Calculating the chord length.
Let x be the radius of the half circle.
a = (x-4) units.
b = (x-9) units.
c = (x-7) units.
d = a+b
d = (x-4)+(x-9)
d = (2x-13) units.
d is the length...
Calculating FM ÷ ML.
Let 2 units be the side length of square.
Calculating FM.
tana = 2/1
a = atan(2)°
a is angle AFB.
Let b, be the radius of the small inscribed circle.
c = (1-b)...
Calculating area of the square.
Let x be the side length of the square.
7² = x²+3²-2*x*3cosy
49 = x²+9-6xcosy
6xcosy = x²-40
cosy = (x²-40)/(6x) --- (1).
5² = x²+3²-2*x*3cos(90-y)
25 =...
Calculating Area Orange ÷ Area Large Square.
Let length AB be 3 units.
Therefore;
AC = 20 unit.
It implies;
Area large square is;
20²
= 40 square units.
Area orange is;
A...
Calculating Area Square ÷ Area Enclosed S
Let the side of the square be 2 units.
Therefore;
Area square is;
2²
= 4 square units.
Area S is;
Area triangle with two side 0.989218...
Calculating Area T ÷ Area (R+S) to 2 d. p.
Let the side of the inscribed square be 2 units.
Therefore;
Area S is;
Area triangle with two side 1.03528 units and 0.53589838486 unit, and angle 45°...
Calculating Area Green Total.
Area green total, in square unit decimal form is;
Area triangle with height 6sin(atan(3/5)) unit and base 6cos(atan(3/5)) unit + Area triangle with height 4 unit...
Calculating the inscribed orange triangle area.
Notice.
a = ½(3)
a = 1.5 units.
a is the radius of the inscribed circle.
tanb = 3/4
b = atan(3/4)°
tan(atan(¾)) = c/1.5
¾ = ⅓(2c)
c...
Calculating x.
a = (x+1) units.
b² = 1²+1²
b² = 2
b = √(2) units.
c = b+r
c = (1+√(2)) units.
Therefore, x is;
(x+1)² = x²+(1+√(2))²
x²+2x+1 = x²+1+2√(2)+2
2x = 2√(2)+2
2x...
Calculating k.
k^(k) = 3^(k)*3⁹
k^(k) = 3^(k)*19683
(k/3)^(k) = 19683
It implies;
k = 9
Checking Accuracy.
(9/3)⁹ = 3⁹ = 19683
