Metrology and Quality Inspection: Key Concepts and Techniques

Posted by on Nov 29, 2025 in Mathematics | 0 comments




Important Instructions to examiners:
SUMMER 18– EXAMINATION
17530
Model AnswerSubject Code:


⦁The answers should be examined by key words and not as word-to-word as given in the model answer scheme.
⦁The model answer and the answer written by candidate may vary but the examiner may try to assess the understanding level of the candidate.
⦁The language errors such as grammatical, spelling errors should not be given more Importance (Not applicable for subject English and Communication Skills.
⦁While
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Essential Calculus Theorems and Formula Reference

Posted by on Nov 25, 2025 in Mathematics | 0 comments

Fundamental Calculus Definitions and Theorems

The Derivative and Integral Definitions

The Derivative Definition

The derivative of a function $f(x)$, denoted $f'(x)$, is defined using the limit of the difference quotient:

$$f'(x) = \lim_{h \to 0} \frac{f(x+h) – f(x)}{h}$$

The Definite Integral (Riemann Sum)

The definite integral of $f(x)$ from $a$ to $b$ is defined as the limit of the Riemann sum:

$$\int_a^b f(x) dx = \lim_{n \to \infty} \sum_{i=1}^n f(x_i^*) \Delta x$$

Key Calculus Theorems

Mean Value Theorem

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Advanced Trigonometric Identities and Ratio Calculations

Posted by on Nov 21, 2025 in Mathematics | 0 comments

1. Proving the Tangent Sum and Difference Identity

Identity to Prove:

\tan (x+y) + \tan (x-y) = \frac{\sin (2x)}{\cos (2y) – \cos (2x)}

Proof Steps

Start with the Left-Hand Side (LHS) using the definition of tangent:

\tan (x+y) + \tan (x-y) = \frac{\sin (x+y)}{\cos (x+y)} + \frac{\sin (x-y)}{\cos (x-y)}

Combine the fractions:

= \frac{\sin (x+y)\cos (x-y) + \sin (x-y)\cos (x+y)}{\cos (x+y)\cos (x-y)}

Using the Sine Addition Formula, $\sin(A+B) = \sin A \cos B + \cos A \sin B$:

= \frac{\sin [ (x+y) + (x-y)

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Developmental Stages in Mathematical Measurement and Number Sense

Posted by on Nov 7, 2025 in Mathematics | 0 comments

Learning Trajectory for Length Measurement

E1: Initial Unit Placement

Places the units from end to end. May not recognize the need for units of the same length or may not be able to measure if there are fewer units than necessary. Can use rulers with substantial guidance.

E2: Ordering and Seriation of Lengths

Orders lengths, marked from 1 to 6 units. Understands, at least intuitively, that any set of objects of different lengths can be placed in a series that is always increasing (or decreasing) in

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Discrete Mathematics Formulas and Proof Techniques

Posted by on Nov 4, 2025 in Mathematics | 0 comments

Problem: what is the power set P(S) of S=(a,b,c) Solution: ∅, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}}.  |p ∨ (p ∧ q) ≡ p|, |p ∧ (p ∨ q) ≡ p|, |p → q ≡ ¬p ∨ q|, |p → q ≡ ¬q → ¬p|, |p ∨ q ≡ ¬p → q|, |p ∧ q ≡ ¬(p → ¬q)|, |¬(p → q) ≡ p ∧ ¬q|, |(p → q) ∧ (p → r) ≡ p → (q ∧ r)|, |(p → r) ∧ (q → r) ≡ (p ∨ q) → r|, |(p → q) ∨ (p → r) ≡ p → (q ∨ r)|, |(p → r) ∨ (q → r) ≡ (p ∧ q) → r|, |p ↔ q ≡

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Essential Physics Formulas: Kinematics and Dynamics

Posted by on Oct 29, 2025 in Mathematics | 0 comments

Cristián Arriagada: Essential Physics Formulas

This compilation provides fundamental equations covering kinematics, dynamics, work, energy, and rotational motion in classical mechanics. These formulas are crucial for solving problems involving motion and forces.

1. Kinematics (Equations of Motion)

1.1. Uniformly Accelerated Motion (MUA)

  • Velocity: V = V0 + a(t – t0)
  • Position: X = X0 + V0t + 1/2 at2
  • Velocity-Position: V2 = V02 + 2a(X – X0)
  • Time: t = (V – V0) / a

1.2. Uniform Rectilinear Motion (MRU)

  • Velocity:
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