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Lera25 [3.4K]
3 years ago
15

When a person is breathing normally the amount of air in their lawns varies sinusoidally. When full Karen’s lungs hold 2.8 L of

air when empty her Lawrence hold 0.6 L of air her brother starts timing her breathing at T equals two seconds she has exhaled completely and at T equals five seconds she has completely inhaled. Create an equation for this
Mathematics
1 answer:
makkiz [27]3 years ago
7 0

Answer:

A(t) = 2.2\sin \frac{(t - 2)\pi }{6} + 0.6

Step-by-step explanation:

Let the function of quantity in the lung of air be A(t)

So A(t) \alpha \sin (\frac{t - \alpha }{k} )

so, A(t) = Amax sin t + b

A(t) = 2.8t⇒ max

A(t) = 0.6t ⇒ min

max value of A(t) occur when sin(t) = 1

and min value of A(t) = 0

So b = 0.6

and A(max) = 2.2

A(t) = 2.2\sin \frac{(t)}{k} + 0.6

at t = 2 sec volume of a is 0.6

So function reduce to

A(t) = 2.2\sin \frac{(t - 2)}{k} + 0.6

and t = 5 max value of volume is represent

so,

\sin \frac{t - \alpha }{k} = 1

\frac{t - 2}{k} = \frac{\pi }{2} when t = 5

\frac{6}{\pi } = k

so the equation becomes

A(t) = 2.2\sin \frac{(t - 2)\pi }{6} + 0.6

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