Inhaled insulin uses the lungs as the absorption site, letting insulin pass across the alveolar surface into the bloodstream for rapid action. This route bypasses the digestive system and hepatic first-pass metabolism, which helps achieve a quick onset around mealtime and a shorter duration of effect. Afrezza and Exubera are both formulated to be inhaled and absorbed through the lungs, not injected under the skin, swallowed, or given intravenously. When using inhaled insulin, proper inhalation technique and lung health are important, and it isn’t suitable for everyone.

Incompressible deformation means volume stays constant as the material deforms. The volume element after deformation is the same as before, so there’s no change in volume even when the shape changes. Because mass is conserved, this also means density doesn’t change during deformation. For isotropic, linear-elastic materials, incompressibility corresponds to Poisson’s ratio approaching 0.5, not zero. So the idea that Poisson’s ratio equals zero isn’t correct for incompressible behavior. The relation between Young’s modulus and shear modulus is E = 2G(1 + ν); with ν near 0.5, this gives E ≈ 3G, so the two moduli are not equal. Finally, density would not increase with compression in an incompressible material, since volume doesn’t contract and mass stays the same. So the statement that volume remains constant during deformation is the correct description.

Acoustic impedance for a plane wave in a medium is the product of its density and the speed of sound: Z = ρ c. With ρ = 1000 kg/m^3 and c = 1540 m/s, multiply to get Z = 1000 × 1540 = 1.54 × 10^6. The units come out as Pa·s/m, since kg/m^3 times m/s equals kg/(m^2 s), which is the standard unit for acoustic impedance. So the correct value is 1.54 × 10^6 Pa·s/m. Other numbers would result from using a different speed or density.

The practical implication is that you must sample biomedical signals at least twice the highest frequency content you care about, and you should filter before sampling to prevent aliasing. This comes from the Nyquist principle: to faithfully reconstruct a signal from its samples, the sampling rate must be at least two times the signal’s bandwidth. If you sample slower than that, higher-frequency components fold into lower frequencies, distorting the signal and potentially creating artifacts. In practice, you place an anti-aliasing (low-pass) filter before the analog-to-digital converter to remove frequency content above half the chosen sampling rate. Then you pick a sampling rate that is at least twice the signal’s bandwidth. For biomedical signals, that means identifying the relevant frequency range—for example, ECG up to about 100 Hz, EEG up to around 100 Hz (depending on application), and EMG that can extend into the kHz range—and selecting a sampling rate accordingly (commonly several hundred hertz to a few kilohertz for safety and fidelity). Why the other ideas don’t fit: sampling at a rate tied only to the highest frequency or using interpolation after cannot guarantee faithful reconstruction if high-frequency content is present or not captured; sampling much slower (or relying on post hoc smoothing) leads to aliasing and loss of information.