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Average rate

  • Thread starter fiziksfun
  • Start date
  • #1
78
0
the rate at which water is sprayed is given by the function f(t)

during the time interval 0<t<4, what is the average rate of water flow??

I'm confused whether to use the formula

f(4)-f(0) / (4-0)

OR

[tex]\frac{1}{4}[/tex][tex]\int[/tex]f(t) evaluated from 0 to 4.

help!!
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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Hi fiziksfun ! :smile:

Hint: Suppose f(t) is a constant, C. Then f(4) = f(0) = C.

So which formula is right? :smile:
 
  • #3
78
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i'm kind of slow, so i still don't understand :[
can you help me more??
 
  • #4
tiny-tim
Science Advisor
Homework Helper
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Sure! :smile:

If f(t) = C, a constant, then obviously the average of f(t) is C.

But f(4)-f(0) / (4-0) = (C - C)/4 = 0, which obviously is wrong. :frown:

And ∫f(t)/4 = ∫C/4 (evaluated from t = 0 to 4) = C, which equally obviously is right! :smile:

This works for any f(t), because f(t) is the rate of water, so ∫f(t) is the total water.

And so the average rate of water = total/time = ∫f(t)/4. :smile:
 
  • #5
78
0
ah, i think i understand, thank you!!!
 

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