The Ungerecht Family Tree urp

urp:00_start

Anonymous (anonymous@undisclosed.example.com) — 2021-11-18T22:43:57+0000

UPchieve Reference Start Page Reference material ("cheat sheets") for tutoring purposes. Common definitions and equations are included, but their derivations and how to use them are generally not included. Final home might be a place like or . (Wikidot supports LaTeX-style equations - nice for visuals, but couldn't copy & paste to chat screen).

urp:algebra

Anonymous (anonymous@undisclosed.example.com) — 2022-02-01T03:07:21+0000

Algebra & Pre-Calc Related pages: * Graphing circles, ellipses, parabolas, hyperbolas * Polynomials, quadratic formula and completing the square * Powers, radicals (roots) & logs quadratic formula: x = (-b ±√(b²-4ac)) / 2a PEMDAS/BODMAS - order of operations: Parentheses/Brackets, Exponents/Order, Multiply-Divide, Add-Subtract System of equations 2 equations, for 2 unknowns (need n equations to solve for n unknowns)

urp:angles

Anonymous (anonymous@undisclosed.example.com) — 2021-11-08T18:18:51+0000

Angles and Vectors Angles and Lines * Complementary angles add up to 90' * Supplementary angles add up to 180' * alternative angles are equal (congruent angles on transversal line intersecting two parallel lines) * vertical angles theorem

urp:circles

Anonymous (anonymous@undisclosed.example.com) — 2021-11-19T02:19:53+0000

Circles * chord has two endpoints on a circle * secant is a line that contains a chord, but extends beyond the circle * tangent is a line that touches a circle at one point (a secant with chord length of zero) * Intercepted arc is the part of the circle contained within the two lines

urp:geometry

Anonymous (anonymous@undisclosed.example.com) — 2021-11-17T06:50:31+0000

Geometry Reference Page * Angles and Vectors * Triangles * Circles, Chords, etc * Polygons misc Truth tables: first columns : True/False values of the variables, such as p, q, or p' or ~p for inverse values. Next columns are logic combinations of the variables p q p ⋂ q p ⋃ q p => q T

urp:graphing

Anonymous (anonymous@undisclosed.example.com) — 2021-10-21T18:26:34+0000

Graphing curves and circles Circles Standard form of a circle: (x-h)² + (y-k)² = r² where point (h,k) is the center, and r is radius This can be expanded to x² + y² + Dx + Ey + F = 0 (aka the General form) Can go from general form to standard form by completing the square

urp:math

Anonymous (anonymous@undisclosed.example.com) — 2021-10-21T18:20:46+0000

Math Reference Pages * Geometry * Trig * Algebra & pre-Calc * Statistics * Calculus See Also Click here for a collection of special characters for common math and physics equations. For more symbols, see: * Math symbols: * Paul Dawkins math cheat-sheets at * Unicode symbols, for fractions, powers, and search for your own:

urp:physelec

Anonymous (anonymous@undisclosed.example.com) — 2021-11-06T20:12:30+0000

Electricity Circuits Power = watts, current (I) = amps, volts (E or V), resistance (R) = ohms * Ohm's Law e = ir * p = ie = i²r Resistors in series add together Resistors in parallel: 1/Rt = 1/R₁ + 1/R₂ + ... current in parallel: if have V, compute R for each path. For two paths, R₁ & R₂: I on R₁ = R₁/(R₁+R₂)

urp:physfreq

Anonymous (anonymous@undisclosed.example.com) — 2021-11-17T06:18:57+0000

Frequency, Oscillations string, frequency, antinodes: Ends of a stretched string are called nodes, N. Point of highest vibrational amplitude is antinode, A. Number of N-1 = harmonic full sine wave (2N) = wavelength Example: Adjacent antinodes are separated by a distance of 20 cm and waves travel at a speed of 1200 cm/s along the string. What frequency is the string vibrating at? wavelength = 40 cm freq = v/wavelength, v = velocity of wave 1200/40 = 30

urp:physgen

Anonymous (anonymous@undisclosed.example.com) — 2022-02-01T02:09:11+0000

General Physics Newton's 3 laws 1) objects in motion stay in motion, a body at rest stays at rest, until a force is applied ("law of inertia") 2) change in momentum of a body is equal in magnitude and direction to the force applied to it (force = mass * acceleration) 3) when two bodies interact, they apply forces that are equal to each other, and opposite in direction ("law of action and reaction")

urp:physheat

Anonymous (anonymous@undisclosed.example.com) — 2021-11-08T04:19:40+0000

Heat Specific heat = ratio of the quantity of heat that we require to raise the temperature of a body by one degree compared to doing the same of an equivalent mass of water. Also, we use the term in a narrower sense to mean the amount of heat, in calories that we require to raise the temperature of one gram of a substance by one Celsius degree.

urp:physics

Anonymous (anonymous@undisclosed.example.com) — 2021-11-16T00:32:58+0000

Physics * General physics (masses and forces) * Electricity * Rotating bodies * Frequency, Oscillations * Heat Back to the start page.

urp:physrot

Anonymous (anonymous@undisclosed.example.com) — 2021-11-08T18:57:39+0000

Rotation Tension on rope being swung = force, centripetal force F = m * v^2/r Example: 4 kg, 2 meter rope, v = 5 m/s F = 4 * 25/2 = 50 ---> now need to subtract gravity, for instance at the top of the swing 50 - 4*9.8 Pendulum simple pendulum: T = 2π * √(L/g) (T = time, L = length, g = gravity) (T/2π)² = L/g

urp:poly

Anonymous (anonymous@undisclosed.example.com) — 2022-01-07T07:17:52+0000

Polynomials Box method [Image from basicmathematics.com] * Make a 2x2 box (for a quadratic equation). * Pull out the greatest common factor of the whole equation and keep it for later, if needed. * The x² coefficient goes in the upper left, the last term goes in the bottom right.

urp:polygons

Anonymous (anonymous@undisclosed.example.com) — 2021-10-13T05:28:21+0000

Polygons The sum of angles in a polygon = 180 (n - 2), where n = number of sides. This can also be written as: 180 + 180 (n-3). (Basically you add in another triangle when adding a side to polygon) Back to geometry or math page.

urp:power

Anonymous (anonymous@undisclosed.example.com) — 2021-11-16T01:19:28+0000

Powers & Radicals Combining powers nᵃnᵇ = nᵃ⁺ᵇ nᵃ/nᵇ = nᵃ⁻ᵇ (nᵃ)ᵇ = nᵃᵇ n⁻ᵃ = 1/nᵃ (Note: The square root sign, √, refers only to the positive root. Use ± to include both roots.) Logs Log is the inverse of a power

urp:specialchars

Anonymous (anonymous@undisclosed.example.com) — 2021-11-08T20:20:51+0000

Copy a symbol below and paste into the UPchieve chat window. On MS Windows you can type in an alt code instead, on Mac OS you can open an on-screen keyboard and press the character. None of these options is particularly speedy, especially when using multiple symbols. Not all characters exist, including apparently a subscript y or t.

urp:texting

Anonymous (anonymous@undisclosed.example.com) — 2021-11-19T01:07:49+0000

Text shortcuts * brb - be right back * idk - I don't know * NOTA - none of the above * np - no problem * nvm - never mind * rn - right now * tbh - to be honest Message starting with an asterisk - corrects a typo or auto-correct error in the previous message.

urp:triangles

Anonymous (anonymous@undisclosed.example.com) — 2021-11-08T18:17:12+0000

Triangles Definitions: * isosceles - (at least) 2 sides the same length, modern definition includes equilateral * equilateral - all 3 sides the same length * acute triangle - all angles are < 90 degrees * obtuse triangle - one angle is > 90 degrees

urp:trig

Anonymous (anonymous@undisclosed.example.com) — 2021-10-21T16:01:49+0000

Trigonometry transformations of sine or cosine function: y = a * sin(b(x - c)) + d [Sine Wave Transformations] (Graphics from www.Desmos.com, labeling was added) a = amplitude, c = phase shift, d = vertical shift, 2π/b = period (for tan the period is π/b) Sin/Cos table Radians