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The Founders
UNIVERSAL CALCULATOR
TI-84
OSCILLOSCOPE
All (77)
⚛ Physics (8)
∑ Math (4)
𝑥 Algebra (8)
△ Geometry (9)
∠ Trig. (7)
∫ Calculus (6)
⚡ Electrical (4)
☁ Atmos. (3)
📐 Units (17)
🌡 Thermo. (3)
🔬 Optics (2)
🪐 Orbital (2)
⚗ Chem. (2)
📡 Signals (2)
⚛
Physics
\[v = u + a\,t\]
Final Velocity
⚛
Physics
\[KE = \tfrac{1}{2} m v^{2}\]
Kinetic Energy
⚛
Physics
\[PE = m\,g\,h\]
Gravitational PE
⚛
Physics
\[F = m\,a\]
Newton F=ma
⚛
Physics
\[v = f\lambda\]
Wave Speed
⚛
Physics
\[F = \dfrac{G\,m_{1}m_{2}}{r^{2}}\]
Gravity (Newton)
⚛
Physics
\[E = m c^{2}\]
E = mc²
⚛
Physics
\[\gamma = \dfrac{1}{\sqrt{1 - v^{2}/c^{2}}}\]
Lorentz Factor
∑
Math
\[x = \dfrac{-b \pm \sqrt{b^{2} - 4ac}}{2a}\]
Quadratic Formula
∑
Math
\[\mu = \dfrac{1}{n}\sum x_i,\quad \sigma = \sqrt{\tfrac{1}{n}\sum (x_i - \mu)^{2}}\]
Descriptive Stats
∑
Math
\[P(n,r) = \dfrac{n!}{(n-r)!},\quad C(n,r) = \dfrac{n!}{r!(n-r)!}\]
Permutations/Combos
∑
Math
\[\log_b(x) = \dfrac{\ln x}{\ln b}\]
Logarithms
⚡
Electrical
\[V = I R,\quad P = I V = I^{2} R = \dfrac{V^{2}}{R}\]
Ohm's Law
⚡
Electrical
\[\tau = RC,\quad V(t) = V_{0}\,e^{-t/\tau}\]
RC Time Constant
⚡
Electrical
\[c = f\lambda\]
Frequency ↔ λ (EM)
⚡
Electrical
\[\mathrm{dB} = 20\,\log_{10}\!\left(\dfrac{V_{2}}{V_{1}}\right)\]
Decibels (dB)
☁
Atmos.
\[h = 44330\left(1 - \left(\dfrac{P}{P_{0}}\right)^{0.1903}\right)\]
Pressure Altitude
☁
Atmos.
\[T_d = \dfrac{243.04\,\gamma}{17.625 - \gamma},\;\; \gamma = \dfrac{17.625\,T}{243.04 + T} + \ln\!\left(\tfrac{RH}{100}\right)\]
Dew Point
☁
Atmos.
\[WC = 13.12 + 0.6215\,T - 11.37\,v^{0.16} + 0.3965\,T\,v^{0.16}\]
Wind Chill
📐
Units
\[K = {}^{\circ}\!C + 273.15,\quad {}^{\circ}\!F = \tfrac{9}{5}\,{}^{\circ}\!C + 32\]
Temperature
📐
Units
\[\text{SI base: Joule (J)}\]
Energy
📐
Units
\[\text{SI base: meter (m)}\]
Length
📐
Units
\[\text{SI base: kilogram (kg)}\]
Mass & Weight
📐
Units
\[\text{SI base: Pascal (Pa)}\]
Pressure
📐
Units
\[\text{SI base: } \mathrm{m/s}\]
Speed & Velocity
📐
Units
\[\text{SI base: } \mathrm{m^{2}}\]
Area
📐
Units
\[\text{SI base: } \mathrm{m^{3}}\]
Volume
📐
Units
\[\text{SI base: Watt (W)}\]
Power
📐
Units
\[1\;\text{byte} = 8\;\text{bits}\]
Data Storage
📐
Units
\[360^{\circ} = 2\pi\;\mathrm{rad} = 400\;\mathrm{grad}\]
Angle
📐
Units
\[\text{SI base: second (s)}\]
Time
📐
Units
\[\text{SI base: Newton (N)}\]
Force
📐
Units
\[\mathrm{mpg} \;\longleftrightarrow\; \mathrm{L}/100\mathrm{km} \;\longleftrightarrow\; \mathrm{km}/\mathrm{L}\]
Fuel Economy
📐
Units
\[\text{US} \;\longleftrightarrow\; \text{Metric} \;\longleftrightarrow\; \text{Imperial}\]
Cooking Measures
📐
Units
\[1\;\mathrm{lux} = 1\;\mathrm{lm/m^{2}}\]
Light & Illuminance
📐
Units
\[1\;\mathrm{Bq} = 1\;\text{decay}/\mathrm{s}\]
Radioactivity & Dose
🌡
Thermo.
\[\eta = 1 - \dfrac{T_{c}}{T_{h}}\]
Carnot Efficiency
🌡
Thermo.
\[PV = nRT\]
Ideal Gas Law
🌡
Thermo.
\[Q = m\,c_{p}\,\Delta T\]
Heat Transfer Q=mcΔT
🔬
Optics
\[\dfrac{1}{f} = \dfrac{1}{d_{o}} + \dfrac{1}{d_{i}}\]
Thin Lens
🔬
Optics
\[n_{1}\sin\theta_{1} = n_{2}\sin\theta_{2}\]
Snell's Law
🪐
Orbital
\[v_{\text{esc}} = \sqrt{\dfrac{2GM}{R}}\]
Escape Velocity
🪐
Orbital
\[T^{2} = \dfrac{4\pi^{2}}{GM}\,a^{3}\]
Kepler's 3rd Law
⚗
Chem.
\[\mathrm{pH} = -\log_{10}[H^{+}]\]
pH Calculator
⚗
Chem.
\[C_{1}V_{1} = C_{2}V_{2}\]
Dilution C₁V₁=C₂V₂
📡
Signals
\[C = B\,\log_{2}\!\left(1 + \dfrac{S}{N}\right)\]
Shannon Capacity
📡
Signals
\[f_{s} \geq 2\,f_{\max}\]
Nyquist Rate
△
Geometry
\[A = \pi r^{2},\quad C = 2\pi r\]
Circle
△
Geometry
\[A = \sqrt{s(s-a)(s-b)(s-c)},\;\; s = \tfrac{a+b+c}{2}\]
Triangle (Heron's)
△
Geometry
\[c = \sqrt{a^{2} + b^{2}}\]
Pythagorean
△
Geometry
\[A = l\,w,\quad V = l\,w\,h\]
Rectangle / Box
△
Geometry
\[V = \tfrac{4}{3}\pi r^{3},\quad A = 4\pi r^{2}\]
Sphere
△
Geometry
\[V = \pi r^{2} h,\quad A = 2\pi r(r+h)\]
Cylinder
△
Geometry
\[V = \tfrac{1}{3}\pi r^{2} h,\quad \ell = \sqrt{r^{2}+h^{2}}\]
Cone
△
Geometry
\[A = \tfrac{1}{4} n s^{2} \cot\!\left(\tfrac{\pi}{n}\right)\]
Regular Polygon
△
Geometry
\[d = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}}\]
Distance 2 Points
𝑥
Algebra
\[\begin{cases} a x + b y = e \\ c x + d y = f \end{cases}\]
Linear System 2×2
𝑥
Algebra
\[A = A_{0}\,e^{r t}\]
Exponential Growth
𝑥
Algebra
\[A = P\!\left(1 + \tfrac{r}{n}\right)^{n t}\]
Compound Interest
𝑥
Algebra
\[a_{n} = a_{1} + (n-1)d,\quad S_{n} = \tfrac{n(a_{1}+a_{n})}{2}\]
Arithmetic Series
𝑥
Algebra
\[a_{n} = a_{1} r^{n-1},\quad S_{n} = \dfrac{a_{1}(1-r^{n})}{1-r}\]
Geometric Series
𝑥
Algebra
\[(a+b)^{n} = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^{k}\]
Binomial Theorem
𝑥
Algebra
\[p(x) = \sum_{k=0}^{n} c_{k} x^{k}\]
Polynomial Evaluate
𝑥
Algebra
\[\log_b(x) = \dfrac{\ln x}{\ln b}\]
Logarithms
∠
Trig.
\[\sin\theta,\;\cos\theta,\;\tan\theta = \tfrac{\sin\theta}{\cos\theta}\]
Trig Functions
∠
Trig.
\[\arcsin x,\;\arccos x,\;\arctan x\]
Inverse Trig
∠
Trig.
\[\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}\]
Law of Sines
∠
Trig.
\[c^{2} = a^{2} + b^{2} - 2 a b \cos C\]
Law of Cosines
∠
Trig.
\[A = \tfrac{1}{2} a b \sin C\]
Triangle Area (SAS)
∠
Trig.
\[360^{\circ} = 2\pi\;\mathrm{rad} = 400\;\mathrm{grad}\]
Angle Convert
∠
Trig.
\[x = r\cos\theta,\quad y = r\sin\theta\]
Polar ↔ Rect
∫
Calculus
\[f'(x) \approx \dfrac{f(x+h) - f(x-h)}{2h}\]
Derivative (numerical)
∫
Calculus
\[\int_{a}^{b} f(x)\,dx\]
Definite Integral
∫
Calculus
\[\lim_{x \to a} f(x)\]
Limit (numerical)
∫
Calculus
\[f(x) \approx \sum_{k=0}^{n} \dfrac{f^{(k)}(a)}{k!}(x-a)^{k}\]
Taylor Series
∫
Calculus
\[L = \int_{a}^{b} \sqrt{1 + f'(x)^{2}}\,dx\]
Arc Length
∫
Calculus
\[x_{n+1} = x_{n} - \dfrac{f(x_{n})}{f'(x_{n})}\]
Newton's Method
TI-84 Calculator
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