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Apuntes

The text provided contains a series of mathematical formulas and expressions. Below is the structured and corrected version: • Subtopic: Thermodynamics and Heat Transfer 1. The formula for heat transfer is given by $Q = mc\Delta T$, where $Q$ is the heat added, $m$ is the mass, $c$ is the specific heat capacity, and $\Delta T$ is the change in temperature. 2. The rate of change of temperature over time is expressed as $\frac{dT}{dt} = -R (T - T_{\text{amb}})$, where $R$ is a constant, $T$ is the temperature, and $T_{\text{amb}}$ is the ambient temperature. 3. The change in volume is given by $\Delta V = Q - W$, where $Q$ is the heat added and $W$ is the work done. • Subtopic: Trigonometry 1. The Pythagorean identity is $\sin^2\theta + \cos^2\theta = 1$. 2. Common angle measures include $\frac{\pi}{2}$, $\frac{\pi}{3}$, $\frac{\pi}{6}$, and $360^\circ$. 3. The tangent of an angle is given by $\tan\theta = \frac{\sin\theta}{\cos\theta}$. • Subtopic: Geometry 1. The volume of a cone is $V = \frac{1}{3} \pi r^2 h$, where $r$ is the radius and $h$ is the height. 2. The circumference of a circle is $C = 2\pi r$, where $r$ is the radius. 3. The diameter of a circle is $D = 2r$...