Gradient of the curve at x = 3 is;
dy/dx = (-19/20)
It implies;
Area yellow exactly in square units decimal is;
Area triangle with height (5/(4sin(atan(19/20)))) units and base (5/(4sin...
a = atan(½)°
b² = 2(10)²
b = 10√(2) units.
c = (45-atan(½))°
cos(atan(½)) = d/20
d = 17.88854382 units.
Area x is;
0.5*17.88854382*10√(2)sin(45-atan(0.5))
= 40 square units.
18² = 14²+16²-2*14*16cosa
448cosa = 14²+16²-18²
a = acos((14²+16²-18²)/448)
a = 73.39845040098°
(18/sin73.39845040098) = (14/sinb)
b = 48.18968510422°
c = 180-48.18968510422-73.3984504009...
Let a be the diameter of the semi circle.
a² = b²+14²
b² = a²-196
b = √(a²-196)
It implies;
b² = 6²+6²-2*6*6(-cosc)
a²-196 = 72+72cosc
a²-196-72 = 72cosc
72cosc = a²-268
cosc = (a²-268...
Let x the the side length of the inscribed green equilateral triangle.
Calculating area green.
a = 180-60
a = 120°
b = 45-30
b = 15°
c = 180-120-15
c = 180-135
c = 45°
d = (4+√(6...
Sir Mike Ambrose is the author of the question.
Let alpha be x.
Therefore;
(12/sin2x)=(8/sinx)
And;
Sin2x = 2sinxcosx
Therefore;
(12/2sinxcos)=(8/sinx)
6 = 8cosx
x = acos(6/8)°...
Sir Mike Ambrose is the author of the question.
Let the side length of the green regular hexagon be 1 unit.
Therefore the angle theta to 2 d. p. is;
(atan(0.5÷(tan72-sin60)) + atan(0.5÷(tan7...
Sir Mike Ambrose is the author of the question.
Area green exactly in cm² is;
Area ABCD - Area trapezoid with parallel sides (9-2√(3)) cm and (24√(3)-39) cm, and height 6 cm.
= (54-6√(3)) - ½...
Area green is;
Area triangle with height 8 units and base 8√(3) units - Area sector with radius 8 units and angle 30° + Area sector with radius 8 units and angle 60° - 2(area triangle with heigh...
