Sir Mike Ambrose is the author of the question.
Notice;
The equation of the curve is;
y = (x²+32)/8
Area S will be;
Area under the curve at the points on the x axis, (16/5) and 8 - Are...
a² = 12²+16²
a = 20 units.
a is BC.
12b+16b+20b = 12*16
48b = 12*16
b = 4 units.
b is the radius of the inscribed circle.
tanc = 12/16
c = atan(3/4)°
d = 16-4
d = 12 units.
e = 9...
a = (10+x) units.
a is the radius of the ascribed semi circle.
sinb = 16/20
b = asin(4/5)°
Calculating x.
It implies;
(10+x)² = 10²+21²-2*10*21cos(asin(4/5))
(10+x)² = 289
10+x = √(...
Green Area is;
Area square with length 4 units - Area quarter circle with radius 2 units - Area square with length 2 units - 3(Area square with length 1 unit) - Area square with length 3 units +...
Sir Mike Ambrose is the author of the question.
Let the single side length of the large square be 2 units.
Therefore;
Area large square is;
2 x 2 = 4 square units.
Calculating Area R....
Let the radius of one of the small congruent circles be x.
Calculating x
Sin(180/7)=x/(x+1)
x = xSin(180/7)+Sin(180/7)
x(1-Sin(180/7))=Sin(180/7)
Therefore;
x = (Sin(180/7))/(1-Sin(18...
Let the radius of inscribed blue semi circle be 2 units.
Therefore the radius of the inscribed blue quarter circle will be 2 units.
The length of the ascribed rectangle will be 4 units.
Th...
Radius, r of the semi circle is;
Cos(2atan(1/(4+√(7))))=(5+√(7))/d
Notice;
d = 2r
Therefore,
d = (5+√(7))/Cos(2atan(1/(4+√(7))))
d = 8 units.
And d = 2r
2r = 8
r (radius semi...
Sir Mike Ambrose is the author of the question.
(a) Exact radius of the circle is;
r = ½√(2²+4²)
r = ½√(20)
r = ½*2√(5) units.
r = √(5) units.
Or
Cos(atan(2)) = (1/r)
Where r is the...
r, radius of the ascribed circle will be;
½(r²)sin60=(256/6)
½√(3)r²=⅓(256)
3√(3)r²=512
r²=(512√(3))/9
r = ⅓√(512√(3)) units.
r = 9.92645183043 units
r ≈ 10 units.
