The temperature of the ice cream 2 hours after it was placed in the freezer is 37.40 °C
From Newton's law of cooling, we have that
Where
From the question,
∴
Therefore, the equation becomes
Also, from the question
After 1 hour, the temperature of the ice-cream base has decreased to 58°C.
That is,
At time ,
Then, we can write that
Then, we get
Now, solve for
First collect like terms
Then,
Now, take the natural log of both sides
This is the value of the constant
Now, for the temperature of the ice cream 2 hours after it was placed in the freezer, that is, at
From
Then
Hence, the temperature of the ice cream 2 hours after it was placed in the freezer is 37.40 °C
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<h3>Answer:</h3>
±12 (two answers)
<h3>Explanation:</h3>
Suppose one root is <em>a</em>. Then the other root will be -3<em>a</em>. The product of the two roots is the ratio of the constant coefficient to the leading coefficient:
(<em>a</em>)(-3<em>a</em>) = -27/4
<em>a</em>² = -27/(4·(-3)) = 9/4
<em>a</em> = ±√(9/4) = ±3/2
Then the other root is
-3<em>a</em> = -3(±3/2) = ±9/2 . . . . . . the roots will have opposite signs
We know the opposite of the sum of these roots will be the ratio of the linear term coefficient to the leading coefficient: b/4, so ...
-(a + (-3a)) = b/4
2a = b/4
b = 8a = 8·(±3/2)
b = ±12
_____
<em>Check</em>
For b = 12, the equation factors as ...
4x² +12x -27 = (2x -3)(2x +9) = 0
It has roots -9/2 and +3/2, the ratio of which is -3.
For b = -12, the equation factors as ...
4x² -12x -27 = (2x +3)(2x -9) = 0
It has roots 9/2 and -3/2, the ratio of which is -3.