Answer:
C. 40π cm²
Explanation:
• The central angle of the sector = 225 degrees
,
• The radius of the sector = 8cm
For a sector of radius r and central angle θ, we calculate the area using the formula below:
Substituting the given values, we have:
The area of the sector is 40π cm².
Answer:
4.9912 or four and nine thousand nine hundred twelve thousandths
Step-by-step explanation:
So you know the whole line is XZ which is 83.Then you find out it is in two parts so that is XY and YZ which are 11 and 4c. You can make the equation:
11+4c=83
4c=72
c=18
c=18 and YZ=72
Answer: 131.1287 square mm (approx)
Step-by-step explanation:
The area of a triangle,
Where 
and 
are adjacent sides and 
is the include angle of these sides,
Here PR and QR are adjacent sides and ∠R is the included angle of these sides,
Thus, we can write,
, 
and 
,
Thus, the area of the triangle PQR,
Let the three gp be a, ar and ar^2
a + ar + ar^2 = 21 => a(1 + r + r^2) = 21 . . . (1)
a^2 + a^2r^2 + a^2r^4 = 189 => a^2(1 + r^2 + r^4) = 189 . . . (2)
squaring (1) gives
a^2(1 + r + r^2)^2 = 441 . . . (3)
(3) ÷ (2) => (1 + r + r^2)^2 / (1 + r^2 + r^4) = 441/189 = 7/3
3(1 + r + r^2)^2 = 7(1 + r^2 + r^4)
3(r^4 + 2r^3 + 3r^2 + 2r + 1) = 7(1 + r^2 + r^4)
3r^4 + 6r^3 + 9r^2 + 6r + 3 = 7 + 7r^2 + 7r^4
4r^4 - 6r^3 - 2r^2 - 6r + 4 = 0
r = 1/2 or r = 2
From (1), a = 21/(1 + r + r^2)
When r = 2:
a = 21/(1 + 2 + 4) = 21/7 = 3
Therefore, the numbers are 3, 6 and 12.
