The amount of oxygen in an adult male’s lungs is measured during a deep breathing experiment. The data is recorded starting after the male has fully exhaled. The graph below gives the volume in liters, y, of oxygen in the male’s lungs x seconds after the experiment began. Point M is a minimum value of the function. What is the equation of a cosine function, using radians, that gives the volume as a function of time?

Enter your numbers in the boxes to complete the equation.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

graph b

step-by-step explanation:

one solution- graph a (clear intercepting point.)

no solution- graph b (they're parallel, there will never be a point of interception.)

infinite solutions- graph c (all points intercept.)

answer: $1794

step-by-step explanation: