1² + 3² + 4² + 4(n - 1)² = ¹/₃n(2n - 1)(2n + 1)
1² + 3² + 4² + (2n - 2)² = ¹/₃n(2n - 1)(2n + 1)
1 + 9 + 16 + (2n - 2)(2n - 2) = ¹/₃n(2n(2n + 1) - 1(2n + 1))
10 + 16 + (2n(2n - 2) - 2(2n - 2)) = ¹/₃n(2n(2n) + 2n(1) - 1(2n) - 1(1) 16 + (2n(2n) - 2n(2) - 2(2n) + 2(2)) = ¹/₃n(4n² + 2n - 2n - 1)
26 + (4n² - 4n - 4n + 4) = ¹/₃n(4n² - 1)
26 + (4n² - 8n + 4) = ¹/₃n(4n² - 1)
26 + 4n² - 8n + 4 = ¹/₃n(4n²) - ¹/₃n(1)
4n² - 8n + 4 + 26 = 1¹/₃n³ - ¹/₃n
4n² - 8n + 30 = 1¹/₃n³ - ¹/₃n
+ ¹/₃n + ¹/₃n
4n² - 7²/₃n + 30 = 1¹/₃n³
-1¹/₃n³ + 4n² - 7²/₃n + 30 = 0
-3(-1¹/₃n³ + 4n² - 7²/₃n + 30) = -3(0)
-3(-1¹/₃n³) - 3(4n²) - 3(-7²/₃n) - 3(30) = 0
4n³ - 12n² + 23n - 90 = 0
There are
ways of pairing up any 2 members from the pool of 
contestants. Note that
so that
Answer:
x=3
Step-by-step explanation:
In(x-1) = In(6) - In(x)
In(x-1) + In(x) = In(6)
In((x-1)x) = In(6)
In(x^2-x) = In(6)
x^2-x=6
x^2-x-6=0
x^2+2x-3x-6=0
x(x+2)-3(x+2)=0
(x-3)(x+2)=0
x=3 because x=-2 need to be cancel out
Answer:5 hours because -2.5*5=-12.5
Step-by-step explanation:
Answer:
exterior angle: 22.5°, interior angle: 157.5°
Step-by-step explanation:
the formula for the measure of each Interior Angle in a regular polygon: 
, n = # of sides
=> 
= 157.5°
the formula for the measure of each Exterior Angle in a regular polygon: 
=> 
= 22.5°
