Geometry Problems: Circles, Chords, and Quadrilaterals

Posted by admin on Jul 13, 2025 in Mathematics | 0 comments

Geometry Problems and Solutions

Here are the solutions to the geometry questions:

1. Cyclic Quadrilateral Angle Sum

   Question: The sum of either pair of opposite angles of a cyclic quadrilateral is 180°. If ‘n’ represents this sum and ‘m’ is also 180°, find ‘m-n’.

   Solution: In a cyclic quadrilateral, the sum of opposite angles is always 180°. Therefore, \(n = 180^\circ\). Given \(m = 180^\circ\), we have:

   \[m – n = 180^\circ – 180^\circ = 0\]

2. Circle’s Largest Chord and Radius

   Question: If the largest chord

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Essential Math Formulas and Definitions

Posted by admin on Jul 9, 2025 in Mathematics | 0 comments

Lines

Slope-Intercept Form

y = mx + b

Point-Slope Form

y – y₁ = m(x – x₁)

Standard Form

Ax + By = C

Rate of Change (Slope)

Δy/Δx = (y₁ – y₂)/(x₁ – x₂)

Algebra Formulas

Quadratic Equations

Standard Form

ax² + bx + c = 0

Quadratic Formula

x = [-b ± √(b² – 4ac)] / (2a)

Binomial Expansions

(a + b)³ Expansion

a³ + 3a²b + 3ab² + b³

(a – b)³ Expansion

a³ – 3a²b + 3ab² – b³

(a + b)² Expansion

a² + 2ab + b²

(a – b)² Expansion

a² – 2ab + b²

Exponent Rules

Product Rule

xᵃ ·

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Core Numerical Methods: Algorithms for Computation

Posted by admin on Jul 4, 2025 in Mathematics | 0 comments

Implementing Euler’s Method

1. Start
2. Define function f(x,y)
3. Read values of initial condition (x₀ and y₀), number of steps (n), and calculation point (x_n)
4. Calculate step size (h) = (x_n – x₀) / n
5. Set i = 0
6. Loop:
   • y_n = y₀ + h * f(x₀ + i*h, y₀)
   • y₀ = y_n
   • i = i + 1
   While i < n
7. Display y_n as result
8. Stop

Implementing Runge-Kutta 4th Order Method

1. Start
2. Define function f(x,y)
3. Read values of initial condition (x₀ and y₀), number of steps (n), and calculation point (x_n)
4. Calculate step size (h) = (x_n – x₀) / n
5. Set i = 0
6. Loop:
   • k₁

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Intangible Capital’s Impact on Investment-Q Relation

Posted by admin on Jul 2, 2025 in Mathematics | 0 comments

Intangible Capital and the Investment-Q Relation

Based on the research by Peters and Taylor (2016).

Introduction: Shifting Investment Landscape

The neoclassical theory of investment was developed when firms primarily owned physical assets. Consequently, empirical tests of this theory have historically focused on physical capital. However, the U.S. economy has since shifted toward service and technology-based industries, where intangible assets have become increasingly important.

The Core Research Question

Is

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Essential Business Math Formulas & Concepts

Posted by admin on Jun 28, 2025 in Mathematics | 0 comments

Applied Business Mathematics Formulas

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1. Polynomials, Exponents, and Roots

Exponent Rules:

• a^m ⋅ aⁿ = a^m+n
• (a^m)ⁿ = a^m⋅n
• a^-n = 1/aⁿ
• a^m/aⁿ = a^m-n

Factoring Techniques:

• Common Factor: ab + ac = a(b + c)
• Difference of Squares: a² – b² = (a – b)(a + b)
• Quadratic Factorization: ax² + bx + c = (px + q)(rx + s)

Quadratic Formula:

x = (-b ± √(b² – 4ac)) / 2a

Example: Solving Quadratic Equations

• Solve x² – 5x + 6 = 0
• Using the quadratic formula:
  • x = (-(-5) ± √((-5)² – 4(1)(6))) / 2(1)
  • x = (5 ± 1) / 2
  • Solutions: x

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Foundational Statistical Concepts for Data Analysis

Posted by admin on Jun 22, 2025 in Mathematics | 0 comments

Types of Research Questions

• Making an Estimate About the Population

  • What is the average number of hours that students study each week?
  • What proportion of all Singaporean students is enrolled in a university?

• Testing a Claim About the Population

  • Does the majority of students qualify for student loans?
  • Is the average course load for a university student greater than 20 units?

• Comparing Two Sub-Populations or Investigating a Relationship Between Two Variables in the Population

  • In University X, do female students

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