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question:A space station, with a 50-meter radius, is designed to spin so that a point on its outer wall attains a linear tangential speed of 22.1 m/s, generating an artificial gravity equivalent to Earth's gravity (1g). If the artificial gravity needs to be increased to 2g, what should the new tangential speed be? a) 44.2 m/s b) 31.3 m/s c) 88.4 m/s d) 27.8 m/s e) 177 m/s
answer:Given: - Radius of the wheel, R = 50 m - Initial tangential speed, V1 = 22.1 m/s - Initial artificial gravity, g1 = 1g (9.81 m/s²) - Desired artificial gravity, g2 = 2g (19.62 m/s²) The relationship between tangential speed and artificial gravity is given by: a = V²/R Since R is constant, we can say: a ∝ V² Thus, (g1/g2) = (V1²/V2²) Substituting the values: (9.81/19.62) = (22.1²/V2²) Solving for V2²: V2² = (22.1² * 19.62) / 9.81 V2² = 976.82 V2 = √976.82 V2 ≈ 31.3 m/s Therefore, the required tangential speed to achieve 2g artificial gravity is approximately 31.3 meters per second. The correct answer is: b) 31.3 m/s
question:Calculate the current ratio for Under Armour.
answer:The current ratio for Under Armour is 3.72, calculated as follows: {eq}begin{align*} &= dfrac{text{Current assets for Under Armour}}{text{Current liabilities for Under Armour}} [0.3 cm] &= dfrac{556}{149} [0.3 cm] &= 3.72 end{align*} {/eq}
question:How can individuals overcome the tendency to give in to short-term impulses?
answer:By considering the long-term consequences of their actions and developing strategies for self-control, such as setting goals and practicing mindfulness.
question:Consider the differential equation -Delta u = f in a different domain Omega := (0,1) times(0,2). How would the Fourier series solution change if the boundary conditions were changed to u(x,0) = u(x,2) = 0?
answer:The eigenfunctions of the Laplace equation would change to: u(x,y) = c_{k,l} sinleft(frac{k pi x}{1}right)sinleft(frac{l pi y}{2}right) The remaining steps to find the Fourier series solution would be the same as in the original answer.