s=250−5T−T2
where s
is the number of seconds and T
is the temperature in degrees Celsius at which the reaction occurred. If a chemical reaction was complete in 200 seconds, what was the temperature at which the reaction occurred?
To find the temperature at which the reaction occurred, we need to solve for T in the equation:
s = 250 - 5T - T^2
Given that the reaction was complete in 200 seconds, we can substitute s = 200 into the equation:
200 = 250 - 5T - T^2
Rearranging the equation, we get:
T^2 + 5T - 50 = 0
This is a quadratic equation that can be solved using the quadratic formula:
T = (-5 ± sqrt(5^2 - 4*1*(-50)) / 2*1
T = (-5 ± sqrt(25 + 200)) / 2
T = (-5 ± sqrt(225)) / 2
T = (-5 ± 15) / 2
T can be either:
T = (-5 + 15) / 2 = 10 / 2 = 5
or
T = (-5 - 15) / 2 = -20 / 2 = -10
Since temperature cannot be negative, the temperature at which the reaction occurred is 5 degrees Celsius.