An audiometer produces a pure tone with a frequency f of 1200 hertz (cycles per second). The maximum pressure P produced from the pure tone is 5 millipascals. Write a sine model that gives the pressure P as a function of the time t (in seconds). Assume P=0 when t=0.

Pressure(t) = 5mP*sin(191.08*t)

Step-by-step explanation:

The information we have:

Maximum pressure P = 5 mP

frequency = 1200Hz

Period = 1/frequency = (1/1200) seconds

when t = 0, P = 0, so we should use a sin function (because sin(0) = 0)

Then we can write this as:

Pressure(t) = P*sin(c*t)

where t is time in secnds, P is the maximum pressure 5mP, and c is a constant that depends on the period.

Pressure(t) = 5*sin(c*t)

knowing that the period is 1/1200 seconds, we have that:

c*1/1200 s = 2*3.14

c = 1200/(2*3.14) 1/s= 600/3.14 1/s

Our function is

Pressure(t) = 5mP*sin(191.08*t)

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be