The equation of the line is:
y - 5 = 3/2 (x - 2)

Transforming the line into the slope intercept form:
y = 3x/2 - 3 + 5
y = 3x/2 + 2

The slope is 3/2 and the y-intercept is 2.

Plotting this on the graph can be done using these steps:
Locate the point (0,2) on the graph.
From (0,2), count 3 units up and 2 units to the left and indicate that point.
Finally, connect the two points and extend the line.

6 0

3 years ago

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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

natka813 [3]

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:

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

8 0

3 years ago