
  • dumbcow
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
anonymous
  • anonymous
Okay so: = \[(7 + 4\sqrt{3})(7 + 4\sqrt{3}) \div (7 - 4\sqrt{3})(7 + 4\sqrt{3})\] = \[49 + 28\sqrt{3} + 28\sqrt{3} + 16\sqrt{9} \div 49 + 28\sqrt{3} - 28\sqrt{3} - 16\sqrt{9}\] = \[121\sqrt{15} \div \]
anonymous
  • anonymous
\[33\sqrt{15}\]
anonymous
  • anonymous
The answer is supposed to be: 97 + 56√3
dumbcow
  • dumbcow
correct until last line...where did 121 come from?
dumbcow
  • dumbcow
also the numbers inside the radicals doNOt change when adding
dumbcow
  • dumbcow
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
dumbcow
  • dumbcow
Top: 16sqrt9 = 16*3 = 48 28sqrt3 + 28sqrt3 = 56sqrt3 49 + 48 = 97 --> 97 + 56sqrt3 Bottom: 49 - 48 = 1 28sqrt3 - 28sqrt3 = 0 --> 1
anonymous
  • anonymous
ohhhh. Thank you!

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