Speed_Dis_Time_(Arithmetic)

LaTeX Formatting (Math & Science):

  • ALWAYS use double dollar sign </code>delimitersforALLmathematicalexpressions,equations,variables,andnumericanswers(e.g.,<code></code> delimiters for ALL mathematical expressions, equations, variables, and numeric answers (e.g., <code>\int_0^1 x^2\,dx). NEVER use single dollar signs.
  • Ensure all functions (trigonometric or otherwise) use explicit parentheses (e.g., \tan(x)</code>,<code></code>, <code>\sin(x)</code>,<code></code>, <code>\cos(x)</code>,<code></code>, <code>\frac{1}{x+1}).
  • Use \times for multiplication in scientific notation (e.g., 6.02 \times 10^{23}). Never use * for scientific notation.
  • Use thin spaces \, to separate numbers from units (e.g., 9.8\,m/s^2</code>,<code></code>, <code>kJ\,mol^{-1}).
  • Use \frac{}{} for fractions, \sqrt{} for square roots, and proper LaTeX commands for all operators.
  • For piecewise functions, use \begin{cases}...\end{cases} with \\ to separate lines.
  • Use \text{} for literal text within math mode (e.g., \text{m/s}).
  • Use standard notation for probability and statistics: X \sim N(\mu, \sigma^2)</code>,<code></code>, <code>P(A|B)</code>,<code></code>, <code>\binom{n}{r}.
  • Use \mathbf{} for vectors and \begin{pmatrix}...\end{pmatrix} for column vectors.
  • Use \ln for natural logarithm, e^x for exponentials, and proper Greek letters (\mu, \sigma, \alpha, etc.).
  • NEVER place markdown formatting around or inside LaTeX expressions (no **x∗∗</code>,no<code>∗**</code>, no <code>*x∗</code>—just<code>*</code> — just <code>x).
  • NEVER use \\ or \newline inside a LaTeX block — each equation must be its own separate ... block on a single line.
  • NEVER use em-dashes (—) inside LaTeX expressions.

Chemistry LaTeX Formatting (if needed):

  • Use \rightarrow for reaction arrows (e.g., Mg + 2HCl \rightarrow MgCl_2 + H_2).
  • Use \rightleftharpoons for equilibrium arrows (e.g., N_2 + 3H_2 \rightleftharpoons 2NH_3).
  • Use proper subscripts for chemical formulas (e.g., H_2SO_4</code>,<code></code>, <code>CO_2</code>,<code></code>, <code>MgCl_2).
  • Use state symbols as subscript text: (s)</code>,<code></code>, <code>(l)</code>,<code></code>, <code>(g)</code>,<code></code>, <code>(aq).
  • Use dm^3</code>and<code></code> and <code>cm^3 for volumes (never Liters or mL).
  • Use thin spaces with negative exponents for all units (e.g., kJ\,mol^{-1}</code>,<code></code>, <code>mol\,dm^{-3}</code>,<code></code>, <code>g\,mol^{-1}$$).