Assume that the volume of air in an average adult’s lung follows a transformed sine
function, as function of time t in seconds,
V (t) = A + B sin(ωt)
Below is a table of measurements of the volume. Identify constants A, B, and ω so
that the function above fits these measurements. After 12 seconds, the measurements
will repeat.
t 0 3 6 9 12
V (t) 7 9 7 5 7

A = 7

B = 2

ω = π/6

Full Equation: V(t) = 7 + 2sin((π/6)t)

Step-by-step explanation:

For this question, you simply have to acquire all the information necessary in order to construct a sine equation. You can easily do this by looking at your table of values (I would recommend graphing it for a visual aid).

From there you can observe that the graph is shifted up by 7 units (here is where we get the A value of 7).

The amplitude of the graph is 2 units (we can see this by comparing the highest point of the graph to its horizontal center line).

Finally, the period of the graph is obtained by setting 2π/ω equal to 12 (12 being the time it takes for the graph to do a full period). Here we get a value of π/6.

the solution is h=10 because you add 9 to each side of the equation.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)