Let the side length of the regular pentagon be 1 unit.
tan36 = a/0.5
a = 0.363271264 unit.
b² = 0.363271264²+0.5²
b = 0.61803398875 unit.
tan72 = c/0.5
c = 1.53884176859 units.
Area Green is;
0...
At point P;
x = (π/6)~30°
y = √(3)-2
Gradient at point P is;
dy/dx = 2/(1+2sinxcosx)
At x = (π/6)~30°
dy/dx = 8-4√(3)
It implies;
yQ exactly as a single fraction in terms of π is;
The coordin...
At t = 2, x = 3 and y = 3/4
dx/dt = 2/3
dy/dt = 13/16
Therefore;
Gradient at the tangent and of the curve at t = 2 is;
dy/dx = dy/dt÷dx/dt
= (13/16)÷(2/3)
dy/dx = 39/32
Notice;
Triangle OPQ...
(x/√(3))+x+2x+3x+(3x/√(3)) = 1
(4√(3)x/3)+6x = 1
(4√(3)x)+18x=3
(4√(3)+18)x = 3
x = 3/(4√(3)+18)
x = 3(18-4√(3))/(324-48)
x = 3(15-4√(3))/276
x = (18-4√(3))/92
x = (9-2√(3))/46 unit.
a = ½(6√(3))
a = 3√(3) units.
b = (6-3√(3)) units.
cosc = 3√(3)/6
c = acos(½(√(3)))
c = 30°
d = 90-30
d = 60°
sin30 = e/6
e = 3 units.
It implies;
Area Blue is;
Area rectangle with length and...
Let the equal lengths be 1 unit.
(1/sin20) = ((1+y)/sin120)
1+y = (sin120/sin20)
y = (sin120/sin20)-1
y = 1.5320888862 units.
z² = 1+1.5320888862²-2*1.5320888862cos40
z = 1 unit.
It implies, the...
The equation of the curve is;
0-32=-a(8-4)²
-32 = -16a
a = 2
Therefore;
y-32 = -2(x-4)²
y = -2(x²-8x+16) +32
y = -2x²+16x-32+32
y = 16x - 2x²
It implies;
(Area (2197/24)+ Area triangle with heig...
a (first term) = 9/7
d (common difference) = 3/7
n (number of terms) = 29
Therefore;
Last term of the sequence of values is;
L = a + d(n-1)
L = (9/7) + (3/7)(29-1)
L = (9/7) + 12
L = ((12*7)+9)/7...
Let the side length of the regular heptagon be 1 unit.
a = ⅐(180*5)
a = ⅐(900)°
b = 0.5(360-2(900/7))
b = ⅐(360)°
c = 2cos(360/7)+1
c = 2.24697960372 units.
d² = 2-2cos(90/7)
d = 1.8019377358 un...
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.
