The temperature of a cup of coffee varies according to Newton's Law of Cooling: dT dt equals negative k times the quantity T minus A, where T is the temperature of the coffee, A is the room temperature, and k is a positive constant. If the coffee cools from 100°C to 90°C in 1 minute at a room temperature of 25°C, find the temperature, to the nearest degree Celsius of the coffee after 4 minutes. 74
67
60
42

  (b)  67

Step-by-step explanation:

A solution to the differential equation describing the temperature according to Newton's Law of Cooling could be written as ...

  T = (final temp) + (initial difference)×(decay factor)^t

where the decay factor is the fraction of change during 1 unit of time period t.

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Here, the initial difference of 100-25 = 75 degrees decays to 90-25 = 65 degrees in 1 minute. So, the units of t are minutes, the decay factor is 65/75, the initial difference is 75 degrees, and the final temperature is 25 degrees. That lets us write the equation as ...

  T = 25 +75(65/75)^t

Then for t=4, the temperature is ...

  T = 25 +75(13/15)^4 ≈ 67.3 . . . . degrees

After 4 minutes the temperature of the coffee is about 67 degrees.

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.

stethere all not eveanp-by-step explanation: