During a regular respiratory cycle, the volume of air in liters in the human lungs can be described by the function V(t) = 0.173t + 0.152t2 - 0.035t3, where t is the time in seconds.
a. Estimate the real zeros of the function by graphing.
b. About how long does a regular respiratory cycle last?
c. Estimates the time in seconds from the beginning of this respiratory cycle for the lungs to fill to
their maximum volume of air.

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step-by-step explanation:

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7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west