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It's easy in the beginning but then I get confused somewhere along the line so please explain fully
It's easy in the beginning but then I get confused somewhere along the line so please explain fully
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Find the two right angled triangles they talk about.
The first has the hypotenuse near the R with the sides 2x and x. Simple to calculate the value for R in terms of x.
The other has the other radius line and the sides are the vertical "2" and "x+2."
You now have two equations where you can solve for x. Since only one soution is real (-1 is imaginary) you can now substitute for R and find the area of the whole circle but divide it half since you have only a semi-circle.
Yes, it is confusing with all the little steps involved. Just solve for all the pits you can find and then some of the questions start to become answers.
As to your "additional details". in the first triangle R^2 is equal to 4x^2 + x^2 or 5x^2. For the second triangle, R^2=x^2 + 4x + 8. Since the two results with "x" are equal to R^2 then they are equal to each other, hence 5x^2 = x^2 + 4x + 8.
The first has the hypotenuse near the R with the sides 2x and x. Simple to calculate the value for R in terms of x.
The other has the other radius line and the sides are the vertical "2" and "x+2."
You now have two equations where you can solve for x. Since only one soution is real (-1 is imaginary) you can now substitute for R and find the area of the whole circle but divide it half since you have only a semi-circle.
Yes, it is confusing with all the little steps involved. Just solve for all the pits you can find and then some of the questions start to become answers.
As to your "additional details". in the first triangle R^2 is equal to 4x^2 + x^2 or 5x^2. For the second triangle, R^2=x^2 + 4x + 8. Since the two results with "x" are equal to R^2 then they are equal to each other, hence 5x^2 = x^2 + 4x + 8.
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R^2 = 5x^2 from the syeeper R in the diagram.
R^2 also = (x + 2)^2 + 2^2 from the flatter R
So 5x^2 = (x + 2)^2 + 2^2 which gives 5x^2 = x^2 +4x + 4 +4
Hence 4x^2 - 4x -8 = 0,so x =2. (not -1).
So r^2 = 5 x 2^2 = 20, so area of whole circle = pi x 20, hence semicircle has area pi x 10.
R^2 also = (x + 2)^2 + 2^2 from the flatter R
So 5x^2 = (x + 2)^2 + 2^2 which gives 5x^2 = x^2 +4x + 4 +4
Hence 4x^2 - 4x -8 = 0,so x =2. (not -1).
So r^2 = 5 x 2^2 = 20, so area of whole circle = pi x 20, hence semicircle has area pi x 10.
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nope sorry confused too