The temperature of a chemical reaction ranges between 20 degrees celsius and 160 degrees celsius. the temperature is at its lowest point when t = 0, and the reaction completes 1 cycle during an 8-hour period. what is a cosine function that models this reaction?

The cosine function that models this reaction is:

Step-by-step explanation:

The general cosine function has the following form

Where A is the amplitude: half the vertical distance between the highest peak and the lowest peak of the wave.

is the period: time it takes the wave to complete a cycle.

k is the vertical displacement.

The maximum temperature is 160 and the minimum is 20. Then the amplitude A is:

The reaction completes a cycle in 8 hours

Then the period is 8 hours.

Thus:

The function is:

when y is minumum therefore

So

Now we substitute in the function and solve for k

Finally

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

answer: the answer is e

step-by-step explanation: