HELP QUICK 10 POINTS!!!!!!
1 answer:
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The information provided is that you have smaller cubes that measure 1 cm on either of the three sides. In order words if you lie each cube side by side you would have the length/width/height of the indicate sides.
For a cube made up of 27 smaller cubes, you can determine the length of each side by factoring the entire size provided. That means for a cube made up of 27 smaller cubes you would have;
This means you would have 3 smaller cubes on the length, 3 smaller cubes on the width and 3 smaller cubes on the height.
Therefore, if you now have 150 of the smaller cubes, by factoring this you would have the following possibility;
This means you would have one side (length) 6 cubes, on another side (width) 5 cubes and on the third side (height) 5 cubes.
That means with 150 smaller cubes you could make a cube with the dimensions,
ANSWER:
The largest big cube you could make would be a 6 cm by 5 cm by 5cm big cube
Answer:
Newton's law of cooling says that:
T(t) = Tₐ + (T₀ - Tₐ)*e^(k*t)
or:
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: