(9^(p)*81)-9^(p) = 240
Let 9^(p) = a.
81a-a = 240
80a = 240
a = 3
It implies;
9^(p) = 3
p = ½
Therefore;
(8p)^(p) is;
√(8*½)
= √(4)
= 2
a² = 6²+9²-2*6*9cos60
a = 7.9372539332 units.
(7.9372539332/sin60) = (6/sinb)
b = 40.8933946491°
(7.9372539332/sin120) = (6/sinc)
c = 40.8933946491°
d = c+b
d = 81.7867892983°
e = 1...
Calculating area of the ascribed square and area of the inscribed blue triangle.
a²+8² = 10²
a = 6 units.
6 - 8
b - x
Cross Multiply.
8b = 6x
b = ¼(3x) units
c²+x² = 8²
c = √(64...
Let AB be 1 unit.
a = 180-18-36
a = 126°
a is angle APB.
(1/sin126) = (b/sin18)
b = 0.3819660113 units
b is BP.
c = 180-(12+18)-(36+36)
c = 180-102
c = 78°
c is angle ACB.
(1/s...
Notice.
The complete plane shape is half a circle with radius 8 cm.
Area green is;
Area semi circle with radius 8cm - 2(area quarter circle with radius 8 cm - area triangle with height and...
Calculating area of the inscribed red circle.
Let the bigger circle radius be a.
Let the big circle radius be b.
It implies;
a+b = 6 --- (1).
½(b²)+½(a²)+14 = 6*a
b²+a²+28 = 12a ---...
a = ⅐(360)°
a is the interior angle of each of the congruent 7 sectors.
Let the radius of the ascribed circle be 1 unit.
Area ascribed circle is;
π(1²)
= π square units.
c = (1-b) uni...
Calculating x.
a²+4² = 5²
a² = 25-16
a = 3 units.
Therefore;
3*(x+5) = 4*(2x-5)
3x+15 = 8x-20
5x = 35
x = 7 units.
It implies;
b = 3+x+5
And x = 7 units.
b = 3+7+5
b = 15 uni...
Calculating the required angle, x.
a = ⅐*180(7-2)
a = ⅐(900)
a is the single interior angle of the regular heptagon.
It implies, the required angle, x is;
Notice.
Length IC is paralle...
Calculating shaded area.
Let the equal lengths of the ascribed trapezoid be a.
Calculating a.
a² = 6²+(18-a)²
0 = 36+324-36a
36a = 360
a = 10 units.
Therefore, shaded area is;
½(1...
