A few nuggets related to STEM: science, technology, engineering, math.

STEM.md

STEM

A few nuggets related to STEM: science, technology, engineering, math. Why? Why not!

Science, Technology, Engineering

• Ideal Gas Law: PV = nRT
• C = (F - 32) * 5 / 9
• F = (C * 9 / 5) + 32
• Speed of sound at STP: 343 m/s, 767 mph, 1125 fps
• Gravitational acceleration on Earth: 9.8 m/s/s
• Mass of a sandard U.S. Nickel: 5.000 g
• Metric system prefixes:

  • The prefixes for the positive exponents SHOULD change from:

    [da, h, k, M, G,  T,  P,  E,  Z,  Y] to:
    [ D, H, K, M, G,  T,  P,  E,  Z,  Y]. e:
    [ 1, 2, 3, 6, 9, 12, 15, 18, 21, 24]

  • The prefixes for the negative exponents are fine. ISO 2955 was on track: µ isn't ASCII but it's easy to enter with a keyboard input like EN INTL.

    [d, c, m, μ, n,  p,  f,  a,  z,  y]. e-:
    [1, 2, 3, 6, 9, 12, 15, 18, 21, 24]

Levers

• https://en.wikipedia.org/wiki/Lever
• A lever is a machine with a beam, a fixed Fulcrum (F), Effort (E), Resistance (R).
• a and b are distances from the fulcrum.
• Mechanical Advantage (MA) = (force at a) / (force at b) = a / b.
• The 3 classes identify which is in the middle: FRE 123
  • Class 1. F in middle. MA <=> 1. E.g. See saw.
  • Class 2. R in middle. MA > 1. E.g. Wheelbarrow.
  • Class 3. E in middle. MA < 1. E.g. Tweezers.

Math

Triangles mnemonic: soh-cah-toa

                B
 hypotenuse   / |
             r  y opposite
           /    |
         A __x_ C
         adjacent

sine(A)    = sin(A)  = opposite/hypotenuse = a/c = y/r
cosine(A)  = cos(A)  = adjacent/hypotenuse = b/c = x/r 
tangent(A) = tan(A)  = opposite/adjacent   = a/b = y/x
           = (a/c)*(c/b) = (a/c)/(b/c) = sin(A)/cos(A)
           = rise/run = slope
x^2 + y^2  = r^2

A combination is a subset from a distinct collection, where order DOESN'T matter and is often written as a set, i.e. {}. The count of combinations for all subset sizes is 2^n.

Given a set S with n elements then the count of combinations where the subset size is k and k > 0:

C(n, k) = n! / (k! * (n - k)!) = P(n, k) / k!

A permutation is a subset from a distinct collection, where order DOES matter and is often written as a tuple, i.e. (). Anagrams are permutations where each letter is considered distinct.

Given a set S with n elements then the count of permutations where the subset size is k and k > 0:

P(n, k) = n! / (n - k)! = C(n, k) * k!

Statistics: 68%: +/- 1 sigma. 95%: +/- 2 sigma. 99.7% +/- 3 sigma.

Probability: The likelihood that an event will occur, i.e. between 0 & 1. Odds: The probability expressed as a ratio of wins to losses.

• P(A). E.g. Roll a 1: 1/6. Odds: 1:5.
• P(!A). E.g. Not roll a 1: 5/6. Odds: 5:1.
• P(A & B). E.g. Snake eyes: 1/6 * 1/6 = 1/36. Odds: 1:35.
• P(A | B). E.g. Roll 1 or 2: 1/6 + 1/6 = 1/3. Odds: 1:2.