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 sides (13/2) units and (10⅔) units, and height (5/3)...
Calculating angle x.
Notice!
x (angle BCD) will sum up the interior reflex angle BCD of the plane shape ABCD to get 360°
Plane shape ABCD is a quadrilateral, therefore the sum of its inte...
Calculating h, height of the triangle.
Notice!
a+b = 28
a = (28-b) units.
It implies;
b² = 5²+h²
h² = b²-25 --- (1).
a² = 9²+h²
And a = (28-b) units.
(28-b)² = 81+h²
h² = 784-5...
2(20x)+2(30x)+2x² = (x+30)(x+20)
Where x is the radius of the inscribed circle.
It implies;
40x+60x+2x² = x²+20x+30x+600
100x+2x² = x²+50x+600
x²+50x-600 = 0
Calculating x via completing th...
Let a be the side length of regular hexagon and the regular triangle (equilateral triangle).
Calculating a.
0.5a²sin60 = √(3)
¼*√(3)a² = √(3)
¼(a²) = 1
a² = 4
a = 2 units.
Again, a is th...
Let AB be 1 unit.
a = 180-12-36-18
a = 180-66
a = 114°
a is angle AEB.
(1/sin114) = (b/sin(18+36))
b = 0.885579352 units.
b is AE.
c = 180-6-36-42
c = 96°
(1/sin96) = (d/sin(42+36...
a = ½(90)
a = 45°
tanb = 2/1
b = atan(2)°
c = 90-b
c = atan(½)°
d = a-c
d = (45-atan(½))°
e = 180-2d
e = 180-2(45-atan(½))
e = (90+2atan(½))°
Therefore, length EF, let it be f,...
a = 7-2.5
a = 4.5 units.
b = 7+1
b = 8 units.
tanc = 4.5/8
c = atan(4.5/8)°
tand = 4.5/3
d = atan(4.5/3)°
e = 180-c-d
e = (180-atan(4.5/8)-atan(4.5/3))°
(4/sin(180-atan(4.5/8)-a...
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Calculating the red angle (angle DAM).
Notice!
ABCD is a regular quadrilateral (square).
Let AB be 1 unit.
tan60 = AB/BK
BK = 1/√(3)
BK = ⅓√(3) units.
CK = 1-BK
CK = ⅓(3-√(3)) uni...
