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Phoenix [80]
2 years ago
12

Water is flowing into and out of a small reservoir. The total amount of water can be modeled by R, where R(t)=20-15sint^2/25 cub

ic feet, t is measured in hours and 0
Mathematics
1 answer:
cestrela7 [59]2 years ago
8 0

9514 1404 393

Answer:

  a) about -1.03 cubic feet per hour

  b) R'(t) = -6/5t·cos(t^2/25); the rate of flow into the reservoir

  c) 0.859 and 5.972 hours

  d) 9.838 hours

Step-by-step explanation:

The rest of the problem statement is in the first attachment. See the second attachment for the graphing calculator input/output.

a) The average rate of change on the interval [0, 8] is ...

  (R(8) -R(0))/(8 -0) ≈ -1.03004 . . . cubic feet per hour

__

b) The derivative can be found using the chain rule.

  R'(t) = -15(2t/25)cos(t^2/25)

  R'(t) = -6/5t·cos(t^2/25)

The derivative of the volume is the rate of change of volume, that is, the flow rate into the reservoir.

__

c) To find the time values when R' = 'average rate of change', we defined the constant a1 to be that average rate of change. The graphing calculator shows the curve R'(t)-a1, which has zeros at the times of interest. The times for which the instantaneous rate of change equals the average rate of change are t = 0.859 and t = 5.972 hours.

__

d) The time of interest is beyond the domain of the function. We cannot use the given function to determine the time of interest.

However, if we extend the domain to include the time of interest, we find it is t = 9.838 hours.

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5 0
3 years ago
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Please help me ......
timama [110]
For the first problem, when you see expression like that it just means to write it twice, then FOIL it.
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If you don't know what FOIL is let me know and I can further explain it!

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3 0
3 years ago
3. Laura walks 3/5 mile to school each day. Isaiah walk to school is 3 times as long as Laura's. Howfar does Isaiah walk to scho
Finger [1]
Lets write down what we know...

Laura walks 3/5 mile to school everyday

Laura=3/5mile

Isaiah's walk is 3 times as long as Lauras, so

Isaiah=Laura*3

We know how far Lauras walk is so we can solve for Isaiah's walk

Isaiah=3/5*3 (or Isaiah=3/5+3/5+3/5 if thats easier for you to solve for)
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9/5=

To solve for this, we have to find out how many times 5 can go into 9. 5 goes into 9 one time with a remainder of 4, so we can write the mixed number as.

9/5= 1 4/5

Isaiah walks 9/5miles or 1 4/5 miles. Both are correct.
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3 years ago
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