#$&*
course Mth 271
I hope this is an improvement compared to the previous quiz, since the problems are similar. I didn't get the chance to send back the corrections to the quiz 1, so this quiz in a way is the correction of the previous one.
If the function y = .028 t2 + -1.3 t + 61 represents depth y vs. clock time t, then what is the average rate of depth change between clock time t = 6.7 and clock time t = 13.4? What is the rate of depth change at the clock time halfway between t = 6.7 and t = 13.4?Y1 = 0.028 * 6.7^2 - 1.3 * 6.7 + 61 = 53.55
Y2 = 0.028 * 13.4^2 - 1.3 * 13.4 + 61 = 48.6
(6.7, 53.55) , (13.4, 48.6)
r = (48.6 - 53.55) / (13.4 - 6.7) = -4.95 / 6.7 = - 0.74
What function represents the rate r of depth change at clock time t? What is the clock time halfway between t = 6.7 and t = 13.4, and what is the rate of depth change at this instant?
y (t) = 2 * 0.028 t- 1.3
y (t) = 0.056 t - 1.3
6.7 + ((13.4 - 6.7)/2) = 6.7 + 3.35 = 10.05
y ( 10.05) = 0.056 * 10.05 - 1.3 = -0.712
@& Your method is fine. Arithmetic might be off in one calculation or the other. The midpoint rate and the average rate for the interval should be equal. Your results don't differ by much, but they do differ.
Nothing to worry about, though. As I said, the method is fine.*@
If the function r(t) = .289 t + -2.7 represents the rate at which depth is changing at clock time t, then how much depth change will there be between clock times t = 6.7 and t = 13.4?
(0.14 * 13.4^2 - 2.7 * 13.4 + c) - (0.14 * 6.7^2 - 2.7* 6.7 + c) = -11.04 +c + 11.8 - c = 0.76
@& Good.
You would have obtained the same result by finding the rate at each clock time, averaging them to get an average rate, and multiplying by the time interval to get the change in depth.
Be sure you understand this as well.*@
* What function represents the depth?
y (t) = 0.289/2 t^2 +-2.7t + c
y(t) = 0.14 t^2 - 2.7t + c
* What would this function be if it was known that at clock time t = 0 the depth is 200 ?
y (t) = 0.14 t^2 - 2.7t + 200
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Self-critique (if necessary):
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Self-critique rating:
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#$&*
@& Nice work. See my notes and let me know if you have questions.*@