Calculating Green Area.
a = 2*4
a = 8 units.
a is the radius of the ascribed quarter circle.
b²+4² = 8²
b² = 64-16
b = √(48)
b = 4√(3) units.
tanc = 4√(3)/4
c = atan(√(3))°
c = 60°...
Inscribed semi circle radius is 4 cm.
Inscribed quarter circle radius is 8 cm.
tana = 4/8
a = atan(½)°
b = 2a
b = 2atan(½)°
c = 180-b
c = 2atan(2)°
Blue Area is;
Area sector wi...
2^(x+1)+2^(x-1) = 320
Let 2^(x) be p.
It implies;
2p+½(p) = 320
½(5p) = 320
5p = 640
p = 128
And
p = 2^(x)
Calculating x.
2^(x) = 128
2^(x) = 2⁷
x = 7
Let b be 1 unit.
a = 50°
b = 40°
a and b are the two interior complementary angles or acute angles of the small right-angled triangle with hypotenuse b.
sin50 = c/b
c = sin50
c = 0.766044...
Calculating angle x.
Let 1 be the base of the ascribed isosceles triangle.
a = 180-39-2(27)
a = 141-54
a = 87°
(1/sin87) = (b/sin(2*27))
b = 0.8101272456 units.
c = 180-27-15-39
c =...
Let AB be a.
b = (a-2) units.
c = ½(a) units.
c is BD.
d = c-2
d = ½(a)-2
d = ½(a-4) units.
It implies;
2 - (a-2)
½(a-4) - 2
Cross Multiply.
4 = ½(a-4)(a-2)
8 = a²-6a+8
a...
Let 1 be the side length of the ascribed regular hexagon.
a = ⅙*180(6-2)
a = 120°
a is the single interior angle of the ascribed regular hexagon.
b² = 1²+1²-2*1*1cos120
b = 1.7320508076 un...
Calculating Alpha.
Let it be a.
Let b be the radius of the ascribed quarter circle.
c = (b-√(2)) units.
d = (b-2√(2)) units.
It implies, observing similar plane shape (right-angled)...
Calculating angle x.
Let AR be 1 unit.
a = 180-24-15
a = 180-39
a = 141°
a is angle ARK.
(1/sin15) = (b/sin141)
b = 2.4315072749 units.
b is AK.
c = 180-12-6
c = 180-18
c = 162°...
Sir Mike Ambrose is the author of the question.
Calculating the equation of the curve.
y-b=a(x-4)² ----- (1)
At coordinate (8, 0)
-b=16a
Therefore;
a = -b/16
Sub. a in (1) to get...
