Let p be 2^(a)
Therefore;
(p³+p²)/(p²+8) = 8
8p²+64 = p³+p²
p³-7p² = 64
p²(p-7) = 64
It implies;
p ≠ 7
p = 8
And;
p = 8 = 2^(a)
2^(a) = 2³
a = 3
10^(2a) + 10^(3a) = 36
Let p be 10^(a)
Therefore;
p² + p³ = 36.
It implies;
p = 3
And;
10^(a) = p = 3
a = log3/log10
a = 0.47712125472
Let the side of the regular pentagon be 1 unit.
Therefore;
Area purple is;
Area trapezium with two parallel side 0.07294901687 unit and 0.38196601125 unit, and height cos18 unit.
= 0.5*cos18*(0.07...
Let the side length of the regular heptagon be 1 unit.
a = ⅐(180(7-2))
a = 128.5714285714°
Where a is the single interior angle of the regular heptagon.
b² = 2-2cos128.5714285714
b = 1.8019377358...
a² = 8-8cos(360-90-108)
a² = 8-8cos162
a = 3.9507533624 units.
b = ½(180-162)
b = 9°
c = 90+9
c = 99°
d² = 3.9507533624²+1-2*3.9507533624cos99
d = 4.2242774658 units.
(4.2242774658/sin99) = (3.9...
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Notice;
Red circle and black circle are congruent, they have equal radius, 1 cm.
Calculating Area Shaded.
a = 60-45
a = 15°
It implies;
Area Shaded is;
Area sector with radius 1 cm...
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Let AB be x.
Therefore BC = 2x.
Calculating x.
Yellow area + Area triangle with height 2x and base ½(3x)sin60 = Area trapezoid with two parallel side ½(3x) and 2x, and height ½(3√(3)x).
Therefore;...
Area blue exactly in cm² decimal is;
Area trapezoid with two parallel sides 12 unit and (12-16tan15) unit, and height 16 unit - Area triangle with height (12-16tan15) unit and base 4 unit - Area tr...
