Note that if m = 3 and n = 2 then
3^2 + 14(3) - 32 = 2(2)^3 + 3
19 = 19
m + n = 5
N^3 = 3N^2 * 2
N^3 - 6N^2 = 0
N^2 ( N - 6) = 0
N - 6 = 0
N = 6
Multiplying top/bottom of each fraction by its conjugate we get
[ sqrt 100 - sqrt 102] / -2 + [ sqrt 102 - sqrt 104 ] / -2 + [ sqrt 104 - sqrt 106] / -2 =
[ sqrt 100 - sqrt 106 ] / -2 =
[ sqrt 106 - sqrt 100] / 2 =
(1/2) (sqrt [ 106] - 10 )
2,3,5,7,11,13,17,19,23,29,31
Sum = 160
160 / 8 = 20
Factor as
(4x - 5) (2x - 7) = 0
The smaller value of x that solves this is
4x - 5 = 0
4x = 5
x = 5/4 = 1.25
l (240/12) * 1.50 - (240/20)* 2.00 l = $6
Area =
Area of rectangle - Area of three right triangles =
(8) (6) - (1/2) [ 4*5 + 2*8 + 3*6 ] =
48 - (1/2) [ 20 + 16 + 18] =
48 - (1/2) [ 54] =
48 - 27 =
21
[ f(10) - f(0) ] / [ 10 - 0 ] = 1
[f (10) - f(0) ] / 10 = 1
f(10) - f(0) = 10 * 1
f(10) - f(0) = 10
a3 = 13
a4 = 17
a5 = 34 not prime
x + y = 13 square both sides x^2 + 2xy + y^2 = 169 (1)
xy = 24 → 2xy = 48 (2)
Sub (2) into (1)
x^2 + 48 + y^2 = 169
x^2 + y^2 = 121
x^2 + y^2 = 11^2
The smallest distance is 11 units
See the graph here : https://www.desmos.com/calculator/6q6v3gi6wa
