Answer:
See explanations below
Step-by-step explanation:
Given the quadratic formula that expresses the temperature of a chemical reaction
C(t)=-12t² +8t +93
Given that C(t) = 110°, we are to find the value of t
Substitute
110 = -12t² +8t +93
-12t² +8t +93-110 = 0
-12t² +8t -17 = 0
12t² -8t + 17 = 0
Using the general formula;
t = -(-8)±√(-8)²-4(12)(17)/2(12)
t = 8±√64-816/24
t = 8±√-752/24
Since the value of t will give a complex number, hence the time doesn't exist when the reaction reaches 110°C
The temperature of the chemical does not reach 110°C
The equation is given as:
[tex]C(t)=-12t\² +8t +93[/tex]
When the reaction reaches 110 degrees, it means that:
C(t) = 110
So, we have:
[tex]110=-12t\² +8t +93[/tex]
Subtract 110 from both sides
[tex]0=-12t\² +8t +93 -110[/tex]
[tex]0=-12t\² +8t-17[/tex]
Rewrite the equation as:
[tex]12t\² -8t+17 = 0[/tex]
Using the quadratic formula, we have:
[tex]t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
So, we have:
[tex]t = \frac{-(-8) \pm \sqrt{(-8)\²-4(12)(17)}}{2(12)}[/tex]
[tex]t = \frac{-(-8) \pm \sqrt{-752}}{24}[/tex]
The square root of -752 is a complex number.
This means that, the equation does not have any solution when C(t) = 110
Hence, the temperature of the chemical does not reach 110°C
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