Scientists believe that the average temperatures at various places on earth vary from cooler to warmer over thousands of years. at one place on earth, the highest average temperature is 800 and the lowest is 600 . suppose it takes 20,000 years to go from the high to low average and the average temperature was at a high point of 800 in year 2000. set up a sinusoidal function t t( ) (where t is time in years) to model this phenomenon.

T (t) = A x cos (2π/40000 x (t - 2000) +π/2)

Explanation:

From the question given, we recall the following,

The co-sinusoidal equation formation is denoted  as:

T (t) = A x cos (2π/p (t - t₀))

At one place on earth the highest temperature = 800

At one place on earth  The lowest temperature = 600

A: represents the wave amplitude, if the max and min are both = 800 and 600  respectively.

Thus,

2 x A = maximum -minimum = 200,

A = 100

P: Represents the wave period

Now suppose it takes 20,000 years to go from the high to the low average

Then,

P/2=20000, P=40000

t₀: Represents  the time at the time of a maximum. t₀=2000

The Relationship  between cos and sin is:

cos (α)= sin ( α + π/2)

In the cosinus equation, all the values are replaced.

Therefore,

We have, T (t) = A x cos (2π/40000 x (t - 2000) +π/2)

work: w = fd (given)

work done by chet   =50*1 = 50 j

work done by mika =40*2 = 80 j

work done by sara =30*1.5 = 45 j

work done by bill =60*0.5 = 30 j

students in order from the greatest amount of work done to the least is mika> chet> sara> bill

hence option (b) is correct.

answer: the exterior temperature of commercial jet planes as they leave the stratosphere and return to the ground increases steadily.

explanation:

the lower most layer of atmosphere is troposphere which extends from 0 to 12 km above the surface of the earth. the temperature initially decreases as distance is increased from the earth's surface. commercial jets fly in lower part of the stratosphere. the stratosphere extends upto 50 km. the temperature in stratosphere starts rising again due to presence of ozone which traps the uv rays.

thus, when the planes leave the stratosphere and return to the ground, the exterior temperature increases steadily.