5x + 6y = 32

Mathematics

1 answer:

velikii [3]3 years ago

3 0

Answer:

The variable y is eliminated.

Step-by-step explanation:

To add a system of equations, we add the common terms. x with x, y with y and values with values.

In this question:

5x + 6y = 32

5x – 6y = 8

Adding:

5x + 5x + 6y - 6y = 32 + 8

10x = 40

So the variable y is eliminated.

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The temperature of a cup of coffee varies according to Newton's Law of Cooling: dT dt equals negative k times the quantity T min

denis23 [38]

Answer:

(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.

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.