The possible sums are all multiples of 3
(18, 21, 24 ......78, 81) =
(81 - 18) / 3 + 1 =
63/3 + 1 =
21 + 1 =
22 distinct sums
Multiplying a polynomial by a non-zero constant does not change its degree
So
If f ( x) is degree 4 and h(x) is degree 6 , then g(x) must be degree 6
No biggie....just a math mistake.....you had the correct approach !!!!
Nice solution Awesomeguy !!!!
single digit primes = 2, 3, 5, 7
2, 3 ⇒ 31 not possible
2 5 ⇒ 31 not possible
2, 7 ⇒ 31 not possible
3, 5 ⇒ (3, 5, 6 ,8 ,9)
3 ,7 ⇒ (3 , 4 , 7 , 8 , 9)
5 , 7 ⇒ (4, 5 , 6, 7 , 9 )
P = (3/6) = (1/2)
Δ = 5
32156 = 3(6)^3 + 2(6)^2 + 1(6) + 5 = 731
5406 = 5(6)^2 + 4(6) = 204
526 = 5(6) + 2 = 32
_____
967
4(6)^3 + 2(6^2) + 5(6) + 1 = 967
2(x^2 + 8x + 4) = 0
2x^2 + 16x + 8 = 0
A = 16 B = 8
A + B = 24
x^2 + 10x + 25 = 18
x^2 + 10x + 7= 0
x = [ -10 - sqrt ( 10^2 - 4 * 7 * ) ] / 2 =
(-10 - sqrt (72) ) /2 =
(-10 - 6sqrt 2) / 2 =
-5 - 3sqrt (2) ≈ .757
Sum of interior angles = (n - 2) * 180 = 180n - 360.....where n = the number of sides
180n - 360 = 1780
180n = 1780 + 360
180n = 2140
We need n to be a whole number > 2140 / 180
ceiling (2140 / 180) = n = 12
(12 - 2) 180 =
10 * 180 =
1800
The missing angle = 1800 - 1780 = 20°
x + y = 9 square both sides
x^2 + y^2 + 2xy = 81
x^2 + y^2 + 2 (18) = 81
x^2 + y^2 + 36 = 81
x^2 + y^2 = 45
And
x^3 + y^3 =
( x + y) ( x^2 - xy + y^2) =
(x + y) ( x^2 + y^2 - xy) =
(9) ( 45 - 18) =
(9) (27) =
243
