Topic: Intro to Permutations Bill has 23 shirts, 7 pants and 3 pairs of shoes. How many different outfits are possible?
We know that Bill has 23 shirts, 7 pants and 3 pairs of shoes. This means every time Bill changed even one article of clothing, he will have a different outfit. To figure this out, we can multiply 23 x 7 x 3 = 483. There are 483 possible outcomes. This is referred to as the 'Fundamental Counting Principle'.
What is the chameleon effect? Provide an example.
The chameleon effect is our tendency to unconsciously copy those around us, for example, when others yawn, we tend to do the same. If you notice the mood of the people around you, you will notice that your emotions and mood will shift to mimic theirs. Autonomic mimicry is an aspect of our ability to empathize with others.
Topic: Law of Conservation of Energy Let's say, in a frictionless world, we are given the initial velocity (v) (10 m/s) and height (5 m) at which a ball is released from a point on a hill. Now, what is the final speed of the ball when it reaches the bottom of the hill?
To answer this question, we must write a work/ energy equation. 1. W = Ef - Ei 2. Now we know that Kinetic Energy (KE) equals (0.5 x mass x velocity^2) and Potential Energy (PE) equals ( mass x-height x acceleration due to gravity [g = 9.8 m/s^2]). At the top of the hill, we have kinetic energy and potential energy. At the bottom, we have kinetic energy but no potential energy as our relative height is 0. So, Work = Energy final - Energy Initial W = (KE) - (KE + PE) W = (0.5 x mass x final velocity^2) - [(0.5 x mass x initial velocity^2) + (mass x height x g)] Since energy is conserved, Work = 0 0 = ( 0.5 x mass x final velocity^2) - [(0.5 x mass x 10^2) - ( mass x 5 x 9.8)] (0.5 x mass x 10^2) - (mass x 5 x 9.8) = 0.5 x mass x final velocity^2 As we can see, we only have two variables: mass and final velocity. Notice that mass is present in all three terms, so we can actually cancel mass out using basic mathematics. We are now left with... (0.5 x 10^2) - (5 x 9.8) = 0.5 x final velocity^2 final velocity = 1 m/s