5 cubed ( or an exponent of three )
Sometimes the best way to tell whether two variables are associated is to ask yourself whether they are not associated. Think backward. In a two-way frequency table, if the relative frequencies for one variable are the same (or close) for all categories of another variable, there is no (or little) association.
x² + y² = 5
y = 2x/3 + 1
In a simple way to find the intersections you can just throw the y value in the other equation, so
x² + y² = 5
x² + (2x/3 + 1)² = 5
x² + (2x/3)² + 2.2x/3.1 + 1² = 5
x² + 4x²/9 + 4x/3 + 1 = 5
13x²/9 + 4x/3 + 1 - 5 = 0
13x²/9 + 4x/3 - 4 = 0
Multiply by 9
13x² + 12x - 36 = 0
Δ = b² - 4.a.c
Δ = 12² - 4 . 13 . -36
Δ = 144 - 4. 13 . -36
Δ = 2016
There are 2 real roots.
x = (-b +- √Δ)/2a
x' = (-12 + √2016)/2.13
x'' = (-12 - √2016)/2.13
x' = 32,8998886412873 / 26
x'' = -56,8998886412873 / 26
x' = 1,2653803323572037
x'' = -2,188457255434127
Rounding
x' = 1,27
x'' = -2,19
Now we need to put this value in the y equation to know the y coordinate.
y = 2x/3 + 1
y' = 2.1,27/3 + 1
y' = 2,54/3 + 1
y' = 1,8466666...
y' = 1,85
y = 2x/3 + 1
y'' = 2.(-2,19)/3 + 1
y'' = -4,38/3 + 1
y'' = -0,46
So the points are: (1,27;1,85) and (-2,19;-0,46)
