Sir Mike Ambrose is the author of the question.
Area purple exactly in decimal is;
Area triangle with height 5cm and base 7.5cm - Area triangle with height 3cm and base 7.5cm - Area triangle wi...
Sir Mike Ambrose is the author of the question.
Notice;
The single length of the square is equal the single side length of half the regular hexagon.
Let it be 2 units.
Therefore area squa...
a = 8+10
a = 18 units.
a is GK.
b² = 18²-9²
b = √(243)
b = 9√(3) units.
b is DK.
tanc = 9√(3)/9
c = atan(√(3))
c = 60°
d² = 9²+8²-2*8*9cos60
d = √(73) units.
d = 8.5440037453 unit...
Sir Mike Ambrose is the author of the question.
Let the bigger regular pentagon side length be 1 unit.
a = √(2-2cos180)
a = 1.61803398875 units.
b = sin36/sin108
b = 0.61803398875 units....
Let the two congruent lengths be a each.
21² = a²+b²+2abcos135
441 = a²+b²+√(2)ab --- (1)
14² = a²+b²-2abcos45
196 = a²+b²-√(2)ab --- (2)
Adding (1) to (2).
637 = 2a²+2b²
b² = ½(637...
Area orange exactly in fraction is:
Area triangle with height 5√(3) cm and base 5 cm.
= ½(5√(3)*5)
= ½(25√(3)) cm²
= 21.6506350946 cm²
a = ½(5)
a = 2.5 units.
a is the radius of the inscribed half circle.
tanb = 2.5/5
b = atan(1/2)°
tan(atan(0.5)) = r/c
½ = r/c
c = 2r units.
d = 5-c
d = (5-2r) units.
e = (2.5-r)...
y = (1+x²)^(-½)
Differentiating via chain rule or function of a function rule.
Let u = (1+x²)
du/dx = 2x
Therefore;
y = u^(-½)
dy/du = -½u^(-3/2)
And;
dy/dx = (dy/du)*(du/dx)
d...
a = ½(5+35)
a = 20 units.
a is the radius of the ascribed semi circle.
b = (20-c) units.
d = a-5
d = 20-5
d = 15 units.
Therefore;
(20-c)² = c²+15²
400-40c+c² = c²+225
175 = 40c...
