answer:According to Graham's law of diffusion, at constant temperature and pressure, the rate of effusion of a gas is inversely proportional to the square root of its molar mass: rate ∝ 1/√M Here, 'rate' represents the effusion rate of the gas, and 'M' is the molar mass of the gas. The molar masses are: - Nitrogen (N2): 28.0 g/mol - Hydrogen (H2): 2.0 g/mol - Chlorine (Cl2): 70.9 g/mol - Carbon Dioxide (CO2): 44.0 g/mol - Argon (Ar): 39.94 g/mol Since the rate is inversely proportional to the square root of molar mass, the gas with the highest molar mass will effuse the slowest, and the one with the lowest molar mass will effuse the fastest. Ordering the gases by their molar masses from highest to lowest: 1. Cl2 (70.9 g/mol) 2. CO2 (44.0 g/mol) 3. Ar (39.94 g/mol) 4. N2 (28.0 g/mol) 5. H2 (2.0 g/mol) Consequently, based on Graham's law, the order of increasing speed of the gases is: Chlorine (Cl2) < Carbon Dioxide (CO2) < Argon (Ar) < Nitrogen (N2) < Hydrogen (H2)

answer:The angles of the triangle are: approx {0.942478, 1.76278, 0.436332} radians The coordinates of the vertices are: A = {0, 0} B = {10.75, 0} C = {14.6766, 20.2006} Please note that the angle measures should be converted to degrees for better understanding if this is intended for a non-radians context.

answer:To find the values of x, y, and z, we can use the method of elimination or substitution. Here, we'll use elimination. First, let's multiply the second equation by 3 and the first equation by 2 to make the coefficients of y equal but opposite: begin{align*} 4x + 6y - 20z &= 20 quad text{(1)} 9x - 15y + 6z &= -3 quad text{(2)} end{align*} Now, add equation (2) to equation (1) to eliminate y: begin{align*} 4x + 6y - 20z + 9x - 15y + 6z &= 20 - 3 13x - 9y - 14z &= 17 quad text{(3)} end{align*} Next, we'll express y from equation (3) in terms of x and z: begin{align*} y &= frac{13x - 17 + 14z}{9} quad text{(4)} end{align*} Substitute equation (4) into the original second equation: begin{align*} 3x - 5left(frac{13x - 17 + 14z}{9}right) + 2z &= -1 3x - frac{65x - 85 + 70z}{9} + 2z &= -1 27x - (65x - 85 + 70z) + 18z &= -9 27x - 65x + 85 + 70z - 18z &= -9 -38x + 52z &= -96 quad text{(5)} end{align*} Now we have a system of two equations with two variables: begin{align*} -38x + 52z &= -96 quad text{(5)} 2x + 3y - 10z &= 10 quad text{(1)} end{align*} To find x, we can multiply equation (5) by 2 and add it to equation (1) to eliminate z: begin{align*} -76x + 104z &= -192 quad text{(6)} 2x + 3left(frac{13x - 17 + 14z}{9}right) - 10z &= 10 2x + frac{39x - 51 + 42z}{9} - 10z &= 10 18x + 39x - 51 + 42z - 90z &= 90 57x - 48z &= 141 quad text{(7)} end{align*} Add equations (6) and (7): begin{align*} -76x + 104z + 57x - 48z &= -192 + 141 -19x + 56z &= -51 end{align*} Now, we can solve for x: begin{align*} x &= frac{51 - 56z}{19} quad text{(8)} end{align*} Substitute equation (8) into equation (5) to find z: begin{align*} -38left(frac{51 - 56z}{19}right) + 52z &= -96 -702 + 728z + 52z &= -1824 780z &= -1122 z &= -frac{1122}{780} z &= -frac{187}{130} z &= -frac{17}{10} z &= -1.7 end{align*} Now, substitute z = -1.7 back into equation (8) to find x: begin{align*} x &= frac{51 - 56(-1.7)}{19} x &= frac{51 + 95.2}{19} x &= frac{146.2}{19} x &= 7.7 end{align*} Finally, substitute z = -1.7 into equation (4) to find y: begin{align*} y &= frac{13(7.7) - 17 + 14(-1.7)}{9} y &= frac{100.1 - 17 - 23.8}{9} y &= frac{59.3}{9} y &= 6.58888... y &= 6.59 quad text{(rounded)} end{align*} Thus, the solution to the system is x = 7.7, y = 6.59, and z = -1.7. However, it's worth noting that the provided answer {21, 16, 8} is incorrect based on our calculations.

answer:A 4-torsion point satisfies the equation 4P = 0. To find these points, we can use the formulas for point addition and doubling in Weierstrass form and solve for points where the coordinates satisfy 4P = 0. Alternatively, we can use computational tools like PARI/GP or the LMFDB database to compute the torsion points directly.