Breathing is cyclic and a full respiratory cycle from the beginning of inhalation to the end of exhalation takes about 7 s. the maximum rate of air flow into the lungs is about 0.3 l/s. this explains, in part, why the function f(t) = 3 10 sin(2πt/7) has often been used to model the rate of air flow into the lungs. use this model to find the volume of inhaled air in the lungs at time t.

In this problem, volume is computed:

volume = ∫(flow rate)·dt 

.. = ∫[0, t] (3/10)*sin(2πt/7)·dt

= (3 / 10)*(7 /(2 π))*(-cos (2 π t/7)+1) 

= (-21 / (20 π))*(cos (2 π t /7) - 1)

Volume is equal to 21 sin^2 (pit/7) / 10pi is the inhaled air in the lungs at time t

Answer: d. 39 cmin the diagram, the approximate length of the minor arc de is 39 centimetres.step-by-step explanation: the formula for the length of an arc in a circle is as displayed below.let the length of the minor arc de = xx = 2( pi )r × angle of sector / 360°from this, we will substitute the values given from the problem into the formula to obtain the length of the minor arc de.x = 2( pi )r × angle of sector / 360°r = radius = 25cmpi as an approximate value = 3.14angle of sector = 120°x = 2( 3.14 )( 25 ) × 120° / 360°x = 157 × 1 / 4x = 39.25x = 39 ( rounded to the nearest whole number as an approximate value )