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x*sqrt(2)/{5 - sqrt(3)} = {5 + sqrt(3)} => x*sqrt(2) = {5 + sqrt(3)} * {5 - sqrt(3)} = 25 - 3 = 22 => x = 22/sqrt(2) = 22*sqrt(2)/{sqrt(2)*sqrt(2)} = 22*sqrt(2)/2 = 11*sqrt(2)
tan theta = sqrt(2)/2 = 1/sqrt(2).
No
A regular hexagon can be divided into 6 equilateral triangles. If a side equals S, then altitude equals S*sqrt(3)/2, and area of that triangle is (S2)*sqrt(3)/4. So the whole hexagon area is 6*(S2)*sqrt(3)/4 = 3*(S2)*sqrt(3)/2. Since S = perimeter/6, then you have: Area = Perimeter2*sqrt(3)/24.
sqrt(8)/[2*sqrt(3)] = 2*sqrt(2)/[2*sqrt(3)] = sqrt(2)/sqrt(3) = sqrt(2/3)
x*sqrt(2)/{5 - sqrt(3)} = {5 + sqrt(3)} => x*sqrt(2) = {5 + sqrt(3)} * {5 - sqrt(3)} = 25 - 3 = 22 => x = 22/sqrt(2) = 22*sqrt(2)/{sqrt(2)*sqrt(2)} = 22*sqrt(2)/2 = 11*sqrt(2)
6
tan theta = sqrt(2)/2 = 1/sqrt(2).
No
A regular hexagon can be divided into 6 equilateral triangles. If a side equals S, then altitude equals S*sqrt(3)/2, and area of that triangle is (S2)*sqrt(3)/4. So the whole hexagon area is 6*(S2)*sqrt(3)/4 = 3*(S2)*sqrt(3)/2. Since S = perimeter/6, then you have: Area = Perimeter2*sqrt(3)/24.
sqrt(8)/[2*sqrt(3)] = 2*sqrt(2)/[2*sqrt(3)] = sqrt(2)/sqrt(3) = sqrt(2/3)
0.2857
1 ------ a+b=4 2 ------ ab=2 ====> 3. b = 2/a Sub 3 into 1 ===> a + 2/a = 4 mutiply both sides by a ===> a2 +2 -4a = 0 use quadratic formula to find a ==> a= 2 +sqrt(2) or a' = 2- sqrt(2) use these two values of a to find a value for b using equation 3 ===> using a, b= 2-sqrt(2) and using a', b= 2+sqrt(2) hence a4 + b4 = (2+sqrt(2))4 + (2-sqrt(2))4 = 136 (for both values of a and b)
g(x) = x + 3 Then f o g (x) = f(g(x)) = f(x + 3) = sqrt[(x+3) + 2] = sqrt(x + 5)
2.5
49
49