Find and show all work for:
a) When the temperature is the hottest.
b) What the temperature is.
Thank you in advance for your help. I certainly do appreciate it!
2007-06-22 08:53:04 · 3 answers · asked by Smarty Pants 2 in Science & Mathematics ➔ Mathematics
Find time of the maximum temperature by finding the zeros of the first derivative of T(t).
T(t) = - 0.5t^2 + 30t^1 + 75
T'(t) = 2(-0.5)t^(2-1) + 1(30)t^(1-1) + 0
T'(t) = -t + 30
T'(t) = 0
-t + 30 = 0
-t = -30
t = 30 minutes
T(30) = -0.5(30)^2 + 30(30) + 75
T(30) = -450 + 900 + 75
T(30) = 525 degrees
Answer: At time t = 30 minutes, the kiln is at its highest temperature of T(30) = 525 degrees.
2007-06-22 09:20:43 · answer #1 · answered by mathjoe 3 · 0⤊ 0⤋
Taking the derivative
T´=-t+30 =0 so the hottest temp.is attained after 30 min and is
T(30) = -0.5*900 +900 +75 = 525 degrees
2007-06-22 16:08:40 · answer #2 · answered by santmann2002 7 · 0⤊ 0⤋
Graph this equation on a calculator w/ T(t) = y and t = x. There will be a maximum in the output. That is the hottest temperature it will reach. (Sorry, I dont have a graphing calculator)...
2007-06-22 16:00:22 · answer #3 · answered by miggitymaggz 5 · 0⤊ 0⤋