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luda_lava [24]
3 years ago
6

-5 + 4 on a number line

Mathematics
1 answer:
alexandr402 [8]3 years ago
7 0
-1 is the answer homie
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the temperature of a cup of coffee obeys newton's law of cooling. The initial temperature of the coffee is 150F and 1 minute lat
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Answer:

Newton's law of cooling says that:

T(t) = Tₐ + (T₀ - Tₐ)*e^(k*t)

or:

\frac{dT}{dt} = -k*(T - T_a)

in the differential form.

where:

T is the temperature as a function of time

Tₐ  is the ambient temperature, in this case, 70F

T₀ is the initial temperature of the object, in this case, 150F

k is a constant, and we want to find the value of k.

Then our equation is:

T = 70F + (150F - 70F)*e^(k*t)

Now we also know that after a minute, or 60 seconds, the temperature was 135F

then:

135F = 70F + (150F - 70F)*e^(k*60s)

We can solve this for k:

135F = 70F + 80F*e^(k*60s)

135F - 70F = 80F*e^(k*60s)

65F =  80F*e^(k*60s)

(65/80) = e^(k*60s)

Now we can apply the Ln(x) function to both sides to get:

Ln(65/80) = Ln(e^(k*60s))

Ln(65/80) = k*60s

Ln(65/80)/60s = k = -0.0035 s^-1

Then the differential equation is:

\frac{dT}{dt} = -0.0035 s^-1*(T - 70F)

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