Let u solve cu = 0. Show that any derivative, say w = uxt, also solves cw = 0. In cu = 0, u = u(t, x) do the change of variables
(ξ, η) specified below, to find the equation for v(ξ, η). Is it vξξ − c 2vηη = 0? (a) Translation ξ = t − T, η = x − y where y, T are fixed. (b) Dilation ξ = at, η = ax for any constant a. (c) Find the change of variables (ξ, η) = (?, ?) such that v(ξ, η) satisfies 1v = vξξ −vηη = 0
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Dimensions of the room in cm = 2.54 x 12 by 15 x 2.54 by 2.54 x 8.5 = 30.48 by 38.1 by 21.59
Volume of the room in cubic cm = 30.48 x 38.1 x 21.59 cubic cm = 25,072.21 cubic cm
Given that the density of air at room temperature is
, thus the mass of air in the room = 25,072.21 x 0.00118 = 29.59 g = 0.0296 kg
Given that the lethal dose of HCN is approximately 300 mg HCN per kilogram of air when inhaled, thus the <span>amount of HCN that gives the lethal dose in the small laboratory room is given by 300 x 0.0296 = 8.88 mg.</span>
Volume of the room in cubic cm = 30.48 x 38.1 x 21.59 cubic cm = 25,072.21 cubic cm
Given that the density of air at room temperature is
Given that the lethal dose of HCN is approximately 300 mg HCN per kilogram of air when inhaled, thus the <span>amount of HCN that gives the lethal dose in the small laboratory room is given by 300 x 0.0296 = 8.88 mg.</span>