Answer: The shaded area is 99.55 units squared.
Step-by-step explanation:
r = 3.2
Now, we can see that the sides of the square are equal to two times the diameter of the circles (or four times the radius of the circles), so the length of the sides of the square is:
L = 2*(2*3.2) = 12.8
The area of the square is A1 = L^2 = 12.8*12.8 = 163.84 units squared.
the shaded semicircle has a diameter of 4 times r (so the radius is 2 times r), and the area is equal to half the area of a circle:
A2 = (1/2)*pi*(2r)^2 = (1/2)*3.14*(6.4)^2 = 64.31 units squared.
And now we must subtract the area of the four smaller circles inside the square, the area of each one is:
A3 = pi*r^2 = 3.14*(3.2)^2 = 32.15 units squared.
Then the shaded area is:
A = A1 + A2 - 4*A3 = 163.84 + 64.31 - 4* 32.15 = 99.55 units squared.
Please, use ( ) around fractional coefficients:
<span>1/3x-9y, 6/5x-15y should (probably) be written as (1/3) - 9y and (6/5)x - 15 y.
The LCD here is 3(5) = 15.
Mult. </span><span>1/3x-9y and 6/5x-15y by 15, and then divide the result by 15:
</span>15 [ (1/3)x - 9y and (6/5)x - 15 y ]
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15
This simplifies to:
5x - 135y and 18x - 225y
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15 15
These fractions are equivalent to the original ones, but now the common denominator, 15, is evident.
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The answer to your question would be 150 (c)
If the -8 is under the square root, then...
OR
If the -8 is not under the square root, then...
Either way, we replace x with -3 and simplify.
For more information, refer to the direct substitution rule for limits.