diff --git a/education/math/Standard forms of circles.md b/education/math/Standard forms of circles.md new file mode 100644 index 0000000..3d37236 --- /dev/null +++ b/education/math/Standard forms of circles.md @@ -0,0 +1,26 @@ +# Notes +## Composition of functions +For $(f\circ g)(x)$ for two sets, you look for $x$ from $f$ and an equivalent $y$ value from $g$, and leftover coordinates are the answer. The order of $f$ and $g$ does matter. +# Formulae +The general equation for a circle: +$$ (x - h)^2 + (y - k)^2 =r $$ +Distance formula: +$$ \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} $$ +Midpoint foruma: +$$ (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}) $$ +Adding functions: +$$ (f + g)(x) = f(x) + g(x) $$ +Multiplying functions: +$$ (f*g)(x)=f(g(x)) $$ + +# Examples +Given the function $f = \{(0, 2), (3, -1), (5, 4), (2, 1)\}$, and $g=\{(2, 0), (3, -1), (4, -2), (5, 2)\}$, and applying $(f+g(x)$, If the same $x$ value exists in both the sets $f$ and $g$, then you can solve for that value by adding $y$ values for the matching x coordinates together. + + +# Terminology + +| Term | Definition | +|--|--| +| $h$ | How far left or right something is shifted from the origin | +| $k$| How far up or down something is shifted from the origin | +| $r$ | The radius of a circle | diff --git a/education/statistics/Correlation and Regression.md b/education/statistics/Correlation and Regression.md index e145fc6..9751b03 100644 --- a/education/statistics/Correlation and Regression.md +++ b/education/statistics/Correlation and Regression.md @@ -4,13 +4,15 @@ ## Scatter Diagrams A scatter diagram or scatter plot shows the relationship between two variables. One variable is on the X axis, the other on the Y axis. ### Association -- Positive association is demonstrated when the dots are trend upward as `x` increases. -- Negative association is demonstrated when the the dots trend downward as `x` increases. +- Positive association is demonstrated when the dots are trend upward as $x$ increases. +- Negative association is demonstrated when the the dots trend downward as $x$ increases. - Strong association is demonstrated when dots are clustered tightly together along a line. - Weak association is demonstrated when dots are not clustered tightly. ## Correlation -Correlation is between `-1` and `1`. Correlation near 1 means tight clustering, and correlation near 0 means loose clustering. +Correlation is between `-1` and `1`. Correlation near 1 means tight clustering, and correlation near 0 means loose clustering. $r$ is -1 if the points are on a line with negative slope, $r$ is positive 1 if the points are on a line with a positive slope. As $|r|$ gets closer to 1, the line points cluster more tightly around a line. # Terminology | Term | Definition | -| `r` | Correlation Coefficient | \ No newline at end of file +| -- | -- | +| $r$ | Correlation Coefficient | +| Linear Correlation | Measures the strength of a line |