8. A colony of bacteria has a total weight which varies according to w(t) = 10.5e-5t (weight in Newtons, time in hours). Find the average weight of the colony over the interval [1,3] and find a value c in [1,3] such that w(c) attains this average.

Q: 324y/" – 180y' + 25y = 0, %3D y(0) = 8, y'(0) = 5. y =

A:

Q: 2. The figure below shows the graph of a function k(x) and its tangent line at a point (a, 2). The…

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Q: Water is being pumped into a 10 m-diameter tank at the rate of 1 m³/min. At the same time, water…

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Q: Find y as a function of t if 25y"- 70y' + 53y = 0, and y(5) = 8, y'(5) = 1. %3D y = %3D

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Q: 8.) For this problem, include any derivatives you compute. The position of a particle moving along…

A: Since you have asked multiple sub parts in a single request so we will be answering only first three…

Q: Differentiate the following function.   r(t)=(t e^-t,5tln t,t sin t)

A: