Shaded Area is;
Area quarter circle with radius 80 cm - Area triangle with height 80 cm and base 80 cm - Area quarter circle with radius 60 cm + Area triangle with height 60 cm and base 60 cm + Are...
a = 3+1
a = 4 units.
b² = (2√(3))²-r²
b = √(12-r²) units.
Observing similar plane shape side lengths.
2√(3) - 4
√(12-r²) - 2r
Cross Multiply.
4√(3)r = 4√(12-r²)
√(3)r = √(12-r²)
3r² = 12-r²
4r²...
Calculating the interior angles.
It the interior angles be a, b and c identifying them clockwise.
Notice.
The plane shape consist of two composite regular nonagon.
It implies;
d = ⅑(180(9-2))
d...
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Sir Mike Ambrose is the author of the question.
Area green exactly in decimal is;
Notice.
Square side is (16/√(17)) units.
Area trapezoid with parallel sides (16/√(17)) units and (4/√(17)) units, an...
Let a be the diameter of the big circle.
Radius = ½(a).
Let b be the diameter of the small inscribed blue circle.
Radius = ½(b).
Diameter of the semi circle is;
2+16+6 = 24 units.
It radiu...
a+a+b = 20
2a+b = 20 --- (1).
20² = c²+10²
c² = 400-100
c = = √(300)
c = 10√(3) units.
It implies;
a+b = c
a+b = 10√(3) --- (2).
Solve (1) and (2) simultaneously, Calculating a and b...
Notice.
The red lengths are equal.
a² = 2-2cos135
a = 1.847759065 units.
b = ½(180+135)
b = 22.5°
c = 22.5+45
c = 67.5°
d² = 1.847759065²+1²-2*1*1.847759065cos67.5
d = 1.7320508075 units.
d is t...
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It implies;
2^(3x)-2^(2x) = 0
Let 2^(x) = p
Therefore;
p³-p² = 0
p³ = p²
p = 1
And p = 2^(x)
It implies;
2^(x) = 1
2^(x) = 2⁰
x = 0
