1)Find the rate of change. Area of a square with respect to its side s when s =
ID: 2857843 • Letter: 1
Question
1)Find the rate of change.
Area of a square with respect to its side s when s = 8.
____ square units per increase
2) The temperature (in degrees C) of an object at time t (in minutes) is T(t) = (3/8)t2 15t + 190 for 0 t 20. At what rate is the object cooling at t = 10?
____ oC/min
3) The position of a particle moving in a straight line during a 10–second trip is s(t)= 2t2 3t + 5 cm. Find a time t at which the instantaneous velocity is equal to the average velocity for the entire trip beginning at t = 0.
Explanation / Answer
1) area of square A=s2
differentiate with respect to time t
dA/dt =2s ds/dt
given s =8
dA/dt =2*8 ds/dt
dA/dt =16 ds/dt
rate of change of area =16 ds/dt square units , where ds/dt is rate of increase of side length
2) T(t) = (3/8)t2 15t + 190
differentiate with respect to time t , d/dx xn =nxn-1
dT/dt = (3/8)2t2-1 15*1 + 0
dT/dt = (3/4)t 15
at t=10
dT/dt = (3/4)*10 15
dT/dt = -22.5
object cooling at 22.5o per minute at t =10
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