9f2c569279
Merge branch 'feature/more-copilot-formulas' of ssh://codeberg.org/alvarogonzalezsotillo/d4rt_formulas into feature/more-copilot-formulas
447 lines
11 KiB
Text
447 lines
11 KiB
Text
[
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// Projectile Motion Range
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{
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"name": "Projectile Range",
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"description": r"""
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Calculates horizontal distance of projectile motion
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$$R = \frac{v^2 \sin(2\theta)}{g}$$
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Where:
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- $v$: Initial velocity
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- $\theta$: Launch angle
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- $g$: Gravitational acceleration
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""",
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"input": [
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{"name": "v", "unit": "meters per second"},
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{"name": "a", "unit": "degree"}
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],
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"output": {"name": "R", "unit": "meter"},
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"d4rtCode": """
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var radians = a * (pi / 180);
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R = (pow(v, 2) * sin(2 * radians)) / 9.80665;
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""",
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"tags": ["physics", "kinematics", "projectile"]
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},
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// Newton's Second Law
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{
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"name": "Newton's Second Law",
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"description": r"""
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Force equals mass times acceleration
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$$F = m \cdot a$$
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Where:
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- $m$: Mass of object ($\mathrm{kg}$)
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- $a$: Acceleration ($\mathrm{m/s^2}$)
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""",
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"input": [
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{"name": "m", "unit": "kilogram"},
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{"name": "a", "unit": "meters per square second"}
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],
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"output": {"name": "F", "unit": "newton"},
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"d4rtCode": "F = m * a;",
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"tags": ["physics", "mechanics", "newton"]
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},
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// Centripetal Force
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{
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"name": "Centripetal Force",
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"description": r"""
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Force required to keep an object moving in circular motion
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$$F = \frac{mv^2}{r}$$
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Where:
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- $F$: Centripetal force (Newtons)
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- $m$: Mass of object (kilograms)
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- $v$: Velocity (m/s)
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- $r$: Radius of circular path (meters)
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This force acts toward the center of the circle.""",
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"input": [
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{"name": "m", "unit": "kilogram"},
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{"name": "v", "unit": "meters per second"},
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{"name": "r", "unit": "meter"}
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],
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"output": {"name": "F", "unit": "newton"},
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"d4rtCode": "F = (m * pow(v, 2)) / r;",
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"tags": ["physics", "circular motion", "centripetal"]
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},
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// Wave Equation
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{
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"name": "Wave Equation",
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"description": r"""
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Relationship between wave speed, frequency, and wavelength
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$$v = f\lambda$$
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Where:
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- $v$: Wave speed (m/s)
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- $f$: Frequency (Hertz)
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- $\lambda$: Wavelength (meters)
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This applies to all types of waves including sound and light.""",
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"input": [
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{"name": "f", "unit": "hertz"},
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{"name": "lambda", "unit": "meter"}
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],
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"output": {"name": "v", "unit": "meters per second"},
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"d4rtCode": "v = f * lambda;",
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"tags": ["physics", "waves", "frequency"]
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},
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// Pythagorean Theorem
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{
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"name": "Pythagorean Theorem",
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"description": r"""
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Fundamental relation in Euclidean geometry among the three sides of a right triangle
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$$a^2 + b^2 = c^2$$
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Where:
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- $a$, $b$: Legs of the right triangle
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- $c$: Hypotenuse of the right triangle
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The square of the hypotenuse is equal to the sum of squares of the other two sides.""",
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"input": [
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{"name": "a", "unit": "meter"},
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{"name": "b", "unit": "meter"}
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],
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"output": {"name": "c", "unit": "meter"},
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"d4rtCode": "c = sqrt(pow(a, 2) + pow(b, 2));",
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"tags": ["trigonometry", "geometry", "pythagorean"]
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},
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// Sine Rule
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{
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"name": "Sine Rule",
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"description": r"""
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Relationship between the sides and angles of any triangle
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$$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$
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Where:
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- $a$, $b$, $c$: Sides of the triangle
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- $A$, $B$, $C$: Angles opposite to sides $a$, $b$, $c$ respectively
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This rule is useful for solving triangles when certain combinations of angles and sides are known.""",
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"input": [
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{"name": "a", "unit": "meter"},
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{"name": "A", "unit": "degree"},
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{"name": "B", "unit": "degree"}
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],
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"output": {"name": "b", "unit": "meter"},
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"d4rtCode": """
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var angleARad = A * (pi / 180);
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var angleBRad = B * (pi / 180);
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b = (a * sin(angleBRad)) / sin(angleARad);
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""",
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"tags": ["trigonometry", "triangle", "sine"]
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},
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// Cosine Rule
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{
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"name": "Cosine Rule",
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"description": r"""
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Generalization of the Pythagorean theorem for any triangle
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$$c^2 = a^2 + b^2 - 2ab\cos(C)$$
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Where:
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- $a$, $b$, $c$: Sides of the triangle
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- $C$: Angle opposite to side $c$
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This rule relates all three sides of a triangle to one of its angles.""",
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"input": [
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{"name": "a", "unit": "meter"},
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{"name": "b", "unit": "meter"},
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{"name": "C", "unit": "degree"}
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],
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"output": {"name": "c", "unit": "meter"},
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"d4rtCode": """
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var angleCRad = C * (pi / 180);
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c = sqrt(pow(a, 2) + pow(b, 2) - 2*a*b*cos(angleCRad));
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""",
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"tags": ["trigonometry", "triangle", "cosine"]
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},
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// Trigonometric Identity
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{
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"name": "Trigonometric Identity",
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"description": r"""
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Fundamental Pythagorean identity in trigonometry
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$$\sin^2(\theta) + \cos^2(\theta) = 1$$
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Where:
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- $\theta$: Any angle in radians or degrees
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This identity is derived from the Pythagorean theorem applied to the unit circle.""",
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"input": [
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{"name": "theta", "unit": "degree"}
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],
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"output": {"name": "result", "unit": "scalar"},
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"d4rtCode": """
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var thetaRad = theta * (pi / 180);
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result = pow(sin(thetaRad), 2) + pow(cos(thetaRad), 2);
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""",
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"tags": ["trigonometry", "identity", "sine", "cosine"]
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},
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// Gravitational Potential Energy
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{
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"name": "Gravitational Potential Energy",
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"description": r"""
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Energy possessed by an object due to its position in a gravitational field
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$$PE = mgh$$
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Where:
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- $m$: Mass of object (kilograms)
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- $g$: Gravitational acceleration ($9.81\ \mathrm{m/s^2}$ on Earth)
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- $h$: Height above reference point (meters)
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This energy increases with height and can be converted to kinetic energy.""",
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"input": [
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{"name": "m", "unit": "kilogram"},
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{"name": "h", "unit": "meter"},
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{"name": "g", "unit": "meters per square second"}
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],
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"output": {"name": "PE", "unit": "joule"},
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"d4rtCode": "PE = m * g * h;",
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"tags": ["physics", "energy", "mechanics", "gravity"]
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},
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// Linear Momentum
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{
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"name": "Linear Momentum",
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"description": r"""
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Quantity of motion possessed by a moving object
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$$p = mv$$
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Where:
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- $p$: Momentum ($\mathrm{kg \cdot m/s}$)
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- $m$: Mass (kilograms)
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- $v$: Velocity (m/s)
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Momentum is conserved in isolated systems.""",
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"input": [
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{"name": "m", "unit": "kilogram"},
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{"name": "v", "unit": "meters per second"}
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],
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"output": {"name": "p", "unit": "kilogram meter per second"},
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"d4rtCode": "p = m * v;",
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"tags": ["physics", "mechanics", "momentum"]
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},
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// Volume of Sphere
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{
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"name": "Volume of Sphere",
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"description": r"""
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Volume enclosed by a sphere
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$$V = \frac{4}{3}\pi r^3$$
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Where:
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- $V$: Volume (cubic meters)
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- $r$: Radius (meters)
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- $\pi$: Pi ($\approx 3.14159$)
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The volume is proportional to the cube of the radius.""",
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"input": [
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{"name": "r", "unit": "meter"}
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],
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"output": {"name": "V", "unit": "cubic meter"},
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"d4rtCode": "V = (4.0/3.0) * pi * pow(r, 3);",
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"tags": ["geometry", "sphere", "volume"]
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},
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// Surface Area of Sphere
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{
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"name": "Surface Area of Sphere",
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"description": r"""
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Total surface area of a sphere
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$$A = 4\pi r^2$$
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Where:
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- $A$: Surface area (square meters)
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- $r$: Radius (meters)
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- $\pi$: Pi ($\approx 3.14159$)
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The surface area is four times the area of a circle with the same radius.""",
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"input": [
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{"name": "r", "unit": "meter"}
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],
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"output": {"name": "A", "unit": "square meter"},
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"d4rtCode": "A = 4 * pi * pow(r, 2);",
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"tags": ["geometry", "sphere", "surface area"]
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},
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// Volume of Cylinder
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{
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"name": "Volume of Cylinder",
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"description": r"""
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Volume enclosed by a cylinder
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$$V = \pi r^2 h$$
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Where:
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- $V$: Volume (cubic meters)
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- $r$: Radius of base (meters)
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- $h$: Height (meters)
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- $\pi$: Pi ($\approx 3.14159$)
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The volume is the area of the base times the height.""",
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"input": [
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{"name": "r", "unit": "meter"},
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{"name": "h", "unit": "meter"}
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],
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"output": {"name": "V", "unit": "cubic meter"},
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"d4rtCode": "V = pi * pow(r, 2) * h;",
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"tags": ["geometry", "cylinder", "volume"]
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},
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// Surface Area of Cylinder
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{
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"name": "Surface Area of Cylinder",
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"description": r"""
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Total surface area of a cylinder (including top and bottom)
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$$A = 2\pi r(r + h)$$
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Where:
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- $A$: Total surface area (square meters)
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- $r$: Radius of base (meters)
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- $h$: Height (meters)
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- $\pi$: Pi ($\approx 3.14159$)
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This includes the lateral surface plus the two circular ends.""",
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"input": [
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{"name": "r", "unit": "meter"},
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{"name": "h", "unit": "meter"}
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],
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"output": {"name": "A", "unit": "square meter"},
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"d4rtCode": "A = 2 * pi * r * (r + h);",
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"tags": ["geometry", "cylinder", "surface area"]
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},
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// Volume of Cone
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{
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"name": "Volume of Cone",
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"description": r"""
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Volume enclosed by a cone
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$$V = \frac{1}{3}\pi r^2 h$$
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Where:
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- $V$: Volume (cubic meters)
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- $r$: Radius of base (meters)
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- $h$: Height (meters)
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- $\pi$: Pi ($\approx 3.14159$)
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The volume is one-third the volume of a cylinder with the same base and height.""",
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"input": [
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{"name": "r", "unit": "meter"},
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{"name": "h", "unit": "meter"}
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],
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"output": {"name": "V", "unit": "cubic meter"},
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"d4rtCode": "V = (1.0/3.0) * pi * pow(r, 2) * h;",
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"tags": ["geometry", "cone", "volume"]
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},
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// Volume of Cube
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{
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"name": "Volume of Cube",
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"description": r"""
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Volume enclosed by a cube
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$$V = s^3$$
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Where:
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- $V$: Volume (cubic meters)
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- $s$: Side length (meters)
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The volume is the cube of the side length.""",
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"input": [
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{"name": "s", "unit": "meter"}
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],
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"output": {"name": "V", "unit": "cubic meter"},
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"d4rtCode": "V = pow(s, 3);",
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"tags": ["geometry", "cube", "volume"]
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},
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// Surface Area of Cube
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{
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"name": "Surface Area of Cube",
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"description": r"""
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Total surface area of a cube
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$$A = 6s^2$$
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Where:
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- $A$: Total surface area (square meters)
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- $s$: Side length (meters)
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The surface area is six times the area of one face.""",
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"input": [
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{"name": "s", "unit": "meter"}
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],
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"output": {"name": "A", "unit": "square meter"},
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"d4rtCode": "A = 6 * pow(s, 2);",
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"tags": ["geometry", "cube", "surface area"]
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},
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// Perimeter of Rectangle
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{
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"name": "Perimeter of Rectangle",
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"description": r"""
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Total distance around a rectangle
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$$P = 2(l + w)$$
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Where:
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- $P$: Perimeter (meters)
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- $l$: Length (meters)
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- $w$: Width (meters)
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The perimeter is twice the sum of length and width.""",
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"input": [
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{"name": "l", "unit": "meter"},
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{"name": "w", "unit": "meter"}
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],
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"output": {"name": "P", "unit": "meter"},
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"d4rtCode": "P = 2 * (l + w);",
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"tags": ["geometry", "rectangle", "perimeter"]
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},
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// Perimeter of Triangle
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{
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"name": "Perimeter of Triangle",
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"description": r"""
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Total distance around a triangle
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$$P = a + b + c$$
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Where:
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- $P$: Perimeter (meters)
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- $a, b, c$: Side lengths (meters)
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The perimeter is the sum of all three sides.""",
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"input": [
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{"name": "a", "unit": "meter"},
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{"name": "b", "unit": "meter"},
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{"name": "c", "unit": "meter"}
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],
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"output": {"name": "P", "unit": "meter"},
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"d4rtCode": "P = a + b + c;",
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"tags": ["geometry", "triangle", "perimeter"]
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}
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]
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