The number of seconds to complete a chemical reaction was determined to be given by the equation 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 (T) when the reaction was complete in 200 seconds (s=200), we can substitute s=200 into the given equation:
200 = 250 - 5T - T^2
Rearranging the equation to standard form:
T^2 + 5T - 50 = 0
Now, we can solve this quadratic equation by factoring or using the quadratic formula:
T^2 + 10T - 5T - 50 = 0
T(T + 10) - 5(T + 10) = 0
(T - 5)(T + 10) = 0
So, T = 5 or T = -10
Since temperature cannot be negative, the temperature at which the reaction occurred is 5 degrees Celsius.