Sir Mike Ambrose is the author of the question.
Let a be the equal lengths inscribing triangle ABC.
Calculating a.
½(a)² = 15
a = √(30) units.
b = 180-60-45
b = 75°
b is angle BAC....
Let R=the bigger inscribed circle radius.
Let r=the smaller inscribed circle radius.
It implies;
R+r=6√(3)-6=4.4
R+r=4.4 -------(1).
And the radius of the ascribed semi circle is 6...
Notice.
Radius rod the half circle is 5 units.
a = (5-x) units.
Calculating x.
5² = 3²+(5-x)²
16 = 25-10x+x²
x²-10x+9 = 0
x = 1 unit.
It implies;
a = 5-x
And x = 1 unit.
a = 4...
a = (2r-14) units.
b = ½(a)
b = (r-7) units.
Calculating r, radius of the half circle.
Therefore;
2r ~ 6
6 ~ (r-7)
Cross Multiply.
2r(r-7) = 36
r²-7r-18 = 0
Resolving the qu...
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...
