more formulas
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@ -173,4 +173,219 @@ Where:
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""",
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"tags": ["comparison", "shopping", "economics"]
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}
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,
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// Einstein's Mass-Energy Equivalence
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{
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"name": "Mass-Energy Equivalence",
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"description": r'''
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Einstein's famous equation showing the relationship between mass and energy
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$$E = mc^2$$
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Where:
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- $E$: Energy (Joules)
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- $m$: Mass (kilograms)
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- $c$: Speed of light ($299,792,458\\ \\mathrm{m/s}$)
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This equation shows that mass can be converted to energy and vice versa.''',
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"input": [
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{"name": "m", "unit": "kilogram"} // Mass
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],
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"output": {"name": "E", "unit": "joule"}, // Energy
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"d4rtCode": "E = m * pow(299792458, 2);",
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"tags": ["physics", "relativity", "energy"]
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},
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// Ohm's Law
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{
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"name": "Ohm's Law",
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"description": r'''
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Relationship between voltage, current, and resistance in electrical circuits
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$$V = IR$$
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Where:
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- $V$: Voltage (Volts)
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- $I$: Current (Amperes)
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- $R$: Resistance (Ohms)
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This fundamental law describes how current flows through resistive materials.''',
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"input": [
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{"name": "I", "unit": "ampere"}, // Current
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{"name": "R", "unit": "ohm"} // Resistance
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],
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"output": {"name": "V", "unit": "volt"}, // Voltage
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"d4rtCode": "V = I * R;",
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"tags": ["physics", "electricity", "electronics"]
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},
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// Hooke's Law
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{
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"name": "Hooke's Law",
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"description": r'''
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Force exerted by a spring is proportional to its displacement
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$$F = -kx$$
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Where:
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- $F$: Restoring force (Newtons)
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- $k$: Spring constant (N/m)
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- $x$: Displacement from equilibrium (meters)
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The negative sign indicates the force opposes the displacement.''',
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"input": [
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{"name": "k", "unit": "newton per meter"}, // Spring constant
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{"name": "x", "unit": "meter"} // Displacement
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],
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"output": {"name": "F", "unit": "newton"}, // Force
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"d4rtCode": "F = -k * x;",
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"tags": ["physics", "elasticity", "oscillations"]
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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"}, // Mass
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{"name": "v", "unit": "meters per second"}, // Velocity
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{"name": "r", "unit": "meter"} // Radius
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],
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"output": {"name": "F", "unit": "newton"}, // Force
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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"}, // Frequency
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{"name": "lambda", "unit": "meter"} // Wavelength
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],
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"output": {"name": "v", "unit": "meters per second"}, // Wave speed
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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"}, // First leg
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{"name": "b", "unit": "meter"} // Second leg
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],
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"output": {"name": "c", "unit": "meter"}, // Hypotenuse
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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"}, // Side a
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{"name": "A", "unit": "degree"}, // Angle A in degrees
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{"name": "B", "unit": "degree"} // Angle B in degrees
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],
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"output": {"name": "b", "unit": "meter"}, // Side b
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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"}, // Side a
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{"name": "b", "unit": "meter"}, // Side b
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{"name": "C", "unit": "degree"} // Angle C in degrees
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],
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"output": {"name": "c", "unit": "meter"}, // Side c
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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"} // Angle in degrees
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],
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"output": {"name": "result", "unit": "scalar"}, // Result (should be 1)
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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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]
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@ -22,7 +22,10 @@ Future<Corpus> createDefaultCorpus() async{
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"assets/units/area.d4rt.units",
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"assets/units/currency.d4rt.units",
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"assets/units/distance.d4rt.units",
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"assets/units/elasticity.d4rt.units",
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"assets/units/electricity.d4rt.units",
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"assets/units/energy.d4rt.units",
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"assets/units/frequency.d4rt.units",
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"assets/units/force.d4rt.units",
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"assets/units/mass.d4rt.units",
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"assets/units/pressure.d4rt.units",
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