course Mth 174 I was wondering if you could send me the grades for Test #1 and Test #2. ??P??~??{~????assignment #012
......!!!!!!!!...................................
15:17:35 Query problem 9.2.8 (3d editin 9.1.6) (was 9.4.6) first term and ratio for y^2 + y^3 + y^4 + ...
......!!!!!!!!...................................
RESPONSE --> The first term is y^2 It is geometric The ratio is n*y y^2*y = y^3 y^3*y = y^4...
.................................................
......!!!!!!!!...................................
15:18:15 either explain why the series is not geometric or give its first term and common ratio
......!!!!!!!!...................................
RESPONSE --> Its first term is y^2 The ratio is a * y
.................................................
......!!!!!!!!...................................
15:20:13 how do you get the common ratio?
......!!!!!!!!...................................
RESPONSE --> I am not sure on a proven system, maybe i missed it in the text. But I just looked at the pattern and found a ratio.
.................................................
......!!!!!!!!...................................
15:21:44 what do you get when you factor out y^2? How does this help you determine the first term?
......!!!!!!!!...................................
RESPONSE --> When I factor out y^2 I get y^2(1 + y + y^2 + y^3...) I just though the first term was the term to the far left of the series (implying there is not a ... preceding the first term).
.................................................
......!!!!!!!!...................................
15:24:36 Query problem 9.2.29 (3d edition 9.1.24) (was 9.4.24) bouncing ball 3/4 ht ratio
......!!!!!!!!...................................
RESPONSE -->
.................................................
......!!!!!!!!...................................
15:43:33 how do you verify that the ball stops bouncing after 1/4 `sqrt(10) + 1/2 `sqrt(10) `sqrt(3/2) (1 / (1-`sqrt(3/4)) sec?
......!!!!!!!!...................................
RESPONSE -->
.................................................
......!!!!!!!!...................................
15:43:35 What geometric series gives the time and how does this geometric series yield the above result?
......!!!!!!!!...................................
RESPONSE -->
.................................................
......!!!!!!!!...................................
15:43:37 How far does the ball travel on the nth bounce?
......!!!!!!!!...................................
RESPONSE -->
.................................................
......!!!!!!!!...................................
15:43:53 How long does it takes a ball to complete the nth bounce?
......!!!!!!!!...................................
RESPONSE -->
.................................................
......!!!!!!!!...................................
15:43:56 Query 9.2.21 (was p 481 #6) convergence of 1 + 1/5 + 1/9 + 1/13 + ...
......!!!!!!!!...................................
RESPONSE -->
.................................................
......!!!!!!!!...................................
15:43:58 with what integral need you compare the sequence and did it converged or diverge?
......!!!!!!!!...................................
RESPONSE -->
.................................................
......!!!!!!!!...................................
15:44:00 Explain in terms of a graph how you set up rectangles to represent the series, and how you oriented these rectangles with respect to the graph of your function in order to prove your result.
......!!!!!!!!...................................
RESPONSE -->
.................................................
?F???????h???b?assignment #012 ??????????? Physics II 07-19-2008
......!!!!!!!!...................................
17:27:57 Query problem 9.2.8 (3d editin 9.1.6) (was 9.4.6) first term and ratio for y^2 + y^3 + y^4 + ...
......!!!!!!!!...................................
RESPONSE -->
.................................................
......!!!!!!!!...................................
17:28:46 either explain why the series is not geometric or give its first term and common ratio
......!!!!!!!!...................................
RESPONSE --> It is geometric. The first term is y^2. The ratio is a * y. y^2 * y = y^3 y^3 * y = y^4...
.................................................
......!!!!!!!!...................................
17:29:12 how do you get the common ratio?
......!!!!!!!!...................................
RESPONSE --> y^3 / y^2 = y
.................................................
......!!!!!!!!...................................
17:30:12 what do you get when you factor out y^2? How does this help you determine the first term?
......!!!!!!!!...................................
RESPONSE --> When I factor out y^2: y^2(1 + y + y^2...) I do not know how this would help me find the first term. I would just think the first term would be on the far left, as long as its not preceded by ...
.................................................
......!!!!!!!!...................................
17:30:15 Query problem 9.2.29 (3d edition 9.1.24) (was 9.4.24) bouncing ball 3/4 ht ratio
......!!!!!!!!...................................
RESPONSE -->
.................................................
......!!!!!!!!...................................
17:36:04 how do you verify that the ball stops bouncing after 1/4 `sqrt(10) + 1/2 `sqrt(10) `sqrt(3/2) (1 / (1-`sqrt(3/4)) sec?
......!!!!!!!!...................................
RESPONSE --> I am not sure if this is correct, but this is what I figured. If it falls at 32 ft/sec^2, then it falls at a velocity of 32(t) ft/sec, which is a displacement function of 16(t)^2. When t = (1/4)sqrt(h), h = 0 16[(1/4)(sqrt(h))]^2 = h = (16)(1/16)(h) = h Once again not real sure what this concludes, but I will look at your notes.
.................................................
......!!!!!!!!...................................
17:45:27 What geometric series gives the time and how does this geometric series yield the above result?
......!!!!!!!!...................................
RESPONSE --> Since it reaches the ground in 1/4 sqrt(h) seconds I used this as my geometric series for time. Not sure about this answer, but it was all I could come up with. (1/4)sqrt(h), I plugged in the series of h, (1/4)sqrt[10(3/4)(1-(3/4) ^ n) / (1-(3/4)] I experimented with this and came out with rediculous results, so I do not think it is correct.
.................................................
......!!!!!!!!...................................
17:46:28 How far does the ball travel on the nth bounce?
......!!!!!!!!...................................
RESPONSE --> S of n bounces = (10(3/4)(1 - (3/4)^n)) / (1 - (3/4))
.................................................
......!!!!!!!!...................................
17:48:15 How long does it takes a ball to complete the nth bounce?
......!!!!!!!!...................................
RESPONSE --> I did not understand the questions on the geometric series involving time so I did not have any idea on this one. But question 29 part b) asks to show that the ball stops bouncing after approx. 11 seconds, so I would guess 11 seconds.
.................................................
......!!!!!!!!...................................
17:50:23 Query 9.2.21 (was p 481 #6) convergence of 1 + 1/5 + 1/9 + 1/13 + ...
......!!!!!!!!...................................
RESPONSE -->
.................................................
......!!!!!!!!...................................
18:00:26 with what integral need you compare the sequence and did it converged or diverge?
......!!!!!!!!...................................
RESPONSE --> The sequence did converge. But I do not full understand the comparing to integrals part of this chapter. Are there any other examples I could look at?
.................................................
......!!!!!!!!...................................
18:08:07 Explain in terms of a graph how you set up rectangles to represent the series, and how you oriented these rectangles with respect to the graph of your function in order to prove your result.
......!!!!!!!!...................................
RESPONSE --> My y axis was the values themselves. For example, my first y coordinate was (1/3)^1, my second was (1/3)^2. My graph showed rectangles, the first having an Area of 1 * (1/3). My second rectangle had an area of (1/9) * 2. I didn't really know how to use this because section 9.3 didn't sink in very well.
.................................................
"