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course Mth 271
resubmission of week 2 quiz 110/8 7p
The depth of water in a certain uniform cylinder is given by the depth vs. clock time function y = .019 t2 + -1.2 t + 50.
What is the average rate at which depth changes between clock times t = 7.4 and t = 14.8?
y=.019(7.4)^2-1.2(7.4)+50
1.04044-8.88+50
= 42.16044
y=.019(14.8)^2-1.2(14.8)+50
4.16176-17.76+50
= 36.40176
dy/dt = (42.16044-36.40176)/(7.4-14.8) = .7782
What is the clock time halfway between t = 7.4 and t = 14.8, and what is the rate of depth change at this instant?
14.8-7.4 = 7.4
2at+b = 2(.019)(7.4)+ - 1.2 = -.9188 rate of depth change at this instant
What function represents the rate r of depth change at clock time t?
2at+b
What is the value of this function at the clock time halfway between t = 7.4 and t = 14.8?
-.9188
If the rate of depth change is given by dy/dt = .25 t + -1.5 then how much depth change will there be between clock times t = 7.4 and t = 14.8?
.25(7.4)-1.5=1.85-1.5 = .35
Give the function that represents the depth.
y=at^2+bt=c
Give the specific function corresponding to depth 190 at clock time t = 0.
190 = 2at + 190
course Mth 271
10/3 930pThis is the quiz after week 2 quiz 2.
The depth of water in a certain uniform cylinder is given by the depth vs. clock time function y = .019 t2 + -1.2 t + 50.
What is the average rate at which depth changes between clock times t = 7.4 and t = 14.8?
y=.019(7.4)^2-1.2(7.4)+50
1.04044-8.88+50
= 42.16044
y=.019(14.8)^2-1.2(14.8)+50
4.16176-17.76+50
= 36.40176
dy/dt = (42.16044-36.40176)/(7.4-14.8) = .7782
What is the clock time halfway between t = 7.4 and t = 14.8, and what is the rate of depth change at this instant?
14.8-7.4 = 7.4
2at+b = 2(.019)(7.4)+ - 1.2 = -.9188 rate of depth change at this instant
What function represents the rate r of depth change at clock time t?
2at+b
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& revisions start here &&&&&&&&&&&&&&
What is the value of this function at the clock time halfway between t = 7.4 and t = 14.8?
&&&& 2at+b = 2(.019)(11.1) + -1.2 = -.7782 &&&&&
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Good, but 7.4 is not halfway between 7.4 and 14.8.
&&&& 14.8-7.4 = 7.4 7.4/2 = 3.7 7.4 +3.7 = 11.1 &&&&
How do you find a number halfway between two given numbers
&&&& Find the difference between the numbers, divide by 2 and add the result to the first number&&&&
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-.9188
If the rate of depth change is given by dy/dt = .25 t + -1.5 then how much depth change will there be between clock times t = 7.4 and t = 14.8?
.25(7.4)-1.5=1.85-1.5 = .35
&&&& .25(14.8) -1.5 = 2.2 .35-2.2 -1.85 depth change &&&&
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2.2 is a rate of depth change.
The change in the rate of depth change is -1.85, but that is not the depth change.
How do you use time interval and rate of depth change to get the change in depth?
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This is the rate of depth change at t = 7.4.
How are the average rate of depth change, the time interval and change in depth related?
&&&& Time interval and change in depth are both used to compute the average rate of depth change.&&&&
How would you use this relationship to find the depth change?
&&&& see preceding q. &&&&
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Give the function that represents the depth.
y=at^2+bt=c
Give the specific function corresponding to depth 190 at clock time t = 0.
190 = 2at + 190
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#$&*
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If the function that represents depth is y = a t^2 + b t + c, then the function that represents the rate of depth change is dy/dt = 2 a t + b.
The rate of depth change is dy/dt = .25 t - 1.5.
What specifically does this tell you about the depth function?
&&&& It is the derivative of the average rate of depth change &&&&
@&
That is so, but what does the derivative tell you about the function?
I'll answer this for you. The derivative tells you the rate of change, as indicated above.
So if you evaluate the derivative for t = 11.1 the result should be close to the average rate of change you got previously.
Check it out and see whether it is so.
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You did pretty well on the first series of questions.
You'll need to clarify your thinking a bit on the last series. Hopefully my notes will help.
&#Please see my notes and submit a copy of this document with revisions, comments and/or questions, and mark your insertions with &&&& (please mark each insertion at the beginning and at the end).
Be sure to include the entire document, including my notes.
&#
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"
Self-critique (if necessary):
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Self-critique rating:
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Good progress, but there are still a couple of issues.
Please submit another revision using #### to mark insertions.
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