A) The differential equation comes from the fact that the rate of temperature change is proportional to the difference in temperatures.

B) Find general solution by separating variables and integrating

:
C) Initial condition is t=0, T = 87

D) Total time elapsed is 10 minutes, new temperature is 84

solve for alpha

E) Temperature function is:

solving for t

Plug in T = 98.6

This is approximately 32 minutes before he arrived or about 1:20 AM
0.15(34) = x......with x representing what they will save
No. The sample size is too small to be reliable. If there were many bags of 500 candies that consistently showed a larger-than-marketed amount of green candy, that will be better proof.
These are the important trigonometric relations to base on:
cot (x) = 1/tan(x)
sec(x) = 1/cos(x)
csc(x) = 1/sin(x)
Following these properties, we could simplify the equation and input into the calculator to determine the exact value.
<span>tan40/cot50 = tan40/(1/tan50) = tan40tan50 = 1
</span><span>sec55/csc35 = (1/cos 55)/(1/sin 35) = sin35/cos55 = 1</span>