# Math Help - SOme help needed thx

1. ## SOme help needed thx

Hi there,

Ok now this problem is

A piston in a large factory engine moves up and down in a cylinder. The height H centimetres of the piston at T seconds is given by the formula H=120sin pi T + 200

A)State the aplitude and period?
B)what are the maximum and minimum height of the piston ?
C)how many complete cycles does the piston make in 30mins?

The volume of air in the lungs can be modelled by a sinusoidal wave.

A) The volume of air in the lungs varies from 1000ML to 5000ML over a period of 6s. Determine an equation for the volume of air over time.

B)Use the equation to determine the amount of air in the lungs at

i)1.5s
ii)4.6s

I answered all my other questions and these questions seems to be giving me grief haha

2. Originally Posted by jamster
Hi there,

Ok now this problem is

A piston in a large factory engine moves up and down in a cylinder. The height H centimetres of the piston at T seconds is given by the formula H=120sin pi T + 200

A)State the aplitude and period?
B)what are the maximum and minimum height of the piston ?
C)how many complete cycles does the piston make in 30mins?
clarify: the formula is $H = 120 \sin \left( \pi T \right) + 200$?

if so, the amplitude is the absolute value of the coefficient of the sine part of the function.

period: the formula for the period gives the period as $\frac {2 \pi}{\pi} = 2$

the max occurs when the sine function has a value of 1 and the minimum occurs when it has a value of -1. do you see why?

for the complete cycles it makes, we need to find for what t does it make one revolution, and multiply that by 30.

3. Originally Posted by jamster
The volume of air in the lungs can be modelled by a sinusoidal wave.

A) The volume of air in the lungs varies from 1000ML to 5000ML over a period of 6s. Determine an equation for the volume of air over time.

B)Use the equation to determine the amount of air in the lungs at

i)1.5s
ii)4.6s
for $y = a \sin k (x - b) + c$

the amplitude is: $|a|$
the period is: $\frac {2 \pi}{|k|}$
the phase (horizontal) shift is: $b$
the vertical shift is: $c$

now, were those the formulas you sued to answer the question? just plug in the corresponding values to get the function. once you have the function, you can calculate anything they ask you to