the volume of air in a person’s lungs can be modeled with a periodic function, v(t)=450 cos((π/4)(t…

the volume of air in a person’s lungs can be modeled with a periodic function, v(t)=450 cos((π/4)(t - 0.5))+1650, where v represents the volume of air, in person’s lungs and time t is measured in seconds. what is the minimum and what does it represent in this context? answer attempt 1 out of 4 the minimum is and it represents

the volume of air in a person’s lungs can be modeled with a periodic function, v(t)=450 cos((π/4)(t - 0.5))+1650, where v represents the volume of air, in person’s lungs and time t is measured in seconds. what is the minimum and what does it represent in this context? answer attempt 1 out of 4 the minimum is and it represents

Answer

Answer:

1200; the minimum volume of air in the person's lungs (in cubic - units, assuming the volume is measured in some cubic units)

Explanation:

Step1: Recall the range of cosine function

The range of $y = \cos(x)$ is $[- 1,1]$.

Step2: Find the minimum of the given function

For $V(t)=450\cos(\frac{\pi}{4}(t - 0.5))+1650$, when $\cos(\frac{\pi}{4}(t - 0.5))=-1$, we have $V(t)=450\times(-1)+1650$.

Step3: Calculate the minimum value

$V(t)=-450 + 1650=1200$. In the context of the problem, since $V$ represents the volume of air in a person's lungs, 1200 represents the minimum volume of air in the person's lungs (the units of volume are not specified in the problem, but it would be in cubic - units of some kind).