Sir Mike Ambrose is the author of the question.
Equation of the curve is;
y = ⅔(8x-x²)
Calculating Area E.
(Area under the curve at x = (3/2) and x = 4) - Area trapezium with parallel sid...
Notice;
Blue area = yellow area.
Let the single side length of blue area be 2 units.
Let the single side length of red area be y.
Therefore;
Tanx=y/(4+y) ------ (1)
Tanx=2/(2+y) -...
a = ½(6)
a = 3 units.
a is the radius of the circle.
b = (5-c) units.
6² = d²+(5-c)²
d² = 36-(25-10c+c²)
d = √(11+10c-c²) units.
e = ½(d)
e = ½√(11+10c-c²) units.
f = (3-c) units....
Sir Mike Ambrose is the author of the question.
Let the side length of the square be 1 unit.
Area square is;
1²
= 1 square unit.
Calculating Area Orange.
a = 45+60
a = 105°
b = ½(...
Calculating angle x.
Let the base of the ascribed quadrilateral be 1 unit.
a = 180-20-60-50
a = 50°
(1/sin50) = (b/sin80)
b = 1.28557521937 units.
(1/sin40) = (c/sin60)
c = 1.347296355...
Let the single side length of the inscribed blue square area be x.
Therefore;
x+(x÷(tan(tan–¹(39/52))))+(x÷(tan(90-tan–¹(39/52))))=65
x=65÷(1+(1÷(tan(tan–¹(39/52))))+(1÷(tan(90-tan–¹(39/52...
Sir Mike Ambrose is the author of the question.
a = ⅛*180(8-2)
a = 135°
a is the single interior angle of the regular octagon.
2² = 2b²
b = √(2) units.
c = 2+b
c = (2+√(2)) units.
tan...
Sir Mike Ambrose is the author of the question.
2² = 2(3²)-2(3²)cosa
18cosa = 18-4
a = acos(7/9)°
a is angle ABC.
Let b be the radius of the inscribed circle.
Calculating b.
c²+1² = 3²...
Sir Mike Ambrose is the author of the question.
Let CD = 1 units.
It implies;
DE = 1 units.
AD = 2 units.
AE = 2 units.
1² = 2²+2²-2*2*2cosa
1 = 8-8cosa
cosa = 7/8
a = acos(⅞)°
b...
Sir Mike Ambrose is the author of the question.
Let the square side length be 2 units.
Calculating Area C and D.
Notice.
Area C = Area D.
C = ½(2²-¼(2*2π))
C = ½(4-π) square units.
T...
