Let the side length of the congruent yellow regular hexagon be 1 unit.
a = 3sin30+1
a = 2.5 units.
sin60 = b/1
b = 0.5√(3) units.
c² = a²+b²
c² = 2.5²+(0.5√(3))²
c = √(7) units.
c = 2.64575131106...
Sir Mike Ambrose is the author of the question.
The vertices coordinates of area purple are;
(6, 12) ((24/5), (36/5)) ((180/29), (168/29)) (12, (21/2))
Area purple is;
½((6, 12) ((24/5), (...
Calculating equation of the curve.
y-6√(2) = a(x-6)² --- (1).
Substituting x = 0, y = 0 to get a.
It implies;
-6√(2) = 36a
a = -(1/(3√(2)) --- (2).
Substituting (2) in (1).
y-6√(2) = -(1/(3√(2))(...
Sir Mike Ambrose is the author of the question.
Let the side of the ascribed regular pentagon be 2 units.
(a) Calculating alpha. Let it be x.
a² = 5-4cos108
a = 2.49721204096 units.
(2.4972120409...
Let the side of the regular hexagon be 1 unit.
(a/sin30) = (1/sin120)
a = 0.57735026919 units.
b² = 0.57735026919²+2²-2*2*0.57735026919cos30
b = 1.52752523165 units.
The required angle, x is;
(1...
Let the side of the regular hexagon be 2 units.
a² = 5-4cos120
a = √(7) units.
(√(7)/sin120) = (1/sinb)
b = 19.10660535087°
c = 60-2*19.10660535087
c = 21.78678929826°
d = 0.5(120-2*19.10660535...
Let the small square side be 2 units.
Area Blue is;
0.5*2*1 = 1 square unit.
a² = 2²+1
a = √(5) units.
a is the side of the big square.
b = (90-atan(½))°
c = 180-(90-atan(½))-60
c = (30+atan(½))...
Calculating p.
p^(⅓)+1 = 6p^(⅙)
Let p^(⅓) = x
x + 1 = 6x^(½)
(x+1)² = 36x
x²+2x+1 = 36x
x²-34x+1 = 0
(x-17)² = -1+(-17)²
x = 17±√(288)
x = 17-12√(2)
Or
x = 17+12√(2)
It implies;
p^(⅓) = x, for x =...
Sir Mike Ambrose is the author of the question.
P(2, (8/3))
Q(4, (32/15))
Gradient of the curve is;
dy/dx = -4x/(x²-1)²
For x = 2.
dy/dx = -8/9
It implies;
R(5, 0)
Area S exactly in square unit...
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