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Tachypnea, also spelt tachypnoea, is a respiratory rate greater than normal, resulting in abnormally rapid and shallow breathing. [1]In adult humans at rest, any respiratory rate of 12–20 per minute is considered clinically normal, with tachypnea being any rate above that. [2]
Tachypnea – increased breathing rate; Orthopnea – Breathlessness in lying down position relieved by sitting up or standing; Platypnea – Breathlessness when seated or standing, relieved by lying flat; Trepopnea – Breathlessness when lying flat relieved by lying in a lateral position; Ponopnea – Painful breathing
Snap, [6] or jounce, [2] is the fourth derivative of the position vector with respect to time, or the rate of change of the jerk with respect to time. [4] Equivalently, it is the second derivative of acceleration or the third derivative of velocity, and is defined by any of the following equivalent expressions: = ȷ = = =.
The respiratory rate in humans is measured by counting the number of breaths for one minute through counting how many times the chest rises. A fibre-optic breath rate sensor can be used for monitoring patients during a magnetic resonance imaging scan. [1] Respiration rates may increase with fever, illness, or other medical conditions. [2]
Labored breathing is distinguished from shortness of breath or dyspnea, which is the sensation of respiratory distress rather than a physical presentation.. Still, many [2] simply define dyspnea as difficulty in breathing without further specification, which may confuse it with e.g. labored breathing or tachypnea (rapid breathing). [3]
In multivariable calculus, the directional derivative measures the rate at which a function changes in a particular direction at a given point. [citation needed]The directional derivative of a multivariable differentiable (scalar) function along a given vector v at a given point x intuitively represents the instantaneous rate of change of the function, moving through x with a direction ...
The nation's busiest runway.An airspace cluttered with passenger planes and military aircraft. A history of near-crashes. And a growing shortage of air traffic controllers available to manage it all.
Construct an equation relating the quantities whose rates of change are known to the quantity whose rate of change is to be found. Differentiate both sides of the equation with respect to time (or other rate of change). Often, the chain rule is employed at this step. Substitute the known rates of change and the known quantities into the equation.