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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Let the square side be 2 units.
Area Square is;
2²
= 4 square units.
tana = ½
a = atan(½)°
b = 2a
b = 2atan(½)°
c = (180-2atan(½))°
d = atan(2)°
e = (180-2atan(½))-atan(2)
e = (90-atan(½))°
t...
Sir Mike Ambrose is the author of the question.
a = atan(2)°
b = (45+atan(½))°
(a) Calculating Alpha.
Let alpha be c.
c = 180-b
c = 180-45-atan(½)
c = (135-atan(½))°
Or
c = 180-(135-atan2)
c = (...
Let the side length of the regular hexagon be 1 unit.
Calculating the side length of the regular pentagon.
Let it be b.
(2/sin72) = (a/sin60)
a = 1.82118599462 units.
(1.82118599462/sin108) = (b/...
Sir Mike Ambrose is the author of the question.
a² = 8²+12²-2*8*12cos60
a = 4√(7) cm.
b = 2a
b = 8√(7) cm.
(4√(7)/sin60) = (8/sinc)
c = 40.89339464928°
(16/sin40.89339464928) = (8√(7)/Sind)
d = 6...
