Polar Coordinates

Today in Mathland we learned about polar coordinates. It's a way of graphing similar to rectangular coordinates. First you fix a point O that is called the pole, and construct from it a ray called the polar axis. Then each point P in the plane can be assigned coordinates in (r, θ). 

You must also know how to convert between rectangular and polar coordinates. The formulas are down below. 

Hyperbolas

Today in Mathland we learned all about hyperbolas! They have a pretty interesting conic section. The formula for a horizontal parabola is (x-h)^2/a^2 - (y-k)^2/b^2=1 and for a vertical hyperbola the formula is (y-k)^2/a^2 - (x-h)^2/b^2. As long as you stick to the formulas you can't go wrong. 

Ellipses

Today in Mathland we learned about the conic known as the ellipse. An ellipse is the set of all points (x,y) the sum of whose distances from two focus points is constant. The standard equation of an ellipse is 

Here is a graph of an ellipse. 

Ellipse can be challenging at times, but if you stick to the formula you can't go wrong. 

Parabolas

Today in Math Land we learned about Parabolas. Parabolas have a lot of rules and a lot going on. 

A parabola is a set of all points (x,y) that are equidistant from a fixed line, and a fixed point on the line.

The formula for a vertical parabola is: (x-h)^2=4p(y-k) and the directrix: y=k-p

The formula for a horizontal parabola is: (y-k)^2=4p(x-h) and the directrix:'x=h-p

Make sure you keep your eye on all the variables and make sure you don't make any silly mistakes. 

Lightning!

The chances of being struck by lighting are 1 in 3000. Yet, Lightning is one of the leading weather related causes of death. And don't think rubber shoes will help. Rubber shoes actually do nothing to protect from lightning. Here is a link to an article explaining the probability of getting struck by lightning: 

http://news.nationalgeographic.com/news/2004/06/0623_040623_lightningfacts.html

Measures of Central Tendency

Today we learned the !easures of Central Tendency. They are mean, median, and mode

Mean: is the average

Median: is the middle number, the set must be in order of least to greatest. 

Mode: the number that occurs most often. 

They are pretty simple to learn, but make sure you don't make any silly mistakes like forgetting to order your sets from least to greatest before searching for the median. 

Standard Deviation

Today in Mathland we learned about the measures of dispersion. Measures of dispersion will give us an idea of how much the numbers in the set differ from the mean of the set. The two measures of dispersion are called the variance of the set and the standard deviation of the set. Finding the standard deviation of a set and the variance of a set take a little effort. But as long as you are careful you can't go wrong.