#$&*
course Mth 271
10/3 930pThis is the quiz after week 2 quiz 2.
The depth of water in a certain uniform cylinder is given by the depth vs. clock time function y = .019 t2 + -1.2 t + 50.
What is the average rate at which depth changes between clock times t = 7.4 and t = 14.8?
y=.019(7.4)^2-1.2(7.4)+50
1.04044-8.88+50
= 42.16044
y=.019(14.8)^2-1.2(14.8)+50
4.16176-17.76+50
= 36.40176
dy/dt = (42.16044-36.40176)/(7.4-14.8) = .7782
What is the clock time halfway between t = 7.4 and t = 14.8, and what is the rate of depth change at this instant?
14.8-7.4 = 7.4
2at+b = 2(.019)(7.4)+ - 1.2 = -.9188 rate of depth change at this instant
What function represents the rate r of depth change at clock time t?
2at+b
What is the value of this function at the clock time halfway between t = 7.4 and t = 14.8?
@&
Good, but 7.4 is not halfway between 7.4 and 14.8.
How do you find a number halfway between two given numbers?
*@
-.9188
If the rate of depth change is given by dy/dt = .25 t + -1.5 then how much depth change will there be between clock times t = 7.4 and t = 14.8?
.25(7.4)-1.5=1.85-1.5 = .35
@&
This is the rate of depth change at t = 7.4.
How are the average rate of depth change, the time interval and change in depth related?
How would you use this relationship to find the depth change?
*@
Give the function that represents the depth.
y=at^2+bt=c
Give the specific function corresponding to depth 190 at clock time t = 0.
190 = 2at + 190
"
#$&*
@&
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?
*@
@&
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. &#
*@