Question

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?

Answer 1

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.