url stringlengths 6 1.61k | fetch_time int64 1,368,856,904B 1,726,893,854B | content_mime_type stringclasses 3 values | warc_filename stringlengths 108 138 | warc_record_offset int32 9.6k 1.74B | warc_record_length int32 664 793k | text stringlengths 45 1.04M | token_count int32 22 711k | char_count int32 45 1.04M | metadata stringlengths 439 443 | score float64 2.52 5.09 | int_score int64 3 5 | crawl stringclasses 93 values | snapshot_type stringclasses 2 values | language stringclasses 1 value | language_score float64 0.06 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
https://nzmaths.co.nz/resource/netball-tournament | 1,621,035,374,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243991829.45/warc/CC-MAIN-20210514214157-20210515004157-00123.warc.gz | 450,449,906 | 10,490 | # The netball tournament
Achievement Objectives
NA2-1: Use simple additive strategies with whole numbers and fractions.
Student Activity
There are six netball teams in the local inter-school netball tournament.
During the tournament, they all need to play each other once.
How many matches will be played altogether?
Specific Learning Outcomes
Solve a problem by being systematic
Description of Mathematics
This problem requires students to make lists, be systematic, maintain a running addition total, eliminate possibilities and explain their results. (Some students may also identify the sequential pattern and devise a rule.)
The rule that comes from this problem (see Solution) is an example of a combination problem. Combination problems are one of several classes of counting problems that become more and more important in statistics as well as in certain branches of mathematics. At senior high school level, combinations are often needed in probability questions.
Required Resource Materials
Copymaster of the problem (English)
Copymaster of the problem (Māori)
6 students could represent the 6 teams and through systematic matching, eliminate all the possible combinations
Activity
### The Problem
There are six netball teams in the local inter-school netball tournament. During the tournament, they all need to play each other once. How many matches will be played altogether?
### Teaching Sequence
1. Invite students to talk about sports they play after school or at the weekend and where they play these.
2. Read the problem, talk about a tournament, and ask why it would be helpful to know how many games will be played e. g., this helps to determine how many courts are required, how tired the players might get, how long the tournament will last etc.
3. Ask students to estimate how many games will be played if each team plays each other once. List the estimations.
4. Ask 6 volunteers stand and represent the 6 netball teams. They can be numbered 1, 2, 3, 4, 5, 6 or given school names of sports’ teams. Have the students work out how many games team 1 (student 1) plays. This could be 'shown' by 1 shaking hands with each student representing the other teams who then sit down once they have been ‘played’. When 1 has shaken hands with each other student, ask thow many ‘games’ have been ‘played’. Then ask student 1 (team 1) to join the rest of the class. Ask the remaining volunteers to stand and repeat the process with student 2 (team 2) until the class see what is occurring.
5. Have the class continue the investigation in their own way and discuss possible strategies they might use e.g., act it out, drawing, making lists etc.
6. Have students share with the class their findings and show the process they used to ensure that every team had been played once. Discuss the different strategies used. Compare with initial estimation and evaluate the reason for the differences between the estimations and the result.
#### Extension
If another team joined the tournament, how many matches would be played?
What is the pattern for the number of games and can you find a rule?
#### Other Contexts for the Problem
Any sports’ team tournament.
Hand shaking at a party
### Solution
With 6 teams, 15 games would be played in total. Students could make lists, act it out, draw or systematically match teams in columns. For clarity of working it may help students to progressively list all the combinations starting with team 1 e.g.,
1 plays 2, 1 plays 3, 1 plays 4, 1 plays 5, 1 plays 6
2 plays 3, 2 plays 4, 2 plays 5, 2 plays 6
3 plays 4, 3 plays 5, 3 plays 6
4 plays 5, 4 plays 6
5 plays 6
Another way to look at this is to see that the each team has to play five others. Since there are 6 teams, at first glance it looks as if there are
6 x 5 = 30 games. But we know that there are only 15 games, so where did we go wrong? What happened is that we counted each game twice. For instance when 1 played 2, we counted that game once as one of the five that 1 played and once as one of the games that 2 played. Since we counted each game twice the final answer should be 30 ÷2 = 15. You might be able to see now that for 10 teams there would be (10 x 9)/ 2 = 45 games. You might now see how to develop a formula for any number of teams. | 984 | 4,280 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.53125 | 5 | CC-MAIN-2021-21 | longest | en | 0.952355 |
https://bettersheets.co/formulas/complex | 1,721,437,333,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514972.64/warc/CC-MAIN-20240719231533-20240720021533-00643.warc.gz | 116,646,144 | 8,078 | Formulas > =COMPLEX()
# How To Use COMPLEX() Function in Google Sheets
Description
Creates a complex number given real and imaginary coefficients.
Common questions about the COMPLEX formula include:
-What is the syntax of the formula?
-How do I use the formula?
-When should I use the formula?
The COMPLEX formula can be used to process multiple operations on the same data set in a single formula. It can also be used to assess data sets with multiple combined operations such as nesting functions or running several calculations on the same data set.
The COMPLEX formula can be mistyped if the syntax of the formula is not correct. Common errors include using incorrect brackets or data types, incorrect ranges or incorrect functions.
Common ways the COMPLEX formula is used inappropriately include using too many functions in a single formula, using unnecessary functions, or using the wrong syntax.
Common pitfalls when using the COMPLEX formula include incorrect brackets, typos, forgetting to enclose ranges in quotation marks, and incorrect order of operation.
Common mistakes when using the COMPLEX Formula include incorrect order of operations, incorrect data from linked cells, incorrect sum ranges or incorrect data formats.
Common misconceptions people might have with the COMPLEX Formula include not realizing that the formula can be used to process multiple operations on the same data set in a single formula, incorrectly assuming that the formula is limited to processing data from two cells, or not understanding the order of operations in which the formula executes.
How To Actually Use COMPLEX() in Sheets
COMPLEX(real_part, imaginary_part, [suffix])
Looking for a video tutorial? Members can email me anytime! Check out the blogs below for more info on this formula. Or generate your formula. Find more formulas here at BetterSheets.co/formulas
Google Sheets, COMPLEX, IMABS, IMARGUMENT, SQRT, SUMSQ, TRANSPOSE
This video shows the use of Google Sheets functions: COMPLEX, IMABS, IMARGUMENT, SQRT, SUMSQ, TRANSPOSE
Generate a COMPLEX() formula for your needs with AI
Whatever you need to do in sheets, you can generate a formula. Use the Better Sheets Formula generator to create a formula for any need. Completely free for members.
Asa
Looking for more help inside sheets get the free Add-on: Asa. Ask Sheets Anything. Go ahead, ask it any problem you migth have. Bring your own APIKEY and generate formulas inside of Google Sheets.
Better Sheets | 505 | 2,487 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2024-30 | latest | en | 0.82241 |
http://www.gregthatcher.com/Stocks/StockFourierAnalysisDetails.aspx?ticker=KOPN | 1,500,994,620,000,000,000 | text/html | crawl-data/CC-MAIN-2017-30/segments/1500549425254.88/warc/CC-MAIN-20170725142515-20170725162515-00022.warc.gz | 428,208,277 | 108,082 | Back to list of Stocks See Also: Seasonal Analysis of KOPNGenetic Algorithms Stock Portfolio Generator, and Fourier Calculator
# Fourier Analysis of KOPN (Kopin Corporation)
KOPN (Kopin Corporation) appears to have interesting cyclic behaviour every 92 weeks (1.9497*sine), 83 weeks (1.7748*sine), and 92 weeks (.6454*cosine).
KOPN (Kopin Corporation) has an average price of 5.86 (topmost row, frequency = 0).
Click on the checkboxes shown on the right to see how the various frequencies contribute to the graph. Look for large magnitude coefficients (sine or cosine), as these are associated with frequencies which contribute most to the associated stock plot. If you find a large magnitude coefficient which dramatically changes the graph, look at the associated "Period" in weeks, as you may have found a significant recurring cycle for the stock of interest.
## Fourier Analysis
Using data from 1/3/2000 to 7/17/2017 for KOPN (Kopin Corporation), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
05.86327 0
13.70387 1.77247 (1*2π)/916916 weeks
22.29737 2.16562 (2*2π)/916458 weeks
32.2418 1.96847 (3*2π)/916305 weeks
41.39548 2.09091 (4*2π)/916229 weeks
51.5218 1.80907 (5*2π)/916183 weeks
61.14054 1.69532 (6*2π)/916153 weeks
7.94473 1.38662 (7*2π)/916131 weeks
81.02618 1.06168 (8*2π)/916115 weeks
91.60504 1.51176 (9*2π)/916102 weeks
10.64544 1.94973 (10*2π)/91692 weeks
11.2666 1.77478 (11*2π)/91683 weeks
12-.00858 1.45027 (12*2π)/91676 weeks
13-.26818 1.52863 (13*2π)/91670 weeks
14-.19873 .98916 (14*2π)/91665 weeks
15-.25596 .97575 (15*2π)/91661 weeks
16-.28805 .79579 (16*2π)/91657 weeks
17-.31703 .59062 (17*2π)/91654 weeks
18-.06038 .47337 (18*2π)/91651 weeks
19-.03734 .66274 (19*2π)/91648 weeks
20-.04678 .46915 (20*2π)/91646 weeks
21-.06248 .52833 (21*2π)/91644 weeks
22-.03354 .47531 (22*2π)/91642 weeks
23-.15258 .46158 (23*2π)/91640 weeks
24-.07752 .31551 (24*2π)/91638 weeks
25.02847 .44127 (25*2π)/91637 weeks
26-.08419 .36472 (26*2π)/91635 weeks
27-.0596 .28762 (27*2π)/91634 weeks
28.09649 .42394 (28*2π)/91633 weeks
29.05646 .46431 (29*2π)/91632 weeks
30.00201 .35859 (30*2π)/91631 weeks
31.02552 .35664 (31*2π)/91630 weeks
32.05864 .23149 (32*2π)/91629 weeks
33.09143 .21365 (33*2π)/91628 weeks
34.22057 .33871 (34*2π)/91627 weeks
35.22251 .34909 (35*2π)/91626 weeks
36.19218 .49638 (36*2π)/91625 weeks
37.15012 .45056 (37*2π)/91625 weeks
38.03867 .5462 (38*2π)/91624 weeks
39-.0346 .60537 (39*2π)/91623 weeks
40-.16959 .53912 (40*2π)/91623 weeks
41-.2028 .36923 (41*2π)/91622 weeks
42-.16736 .31365 (42*2π)/91622 weeks
43-.11193 .22542 (43*2π)/91621 weeks
44-.04639 .14327 (44*2π)/91621 weeks
45-.00676 .29083 (45*2π)/91620 weeks
46-.02675 .22394 (46*2π)/91620 weeks
47.12242 .28372 (47*2π)/91619 weeks
48.04419 .38991 (48*2π)/91619 weeks
49-.02571 .41626 (49*2π)/91619 weeks
50-.0904 .34652 (50*2π)/91618 weeks
51-.09074 .31088 (51*2π)/91618 weeks
52-.0475 .23756 (52*2π)/91618 weeks
53-.01894 .29226 (53*2π)/91617 weeks
54-.01615 .32401 (54*2π)/91617 weeks
55-.00572 .38592 (55*2π)/91617 weeks
56-.06014 .40527 (56*2π)/91616 weeks
57-.17802 .44271 (57*2π)/91616 weeks
58-.24089 .34691 (58*2π)/91616 weeks
59-.25651 .30749 (59*2π)/91616 weeks
60-.2752 .23427 (60*2π)/91615 weeks
61-.21811 .18536 (61*2π)/91615 weeks
62-.29777 .17999 (62*2π)/91615 weeks
63-.2197 .1278 (63*2π)/91615 weeks
64-.21559 .0701 (64*2π)/91614 weeks
65-.10238 .07744 (65*2π)/91614 weeks
66-.10677 .08757 (66*2π)/91614 weeks
67-.08632 .14145 (67*2π)/91614 weeks
68-.17794 .14256 (68*2π)/91613 weeks
69-.22244 .14758 (69*2π)/91613 weeks
70-.21896 .02819 (70*2π)/91613 weeks
71-.26852 -.00306 (71*2π)/91613 weeks
72-.17353 .00745 (72*2π)/91613 weeks
73-.13724 -.0612 (73*2π)/91613 weeks
74-.07646 -.10972 (74*2π)/91612 weeks
75-.04706 -.0749 (75*2π)/91612 weeks
76-.02389 -.0511 (76*2π)/91612 weeks
77.04657 -.07612 (77*2π)/91612 weeks
78.11629 -.05449 (78*2π)/91612 weeks
79.14135 .03427 (79*2π)/91612 weeks
80.12397 .07838 (80*2π)/91611 weeks
81.05839 .12632 (81*2π)/91611 weeks
82.06357 .19199 (82*2π)/91611 weeks
83.00888 .19402 (83*2π)/91611 weeks
84-.02353 .16308 (84*2π)/91611 weeks
85-.01877 .10325 (85*2π)/91611 weeks
86.02145 .1077 (86*2π)/91611 weeks
87.02363 .23355 (87*2π)/91611 weeks
88-.09083 .21193 (88*2π)/91610 weeks
89-.07971 .15385 (89*2π)/91610 weeks
90-.10092 .17837 (90*2π)/91610 weeks
91-.14413 .13315 (91*2π)/91610 weeks
92-.12527 .14475 (92*2π)/91610 weeks
93-.16392 .12285 (93*2π)/91610 weeks
94-.22119 .05147 (94*2π)/91610 weeks
95-.14435 .00292 (95*2π)/91610 weeks
96-.11964 .01941 (96*2π)/91610 weeks
97-.11497 -.02942 (97*2π)/9169 weeks
98-.06929 -.06403 (98*2π)/9169 weeks
99-.05239 -.03672 (99*2π)/9169 weeks
100-.02376 -.02848 (100*2π)/9169 weeks
101.00676 -.00847 (101*2π)/9169 weeks
102-.00937 .00069 (102*2π)/9169 weeks
103-.00919 -.0188 (103*2π)/9169 weeks
104.0292 -.03686 (104*2π)/9169 weeks
105.02355 .0257 (105*2π)/9169 weeks
106.00245 .01001 (106*2π)/9169 weeks
107-.00977 .01818 (107*2π)/9169 weeks
108.04036 -.01573 (108*2π)/9168 weeks
109.06502 .02368 (109*2π)/9168 weeks
110.0846 .01433 (110*2π)/9168 weeks
111.06129 .0469 (111*2π)/9168 weeks
112.06763 .0564 (112*2π)/9168 weeks
113.05163 .07778 (113*2π)/9168 weeks
114.0643 .09668 (114*2π)/9168 weeks
115.0156 .11941 (115*2π)/9168 weeks
116.024 .12685 (116*2π)/9168 weeks
117.01785 .11616 (117*2π)/9168 weeks
118-.0139 .14857 (118*2π)/9168 weeks
119-.0029 .12174 (119*2π)/9168 weeks
120-.04463 .15849 (120*2π)/9168 weeks
121-.08217 .15166 (121*2π)/9168 weeks
122-.10337 .12622 (122*2π)/9168 weeks
123-.08321 .06603 (123*2π)/9167 weeks
124-.1158 .05641 (124*2π)/9167 weeks
125-.07428 .04306 (125*2π)/9167 weeks
126-.1013 .00687 (126*2π)/9167 weeks
127-.09087 .00136 (127*2π)/9167 weeks
128-.03153 -.00389 (128*2π)/9167 weeks
129.00654 .02299 (129*2π)/9167 weeks
130-.0309 .03098 (130*2π)/9167 weeks
131.00379 .03363 (131*2π)/9167 weeks
132-.04904 .0382 (132*2π)/9167 weeks
133-.01683 .02293 (133*2π)/9167 weeks
134-.00746 .01139 (134*2π)/9167 weeks
135.01541 .05336 (135*2π)/9167 weeks
136-.03699 .03881 (136*2π)/9167 weeks
137-.02621 .06632 (137*2π)/9167 weeks
138-.03289 .04158 (138*2π)/9167 weeks
139-.04131 .02961 (139*2π)/9167 weeks
140-.01335 .05154 (140*2π)/9167 weeks
141-.0679 .06787 (141*2π)/9166 weeks
142-.11522 .04103 (142*2π)/9166 weeks
143-.0955 -.00224 (143*2π)/9166 weeks
144-.07029 -.00641 (144*2π)/9166 weeks
145-.05376 -.02347 (145*2π)/9166 weeks
146-.07208 -.01758 (146*2π)/9166 weeks
147-.03088 -.04534 (147*2π)/9166 weeks
148-.03157 -.02567 (148*2π)/9166 weeks
149-.01469 -.03122 (149*2π)/9166 weeks
150-.03862 -.0141 (150*2π)/9166 weeks
151-.0157 -.03006 (151*2π)/9166 weeks
152-.01834 -.03666 (152*2π)/9166 weeks
153.01393 -.04529 (153*2π)/9166 weeks
154.0013 -.03671 (154*2π)/9166 weeks
155-.00604 -.05419 (155*2π)/9166 weeks
156.00046 -.07629 (156*2π)/9166 weeks
157.01388 -.06227 (157*2π)/9166 weeks
158.04316 -.06203 (158*2π)/9166 weeks
159.06191 -.08187 (159*2π)/9166 weeks
160.06068 -.07058 (160*2π)/9166 weeks
161.08597 -.05327 (161*2π)/9166 weeks
162.08463 -.0405 (162*2π)/9166 weeks
163.10712 -.03482 (163*2π)/9166 weeks
164.10096 -.00212 (164*2π)/9166 weeks
165.10555 -.008 (165*2π)/9166 weeks
166.11914 .00668 (166*2π)/9166 weeks
167.12063 .01089 (167*2π)/9165 weeks
168.12451 .02777 (168*2π)/9165 weeks
169.14014 .06483 (169*2π)/9165 weeks
170.09428 .10283 (170*2π)/9165 weeks
171.07841 .11442 (171*2π)/9165 weeks
172.04414 .11903 (172*2π)/9165 weeks
173.05038 .13094 (173*2π)/9165 weeks
174-.00631 .09896 (174*2π)/9165 weeks
175.03201 .09722 (175*2π)/9165 weeks
176-.00162 .10456 (176*2π)/9165 weeks
177.00745 .10902 (177*2π)/9165 weeks
178.00509 .11376 (178*2π)/9165 weeks
179-.05057 .11658 (179*2π)/9165 weeks
180-.08846 .1001 (180*2π)/9165 weeks
181-.06201 .06086 (181*2π)/9165 weeks
182-.06771 .05908 (182*2π)/9165 weeks
183-.05336 .03685 (183*2π)/9165 weeks
184-.04911 .04956 (184*2π)/9165 weeks
185-.05848 .03393 (185*2π)/9165 weeks
186-.05645 .03696 (186*2π)/9165 weeks
187-.06067 .0331 (187*2π)/9165 weeks
188-.0688 .01429 (188*2π)/9165 weeks
189-.0533 -.02361 (189*2π)/9165 weeks
190-.0425 .00061 (190*2π)/9165 weeks
191-.02909 -.02335 (191*2π)/9165 weeks
192-.01904 -.00759 (192*2π)/9165 weeks
193-.01255 -.00375 (193*2π)/9165 weeks
194-.0287 -.0104 (194*2π)/9165 weeks
195-.01923 -.00355 (195*2π)/9165 weeks
196-.03854 -.00197 (196*2π)/9165 weeks
197-.03784 -.03876 (197*2π)/9165 weeks
198-.02233 -.06832 (198*2π)/9165 weeks
199.00639 -.07816 (199*2π)/9165 weeks
200.05403 -.08366 (200*2π)/9165 weeks
201.08261 -.0662 (201*2π)/9165 weeks
202.08271 -.03155 (202*2π)/9165 weeks
203.07065 .00597 (203*2π)/9165 weeks
204.05973 .01355 (204*2π)/9164 weeks
205.0694 .02152 (205*2π)/9164 weeks
206.04873 .00954 (206*2π)/9164 weeks
207.04782 .00252 (207*2π)/9164 weeks
208.0449 .00007 (208*2π)/9164 weeks
209.06607 .00321 (209*2π)/9164 weeks
210.07321 .01576 (210*2π)/9164 weeks
211.08755 .01932 (211*2π)/9164 weeks
212.05564 .05369 (212*2π)/9164 weeks
213.04032 .03604 (213*2π)/9164 weeks
214.04039 .03076 (214*2π)/9164 weeks
215.06613 .04335 (215*2π)/9164 weeks
216.03455 .05601 (216*2π)/9164 weeks
217.0182 .04206 (217*2π)/9164 weeks
218.01065 .02938 (218*2π)/9164 weeks
219.05019 .00325 (219*2π)/9164 weeks
220.07226 .02299 (220*2π)/9164 weeks
221.0559 .04927 (221*2π)/9164 weeks
222.06275 .03491 (222*2π)/9164 weeks
223.05554 .05745 (223*2π)/9164 weeks
224.06445 .06539 (224*2π)/9164 weeks
225.04551 .06372 (225*2π)/9164 weeks
226.05609 .05771 (226*2π)/9164 weeks
227.03721 .07438 (227*2π)/9164 weeks
228.06017 .08091 (228*2π)/9164 weeks
229.02558 .09244 (229*2π)/9164 weeks
230.02707 .09406 (230*2π)/9164 weeks
231.02275 .07611 (231*2π)/9164 weeks
232-.017 .09095 (232*2π)/9164 weeks
233-.00879 .07059 (233*2π)/9164 weeks
234-.01722 .06388 (234*2π)/9164 weeks
235-.012 .04661 (235*2π)/9164 weeks
236.00646 .05644 (236*2π)/9164 weeks
237.00396 .05344 (237*2π)/9164 weeks
238-.02329 .06026 (238*2π)/9164 weeks
239-.00783 .07194 (239*2π)/9164 weeks
240-.03206 .05086 (240*2π)/9164 weeks
241-.01551 .04671 (241*2π)/9164 weeks
242-.02433 .042 (242*2π)/9164 weeks
243-.00998 .04545 (243*2π)/9164 weeks
244-.01566 .0416 (244*2π)/9164 weeks
245-.01092 .04807 (245*2π)/9164 weeks
246-.00063 .02823 (246*2π)/9164 weeks
247.01694 .04521 (247*2π)/9164 weeks
248-.00582 .0836 (248*2π)/9164 weeks
249-.02896 .07491 (249*2π)/9164 weeks
250-.03186 .05347 (250*2π)/9164 weeks
251-.04542 .04832 (251*2π)/9164 weeks
252-.02702 .05114 (252*2π)/9164 weeks
253-.05389 .06459 (253*2π)/9164 weeks
254-.06025 .04431 (254*2π)/9164 weeks
255-.04926 .02616 (255*2π)/9164 weeks
256-.03786 .00695 (256*2π)/9164 weeks
257-.05246 .00994 (257*2π)/9164 weeks
258-.04233 -.00218 (258*2π)/9164 weeks
259-.04231 .01426 (259*2π)/9164 weeks
260-.06292 -.00528 (260*2π)/9164 weeks
261-.02045 -.02312 (261*2π)/9164 weeks
262-.03626 .01322 (262*2π)/9163 weeks
263-.05157 -.00334 (263*2π)/9163 weeks
264-.04837 -.02963 (264*2π)/9163 weeks
265-.03141 -.03862 (265*2π)/9163 weeks
266-.00823 -.04211 (266*2π)/9163 weeks
267.0042 -.02302 (267*2π)/9163 weeks
268.0011 -.0226 (268*2π)/9163 weeks
269.00177 -.01356 (269*2π)/9163 weeks
270.01827 -.01599 (270*2π)/9163 weeks
271.01441 -.00736 (271*2π)/9163 weeks
272.00371 -.00531 (272*2π)/9163 weeks
273.01622 .00346 (273*2π)/9163 weeks
274.02478 -.00157 (274*2π)/9163 weeks
275.03077 .00187 (275*2π)/9163 weeks
276.02733 .02931 (276*2π)/9163 weeks
277.00648 .03133 (277*2π)/9163 weeks
278-.00069 .02082 (278*2π)/9163 weeks
279-.00408 .00701 (279*2π)/9163 weeks
280.00635 .00467 (280*2π)/9163 weeks
281.00139 .0264 (281*2π)/9163 weeks
282-.00448 .01421 (282*2π)/9163 weeks
283.00373 .0179 (283*2π)/9163 weeks
284.00993 .01351 (284*2π)/9163 weeks
285.00676 .02155 (285*2π)/9163 weeks
286-.00627 .01975 (286*2π)/9163 weeks
287-.02541 .00106 (287*2π)/9163 weeks
288-.02293 -.01451 (288*2π)/9163 weeks
289.00125 -.01267 (289*2π)/9163 weeks
290.0001 -.01285 (290*2π)/9163 weeks
291.00356 -.00543 (291*2π)/9163 weeks
292.0081 -.0005 (292*2π)/9163 weeks
293.00557 .00262 (293*2π)/9163 weeks
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748.12451 -.02777 (748*2π)/9161 weeks
749.12063 -.01089 (749*2π)/9161 weeks
750.11914 -.00668 (750*2π)/9161 weeks
751.10555 .008 (751*2π)/9161 weeks
752.10096 .00212 (752*2π)/9161 weeks
753.10712 .03482 (753*2π)/9161 weeks
754.08463 .0405 (754*2π)/9161 weeks
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756.06068 .07058 (756*2π)/9161 weeks
757.06191 .08187 (757*2π)/9161 weeks
758.04316 .06203 (758*2π)/9161 weeks
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761-.00604 .05419 (761*2π)/9161 weeks
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785.00379 -.03363 (785*2π)/9161 weeks
786-.0309 -.03098 (786*2π)/9161 weeks
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788-.03153 .00389 (788*2π)/9161 weeks
789-.09087 -.00136 (789*2π)/9161 weeks
790-.1013 -.00687 (790*2π)/9161 weeks
791-.07428 -.04306 (791*2π)/9161 weeks
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793-.08321 -.06603 (793*2π)/9161 weeks
794-.10337 -.12622 (794*2π)/9161 weeks
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800.024 -.12685 (800*2π)/9161 weeks
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816-.02376 .02848 (816*2π)/9161 weeks
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818-.06929 .06403 (818*2π)/9161 weeks
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820-.11964 -.01941 (820*2π)/9161 weeks
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830.02145 -.1077 (830*2π)/9161 weeks
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832-.02353 -.16308 (832*2π)/9161 weeks
833.00888 -.19402 (833*2π)/9161 weeks
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835.05839 -.12632 (835*2π)/9161 weeks
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837.14135 -.03427 (837*2π)/9161 weeks
838.11629 .05449 (838*2π)/9161 weeks
839.04657 .07612 (839*2π)/9161 weeks
840-.02389 .0511 (840*2π)/9161 weeks
841-.04706 .0749 (841*2π)/9161 weeks
842-.07646 .10972 (842*2π)/9161 weeks
843-.13724 .0612 (843*2π)/9161 weeks
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846-.21896 -.02819 (846*2π)/9161 weeks
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858-.24089 -.34691 (858*2π)/9161 weeks
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860-.06014 -.40527 (860*2π)/9161 weeks
861-.00572 -.38592 (861*2π)/9161 weeks
862-.01615 -.32401 (862*2π)/9161 weeks
863-.01894 -.29226 (863*2π)/9161 weeks
864-.0475 -.23756 (864*2π)/9161 weeks
865-.09074 -.31088 (865*2π)/9161 weeks
866-.0904 -.34652 (866*2π)/9161 weeks
867-.02571 -.41626 (867*2π)/9161 weeks
868.04419 -.38991 (868*2π)/9161 weeks
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870-.02675 -.22394 (870*2π)/9161 weeks
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903-.26818 -1.52863 (903*2π)/9161 weeks
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905.2666 -1.77478 (905*2π)/9161 weeks
906.64544 -1.94973 (906*2π)/9161 weeks
9071.60504 -1.51176 (907*2π)/9161 weeks
9081.02618 -1.06168 (908*2π)/9161 weeks
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9101.14054 -1.69532 (910*2π)/9161 weeks
9111.5218 -1.80907 (911*2π)/9161 weeks
9121.39548 -2.09091 (912*2π)/9161 weeks
9132.2418 -1.96847 (913*2π)/9161 weeks
9142.29737 -2.16562 (914*2π)/9161 weeks | 15,847 | 35,539 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.921875 | 3 | CC-MAIN-2017-30 | longest | en | 0.775355 |
https://number.academy/209557 | 1,660,481,979,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882572033.91/warc/CC-MAIN-20220814113403-20220814143403-00212.warc.gz | 398,320,083 | 12,254 | # Number 209557
Number 209,557 spell 🔊, write in words: two hundred and nine thousand, five hundred and fifty-seven . Ordinal number 209557th is said 🔊 and write: two hundred and nine thousand, five hundred and fifty-seventh. Color #209557. The meaning of number 209557 in Maths: Is Prime? Factorization and prime factors tree. The square root and cube root of 209557. What is 209557 in computer science, numerology, codes and images, writing and naming in other languages. Other interesting facts related to 209557.
## What is 209,557 in other units
The decimal (Arabic) number 209557 converted to a Roman number is (C)(C)(IX)DLVII. Roman and decimal number conversions.
#### Weight conversion
209557 kilograms (kg) = 461989.4 pounds (lbs)
209557 pounds (lbs) = 95054.4 kilograms (kg)
#### Length conversion
209557 kilometers (km) equals to 130213 miles (mi).
209557 miles (mi) equals to 337250 kilometers (km).
209557 meters (m) equals to 687515 feet (ft).
209557 feet (ft) equals 63874 meters (m).
209557 centimeters (cm) equals to 82502.8 inches (in).
209557 inches (in) equals to 532274.8 centimeters (cm).
#### Temperature conversion
209557° Fahrenheit (°F) equals to 116402.8° Celsius (°C)
209557° Celsius (°C) equals to 377234.6° Fahrenheit (°F)
#### Time conversion
(hours, minutes, seconds, days, weeks)
209557 seconds equals to 2 days, 10 hours, 12 minutes, 37 seconds
209557 minutes equals to 5 months, 5 days, 12 hours, 37 minutes
### Codes and images of the number 209557
Number 209557 morse code: ..--- ----- ----. ..... ..... --...
Sign language for number 209557:
Number 209557 in braille:
QR code Bar code, type 39
Images of the number Image (1) of the number Image (2) of the number More images, other sizes, codes and colors ...
## Mathematics of no. 209557
### Multiplications
#### Multiplication table of 209557
209557 multiplied by two equals 419114 (209557 x 2 = 419114).
209557 multiplied by three equals 628671 (209557 x 3 = 628671).
209557 multiplied by four equals 838228 (209557 x 4 = 838228).
209557 multiplied by five equals 1047785 (209557 x 5 = 1047785).
209557 multiplied by six equals 1257342 (209557 x 6 = 1257342).
209557 multiplied by seven equals 1466899 (209557 x 7 = 1466899).
209557 multiplied by eight equals 1676456 (209557 x 8 = 1676456).
209557 multiplied by nine equals 1886013 (209557 x 9 = 1886013).
show multiplications by 6, 7, 8, 9 ...
### Fractions: decimal fraction and common fraction
#### Fraction table of 209557
Half of 209557 is 104778,5 (209557 / 2 = 104778,5 = 104778 1/2).
One third of 209557 is 69852,3333 (209557 / 3 = 69852,3333 = 69852 1/3).
One quarter of 209557 is 52389,25 (209557 / 4 = 52389,25 = 52389 1/4).
One fifth of 209557 is 41911,4 (209557 / 5 = 41911,4 = 41911 2/5).
One sixth of 209557 is 34926,1667 (209557 / 6 = 34926,1667 = 34926 1/6).
One seventh of 209557 is 29936,7143 (209557 / 7 = 29936,7143 = 29936 5/7).
One eighth of 209557 is 26194,625 (209557 / 8 = 26194,625 = 26194 5/8).
One ninth of 209557 is 23284,1111 (209557 / 9 = 23284,1111 = 23284 1/9).
show fractions by 6, 7, 8, 9 ...
### Calculator
209557
#### Is Prime?
The number 209557 is not a prime number. The closest prime numbers are 209549, 209563.
#### Factorization and factors (dividers)
The prime factors of 209557 are 367 * 571
The factors of 209557 are 1 , 367 , 571 , 209557
Total factors 4.
Sum of factors 210496 (939).
#### Powers
The second power of 2095572 is 43.914.136.249.
The third power of 2095573 is 9.202.514.649.931.692.
#### Roots
The square root √209557 is 457,773962.
The cube root of 3209557 is 59,397394.
#### Logarithms
The natural logarithm of No. ln 209557 = loge 209557 = 12,252751.
The logarithm to base 10 of No. log10 209557 = 5,321302.
The Napierian logarithm of No. log1/e 209557 = -12,252751.
### Trigonometric functions
The cosine of 209557 is 0,979338.
The sine of 209557 is 0,20223.
The tangent of 209557 is 0,206497.
### Properties of the number 209557
Is a Friedman number: No
Is a Fibonacci number: No
Is a Bell number: No
Is a palindromic number: No
Is a pentagonal number: No
Is a perfect number: No
## Number 209557 in Computer Science
Code typeCode value
PIN 209557 It's recommendable to use 209557 as a password or PIN.
209557 Number of bytes204.6KB
CSS Color
#209557 hexadecimal to red, green and blue (RGB) (32, 149, 87)
Unix timeUnix time 209557 is equal to Saturday Jan. 3, 1970, 10:12:37 a.m. GMT
IPv4, IPv6Number 209557 internet address in dotted format v4 0.3.50.149, v6 ::3:3295
209557 Decimal = 110011001010010101 Binary
209557 Decimal = 101122110101 Ternary
209557 Decimal = 631225 Octal
209557 Decimal = 33295 Hexadecimal (0x33295 hex)
209557 BASE64MjA5NTU3
209557 SHA224f2034e2d8ef5e69e62bbbef73a29d4e4a3e68a73931dbaf5f8843927
209557 SHA256fc7b380613c54fe6e110f0deac1167ce642c611e3d4d9fd78b6b284094c2fd5d
More SHA codes related to the number 209557 ...
If you know something interesting about the 209557 number that you did not find on this page, do not hesitate to write us here.
## Numerology 209557
### Character frequency in number 209557
Character (importance) frequency for numerology.
Character: Frequency: 2 1 0 1 9 1 5 2 7 1
### Classical numerology
According to classical numerology, to know what each number means, you have to reduce it to a single figure, with the number 209557, the numbers 2+0+9+5+5+7 = 2+8 = 1+0 = 1 are added and the meaning of the number 1 is sought.
## Interesting facts about the number 209557
### Asteroids
• (209557) 2004 WJ12 is asteroid number 209557. It was discovered by LINEAR, Lincoln Near-Earth Asteroid Research from Lincoln Laboratory, ETS in Socorro on 11/19/2004.
## № 209,557 in other languages
How to say or write the number two hundred and nine thousand, five hundred and fifty-seven in Spanish, German, French and other languages. The character used as the thousands separator.
Spanish: 🔊 (número 209.557) doscientos nueve mil quinientos cincuenta y siete German: 🔊 (Anzahl 209.557) zweihundertneuntausendfünfhundertsiebenundfünfzig French: 🔊 (nombre 209 557) deux cent neuf mille cinq cent cinquante-sept Portuguese: 🔊 (número 209 557) duzentos e nove mil, quinhentos e cinquenta e sete Chinese: 🔊 (数 209 557) 二十万九千五百五十七 Arabian: 🔊 (عدد 209,557) مئتان و تسعة ألفاً و خمسمائة و سبعة و خمسون Czech: 🔊 (číslo 209 557) dvěstě devět tisíc pětset padesát sedm Korean: 🔊 (번호 209,557) 이십만 구천오백오십칠 Danish: 🔊 (nummer 209 557) tohundrede og nitusindfemhundrede og syvoghalvtreds Dutch: 🔊 (nummer 209 557) tweehonderdnegenduizendvijfhonderdzevenenvijftig Japanese: 🔊 (数 209,557) 二十万九千五百五十七 Indonesian: 🔊 (jumlah 209.557) dua ratus sembilan ribu lima ratus lima puluh tujuh Italian: 🔊 (numero 209 557) duecentonovemilacinquecentocinquantasette Norwegian: 🔊 (nummer 209 557) to hundre og ni tusen, fem hundre og femti-syv Polish: 🔊 (liczba 209 557) dwieście dziewięć tysięcy pięćset pięćdziesiąt siedem Russian: 🔊 (номер 209 557) двести девять тысяч пятьсот пятьдесят семь Turkish: 🔊 (numara 209,557) ikiyüzdokuzbinbeşyüzelliyedi Thai: 🔊 (จำนวน 209 557) สองแสนเก้าพันห้าร้อยห้าสิบเจ็ด Ukrainian: 🔊 (номер 209 557) двiстi дев'ять тисяч п'ятсот п'ятдесят сiм Vietnamese: 🔊 (con số 209.557) hai trăm lẻ chín nghìn năm trăm năm mươi bảy Other languages ...
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If you know something interesting about the number 209557 or any natural number (positive integer) please write us here or on facebook. | 2,513 | 7,435 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2022-33 | latest | en | 0.653271 |
https://ythi.net/practice-spoken-english/yvuE9HSqL3k/ | 1,660,490,007,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882572043.2/warc/CC-MAIN-20220814143522-20220814173522-00241.warc.gz | 958,879,671 | 17,853 | # Practice English Speaking&Listening with: How Old Is the Universe?
Normal
(0)
Difficulty: 0
Have you ever gazed out at the night sky and been fascinated by a bright band of stars
that lights it up?
Thats the Milky Way.
And over there is the Mars Bar.
The sky is full of candy bars.
Nope, just kidding!
The Milky Way is really the galaxy where our sun hangs out.
And the sun is not the only star in the Milky Way, and the Milky Way is not the only galaxy
in the universe.
Astronomers have long since been in the quest to find out exactly how many galaxies there
are in the universe, and you wont believe the numbers theyve come up with!
With time, as humans progressed, the scope of what we considered the universe also advanced.
First, we thought that the earth we lived on, the Sun, the Moon and the stars that we
could see with our naked eyes made up the entire universe.
So, effectively, for a large part of human history, we considered the Milky Way to be
the only universe.
We thought that all the stars that we see belong to it.
This belief didnt change until the 1900s, when scientists like Henrietta Swan Leavitt
and Edwin Hubble identified stars whose brightness seemed to change when observed from the earth.
They called these the Variable Stars.
Leavitt had intensely studied thousands of Variable stars.
She found that certain stars, called Cepheid variables, have the same brightness if they
twinkle at the same speed.
This discovery proved to be a milestone in measuring the distance of stars and galaxies.
It provided a way to relate brightness to distance.
Then came Hubble, who, using the Hooker telescope at Mount Wilson Observatory, California, identified
several of these variable stars.
He then used some complex mathematics to calculate the distance of these stars.
His calculations showed that these stars were way too distant to belong to our galaxy.
So, he concluded that they must be members of some other faraway galaxies, and not the
Milky Way.
This discovery motivated astronomers to find out exactly how many galaxies are out there
in the universe.
To aid this mission, more and more powerful telescopes were developed.
Today we have telescopes both on the ground, and in outer space, that regularly stare into
the vast universe to detect the faintest and most distant galaxies.
A major contributor to this quest, and towards making astronomy popular, is the Hubble Space
Telescope.
Named after famous astronomer Edwin Hubble, this telescope was launched into the low Earth
orbit in 1990 and remains operational.
It tried to investigate deep space for the first time in 1995.
The image that the telescope captured is known as the Hubble Deep Field, and in it, scientists
could identify 3000 distinct galaxies.
Similar deep observations using the Hubble and other telescopes followed its success,
and they found even more galaxies.
Using these experiments, scientists determined that there are about 125 billion galaxies.
But that large number appears faint compared to what scientists would discover a few years
later.
In 2016, a study conducted by a team of astronomers, led by an astrophysicist from the University
of Nottingham, used 3D modeling of images collected over 20 years by the Hubble Space
Telescope to determine the number of galaxies.
What they found was startling.
According to them, there are over 2 trillion galaxies.
These galaxies lie in what is known as the observable universe.
The observable universe is the part of the universe that can be seen from Earth or from
space-based telescopes like the Hubble.
Right now, its 93 billion light-years in diameter.
These galaxies are those from which light has reached us since the beginning of the
universe.
Have we blown your mind yet?
Well hang on
Improved technology in finding the light thats not visible to human eyes has now made it
possible for us to reveal galaxies that couldnt be detected by Hubble.
These galaxies mostly lie in an area called the Zone of Avoidance; that is, the region
in the sky thats obscured by the Milky Way.
The farthest galaxy that weve been able to observe till now is named EGS-zs8-1.
I think we should nickname itbob”.
Its so far out that the light from there took a little over 13 billion years to reach
us.
We studied in our Physics class that we cant see an object until its light reaches us.
And although light travels extremely fast, it still takes time to cover such long distances.
For example, the light from our Sun, which is just about 93 million miles away from the
Earth, takes 8 minutes and 20 seconds to get here.
And so, if the light from the nearest star, Alpha Centauri, takes more than 4 years to
reach us, it means we're seeing that star 4 years in the past.
The light you see from your computer or your smartphone screen is just nanoseconds old.
So, now lets go back to the farthest known galaxy, the EGS-zs8-1, or Bob.
Since its light took about 13 billion years to reach us, it means that what we see of
this galaxy today is how the galaxy looked about 13 billion years ago, long before the
earth, or even our sun, came into existence.
The discovery of such galaxies has helped astronomers to understand how the universe
began and how its evolved since then.
Its now generally accepted that the universe is about 13.8 billion years old; so the galaxy
Bob is certainly one of the earliest galaxies to have formed in the cosmos.
Looking at it is like looking at the universes past.
A very fascinating, and yet sometimes confusing, aspect of the universe is that its size is
not permanent.
Instead, its been growing ever since it was created by the Big Bang.
And the farther an object is from us, the faster its moving away from us.
So, by the time light from a faraway galaxy reaches us, the same galaxy has already moved
farther away.
This makes it difficult to calculate the actual distance of faraway galaxies, because by the
time we see them, the distance has changed.
So, according to some complex calculations, the most distant galaxy is about 32 billion
light-years away from us now, and is still moving away from us, picking up speed as it
goes.
The expanding universe theory also means that theres a point in the universe from which
things are moving away from us at a speed faster than the speed of light; a point beyond
which, given our current scientific knowledge and technology, we cant investigate.
This is a place from where light can never reach us.
The enormous blue star nicknamed Icarus is the farthest individual star weve seen
to date.
Normally, it wouldve been too faint to view, even with the largest and most powerful
telescopes that we have today.
But it seems like nature wanted us to have a look at it.
It was because of a fluke of nature that the stars weak glow got extremely bright.
Astronomers using NASAs Hubble Space Telescope were, therefore, able to pinpoint this faraway
star and set a new distance record.
The star is in a very distant spiral galaxy.
Its so far away that its light took 9 billion years to reach Earth.
All these discoveries have been amazing.
But scientists are never satisfied with what they know or have.
They have an unquenchable thirst to know and develop new things.
So, to look at objects far, far away, and more difficult to be detected by telescopes,
they developed an observation network in the Netherlands that can see light sources that
regular telescopes cant.
This newer telescope works by detecting radiation produced by the interaction of huge cosmic
objects.
This telescope network is called Low-Frequency Array or LOFAR.
Over 200 scientists from 18 different countries teemed in an awe-inspiring study, using radio
astronomy to analyze a tiny section of sky above the northern hemisphere.
During this experiment, they were able to identify 300,000 new galaxies.
But even with such advanced systems, scientists say that theyve only been able to chart
2 percent of the sky so far.
The team of scientists now plan to set their eyes on the entire northern sky.
They hope to be able to discover many more new galaxies that can shed light on various
other research areas, including the physics of black holes as well as research into how
galaxy clusters evolve.
But will we stop with the LOFAR systems?
Obviously Not.
If theres been something constant in the evolution of humans, its the fact that
And with time, the rate of this progress has only sped up.
The universe, as I see it, is far vaster than we can ever discover, but it surely doesnt
discourage those searching; itll only make them push harder.
It wouldnt surprise me if, someday soon, we discover even more galaxies at even farther
distances.
Do you think we will discover more galaxies than we have till now, before the end of the
Let me know down in the comments!
If you learned something new today, then give this video a like and share it with a friend.
Buthey! – dont go star trekking just yet!
We have over 2,000 cool videos for you to check outright here on Earth.
All you have to do is pick the left or right video, click on it, and enjoy!
Stay on the Bright Side of life!
The Description of How Old Is the Universe? | 1,996 | 9,252 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2022-33 | latest | en | 0.95207 |
http://spendmatters.com/2016/02/23/the-spend-uncertainty-principle/ | 1,484,628,200,000,000,000 | text/html | crawl-data/CC-MAIN-2017-04/segments/1484560279468.17/warc/CC-MAIN-20170116095119-00265-ip-10-171-10-70.ec2.internal.warc.gz | 275,432,477 | 24,490 | # The Spend Uncertainty Principle
Spend Matters welcomes this guest post from Paul Blake, of GEP.
Sometimes the certainties in life can suddenly seem anything but. We’re not talking here about the classical “death and taxes” certainties attributed to Benjamin Franklin, but those things known to be “just so,” turning out to have a surprising degree of fuzziness about them.
Take the geometry we all learn at school. Despite however many intervening years there may be between school days and the present, I’d wager a good percentage of procurement professionals could still offer an instant answer when asked for the formula for how to calculate the circumference of a circle.
2πr — simple. If we know the radius we can calculate the circumference and vice versa. Then there’s the area of said circle, πr2, and the volume of a sphere, 4/3 πr3 and so on. If we can remember the formula, then the rest is simple calculation.
But there’s a funny thing about all this that rather defies rational thinking. Pi is one of those curious numbers that can’t be pinned down exactly. You’ll probably remember this as well. Pi is a bit more than 3. A bit more than 3.1, actually. Or rather a bit more than 3.14. To be precise, it’s a bit more than 3.141592653589. In reality, it’s a bit more than that. However many numbers one adds to the right of the decimal, friendly old pi is, well, it’s just a bit more than that.
What this means, of course, is that for a circle with a radius of 10 cm the circumference is a bit more than 62.8 cm. It’s a bit more than 62.83185307 cm. Actually it’s a bit more than a bit more — forever.
But surely that’s not possible? It’s a circle! It must have a definite length! It can’t just be “a bit more!”
Let’s do it in reverse then. Let’s say we take a piece of string precisely 62.83 cm long and form it into a perfect circle. We then calculate the radius as being just a bit more than 9.999705074 cm. Again, just a bit more — forever.
But surely that’s not possible either? It’s a straight line between two points on a perfect circle, how can it possibly be always just a bit longer?
And what on Earth has this got to do with procurement?
Quite a lot, as it turns out.
The pursuit of an absolute answer to a seemingly trivial problem can result in one falling down the rabbit hole of confusion. In geometrical terms the measurement of diameters and circumferences can never be carried out with absolute precision. The one can be calculated from the other but the precision of measuring tools is simply insufficient to permit that absolute resolution.
But in every practical sense — and this is important — getting to a certain percentage of the “truth” is perfectly adequate.
Applying that insight to our procurement experience, we can get to thinking about tail spend and about cost management. Software tools exist today to provide you with unprecedented visibility of spend across the enterprise, categorized with high accuracy to your chosen sourcing taxonomy. It is reasonable to expect to have more than 90% of your spend classified in a way that lets you make qualified, intelligent decisions about where to look for savings opportunities and the like.
Following the Pareto principle, it won’t come as any surprise to know that, of that 90%, a good majority will be represented in just a few supplier dealings and perhaps in just a few transactions.
The chances are, then, that the majority of the transactions (orders, invoices, whatever), or at least a high minority of them, will fall into the segment that is hard to analyze, tough to define, difficult to categorize. And this can cause some concern.
If your spend analysis solution is only correctly categorizing 50% of your transactions, then surely it’s not working. But if 95% of your spend is categorised correctly, then surely it is working.
Dedicating effort and funds to classifying the final 5% might very well serve to satisfy the intellectual need for complete spend visibility, but what impact will that new knowledge have on savings realized? Probably negative, I’d wager.
Like the procurement equivalent of Heisenberg’s uncertainty principle, you can either know enough about your spend for that knowledge to deliver ROI, or you can know everything about your spend but derive no ROI whatsoever. The trick is to know where to draw the line.
This is where we reach the confluence of spend analysis and tail spend management. Spend analysis is emphatically not an intellectual exercise, despite the brainpower behind the algorithms and classification rules. It is a practical exercise, designed to achieve one goal: revealing opportunities for improvement.
Tail spend management is about reducing the noise in that final block of data, for however insignificant the spend may be in the tail, the overhead in terms of processing costs can be huge.
A final thought is that adding a structured, controlled and easy to use P2P system can serve to not only reduce that processing overhead but prevent the tail from growing again.
Combining spend analysis, tail spend management and a solid purchasing system can reduce the uncertainty. It’s fair to say you’ll never reach the “real” answer, because as basic school geometry shows us, it’s just not really real at all. Of that you can be certain.
For more creative thinking on procurement, visit the GEP Knowledge Bank.
### First Voice
1. Bill Kohnen:
Certainly there is no organization that has 95% category accuracy as the reality is even world class purchasing organizations struggle even to get access to comprehensive spend data.
Sure most CPOs will say they have something (mostly out of embarrassment) but reality is most are still using homegrown partial data extracts dumped into excel and even then only for their most critiCal items.
Everyone knows from experience the big ERP solutions are no help and it has come as an unpleasant surprise that cloud solutions are not much better. In fact many cloud solutions require so much data prep and interaction with the cloud provider team (often in India) that it feels like a manual process still, at least initially.
Perhaps some of the “big data” solutions deployed in other parts of organizations will ultimately be a better answer and even help look into the tail spend “weeds” | 1,320 | 6,305 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.84375 | 4 | CC-MAIN-2017-04 | longest | en | 0.920853 |
https://www.wyzant.com/resources/answers/word_problem?f=active&pagesize=20&pagenum=4 | 1,454,991,104,000,000,000 | text/html | crawl-data/CC-MAIN-2016-07/segments/1454701156448.92/warc/CC-MAIN-20160205193916-00224-ip-10-236-182-209.ec2.internal.warc.gz | 891,710,382 | 16,808 | Search 79,462 tutors
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### syed
1. 1. C# Practical File 2013 By: Syed Mohd Naqi Zaidi using System; using System.Collections.Generic; using System.Linq; using System.Text; namespace neha { class MATRIX { static void Main(string[] str) { Console.WriteLine(" Program to calculate addition of two matrix of size 2*2 "); int[,] m1 = new int[3, 3]; Console.WriteLine(); Console.WriteLine("Enter the Values of 1st matrix : "); for (int i = 0; i < 2; i++) { for (int j = 0; j < 2; j++) { m1[i, j] = int.Parse(Console.ReadLine()); } } int[,] m2 = new int[3, 3]; Console.WriteLine("Enter the Values of 2nd matrix :"); for (int i = 0; i < 2; i++) { for (int j = 0; j < 2; j++) { m2[i, j] = int.Parse(Console.ReadLine()); } } int[,] c = new int[3, 3]; Console.WriteLine("The Addtion of Matrix is : "); for (int i = 0; i < 2; i++) { for (int j = 0; j < 2; j++) { Console.Write((m1[i, j] + m2[i, j]) + " "); } Console.WriteLine(); } Console.ReadLine(); } } } /***WAP to calculate addition of two 2*2 matrix***/
2. 2. C# Practical File 2013 By: Syed Mohd Naqi Zaidi OUTPUT
3. 3. C# Practical File 2013 By: Syed Mohd Naqi Zaidi using System; using System.Collections.Generic; using System.Linq; using System.Text; namespace NEHA { class STRING { public static void length() { string s; Console.WriteLine("Enter The String "); s = Console.ReadLine(); Console.WriteLine("Lenght of the String is :" + s.Length); } public static void palindrome() { string str, revstr; Console.WriteLine("Enter Any String to Know It is Palindrome or not"); str = Console.ReadLine(); char[] tempstr = str.ToCharArray(); Array.Reverse(tempstr); revstr = new string(tempstr); bool caseignore = str.Equals(revstr, StringComparison.OrdinalIgnoreCase); if (caseignore == true) { Console.WriteLine("............" + str + " Is a Palindrome.........."); } else { Console.WriteLine("............" + str + " Is Not a Palindrome........"); } } static void Main(string[] args) { length(); palindrome(); Console.ReadLine(); } } } /*** create a class to perform following operations:- Calculate the length of string. Check whether the string is a palindrome or not. ***/
4. 4. C# Practical File 2013 By: Syed Mohd Naqi Zaidi OUTPUT
5. 5. C# Practical File 2013 By: Syed Mohd Naqi Zaidi using System; using System.Collections.Generic; using System.Linq; using System.Text; namespace neha { class EVENODD { static void Main(string[] str) { Console.WriteLine("Even" + " " + "ODD"); for (int i = 0; i < 50; i++) { if ((i % 2) == 0) Console.Write(i + " "); else { if ((i % 2) != 0) Console.WriteLine(i); } } Console.ReadLine(); } } } /***WAP to generate series of even and odd numbers separately between 1to50***/
6. 6. C# Practical File 2013 By: Syed Mohd Naqi Zaidi OUTPUT
7. 7. C# Practical File 2013 By: Syed Mohd Naqi Zaidi
8. 8. C# Practical File 2013 By: Syed Mohd Naqi Zaidi using System; using System.Collections.Generic; using System.Linq; using System.Text; namespace neha { class FACTORIAL { public static string rev(string st) { char[] ar = st.ToCharArray(); Array.Reverse(ar); return new string(ar); } static int a, b = 1; static string st; static void Main(string[] str) { Console.Write(" Program to Calculate the Factorial, length, Reverse of the string "); Console.WriteLine(); Console.WriteLine(); Console.Write("Enter the any value:"); a = int.Parse(Console.ReadLine()); for (int i = a; i > 1; i--) { b = b * i; } Console.Write("Factorial number: "); Console.WriteLine(b); st = b.ToString(); st = rev(st); Console.Write("Length of string: "); Console.WriteLine(st.Length); Console.Write("Reverse String: "); Console.WriteLine(st); Console.ReadKey(); } } } /***WAP to find the factorial of given integer, inverse of the number, calculate sum of the digits***/
9. 9. C# Practical File 2013 By: Syed Mohd Naqi Zaidi OUTPUT
10. 10. C# Practical File 2013 By: Syed Mohd Naqi Zaidi Define a class to represent a bank account having following members name, acc. No, type, initial values deposited amt, withdraw amt and display balance. using System; using System.Collections.Generic; using System.ComponentModel; using System.Data; using System.Drawing; using System.Linq; using System.Text.RegularExpressions; using System.Windows.Forms; using System.Collections; using System.Media; using System.Resources; using System.Reflection; using System.Diagnostics; using System.IO; namespace timer_and_acount_prog { public partial class Form1 : Form { public Form1() { InitializeComponent(); } Form2 frm = new Form2(); private void button1_Click(object sender, EventArgs e) { if (textBox1.Text == "" || textBox3.Text == "" || (!Regex.IsMatch(textBox1.Text, @"[0-9]") || !(Regex.IsMatch(textBox3.Text, @"[0- 9]")))) { MessageBox.Show("Please Enter the integer value in: " + 'n' + 'n' + " ACCOUNT NO. AND TOTAL AMOUNT", "MANI MESSAGE"); } else if (textBox2.Text == "" || textBox4.Text == "" || (!Regex.IsMatch(textBox2.Text, @"[a-zA-Z]") || !(Regex.IsMatch(textBox4.Text, @"[a-zA-Z]")))) { MessageBox.Show("Please Enter the String in: " + Environment.NewLine+'n' + "NAME AND ACCOUNT TYPE", "MANI MESSAGE"); } else { frm.a = int.Parse(textBox1.Text); frm.b = int.Parse(textBox3.Text); frm.d = button1.Text; frm.Show();
11. 11. C# Practical File 2013 By: Syed Mohd Naqi Zaidi this.Hide(); } } private void button3_Click(object sender, EventArgs e) { if (textBox1.Text == "" || textBox3.Text == "" || (!Regex.IsMatch(textBox1.Text, @"[0-9]") || !(Regex.IsMatch(textBox3.Text, @"[0- 9]")))) { MessageBox.Show("Please Enter the integer value in: " + 'n' + 'n' + " ACCOUNT NO. AND TOTAL AMOUNT", "MANI MESSAGE"); } else if (textBox2.Text == "" || textBox4.Text == "" || (!Regex.IsMatch(textBox2.Text, @"[a-zA-Z]") || !(Regex.IsMatch(textBox4.Text, @"[a-zA-Z]")))) { MessageBox.Show("Please Enter the String in: "+ Environment.NewLine+'n' +"NAME AND ACCOUNT TYPE", "MANI MESSAGE"); } else { frm.a = int.Parse(textBox1.Text); frm.b = int.Parse(textBox3.Text); frm.d = button3.Text; frm.Show(); this.Hide(); } } private void Form1_Load(object sender, EventArgs e) { } private void button4_Click(object sender, EventArgs e) { this.Close(); } private void button2_Click(object sender, EventArgs e) { MessageBox.Show("Account No.: " + textBox1.Text.ToString() + 'n' + 'n' + "Name Is: " + textBox2.Text + 'n' + 'n' + "Total Amount: " + textBox3.Text.ToString() + 'n' + 'n' + label4.Text + ": " + textBox4.Text, "MANI MESSAGE"); } } } FORM 2 using System;
12. 12. C# Practical File 2013 By: Syed Mohd Naqi Zaidi using System.Collections.Generic; using System.ComponentModel; using System.Data; using System.Drawing; using System.Linq; using System.Text.RegularExpressions; using System.Windows.Forms; namespace timer_and_acount_prog { public partial class Form2 : Form { public int a, b, c; public string d,s; public Form2() { InitializeComponent(); } private void button1_Click(object sender, EventArgs e) { Form1 f = new Form1(); if (textBox5.Text == "" || (!Regex.IsMatch(textBox5.Text,@"[0-9]"))) { MessageBox.Show("Please Enter the integer value"); } else { c = int.Parse(textBox5.Text); if (label5.Text == "Deposit") { textBox2.Text = (b + c).ToString(); } else { if (b > c) { textBox2.Text = (b - c).ToString(); } else MessageBox.Show("Your Amount Is More than total Amount "+'n'+" Your Current Balance is: "+b); } MessageBox.Show("ACCOUNT NO. " + textBox1.Text + " " + " Balance Is " + textBox2.Text, "KALRA BANK ;) :P"); } } private void Form2_Load(object sender, EventArgs e) { Form1 f = new Form1(); f.Hide(); textBox1.Text = a.ToString(); label5.Text = d; label5.Visible = true; textBox5.Visible = true; textBox1.ReadOnly = true; }
13. 13. C# Practical File 2013 By: Syed Mohd Naqi Zaidi private void button2_Click(object sender, EventArgs e) { Form1 frm = new Form1(); this.Close(); frm.Show(); } } }
14. 14. C# Practical File 2013 By: Syed Mohd Naqi Zaidi OUTPUT:-
15. 15. C# Practical File 2013 By: Syed Mohd Naqi Zaidi Swap two values using call by reference . a) Create a method using reference parameter to calculate square of no. b) Create a class by name decompose that separates the integer no and fractional part of given floating point no. using System; using System.Collections.Generic; using System.Linq; using System.Text; namespace Swap { class Swapping { class Swap { public void swap(ref int a, ref int b) { int t; t = a; a = b; b = t; } static void squareRef(ref int refParameter) { refParameter *= refParameter; } public class SwapDemo { public static void Main() { Swap ob = new Swap(); int x = 10, y = 20; Console.WriteLine("X and Y Before call: " + x + " " + y); ob.swap(ref x, ref y); Console.WriteLine("X and Y After call: " + x + " " + y); int arg; arg = 5; squareRef(ref arg); Console.WriteLine("Square Of a Number is :"+arg); Console.Read(); } } } } }
16. 16. C# Practical File 2013 By: Syed Mohd Naqi Zaidi | 2,537 | 9,138 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.421875 | 3 | CC-MAIN-2016-07 | latest | en | 0.355038 |
https://www.mapleprimes.com/tags/summation | 1,503,317,761,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886108268.39/warc/CC-MAIN-20170821114342-20170821134342-00631.warc.gz | 923,459,294 | 53,264 | ## is it possible to evaluate or how to evaluate this...
updated
after refer from
https://en.wikipedia.org/wiki/List_of_representations_of_e
exponential1 := sum((1/n!), n=0..infinity);
exponential1 is not a decimal number, it is exp(1)
hoyeung1:= sum((Int(exp(LambertW(1/(-1+x))*(-1+x)), x)), x=0..infinity);
hoyeung2:= sum((Int(exp(LambertW(1/(-1+x!))*(-1+x!)), x)), x=0..infinity);
how to evalute hoyeung1 or hoyeung2 as a decimal number?
how to evalute hoyeung^x as a decimal number function is func1 := proc(x) return hoyeung^x end proc:
but i do not know whether sum((Int(exp(LambertW(1/(-1+x))*(-1+x)), x))*m^x, x=0..infinity) = hoyeung^x
can limit(1+(Int(exp(LambertW(1/(-1+x))*(-1+x)), x)))^x, x=infinity) = hoyeung^1 ?
## how to find back the term in summation?...
Lee := (-1+Int(exp(LambertW(1/(-1+t))*(-1+t)), t=1..x))/(Int(exp(LambertW(1/(-1+t))*(-1+t)), t=1..x));
sum(unknown, n=1..infinity) = Lee
how to find unknown?
## Summation giving unexpected result...
I am trying to evaluate the following summation which gives the result 0. But I think answer is not correct.
>
(1)
>
## Derivative of a summation in order to a single ter...
doubt.mw
Equation21v2.mw
Hi,
When I do the derivation of a summation in order to one single term should not the result come out of the summation in the example attached in the file doubt? for example the derivative should not have yielded Ci and not the summation of Ci because for example if want the derivative in order to y1 it should be only C1 and not the summation of Ci.
The same happen when I go to a more complex case like in the file Equation21v2, should the result in the last double summation before T drop the summation over i to NC?
## Not solving integration...
Hello everybody,
I am trying to solve the following integral which also has summation but it gives me strange results. Do anyone know if I am doing something wrong?
The equation is in black and the strange result is in blue.
Thank you !
## How I can display particular term from summation ?...
Dear All
Suppose I have a expression whose terms are in summation:
>
(1)
>
(2)
In above summation, how I can write specific term ? For example, how I can display term for etc.
>
## How to solve sum in maple?...
Consider the expression n=1 (-1)n e*n/n2
1. Find the symbolic value of this sum.
2. Find an approximation for the value when = -2.
3. Build a function to calculate an approximation for the value of the given expression for
any value for
## Numerical Solutions to Matrix/Lattice Based Proble...
Hi, so I have few problems here. I need to;
Create a MxN Matrix/Lattice, where N and M can be any positive integer, that contains a random selection of -1/1s at each entry.
Need to sum every entry, then multiply by -1 to find “H”.
Need to multiply each neighbour to find its bond energy, so if it’s the same you get 1 else -1, but only its direct neighbours once, so if it was a 2x2 matrix there would be only 4 values and then sum them.
I don’t seem to be able to set up the code so that it does it for any size matrix, as I only know how to write it out basic for a 2x2. Also, not so important, but I wanted to know if could create a loop that would find every iteration of possible setups i.e. for a 2x1 you can have 1.1, -1.1, 1.-1, -1.-1. And then give the solutions outlined earlier for each of the the possibilities [There being 2MxN ]
## Symbolic summation gives wrong result?...
Hi,
I have encountered some strange issue with symbolic summation. Would be grateful for any help.
Here is the code (inserted as image):
Code in text:
`restart;F:=(n,a,b)->sum(r^(a+b)*cos(2*Pi/n*j+t)^a*sin(2*Pi/n*j+t)^b,j=0..n-1);F(n,2,2);F(4,2,2); `
The issue is that symbolic summation produces the formula (for general n) which contradicts the particular case (n=4).
Could somebody explain why this is happening? Is it a bug or am I missing something here?
I have tried all versions of Maple downto 14 - same situation.
Also Mathematica givers the same answer.
Pavel Holoborodko.
--
Multiprecision Computing Toolbox
## distributing limit to each terms...
Hello people in mapleprimes,
I want to distribute limit or Limit to each terms of summation.
Limit(f(a+h)-f(a),h=0);
But, the output is not distributed one, but the same as the input, though
I want it to become Limit(f(a+h),h=0)+Limit(f(a),h=0), or
Limit(f(a+h),h=0)+f(a).
Isn't there any way for it, other than a trivial one that is
subs(Limit(f(a+h)-f(a),h=0)=Limit(f(a+h),h=0)+Limit(f(a),h=0),Limit(f(a+h)-f(a),h=0));
?
I hope someone will teach me.
taro
## Fibonacci sequence...
Hello
Any idea about the summation of Fibonacci sequence
Fibonacci.mw
Best regards
## Manipulating Series Equations...
How do I multiply the 4x into the summation to get and same idea for the 3rd third?
Also, how do I go from to by manipulating the indices?
## How to take derivative of sum?...
I have the following expression.
What I want to do is take the derivative of this expression with respect to,
Where L is somewhere between 1 and n.
Using the diff operator, I would like to get something like,
But I don't. Instead, I get zero. I want to leave n undefined so that the summation isn't automatically expanded out to alot of terms, thereby making it much more difficult to read. This is especially true as my formulas become more complicated.
Thanks!!
## Сurse of dimensionality...
I'm trying to solve a system of equations thats expressed as a summation (the original has the summation symbol as opposed to 'sum'):
d_actual := solve(W_actual = sum(W_guess(def-asp_rad_inverse[i], E, asp_rad[i]), i = 1 .. n), def);
When n<5, I get an answer after a few seconds, but when n is higher, the program sits and 'evaluates' forever...I've waited up to 30 min.
Background:
I have a plate with a number of hemispheres on the surface (# of impacted hemispheres given a force = n). Each has a unique radius and they're listed from largest to smallest in 'asp_rad[]'. I have an equation for the deflection of a single hemisphere as a function of Force and material properties that I have rearranged with respect to Force (W_guess(deflection, E, r)). There's an opposing plate that stays parallel to the original plate while pushing down on the asperities with Force W_actual. The total deflection of the opposing plate is the sum of: 1) the difference between the tallest radius and the impacted radius in question (asp_rad_inverse[]), and 2) the deflection of the impacted radius in question.
I'm attempting to solve for the total deflection of the opposing plate via solving for the 'def' in the summation above, but when I run it, the program is not able to compute a solution.
## How can I animate this stiff function?...
Hi,
I have a problem with creating a function contains n-dimensional independent variables with random function .. The function looks like:
where U is a random between 0 and 1
For 1-dimensional problem, it will be like:
The plot by MATLAB will be:
While, for 2-dimensional problem, it will be like:
and the plot with MATLAB will be:
The MATLAB code is:
x1min=-5;
x1max=5;
x2min=-5;
x2max=5;
R=1000; % steps resolution
x1=x1min:(x1max-x1min)/R:x1max;
x2=x2min:(x2max-x2min)/R:x2max;
for j=1:length(x1)
% For 1-dimensional plotting
f1(j)=rand*abs(x1(j));
% For 2-dimensional plotting
for i=1:length(x2)
fn(i)=f1(j)+rand*abs(x2(i))^2;
end
fn_tot(j,:)=fn;
end
figure(1)
plot(x1,f1);
figure(2)
meshc(x1,x2,fn_tot);
I have used Maple because of its great graphics and animation, and for the mathematical analysis capability. However, to animate the above problem for 1- and 2-dimensional problems, I always fail!
My attempt has been just successed to plot 1-dimensional problem (without animation) .. And it tooks long-time with many codes!
restart;
X := Statistics:-RandomVariable(('Uniform')(0, 1));
R := Statistics:-Sample(X, 1000);
Vect := abs(Vector[column]([seq(0 .. 10, 10/999)]));
V := `~`[`-`](Vect, 5);
with(LinearAlgebra);
Mat := Multiply(V, R);
with(ArrayTools);
f := ArrayTools:-Diagonal(Mat);
F := abs(f);
Axis := Transpose(V);
f5 := plot(Axis, F, style = line);
And finally I got the graph:
But the problem is:
How can I animate it? Maybe I need to express it with new Maple code?
How can I plot and animate it when n=2?
Thanks
1 2 3 Page 1 of 3
| 2,288 | 8,376 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.625 | 4 | CC-MAIN-2017-34 | latest | en | 0.829859 |
https://www.sanfoundry.com/physics-questions-answers-ray-optics-refraction-prism/ | 1,717,048,258,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971059506.69/warc/CC-MAIN-20240530052602-20240530082602-00624.warc.gz | 835,939,133 | 23,289 | Class 12 Physics MCQ – Ray Optics – Refraction through a Prism
This set of Class 12 Physics Chapter 9 Multiple Choice Questions & Answers (MCQs) focuses on “Ray Optics – Refraction through a Prism”.
1. What is the angle between the incident ray and the emergent ray in a prism called?
a) Angle of deviation
b) Angle of refraction
c) Angle of reflection
d) Angle of dispersion
Explanation: A prism is a homogenous, transparent medium enclosed two plane surfaces inclined at an angle. These surfaces are called the refracting surfaces and the angle between the incident ray and emergent ray is known as the angle of deviation.
2. Identify the prism formula from the following.
a) μ=$$\frac {sin [ \frac {A – \delta_m}{2} ] }{ sin(\frac {A}{2}) }$$
b) μ=$$\frac {sin [ \frac {A + \delta_m}{4} ] }{ sin(\frac {A}{2}) }$$
c) μ=$$\frac {sin [ \frac {A + \delta_m}{2} ] }{ sin(\frac {A}{2}) }$$
d) μ=$$\frac {sin [ \frac {A + \delta_m}{2} ] }{ cos(\frac {A}{2}) }$$
Explanation: The refractive index of the material of the prism is given as:
μ=$$\frac {sin [ \frac {A + \delta_m}{2} ] }{ sin(\frac {A}{2}) }$$
Where A ➔ Angle of the prism and δm ➔ angle of minimum deviation. This is known as the prism formula.
3. Which of the following is Cauchy’s formula?
a) μ=A+Bλ2+Cλ4
b) μ=A+$$\frac {B}{\lambda^2} + \frac {C}{\lambda^4}$$
c) μ=A+B+CBλ
d) μ=A+$$\frac {B}{\lambda}+\frac {C}{\lambda^2}$$
Explanation: Cauchy’s dispersion formula is an empirical expression that gives an approximate relation between the refractive index of a medium and the wavelength of the light. Cauchy’s formula is given as:
μ=A+$$\frac {B}{\lambda^2} + \frac {C}{\lambda^4}$$
Where A, B, and C are the arbitrary constants of the medium.
4. The Refractive index of a material of a prism is different for different colors.
a) True
b) False
Explanation: Yes, this statement is true. The Refractive index is the property of a material. Since δ=(μ-1)A, different colors turn through different angles on passing through the prism. This is the cause of dispersion. Therefore, the refractive index of a material of a prism is different for different colors.
5. What is the difference in a deviation between any two colors called?
a) Linear dispersion
b) Angular dispersion
c) Mean deviation
d) Mean dispersion
Explanation: The difference in a deviation between any two colors is known as angular dispersion. Angular dispersion is given as:
δVR=(μVR)A
Where μV and μR are the refractive index for violet rays and red rays, respectively. Mean deviation is δ = $$( \frac {\delta_V + \delta_R}{2} )$$.
6. Pick out the formula for dispersive power from the following.
a) Dispersive power = $$\frac {mean \, deviation}{angular \, dispersion }$$
b) Dispersive power = mean deviation * angular dispersion
c) Dispersive power = mean deviation + angular deviation
d) Dispersive power = $$\frac {angular \, dispersion}{mean \, deviation}$$
Explanation: The formula for dispersive power is given as:
Dispersive power (ω)=$$\frac {Angular \, dispersion (\delta_V-\delta_R)}{Mean \, deviation (\delta)}$$
ω=$$\frac {\mu_V-\mu_R}{\mu-1}$$
Where μ=$$\frac {\mu_V+\mu_R}{2}$$ = mean refractive index
7. What is the condition for dispersion without deviation?
a) δ-δ’=0
b) δ+δ’=0
c) δ × δ=0
d) $$\frac {\delta}{\delta^{‘}}$$=0
Explanation: Consider combining two prisms of refracting angles A and A’, and dispersive powers ω and ω’ respectively in such a way that their refracting angles are reversed concerning each other. For no deviation, the condition is:
δ+δ’=0
So, (μ-1)A+(μ’-1)A’=0 or A’=-$$\frac {(\mu -1)A}{(\mu^{‘}-1)}$$
8. The Refractive index and wavelength are directly proportional to each other.
a) True
b) False
Explanation: No, this statement is false. The Refractive index of material and wavelength of color are inversely proportional to each other. For example, the wavelength of the color red is the longest, so the refractive index of the same will be the smallest. Similarly, violet has the greatest refractive index and the shortest wavelength.
9. Calculate the dispersive power of crown glass where μV=1.456 and μR=1.414.
a) 0.0096
b) 0.45
c) 0.96
d) 0.096
Explanation: Given: The refractive index for violet color = 1.456; Refractive index for red color = 1.414
Required equation ➔
ω=$$\frac {\mu_V – \mu_R}{\mu – 1}$$
Also, μ=$$\frac {(\mu_V+\mu_R)}{2}$$
μ=$$\frac {1.456+1.414}{2}$$=1.435
Thus, ω=$$\frac {1.456-1.414}{1.435-1}$$
ω=$$\frac {0.042}{0.435}$$
ω=0.096
Therefore, the dispersive power of crown glass is 0.096.
10. A thin prism with an angle of 3o and made from glass of refractive index 1.15 is combined with another prism made from glass and has a refractive index of 1.45. If the dispersion were to occur without deviation then what should be the angle of the second prism?
a) 3o
b) 0o
c) 1o
d) 2o
Explanation: The required equation ➔ δ=(μ-1)A
When two prisms are combined, then:
δ=δ+δ’=(μ-1)A+(μ’-1)A’=0
So, A’=-$$\frac {(\mu-1)A}{\mu^{‘}-1}$$
A’=-$$\frac {(1.15-1)}{1.45-1}$$ × 3
A’=-1o
Therefore, the angle of the other prism is 1o and opposite of the first prism.
Sanfoundry Global Education & Learning Series – Physics – Class 12.
To practice all chapters and topics of class 12 Physics, here is complete set of 1000+ Multiple Choice Questions and Answers.
If you find a mistake in question / option / answer, kindly take a screenshot and email to [email protected] | 1,655 | 5,389 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.15625 | 4 | CC-MAIN-2024-22 | latest | en | 0.809839 |
http://lesswrong.com/lw/li/unbounded_scales_huge_jury_awards_futurism/ | 1,519,111,258,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891812913.37/warc/CC-MAIN-20180220070423-20180220090423-00242.warc.gz | 201,283,701 | 14,251 | # Unbounded Scales, Huge Jury Awards, & Futurism
21 29 November 2007 07:45AM
Followup toEvaluability
"Psychophysics", despite the name, is the respectable field that links physical effects to sensory effects. If you dump acoustic energy into air—make noise—then how loud does that sound to a person, as a function of acoustic energy? How much more acoustic energy do you have to pump into the air, before the noise sounds twice as loud to a human listener? It's not twice as much; more like eight times as much.
Acoustic energy and photons are straightforward to measure. When you want to find out how loud an acoustic stimulus sounds, how bright a light source appears, you usually ask the listener or watcher. This can be done using a bounded scale from "very quiet" to "very loud", or "very dim" to "very bright". You can also use an unbounded scale, whose zero is "not audible at all" or "not visible at all", but which increases from there without limit. When you use an unbounded scale, the observer is typically presented with a constant stimulus, the modulus, which is given a fixed rating. For example, a sound that is assigned a loudness of 10. Then the observer can indicate a sound twice as loud as the modulus by writing 20.
And this has proven to be a fairly reliable technique. But what happens if you give subjects an unbounded scale, but no modulus? 0 to infinity, with no reference point for a fixed value? Then they make up their own modulus, of course. The ratios between stimuli will continue to correlate reliably between subjects. Subject A says that sound X has a loudness of 10 and sound Y has a loudness of 15. If subject B says that sound X has a loudness of 100, then it's a good guess that subject B will assign loudness in the range of 150 to sound Y. But if you don't know what subject C is using as their modulus—their scaling factor—then there's no way to guess what subject C will say for sound X. It could be 1. It could be 1000.
For a subject rating a single sound, on an unbounded scale, without a fixed standard of comparison, nearly all the variance is due to the arbitrary choice of modulus, rather than the sound itself.
"Hm," you think to yourself, "this sounds an awful lot like juries deliberating on punitive damages. No wonder there's so much variance!" An interesting analogy, but how would you go about demonstrating it experimentally?
Kahneman et. al., 1998 and 1999, presented 867 jury-eligible subjects with descriptions of legal cases (e.g., a child whose clothes caught on fire) and asked them to either
1. Rate the outrageousness of the defendant's actions, on a bounded scale
2. Rate the degree to which the defendant should be punished, on a bounded scale, or
3. Assign a dollar value to punitive damages
And, lo and behold, while subjects correlated very well with each other in their outrage ratings and their punishment ratings, their punitive damages were all over the map. Yet subjects' rank-ordering of the punitive damages—their ordering from lowest award to highest award—correlated well across subjects.
If you asked how much of the variance in the "punishment" scale could be explained by the specific scenario—the particular legal case, as presented to multiple subjects—then the answer, even for the raw scores, was .49. For the rank orders of the dollar responses, the amount of variance predicted was .51. For the raw dollar amounts, the variance explained was .06!
Which is to say: if you knew the scenario presented—the aforementioned child whose clothes caught on fire—you could take a good guess at the punishment rating, and a good guess at the rank-ordering of the dollar award relative to other cases, but the dollar award itself would be completely unpredictable.
Taking the median of twelve randomly selected responses didn't help much either.
So a jury award for punitive damages isn't so much an economic valuation as an attitude expression—a psychophysical measure of outrage, expressed on an unbounded scale with no standard modulus.
I observe that many futuristic predictions are, likewise, best considered as attitude expressions. Take the question, "How long will it be until we have human-level AI?" The responses I've seen to this are all over the map. On one memorable occasion, a mainstream AI guy said to me, "Five hundred years." (!!)
Now the reason why time-to-AI is just not very predictable, is a long discussion in its own right. But it's not as if the guy who said "Five hundred years" was looking into the future to find out. And he can't have gotten the number using the standard bogus method with Moore's Law. So what did the number 500 mean?
As far as I can guess, it's as if I'd asked, "On a scale where zero is 'not difficult at all', how difficult does the AI problem feel to you?" If this were a bounded scale, every sane respondent would mark "extremely hard" at the right-hand end. Everything feels extremely hard when you don't know how to do it. But instead there's an unbounded scale with no standard modulus. So people just make up a number to represent "extremely difficult", which may come out as 50, 100, or even 500. Then they tack "years" on the end, and that's their futuristic prediction.
"How hard does the AI problem feel?" isn't the only substitutable question. Others respond as if I'd asked "How positive do you feel about AI?", only lower numbers mean more positive feelings, and then they also tack "years" on the end. But if these "time estimates" represent anything other than attitude expressions on an unbounded scale with no modulus, I have been unable to determine it.
Part of the Death Spirals and the Cult Attractor subsequence of How To Actually Change Your Mind
Next post: "The Halo Effect"
Previous post: "Evaluability (And Cheap Holiday Shopping)"
Kahneman, D., Schkade, D. A., and Sunstein, C. 1998. Shared Outrage and Erratic Awards: The Psychology of Punitive Damages. Journal of Risk and Uncertainty 16, 49-86.
Kahneman, D., Ritov, I. and Schkade, D. A. 1999. Economic Preferences or Attitude Expressions? An Analysis of Dollar Responses to Public Issues. Journal of Risk and Uncertainty, 19: 203-235.
Sort By: Old
Comment author: 29 November 2007 11:35:11AM 7 points [-]
If you are asked to estimate a number that is a product (or sum) of many numbers, and you have good estimates for all those numbers but one, well variance in that last number you can't estimate well will dominate the variance of your answer. It just takes one.
Comment author: 29 November 2007 12:52:05PM 0 points [-]
I strongly encourage any AI worker who hasn't already done so to read Ian McDonald's 'River of Gods'. He's pretty positive (in timescale terms...) on AI, his answer to the question "How long will it be until we have human-level AI?" is 2047 AD, and it's a totally gob-smacking, brilliant, read.
Comment author: 13 February 2011 12:11:45PM 0 points [-]
Is this the one you mean: River of gods ?
if so - it's a novel... and it includes aliens... I admit I haven't read it, but I'm skeptical as to how much you might deduce about AI's likelihood...
Comment author: 29 November 2007 01:03:35PM 0 points [-]
Derrida must have done a thousand essays on how an author trying to be very precise about how language could possibly work, winds up in an infinte loop clarifying a final point that amounts to in effect starting over.
This contributes a lot to an indefinite future, whatever the modulus problem, if you take AI as just such a project.
Comment author: 29 November 2007 01:25:04PM 9 points [-]
I observe that many futuristic predictions are, likewise, best considered as attitude expressions. Take the question, "How long will it be until we have human-level AI?" The responses I've seen to this are all over the map. On one memorable occasion, a mainstream AI guy said to me, "Five hundred years." (!!)
Did you ask any of them how long they felt it would take to develop other "futuristic" technologies? (in other words, their rank ordering of technological changes).
Comment author: 29 November 2007 02:36:01PM 0 points [-]
The damages experiment, as described here, seems not to nail things down enough to say that what's going on is that damages are expressions of outrage on a scale with arbitrary modulus. Here's one alternative explanation that seems consistent with everything you've said: subjects vary considerably in their assessment of how effective a given level of damages is in deterring malfeasance, and that assessment influences (in the obvious way) their assessment of damages.
(I should add that I find the arbitrary-modulus explanation more plausible.)
Comment author: [deleted] 28 October 2012 12:48:19AM 0 points [-]
500 years still sounds optimistic to me.
Comment author: 20 February 2014 05:50:40AM 1 point [-]
Interesting, but without the dollar values adjusted for inflation, I feel like the point is lost on me of that part of the data, all though get the idea.
Edit: It only went up to \$.84, so I guess it doesn't matter that much (used the Inflation Calculator)
Comment author: 21 January 2018 05:58:27PM 0 points [-]
''Assign a dollar value to punitive damages''' - does this corelated with the ammount of money, that peoples, who responded to this earn? It look plausible that people who earn more can assign a highely money punishement for body harm | 2,191 | 9,401 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.109375 | 3 | CC-MAIN-2018-09 | latest | en | 0.927378 |
http://math.stackexchange.com/questions/111692/partial-derivatives-and-linear-map | 1,469,456,150,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469257824230.71/warc/CC-MAIN-20160723071024-00143-ip-10-185-27-174.ec2.internal.warc.gz | 152,734,981 | 18,738 | # Partial Derivatives and Linear Map
Proposition:
Suppose that $T : R^n \to R^m$ is the linear transformation defined by
$T(x) = Mx$
for some m × n matrix $M$. Then
$DT(x) = M$
for all points $x \in R^n$
where $D$ is the partial derivative matrix. (Jacobian?)
Question:
I don't understand what is being said. $T(x)$ is a linear transformation on $x$. How does the partial derivative of $T(x)$ lead to the transformation matrix. Neither do I have an algebraic intuition nor a geometric one.
Further, How is the total derivative of $g(x,y,z)$ equal to $Dg(x,y,z) \begin{pmatrix} x \\ y\\ z \end{pmatrix}$?
This is stated without proof. There is a chance, I made a wrong interpretation so I am pasting the portion of the text where it appears.
Is it that the change in $x$ in all dimensions of the output of $g(x,y,z)$ multiplied by $x$ and similar for y and z gives a total derivative. I don't seem to understand.I know the total derivative is a derivative taking into account that other variables are not constant during differentiation by one variable.
-
Regarding the second part: Confusingly, there are many things which are given the name "total derivative". But this doesn't appear to match up with any of them. Are you sure of the transcription? It could be that $x, y, z$ are functions of a single variable $t$, and the matrix on the right could be $\begin{pmatrix}x'(t) \\ y'(t) \\ z'(t)\end{pmatrix}$. Then this would just be the chain rule. – Dylan Moreland Feb 21 '12 at 15:08
@DylanMoreland, I have added a picture of the part where it appears. – Inquest Feb 21 '12 at 15:14
Thanks for scanning; that really helps us. [It would be good to say what $g$ and $f$ are, too.] I would not use the same letters for $(1, 0)$ (the point at which you're finding the total derivative; maybe write a general point as $(a, b)$) and the vector $(x, y)$ on which you are evaluating the derivative. – Dylan Moreland Feb 21 '12 at 15:16
@DylanMoreland, I added the whole problem. – Inquest Feb 21 '12 at 15:19
For algebraic intuition: The derivative of a function is the best linear approximation to it. In the case when the function is linear already, it's its own best linear approximation, hence it's its own derivative.
As a reminder, for multivariate $f:\mathbb{R}^m\rightarrow\mathbb{R}^n$, the derivative $Df(x)$ at the point $x\in \mathbb{R}^m$ is defined to be a linear map $A:\mathbb{R}^m\rightarrow\mathbb{R}^n$ satisfying
$$\lim_{h\rightarrow 0} \dfrac{f(x+h)-f(x) - Ah}{\|h\|}=0$$
It's not too hard to show that if $A$ exists, it's unique.
Now, we simply check that for $T(x) = Mx$, everything works.
$$\lim_{h\rightarrow 0} \dfrac{T(x+h)-T(x) - Mh}{\|h\|} = \lim_{h\rightarrow 0} \dfrac{M(x+h)-Mx-Mh}{\|h\|} = \lim_{h\rightarrow 0}\dfrac{Mx+Mh-Mx-Mh}{\|h\|}=0$$ since the numerator is $0$.
In answer to the comment, the derivative at a point is the best linear approximation at that point (though we think of the point as being shifted to the origin). Thus, in your example of $f(x) = x^3$, the derivative, $3x^2$, at a point (say $x=2$) gives a slope of $12$. The linear approximation this corresponds to is $12x$.
In fact, this issue is one it took me a long time to come to terms with. For functions $f:\mathbb{R}\rightarrow\mathbb{R}$, we think of the derivative of the whole function as a new function $f'(x)$. With more variables, we change view point: The derivative of a function at a point is itself a function (linear transformation). The relationship between the 2 is that a linear transformation from $\mathbb{R}\rightarrow\mathbb{R}$ can be identified with a single real number $\mathbb{R}$ via a pretty canonical choice of basis. The derivative of a function $f:\mathbb{R}\rightarrow\mathbb{R}$ at a point $p$ is the linear map "multiply by $f'(p)$".
1. In the definition of the derivative, should it be $f(x+h) - f(x)$ instead of $f(x+h) - f(h)$ or am I missing something. 2. I understood the interpretation but I can't seem to completely appreciate the fact that a derivative is a linear approximation. How is $3x^2$ a linear approximation to $x^3$? – Inquest Feb 21 '12 at 15:39 | 1,194 | 4,123 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.796875 | 4 | CC-MAIN-2016-30 | latest | en | 0.928496 |
https://prezi.com/bggjvjqkjcej/how-does-the-slope-of-a-ramp-affect-the-rate-at-which-a-ball/ | 1,542,068,138,000,000,000 | text/html | crawl-data/CC-MAIN-2018-47/segments/1542039741176.4/warc/CC-MAIN-20181113000225-20181113022225-00144.warc.gz | 723,218,406 | 21,613 | ### Present Remotely
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# How does the slope of a ramp affect the rate at which a ball
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## zahaara younis
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#### Transcript of How does the slope of a ramp affect the rate at which a ball
Discussion
Variables
conclusion
The method
Variables:
The increasing of the angle will make the speed of the ball travel faster due to gravity
Dependent variables-time
Independent variables - angle of the textbook(ramp)
Controlled variables - distance, ball, accurate and same stopwatch, protractor, measuring tape/ruler, surface and the same person
Materials:
PLATFORMS
Social
SOCIAL
SEO
CMS
1. gather all materials and equipments
2. set up equipment/materials as shown in the diagram:
textbooks(ramp)
How does the slope of a ramp affect the rate at which a ball rolls down it?
HYPOTHESIS
Stopwatch
measuring tape/ruler
protractor
textbooks(ramp)
ball
(2 people)
METHOD
ball
3. Use the protractor to measure the angle wanted
4. Make the ball roll down the ramp with the chosen angle
5. Using the stopwatch, find the speed by S= D/T(speed= distance over time)
6. Add an extra textbook when wanting to make the height of the ramp larger/increasing angle
7. Record the information in the table below
8. Repeat 3 times
results
p
stopwatch
measuring tape/ruler
protractor
calculations:
2 textbooks= 62.5
4 textbooks= 65.2
6 textbooks= 81.5
8 textbooks= 105.6
The slope of the ramp affects the rate at which the ball rolls down it as the more textbooks stacked the faster it rolls down and for the improvement of this experiment i could have performed this on a even surface for accurate results
As much as textbooks I added, the faster the ball rolled down the ramp due to gravity pushing it down which resulted in the ball rolling down in the increasing height of the ramp. The equipment was accurate as I was using a digital stopwatch which was precise, I was using a ruler not estimating and I used the same ball throughout the experiment. The dependent variable was the time; so when I let the ball roll down the textbook(ramp) I timed it by the stopwatch and stopped it when it landed on the point I wanted, the dependent variable was the angle of the textbook; using the protractor I measured the angle so the ramp would be the same for all the times I repeated it and the controlled variables are the distance, ball, stopwatch and protractor. I repeated the experiment 3 times so it was reliable. My hypothesis was right about 'the increasing of the angle will make the speed of the ball go faster due to gravity.'
THE END
By:Zahaara Mohammed.Younis-Khan
Aim
TO DETERMINE IF THE SLOPE OF THE RAMPS HEIGHT EFFECTS THE WAY THE BALL ROLLS DOWN IT
Full transcript | 721 | 3,063 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.109375 | 3 | CC-MAIN-2018-47 | latest | en | 0.881245 |
https://extraboneiru.com/d53adw5p/e1zl5.php?id=856c97-minimum-of-exponential-random-variables | 1,627,571,454,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046153860.57/warc/CC-MAIN-20210729140649-20210729170649-00445.warc.gz | 240,001,903 | 8,478 | ## minimum of exponential random variables
Exponential random variables. value - minimum of independent exponential random variables ... Variables starting with underscore (_), for example _Height, are normal variables, not anonymous: they are however ignored by the compiler in the sense that they will not generate any warnings for unused variables. Let X 1, ..., X n be independent exponentially distributed random variables with rate parameters λ 1, ..., λ n. Then. Let Z = min( X, Y ). From Eq. Lecture 20 Memoryless property. The expectations E[X(1)], E[Z(1)], and E[Y(1)] of the minimum of n independent geometric, modified geometric, or exponential random variables with matching expectations differ. μ, respectively, is an exponential random variable with parameter λ + μ. Poisson processes find extensive applications in tele-traffic modeling and queuing theory. Minimum of independent exponentials Memoryless property. I assume you mean independent exponential random variables; if they are not independent, then the answer would have to be expressed in terms of the joint distribution. Let we have two independent and identically (e.g. The distribution of the minimum of several exponential random variables. For some distributions, the minimum value of several independent random variables is a member of the same family, with different parameters: Bernoulli distribution, Geometric distribution, Exponential distribution, Extreme value distribution, Pareto distribution, Rayleigh distribution, Weibull distribution. is also exponentially distributed, with parameter. Of course, the minimum of these exponential distributions has Stack Exchange Network Stack Exchange network consists of 176 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Proposition 2.4. The Expectation of the Minimum of IID Uniform Random Variables. as asserted. If X 1 and X 2 are independent exponential random variables with rate μ 1 and μ 2 respectively, then min(X 1, X 2) is an exponential random variable with rate μ = μ 1 + μ 2. In this case the maximum is attracted to an EX1 distribution. The failure rate of an exponentially distributed random variable is a constant: h(t) = e te t= 1.3. The transformations used occurred first in the study of time series models in exponential variables (see Lawrance and Lewis [1981] for details of this work). Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … Let X 1, ..., X n be independent exponentially distributed random variables with rate parameters λ 1, ..., λ n. Then is also exponentially distributed, with parameter However, is not exponentially distributed. exponential) distributed random variables X and Y with given PDF and CDF. I How could we prove this? A plot of the PDF and the CDF of an exponential random variable is shown in Figure 3.9.The parameter b is related to the width of the PDF and the PDF has a peak value of 1/b which occurs at x = 0. Relationship to Poisson random variables. pendent exponential random variables as random-coefficient linear functions of pairs of independent exponential random variables. For a collection of waiting times described by exponen-tially distributed random variables, the sum and the minimum and maximum are usually statistics of key interest. Something neat happens when we study the distribution of Z , i.e., when we find out how Z behaves. Using Proposition 2.3, it is easily to compute the mean and variance by setting k = 1, k = 2. The PDF and CDF are nonzero over the semi-infinite interval (0, ∞), which … Find the expected value, variance, standard deviation of an exponential random variable by proving a recurring relation. Sep 25, 2016. Minimum of independent exponentials is exponential I CLAIM: If X 1 and X 2 are independent and exponential with parameters 1 and 2 then X = minfX 1;X 2gis exponential with parameter = 1 + 2. We introduced a random vector (X,N), where N has Poisson distribution and X are minimum of N independent and identically distributed exponential random variables. In my STAT 210A class, we frequently have to deal with the minimum of a sequence of independent, identically distributed (IID) random variables.This happens because the minimum of IID variables tends to play a large role in sufficient statistics. Suppose that X 1, X 2, ..., X n are independent exponential random variables, with X i having rate λ i, i = 1, ..., n. Then the smallest of the X i is exponential with a rate equal to the sum of the λ Minimum and Maximum of Independent Random Variables. An exercise in Probability. For instance, if Zis the minimum of 17 independent exponential random variables, should Zstill be an exponential random variable? Minimum of two independent exponential random variables: Suppose that X and Y are independent exponential random variables with E (X) = 1 / λ 1 and E (Y) = 1 / λ 2. Because the times between successive customer claims are independent exponential random variables with mean 1/λ while money is being paid to the insurance firm at a constant rate c, it follows that the amounts of money paid in to the insurance company between consecutive claims are independent exponential random variables with mean c/λ. We … The answer 4. Thus, because ruin can only occur when a … two independent exponential random variables we know Zwould be exponential as well, we might guess that Z turns out to be an exponential random variable in this more general case, i.e., no matter what nwe use. Proof. Distribution of the minimum of exponential random variables. Similarly, distributions for which the maximum value of several independent random variables is a member of the same family of distribution include: Bernoulli distribution , Power law distribution. Parametric exponential models are of vital importance in many research fields as survival analysis, reliability engineering or queueing theory. We show how this is accounted for by stochastic variability and how E[X(1)]/E[Y(1)] equals the expected number of ties at the minimum for the geometric random variables. 18.440. Continuous Random Variables ... An interesting (and sometimes useful) fact is that the minimum of two independent, identically-distributed exponential random variables is a new random variable, also exponentially distributed and with a mean precisely half as large as the original mean(s). The m.g.f.’s of Y, Z are easy to calculate too. An exponential random variable (RV) is a continuous random variable that has applications in modeling a Poisson process. Sum and minimums of exponential random variables. Remark. It can be shown (by induction, for example), that the sum X 1 + X 2 + :::+ X n Parameter estimation. Suppose X i;i= 1:::n are independent identically distributed exponential random variables with parameter . If the random variable Z has the “SUG minimum distribution” and, then. Proof. On the minimum of several random variables ... ∗Keywords: Order statistics, expectations, moments, normal distribution, exponential distribution. I Have various ways to describe random variable Y: via density function f Y (x), or cumulative distribution function F Y (a) = PfY ag, or function PfY >ag= 1 F †Partially supported by the Fund for the Promotion of Research at the Technion ‡Partially supported by FP6 Marie Curie Actions, MRTN-CT-2004-511953, PHD. Distribution of the minimum of exponential random variables. [2 Points] Show that the minimum of two independent exponential random variables with parameters λ and. Expected Value of The Minimum of Two Random Variables Jun 25, 2016 Suppose X, Y are two points sampled independently and uniformly at random from the interval [0, 1]. 4.2 Derivation of exponential distribution 4.3 Properties of exponential distribution a. Normalized spacings b. Campbell’s Theorem c. Minimum of several exponential random variables d. Relation to Erlang and Gamma Distribution e. Guarantee Time f. 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| October 3, 2018
MAT540 Homework
Week 8
Page 1 of 4
MAT540
Week 8 Homework
Chapter 4
1.
Grafton
Metalworks Company produces metal alloys from six different ores it mines. The
company has an order from a customer to produce an alloy that contains four
metals according to the following specifications: at least 21% of metal A, no
more than 12% of metal B, no more than 7% of metal C and between 30% and 65% of
metal D. The proportion of the four metals in each of the six ores and the
level of impurities in each ore are provided in the following table:
Metal (%)
Impurities
Ore
A
B
C
D
(%)
Cost/Ton
1
19
15
12
14
40
27
2
43
10
25
7
15
25
3
17
0
0
53
30
32
4
20
12
0
18
50
22
5
0
24
10
31
35
20
6
12
18
16
25
29
24
When the metals are processed and refined, the impurities are removed.
The company wants to know the amount of each ore
to use per ton of the alloy that will minimize the cost per ton of the alloy.
a.
Formulate a
linear programming model for this problem.
b. Solve the model by using the computer.
2.
As a result of a recently passed bill, a
congressman’s district has been allocated \$4 million for programs and projects.
It is up to the congressman to decide how to distribute the money. The
congressman has decided to allocate the money to four ongoing programs because
of their importance to his district – a job training program, a parks project,
a sanitation project, and a mobile library. However, the congressman wants to
distribute the money in a manner that will please the most voters, or, in other
words, gain him the most votes in the upcoming election. His staff’s estimates
of the number of votes gained per dollar spent for the various programs are as
follows.
Program
Job training
0.02
Parks
0.09
Sanitation
0.06
Mobile library
0.04
In order also to satisfy several local
influential citizens who financed his election, he is obligated to observe the
following guidelines:
MAT540 Homework
Week 8
Page 2 of 4
·
None of the
programs can receive more than 40% of the total allocation.
·
The amount
allocated to parks cannot exceed the total allocated to both the sanitation
project and the mobile library
·
The amount
allocated to job training must at least equal the amount spent on the
sanitation project.
Any money not spent in the district will be
returned to the government; therefore, the congressman wants to spend it all.
The congressman wants to know the amount to allocate to each program to
a. Formulate a linear programming model for this
problem.
b. Solve the model by using the computer.
3.
Anna
Broderick is the dietician for the State University football team, and she is
attempting to determine a nutritious lunch menu for the team. She has set the
following nutritional guidelines for each lunch serving:
·
Between
1,500 and 2,000 calories
·
At least 5
mg of iron
·
At least 20
but no more than 60 g of fat
·
At least 30
g of protein
·
At least 40
g of carbohydrates
·
No more
than 30 mg of cholesterol
She selects the menu from seven basic food items,
as follows, with the nutritional contributions per pound and the cost as given:
Calories
Iron
Protein
Carbo-
Fat
Chol-
Cost
(per lb.)
(mg/lb.)
(g/lb.)
hydrates
(g/lb.)
esterol
(g/lb.)
(mg/lb.)
\$/lb.
Chicken
520
4.4
17
0
30
180
0.80
Fish
500
3.3
85
0
5
90
3.70
Ground beef
860
0.3
82
0
75
350
2.30
Dried beans
600
3.4
10
30
3
0
0.90
Lettuce
50
0.5
6
0
0
0
0.75
Potatoes
460
2.2
10
70
0
0
0.40
Milk (2%)
240
0.2
16
22
10
20
0.83
The dietician wants to select a menu to meet the
nutritional guidelines while minimizing the total cost per serving.
a. Formulate a linear
programming model for this problem.
MAT540 Homework
Week 8
Page 3 of 4
b. Solve the model by using the computer
c. If a serving of each of the food items (other
than milk) was limited to no more than a half pound, what effect would this
have on the solution?
4.
The Cabin
Creek Coal (CCC) Company operates three mines in Kentucky and West Virginia,
and it supplies coal to four utility power plants along the East Coast. The
cost of shipping coal from each mine to each plant, the capacity at each of the
three mines and the demand at each plant are shown in the following table:
Plant
Mine Capacity
Mine
1
2
3
4
(tons)
1
\$ 7
\$ 9
\$10
\$12
220
2
9
7
8
12
170
3
11
14
5
7
280
Demand
(tons)
110
160
90
180
The cost of mining and processing coal is \$62 per
ton at mine 1, \$67 per ton at mine 2, and \$75 per ton at mine 3. The percentage
of ash and sulfur content per ton of coal at each mine is as follows:
Mine
% Ash
% Sulfur
1
9
6
2
5
4
3
4
3
Each plant has different cleaning equipment.
Plant 1 requires that the coal it receives have no more than 6% ash and 5%
sulfur; plant 2 coal can have no more than 5% ash and sulfur combined; plant 3
can have no more than 5% ash and 7% sulfur; and plant 4 can have no more than
6% ash and sulfur combined. CCC wabts to determine the amount of coal to
produce at each mine and ship to its customers that will minimize its total
cost.
a. Formulate a linear programming model for this
problem.
b. Solve this model by using the computer.
5.
Joe
Henderson runs a small metal parts shop. The shop contains three machines – a
drill press, a lathe, and a grinder. Joe has three operators, each certified to
work on all three machines. However, each operator performs better on some
machines than on others. The shop has
MAT540 Homework
Week 8
Page 4 of 4
contracted to do a big job that requires all
three machines. The times required by the various operators to perform the
required operations on each machine are summarized as follows:
Operator
Drill Press
Lathe
Grinder
(min)
(min)
(min)
1
23
18
35
2
41
30
28
3
25
36
18
Joe Henderson wants to assign one operator to
each machine so that the topal operating time for all three operators is
minimized.
a. Formulate a linear programming model for this
problem.
b. Solve the model by using the computer
c.
Joe’s
brother, Fred, has asked him to hire his wife, Kelly, who is a machine
operator. Kelly can perform each of the three required machine operations in 20
minutes. Should Joe hire his sister-in-law?
6.
The Cash
and Carry Building Supply Company has received the following order for boards
in three lengths:
Length
Order (quantity)
7 ft.
700
9 ft.
1,200
10 ft.
300
The company has 25-foot standard-length boards in stock. Therefore,
the standard-length boards must be cut into the lengths necessary to meet order
requirements. Naturally, the company wishes to minimize the number of
standard-length boards used.
a. Formulate a linear programming model for this
problem.
b. Solve the model by using the computer
c.
When a
board is cut in a specific pattern, the amount of board left over is referred
to as “trim-loss.” Reformulate the linear programming model for this problem,
assuming that the objective is to minimize trim loss rather than to minimize
the total number of boards used, and solve the model. How does this affect the
solution?
Get a 33 % discount on an order above \$ 40
Use the following coupon code:
MERRYXMAS
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Solved
# FIND THE SUM TOTAL OF AN --ISNUMBER REESULT
Posted on 2014-09-05
Medium Priority
147 Views
I have a spreadsheet that finds the total number of times a category reason code is noted on another worksheet, but now I have to find what the total dollars are for that category reason code. How do I proceed? Use an "If" statement, a "Match" + Sumproduct statement, or ???
Attached is a sample of the spreadsheet; the Review worksheet has the categories with their count + dollar columns and the Detail worksheet the codes used with the claim value.
EE-ISNUMBER-MATCH.xls
0
Question by:castlerj
[X]
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Accepted Solution
Glenn Ray earned 2000 total points
ID: 40306659
Great formula. You only have to add a reference to the "Except Amt" column in the SUMPRODUCT formula to return the total amount for any category:
=IF(C6="","",SUMPRODUCT(--(ISNUMBER(FIND(","&C6&",",","&SUBSTITUTE(Detail!B\$2:B\$41," ","")&","))),Detail!\$C\$2:\$C\$41))
Regards,
-Glenn
0
Author Comment
ID: 40306744
Thanks for pointing that out! Worked!
0
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Expert Comment
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Hi,
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## To reduce waste of raw materials, the government
tagged by: NandishSS
This topic has 1 expert reply and 2 member replies
### Top Member
NandishSS Master | Next Rank: 500 Posts
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#### To reduce waste of raw materials, the government
Mon Aug 29, 2016 3:18 am
To reduce waste of raw materials, the government of Sperland is considering requiring household appliances to be broken down for salvage when discarded. To cover the cost of salvage, the government is planning to charge a fee, which would be imposed when the appliance is first sold. Imposing the fee at the time of salvage would reduce waste more effectively, however, because consumers tend to keep old appliances longer if they are faced with a fee for discarding them.
Which of the following, if true, most seriously weakens the argument?
A. Increasing the cost of disposing of an appliance properly increases the incentive to dispose it improperly.
B. The fee provides manufacturers with no incentive to produce appliances that are more durable.
C. For people who have bought new appliances recently, the salvage fee would not need to be paid for a number of years.
D. People who sell their used, working appliances to others would not need to pay the salvage fee.
E. Many nonfunctioning appliances that are currently discarded could be repaired at relatively little expense.
Source:OG
OA:A
Experts how do I break down this argument and down with correct ans. Advice Please.
@GMATGuruNY, Matt@VeritasPrep, DavidG@VeritasPrep
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Hello Experts ,
Thanks,
Rashi
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Fri Jan 06, 2017 11:50 pm
Premise: A charge at the time of disposal will push people to use the product for a long time, so that they don't throw it and fully utilise it.
Conclusion : this will reduce wastage.
A. Correct, people might just throw anywhere rather than disposing it properly.
B. Out of scope, manufactures intent is not at the core, the user's intent is at the core of the argument.
C. Irrelevant.. fee is only charged at the time of disposal... Timing of salvage fee is not queationed.
Both D and E are strengthners..Both increases the life of the product therefore reducing waste, an idea that we have to weaken...
Surely, tough one..
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Sat Jan 07, 2017 10:52 am
NandishSS wrote:
To reduce waste of raw materials, the government of Sperland is considering requiring household appliances to be broken down for salvage when discarded. To cover the cost of salvage, the government is planning to charge a fee, which would be imposed when the appliance is first sold. Imposing the fee at the time of salvage would reduce waste more effectively, however, because consumers tend to keep old appliances longer if they are faced with a fee for discarding them.
Which of the following, if true, most seriously weakens the argument?
A. Increasing the cost of disposing of an appliance properly increases the incentive to dispose it improperly.
B. The fee provides manufacturers with no incentive to produce appliances that are more durable.
C. For people who have bought new appliances recently, the salvage fee would not need to be paid for a number of years.
D. People who sell their used, working appliances to others would not need to pay the salvage fee.
E. Many nonfunctioning appliances that are currently discarded could be repaired at relatively little expense.
Source:OG
OA:A
Experts how do I break down this argument and down with correct ans. Advice Please.
@GMATGuruNY, Matt@VeritasPrep, DavidG@VeritasPrep
The conclusion: It's better to charge a fee at the time of disposal/salvage than when an appliance is first sold.
Premise: If people have to pay a fee at the time of salvage, they'll hold on to the appliance longer.
We want to weaken this conclusion, so we want to show that charging a fee at the time of disposal/salvage won't work to reduce waste. In effect, we're looking for problems with charging a fee at the time of salvage.
A gives us a pretty compelling problem. If people dispose of the appliance improperly they'll 1) avoid the fee associated with proper disposal and thus 2) have no incentive to hold on to the appliance for a longer period of time.
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https://hackaday.com/2015/09/28/navigating-the-oceans-is-deadly-without-a-clock/?replytocom=2747048 | 1,618,160,666,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038064520.8/warc/CC-MAIN-20210411144457-20210411174457-00066.warc.gz | 401,454,061 | 40,114 | # Navigating The Oceans Is Deadly Without A Clock
I came across an interesting question this weekend: how do you establish your East/West location on the globe without modern technology? The answer depends on what you mean by “modern”, it turns out you only have to go back about three centuries to find there was no reliable way. The technology that changed that was a clock; a very special one that kept accurate time despite changing atmospheric conditions and motion. The invention of the Harrison H1 revolutionized maritime travel.
We can thank Andy Weir for getting me onto this topic. I just finished his amazing novel The Martian and I can confirm that George Graves’ opinion of the high quality of that novel is spot on. For the most part, Andy lines up challenges that Mark Watney faces and then engineers a solution around them. But when it came to plotting location on the surface of Mars he made just a passing reference to the need to have accurate clocks to determine longitude. I had always assumed that a sextant was all you needed. But unless you have a known landmark to sight from this will only establish your latitude (North/South position).
### Watching the Sun
If you’re standing still, you can plot the location of the sun in the sky each day. If you move West from that point, the Sun will be lower in the sky at the same exact time because your new location takes longer to move toward the horizon line. Knowing this and combining it with sextant readings lets you easily calculate your exact position. But you need a very accurate clock to make the first measurement.
The pendulum clock is a very accurate method of keeping time. It was invented in 1656 by [Christiaan Huygens] but you can’t take one on a ship. The rocking of the boat to which the clock is affixed disturbs the regular oscillation and renders it useless. Add to this the conditions the mechanism has to hold up to at sea (changes in temperature, humidity, saltwater, etc) and it’s worthless for navigation. So what did they do? Dead Reckoning. That’s right, measure (estimate really) the speed of travel and plot it on the map the best you can combined with Sextant readings. The resulting navigation system put mariners hundreds of miles off course and was one of the biggest contributors to maritime deaths.
### John Harrison; The Legend
This guy is our guy. You have to sympathize with someone who spent 31 years of his life trying to solve a really important problem, killed it with his invention, and was only marginally recognized for the accomplishment.
His first stab at a maritime chronometer started in 1730 and resulted in the Harrison H1 which was given a sea trial in 1736. It wasn’t the very first clock designed for a ship, but it did overcome the problems faced by earlier designs.
First off, you can eliminate many of the problems of pendulums by using a horizontal balance wheel. Balance wheels had already been tried and were proven to be imprecise, especially because of changes in temperature affecting the metal spring used in the system.
The H1 used a novel approach that fixes almost all of the issues. In it, Harrison implemented a double beam system. The two were mounted in a vertical position with the pivot in the middle and weights at both ends. These oscillate opposite of each other and have springs on both ends that pull them toward the center point of the chronometer and push them back out again. This continued shift of momentum is not affected by the motion of the ship or by changes in atmospheric conditions.
You can see the top weights of a replica H1 shown to the left. This is a screen capture from a very quick clip video showing the clock in action at the Royal Observatory in Greenwich. Take a look and you’ll get a glimpse of how large the device is.
Although the H1 worked extremely well in many cases, it was still vulnerable to centrifugal forces and tested rather sporadically. He refined the design twice and by the time he built the H3 in 1759 it included more balancing weights to combat this weakness.
But in the end the entire design was scrapped for a huge leap forward which would become the standard for mechanical watches. It was back to that horizontal balance wheel and spring that proved the ultimate solution. Harrison solved the problem of temperature swings killing accuracy by using a bimetal spring that adjusted its own tension as it warmed or cooled. He also increased the speed of the balance wheel to improve performance. This was realized in the H4 which was completed in 1761.
But don’t forget that I mentioned his discovery was somewhat marginalized. One contributing factor to his drive to solve the issue was the Longitude Reward the British Government was offering. The H4 qualified for the highest prize of 20,000 pounds sterling (2.8M at modern value) because it achieved accuracy of less than 30 minutes of longitudinal error. The Longitude Board, which was responsible for making the determination of a winner, asserted that he had to produce multiple copies of the H4. He eventually received the full reward… about 36 years after the first copy of the H4 was shown to be reliable. Better late than never, although the then 80-year-old Harrison might not have been so upbeat about it.
### We’re Still Using Clocks for Navigation
It would be really interesting to know Harrison’s reaction if we were somehow able to explain today’s navigation practices to him. Obviously we’re not using the H4 to navigate our ocean-going vessels. Modern ships are simply incredible. They have highly advanced navigation and control systems; they even include automatic pirate detectors (arg!). But boats, cars, and your smartphone alike are all still using extremely accurate clocks to get a perfect fix on your global location.
GPS, the Global Positioning System, uses time to triangulate between satellites. There are 24 satellites in the GPS system each with 4 atomic clock sources (Rubidium or Cesium). A GPS receiver locks onto satellites, receiving a chirp from each that includes a time stamp from their clock standard. If you don’t already know how this works you need to watch Grace Hopper’s explanation of how far a nanosecond is. When you’re talking about distances like those from an orbiting satellite to the earth, the speed of light comes into play big time. Calculate the amount each satellite timestamp is off from each other and you can triangulate your location in 3D space: latitude, longitude, and elevation.
We’ve far surpassed the Harrison H4, but clock accuracy has never been more important for finding our way.
## 66 thoughts on “Navigating The Oceans Is Deadly Without A Clock”
1. Jomegat says:
There is another way as described by Gavin Menzies in his book 1492 (not endorsing – it’s a controversial book). Menzies asserts that the Chinese were using lunar eclipses to determine longitude in the 15th century by noting what stars were at the zenith during the various phases of an eclipse. Since the eclipse happens at the same time no matter where you are, you can grok your longitude by knowing the offset between the stars at zenith at the two locations. Not exactly real-time, and useless for navigation. But still cool. I thought about noting the zenith last night, but didn’t bother.
1. bl says:
does that also work for magnavox?
(sorry) ;)
2. static says:
The Nova episode on this topic did mention using the eight sky, but also mention even if it wasn’t overcast the rocking of the ship at sea made it difficult to get the sighting the need, and if the did gt the sighting, the math required took a very long time. Meaning by the time they fixed their location they would have been well beyond that point
3. Chris says:
Even after Harrison’s chronometer, astronomical events (especially transits and occlusion of Jovian moons) were used to correct chronometers during long voyages, or in those rare instances where the punishment of lashes didn’t prevent a seaman from letting a ships chronometer from winding down…
2. Miroslav says:
Harrison was a real genius. And they just barely paid him after a lot of wrangling. Interestingly, I read somewhere that gears, at least in the 1st version, were made of wood.
1. Sweeney says:
They were wood, but wood chosen for both its hardness and self lubricating nature. The older H series chronometers still work today. The H4 was made from metal, and the acids in oil mean it doesn’t work any more.
3. Rich says:
There is a great PBS Nova episode about the Longitude Reward and Harrison. It’s worth the watch.
1. nitePhyyre says:
Har har har.
2. Ren says:
IIRC, the name of the show was “Longitude” it also starred Jeremy Irons as a man who centuries later worked to renovate the Harrison clocks. I was surprised to hear them pronounce Longitude with a “hard g”. The movie is available on the PBS store.
1. FastEddy says:
I have only ever heard the hard “G” version in England.
Longitude (/ˈlɒndʒɨtjuːd/ or /ˈlɒndʒɨtuːd/, British also /ˈlɒŋɡɨtjuːd/)
1. We Yanks (i.e. Americans) say “lawn-jah-two-d” for longitude. Brits (i.e. UK) say a lot of stuff weirder to our ears like “shed-jewel” for schedule. Why don’t they say “shoe-el” for school? We say “skool” just like they do. I love it when they try and imitate our accents like we all have Boston or Texas accents right? I think actor Idris Elba is one of few Brits that can do our accents correctly. Jeremy Irons doesn’t usually try to but he’s not to good at it either. I think he sticks with his own accent when acting.
1. jalnl says:
Don’t forget Hugh Laurie, as a Brit who can do a perfect version (so I’m told, not a native speaker myself) of American English.
4. Gary says:
And watching the occultations of Jupiter’s moons with a telescope can get you to within a minute or so.
That was used before good clocks. But hard to use on a pitching ship.
1. True but you’d need a lens at least with 2.75″ aperture and 50X magnification. Binoculars like that are rare. A T-scope like that would need to be on a tripod or deck gimble-mount. Of course, like you said, any pitching and yawing would negate your efforts. I think shooting LUNA would be easier (i.e. Lunar chronometer method with sextant). I wonder if an Arduino with a home made sextant could be programmed to equivocate that method. Or a homemade automatic web cam lunar tracker. Initially aim it at moon and it tracks the moon’s movement. It would use 2 linear potentiometers to read azimuth and elevation into a ADC to the Arduino. The motors would be stepper motors. Or maybe steppers would not need position feedback? Just brainstorming here…
1. sdphotoau says:
I was about to leave the same comment. What an amazing book and story.
5. Leithoa says:
Another hero in this is Nathaniel Bowditch. He compiled “The American Practical Navigator” in 1802, a book that is still updated by the USCG and continues to be in print. This book provides a foundation for celestial navigation and was used to teach generations of navigators with little formal education.
Celestial navigation is still used in military roles via computer vision when the prospect of GPS being jammed (such as the retired SR-71) would prove problematic to the mission.
The PDF is available for free (as it’s maintained by taxes) and worth having in every hackers library. ftp://ftp.flaterco.com/xtide/Bowditch.pdf
And wiki format
https://en.wikisource.org/wiki/The_American_Practical_Navigator
1. Leithoa says:
Dead reckoning is what you do without any instrument readings, based solely on estimated direction, speed, and duration of travel. This is what robots and submarines do when they use their IMU to determine location (albeit less precise).
Navigators with celestial readings but no clock would use what is referred to as ‘parallel sailing’. That is sailing due east-west along a parallel (latitude) until landmarks or navigational aids are available to follow.
1. Whatnot says:
I’m sure subs use a host of tricks, not just IMU but there are many other things, like possibly variation in the earth’s magnetic field and such, which makes me wonder, is there any particle the sun emits that goes right through an ocean like neutrinos BUT are detectable in a usable manner? Because then you could locate the sun, which might be a handy aid.
I’m sure the US navy won’t tell but maybe somebody can reverse engineer, for lack of a better word.
1. Leithoa says:
Magnetometers are integrated into IMUs, Basically it’s a digital compass that adds precision to changes in course. But even these have their flaws since large ore bodies or underwater cables (power in particular) would influence them, forcing you to trust in your accelerometers.
Any particle that makes it through the atmosphere and a few hundred feet of water is either going to scream right on through a few tons of steel, or get absorbed by the hull. Placing sensors outside the hull to detect such a particle would introduce many engineering problems, that in general aren’t worth the effort since being able to detect the sun is less useful than knowing which way is north.
1. Whatnot says:
About those particles, some particles could be coaxed into reacting with specific setups. And combining the location of the sun with a precise clock will give you more info than a rough magnetic north.
As for those ores and cables, that is precisely the advantage, since there are variation in the magnetic field depending on the location it would actually aid you with determining where you are. If for instance you can detect an underwater cable, which is in a known locations, you automatically know you are somewhere along the line of that cable.
2. Leithoa says:
Ahh, I was thinking along the lines of how magnetometers generally function w/i the IMU. Being able to locate yourself on the map is important but if you’re navigating a submarine canyon and your instruments go nuts you’re in trouble.
Unless it’s been navigated before and you know to turn port 20*, bow up 5* when the instruments flip out.
3. @Leithoa – Here’s a scenario for you (use Gene Hackman’s voice) “COB turn to port 20°, bow 5° up bubble. Make your depth two five zero, hover, and float the buoy.”, “The comm-buoy skipper?”, “No that new KVH thermal-sun-tracker thing with the 500 foot fiber-optic cable we got at NLON last week during our IMU system’s retrofit… COB?!”,”Aye aye captain! Quartermaster,,, prepare for SolarShot deployment…”.
Of course there is no such thing but that would make for a great HaD project to sell (or give) to DoD SBIR or DARPA! It could even use an Arduino. It would have to by HaD tradition I think. 8-P
4. @Whatnot – Well SOLAR FLARES can penetrate seawater up to 33 feet. That’s within periscope depth. So maybe some sort of underwater SF detector could be invented and used by USN for emergency navigation? According to a hobbyists radio astronomer, the sub already has the equipment in the form of their VLF radio they use(d) for EAM’s. Some how the absorption of SF SIDs (Sudden Ionospheric Disturbance) can be detected on a VLF radio around 24 Khz. http://tinyurl.com/pzgubu7 (a PDF file)
2. AKA the A says:
At least modern NATO subs tend have very sensitive gravitational sensors, that allow them to detect fluctuations of the ocean floor without having to use sonar…
Also, very sensitive and complicated magnetometers, both for navigation and enemy subs…
1. @AKA the A – the latest USN super-sensitive magnetometer uses UV light…
3. @Whatnot – Leithoa is 100% accurate (as usual!). There is also the Laser Gyro Compass that does not depend on geomagnetics nor outside RF or photonic signals. It needs to be initialized at a fixed surface point though. USN uses some pretty sophisticated stuff too. The accelerometers they use (i.e. FOLA’s) are not from Radio Shack – LOL
Your neutrino idea wont work as they mostly go through everything. One thing you could do was have a huge vat (470 metric tons) of dry cleaning fluid (perc – C2Cl4) and maybe a argon proton or two might become visible as a neutrino passes by; but a submarine has no room for that *-) – There are other ways but all still too big for a sub.
(Just like it has no room for exterior screen doors either – LOL)
An ancient method of navigation needs to be reintroduced to science today. A piece of feldspar called Icelandic Calcite could be used to find the sun even at twilight when the sun has gone below the horizon. Also works during periods of overcast and precipitation (i.e. occulting of the sun). You use your fovea (in your eye) to peripherally detect a streak of light from polarized sunlight. Probably helped Lief Erickson in 11 century CE find North America.
Some insects use polarized sunlight for navigation: bees and ants – maybe others too.
Also the Polynesians used known ocean currents and other ancient maritime navigational methods (i.e. stellar, marine life behavior, meteorology, sea color, etc.) to trek out to remote places like Easter Island, Tahiti, and other Pacific islands. This even may account for pre-Colombian treks to North America. A theory says that the so-called Indians Columbus and other Conquistadors had first contact with may have actually been people with Polynesian DNA.
eot
1. Whatnot says:
I made it clear that I was aware that neutrinos won’t work, they merely served as an example that some particles have no issue penetrating the ocean, or in fact the entire planet. But my point was that there might be other particles that can penetrate a large volume of water but which through technical means would still be detectable in a sub.
And although a sub has little room, it does have a lot of electrical power if it’s a nuclear type I expect.
As for polarization, I’m not sure that would work at the depth moderns subs can travel. The photons if any are probably scattered or coming from bio-luminescence – if there are any. Although I guess you didn’t refer to use with submarines on that subject.
But your maria life and water color example is something that could aid even in a sub, I wonder if you could just combine a shitload of vague clues into a semblance of actual coordinates.
2. @Whatnot – OK duly noted about the neutrinos. They are working on something that uses Blue-Green-Ultraviolet light to penetrate seawater for something (not from sunlight but from an overhead plane, ship, or satellite).. Whatever it does is light-years way over my pay grade :-)
(Checkout QInetQ in UK. I think they are working on it for USN – I’m not talking about SLC comm either…)
Yes you are right I did not offer that information about Icelandic “sunstones” for underwater navigation. The sub would have to surface and use it to take a sun bearing. But sub’s wouldn’t need it with all the high-tech gadgets they have for navigation. I think they have a AI-based gadget that if they lost all power at sea (virtually impossible for a nuke), you could aim this palm sized thingy at the night sky and it would figure out where you are by stellar navigation. You don’t need to tell it anything as it automatically figures out which way is north, what time it is, and by pattern-recognition figures out constellations and individual stars and planets. Of course you need to put batteries in it. Of course you must be top-side for it to work too.
Regarding the Polynesians, I don’t think they thought like Westerners who need to know their EXACT COORDINATES. Just like how Europeans needed to OWN LAND in North America and the natives where going “Huh? What’s that?”. I think they were happy if they could come within spotting distance of familiar landfall when traveling the Pacific. I imagine a AI-based computer program could take a “shitload” of diverse data like that and come up with a close approximation of your global position at sea. Sounds like a good HaD Arduino or Raspberry PI project? 8-D
They still teach PN somewhere in South Pacific. Here are some references to literature on it:
* Kawaharada, Dennis. “Wayfinding: Modern Methods and Techniques of Non-Instrument Navigation, Based on Pacific Traditions”. Wayfinding Strategies and Tactics. Honolulu, HI, USA.
* “Wayfinding”. Honolulu, HI, USA: Polynesian Voyaging Society.
* Exploratorium. “Never Lost | Polynesian Navigation”. San Francisco, CA, USA.
6. If you’re looking for modern navigation, HFOS might be interesting for you. It won’t really work without a clock either, but what does, these days ;-)
It strives to be a very collaborative crew/ship management system with open charts and a lot of “multiplayer” goodies.
One of the most important things it aims to do, is bring the navigation desk to the crew’s pockets – BYOD-style.
Another point is to aggregate sensor data to collaborate back to the open sea map and other open datasources.
HFOS lives on your ship computer (aimed for embedded hardware) and loves if you have Wifi on your vessel already, but you can use it on your localhost, too – the frontend is built with HTML5, the backend constructed in Python. The sourcecode lives on github: https://github.com/Hackerfleet/hfos
I am the developer. AMA ;)
1. nitePhyyre says:
You need better SEO, lol ;)
1. Thanks for the headsup, that should be “fixed” again – we’re working on a new homepage.
2. @riot – Technically even GPS won’t work without a local clock too. It must be set correctly before you use it. The satellites use a clock too but way over our pay grade they are… ATOMIC
1. drew says:
The satellites’ atomic clocks also have to be regularly updated to correct for relativity: they’re far enough out of earth’s gravity well and have sensitive enough clocks you can actually observe their clocks running fast relative to an earthbound clock.
1. @drew – That’s pretty much the reason why serious TIME MACHINE advocates like physics professor Dr. Ron Mallet at UCONN.edu (and others) refuse to give up the notion that time-travel is possible. Dr. Mallet claims he has successfully sent a gauge boson BACK 1-second in time using a ring laser and photonic crystals. I’m still very skeptical even though I have visited the location a few times. His supervisor says he is very serious about it and is not some crack-pot. The jury is still out I think on that. Ken Olum and Allen Everett say he is wrong: http://arxiv.org/abs/gr-qc/0410078
I still haven’t read his book on my shelf yet. I wish someone would read it to me… (LOL)
7. silencio says:
There’s one with wooden gears that’s still operational. From Wikipedia:
“In the early 1720s, Harrison was commissioned to make a new turret clock at Brocklesby Park, North Lincolnshire. The clock still works, and like his previous clocks has a wooden movement of oak and lignum vitae.”
1. Ren says:
Yes, Lignum vitae is an “oily” wood.
2. Drew says:
Yes- that is for real. It was stopped once, I believe, sometime in the 1880s I think, for basic service.
The thing is STILL RUNNING. Accurate too. To call Harrison a genius is almost an understatement- there are people working nearly 300 years after his death that still can’t make a clock that can run that long or accurate.
The guy was a god of horologists, the only man among horologists that makes even A.L. Breguet look small by comparison. They still haven’t figured out how he formed the curved planes of the diamond pallets for the H4.
For those interested- and to further prove the point that this man is equivalent to Einstein in the world of horology, he designed a clock before he died that was never built- but he claimed it should keep time to within ONE SECOND in 100 days- using a pendulum. Keep in mind- this is an insane feat even to this day. It really shouldn’t be possible.
Martin Burgess, a Brittish clockmaker, replicated Harrison’s design recently- Google Burgess B Clock. It really did work- and it is now in the Guinness Book Of World Records for most accurate mechanical clock ever made.
It was designed over 250 years ago. Design existed- but no maker ever made a clock near that accurate, without aide of something electrical. It’s totally mechanical.
It’s not hyperbole to say John Harrison is the horological equivalent of Einstein. Genius is too small a word for some people- Harrison is one of them. Long after he’s dead- he’s still reinventing our understanding of timekeeping. And his story is one of the best reads you’ll ever pick up. The guy was absolute tenaciousness incarnate.
1. What did Einstein ever invent with his hands? Just asking…
1. @tag – Actually according to Gene Dannen of Scientific American, he says his Hungarian student Leo Szilard did all the “hands-on” work and Albert just did the paper work for the patent applications. Just saying…
2. Dan says:
You know in 100 years from now robots will be making the same bitchy comments about humans.
1. h3ll0_w0rld says:
Einstein’s mind was a much better tapestry than physical space for his ideas. I think if he was too focused on classical mechanics he would have never redefined them using non-euclidean geometry. He was able to look at what everyone else saw and say it was not accurate just by knowing that it wasn’t pretty enough to be true nature. He literally redefined reality in a time when physics as a science was in its infancy. Its truly comparing apples and oranges but I glorify the complete redefinition of time over building a badass clock before its time.
8. TheRegnirps says:
You can easily navigate today without (carrying) modern instruments or a compass. For example, to got to Hawaii from Seattle, go out the straights and head for the setting sun a day or two. Turn South till your butter melts then follow the jet contrails from LAX to Honolulu. Your passengers will first be panicked and then amazed at your navigation sense.
1. Dan says:
You don’t even need the butter if you do a statistical analysis of the changes in the passenger’s clothing choices, except this is not very popular with most captains on account of the requirement that they do not skew the results by attempting to disrobe any of the passengers themselves.
2. Polynesians had no trouble navigating between Hawaii and mainland North America. Just used sea color. bird behavior, ocean currents, cloud formations, and apparent star movements. Also the ancient Japanese fishermen had no trouble navigating to Peru (albeit mostly by accident). The ancient Chinese (under first emperor Qin Shi Huang) supposedly trekked to California coastline and interacted with local Natives there many centuries before Columbus (just circa 220 years before Jesus Christ’s birth in Israel).
9. If you are ever in DC, visit the Time and Navigation exhibit at the National Air and Space Museum. They also have a good online version that goes into the the history of maritime navigation – timeandnavigation.si.edu/navigating-at-sea
10. Drew says:
If any of you ever get a chance to go to England, you’ll probably be in London. The Royal Observatory in Greenwich is right next to London. It’s the place where the Prime Meridian is measured from.
If you can, absolutely go see it. There is simply no place else like it in the world- and it has one of the world’s most impressive collection of timekeepers. Harrison’s H1, H2, H3 are there, and a replica of the H4 is on display. The Worshipful Company Of Clockmakers guildhall in London has an incredible museum too.
I went to school to learn watchmaking, and going to that museum and seeing Harrison’s pieces, actually before I realized their true importance, was what made me want to be a watchmaker. The entire place was a huge inspiration, and one of the coolest places you’ll ever visit if you are a fan of timekeepers, mechanics, history, or geography. Students today still learn about Harrison in modern curriculum as watchmakers- he was simply that important to our modern era.
1. John Spencer says:
Greenwich was the Prime Meridian, by definition and by International Treaty. Today latitude and longitude is defined by reference to a mathematical model of the, slightly lumpy, Earth, not to any physical place on the Earth. There are lots of mathematical models of the Earth (or regions of the earth) and they all differ slightly. Google Earth can zoom in to show the Prime Meridian carved into the pavement at the Greenwich Observatory, and it marks 0° as being a few feet away. Both the groove on the ground and the Google 0° line are correct.
It is odd that now we have astonishingly accurate means to measure our longitude and latitude the definition of latitude and longitude is imprecise unless we specify which model we are referring to.
11. Drew says:
….and congrats ladies & gents, we’ve been slashdotted. The only other site I visit daily. I’m honored I posted here. Never thought John Harrison would get slashdotted, but I think he’d like it.
12. tim says:
Great movie on Harrison, the quality is a bit rough though
13. FastEddy says:
As I recall, one of Darwin’s task on the Beagle was to wind and tend to the chronometers (plural, since you would not want to trust your longitude to a single, malfunctioning unit).
1. BillT says:
If you had 2 clocks, you’d be more confused than if you had just one.
14. MonsieurET says:
Lewis and Clark used a Thomas Parker Chronometer (cost \$250.00) for their maps. Sadly, they often forgot or were too busy to keep it wound. It was found to lose 14 seconds in 24 hours each day after initial calibration. When found stopped, they had to resort to celestial sightings to reset the clock.
1. @MonsieurET – No worries mate… Sacajawea,their Lemhi Shoshone assistant, probably knew her way anyway. We NA’s seem to have a natural instinct for navigation. I’ve never been lost anywhere until I went to Camden NJ or Waterbury CT (two of the worst planned cities ever!). California is very easy to navigate without instruments. Mexico and Canada also no challenge for NOT getting lost. NYC is a piece of cake when you get the numbering plan straight in your head. In Lewis & Clark’s situation, even applies today, if you ever get lost in the woods just follow any river downstream. You’ll run into somebody (or some animal) eventually as every creature needs water. And humans tend to build villages. towns. and cities next to rivers.
What really astounds me is that they brought an almost silent-firing air rifle along and amazed the NA’s! I still can’t see how the inventor did that. Much better than a musket.
15. Andrew says:
It looks like a bomb.
Phil Derry, Commodore of Coquet Yacht Club (coquetyachtclub(dot)co(dot)uk) is a direct descendant of John Harrison. He and his son Simon continue the entrepreneurial lineage with their location company trackaphone(dot)com. Their technology enables them to pinpoint and track the exact location of any individual and asset across the globe. Phil said “John Harrison was my (times 6) great-grandfather on my mother’s side. From what I have read about him, I am sure my son has inherited his disposition. He has the same stubbornness and attitude towards quality and attention to detail.”
Remove (dot) and replace with period to go to websites
1. h3ll0_w0rld says:
17. I don’t mean to nickpick, but GPS uses trilateration and not triangulation.
1. @rotatetechnology – Correct. Much the same way LORAN-C navigation systems worked. The computer is measuring the distance along a hyperbolic line of the RF signal (oversimplifying it of course – the GPS process is very complex). Radio triangulation would be measuring the azimuth in degrees to an RF source from your point.
I would love to know who invented GPS and the evolution of thought leading up to it. NEVER MIND it was Roger Lee Easton, Sr. who died last May… :-(
18. xorpunk says:
They did longitude and latitude doing different purely mechanical methods on that show Rough Science.
19. Garry says:
Clearly most of these comments are irrelevant. The principal contender for the royal prize was the method of lunar distances proposed by Sir Nevil Maskelyn, the Astronomer Royal. Although Harrison won the prize, most mariners used “lunars” because chronometers were extremely expensive until the 20th century. “Lunars” required only a sextant and the navigational almanac’s tables and the calculations are surprisingly easy to do. Since every navigator had a sextant and the tables anyway it was much cheaper to do “lunars” than a “time sight. Sights from the deck of a vessel at sea are not particularly difficult except for the requirement that you use both hands to adjust the sextant and have to hang on to the boat with your teeth or wrap your self around a shroud or a stay. As mentioned two chronometers that disagree are as bad a no chronometers. Royal Navy warships carried three. For an explanation of how to do “lunars” see Chapter 8 in “Celestial Navigation in the GPS Age” by John Karl. Joshua Slocum sailed around the world alone and his only timepiece was a tin alarm clock without a minute hand. LUNARS RULE!!
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This site uses Akismet to reduce spam. Learn how your comment data is processed. | 7,380 | 33,106 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2021-17 | latest | en | 0.951139 |
http://mathhelpforum.com/algebra/189497-lines.html | 1,527,360,938,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794867841.63/warc/CC-MAIN-20180526170654-20180526190654-00331.warc.gz | 184,826,435 | 9,695 | 1. ## Lines
Hi I'm new here. Can someone check my work to see what I should do to correct my mistake?
Find the slope of the line through (6, -4) and (2, 10).
I solved it this way:
$\displaystyle (10-4)/(2-6)=-6/4 = -3/2$
$\displaystyle m=-3/2$
However my answer is wrong. What should I do?
Also, I have a few other math questions... should I post in a different thread for the other questions?
Thank you.
2. ## Re: Lines
Your numerator should be 10-(-4) not 10-4
3. ## Re: Lines
Close. What happened to the sign on "-4"?
10 - (-4) = 10+4 = 14 | 175 | 554 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.78125 | 4 | CC-MAIN-2018-22 | latest | en | 0.909318 |
https://onlinetest.ibpsexamguru.in/questions/Clerk-Reasoning-Test/CR-Quiz-133 | 1,534,512,266,000,000,000 | text/html | crawl-data/CC-MAIN-2018-34/segments/1534221212323.62/warc/CC-MAIN-20180817123838-20180817143838-00084.warc.gz | 756,326,783 | 9,173 | # Bank Clerk :: Clerk Reasoning Test CR Quiz 133
## Home Bank Clerk / Clerk Reasoning Test CR Quiz 133 Questions and Answers
1 .
Which will be the next in the following series ?
AZY, BYX, CXW, DWV,__________
GHS
EVU
FUT
EUT
2 .
Rakesh walked 100 metres towards north, took a left turn and walked 75 metres, again took a left turn and walked 100 metres and stopped walking. Towards what direction was he facing when he stopped walking ?
North
South
North-East
South-East
3 .
There are seven persons up on a ladder A, B, C, D, E, F and G A is above E by three steps but is lower than only C. B's position is exactly in the middle. G is between A and B. E is between B and F. Who is on the bottom step of the ladder ?
D
B
F
E
4 .
A + B means B is brother of A; A⋆ B means B is husband of A; A - B means A is brother of B; and A ⋆ B means A is father of B. Then which of the following expressions indicates 'R' is the grandfather of 'S' ?
R - Q - Y + S
R - P + T - S
S - Q - Y + R
R ⋆ Q - T - S
5 .
Pointing to a gentleman, Prasad said, "His only sister is the mother of my daughter's father." How is the gentleman related to Prasad ?
Uncle
Maternal Uncle
Brother in-law
Father
6 .
Direction (Q. 6 - 10): In the following questions the symbols #, @, ©, $, ⋆ are used with the following meanings: P # Q means P is greater than Q. P @ Q means P is either greater than or equal to Q. P © Q means P is equal to Q. P$ Q means P is smaller than Q.
P ⋆ Q means P is either smaller than or equal to Q.
Now in each of the following questions assuming the given statements to be true, find which of the two conclusions I and II given below them is/are definitely true.
Statement: Y#E, U@B, E⋆ B
Conclusions: I. Y # U II.B@Y
if only conclusion I is true.
if only conclusion II is true.
if either I or II is true.
if neither I nor II is true.
7 .
Statement: A @ B R$L, L # A Conclusions: I. R# A II. L#B if only conclusion I is true. if only conclusion II is true. if either I or II is true. if neither I nor II is true. View Answer Discuss in Forum 8 . Statement: RSM, N@Q, ROQ Conclusions: I . M # N II. N@R if only conclusion I is true. if only conclusion II is true. if either I or II is true. if neither I nor II is true. View Answer Discuss in Forum 9 . Statement:K$Z, K@P, Z⋆ L
Conclusions: I. P • L II. PSL
if only conclusion I is true.
if only conclusion II is true.
if either I or II is true.
if neither I nor II is true.
10 .
Statements: 1 # 9, 8 @ 9, 7 \$ 8
Conclusions: 1 .7@9 II. 7© 1
if only conclusion I is true.
if only conclusion II is true.
if either I or II is true.
if neither I nor II is true. | 814 | 2,625 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.59375 | 4 | CC-MAIN-2018-34 | latest | en | 0.922593 |
https://www.physicsforums.com/threads/superluminal-propagation-of-fields.798156/ | 1,531,711,694,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676589172.41/warc/CC-MAIN-20180716021858-20180716041858-00239.warc.gz | 974,683,375 | 13,373 | # Superluminal propagation of fields
Tags:
1. Feb 16, 2015
### Jesus
I am reading about the Velo-Zwanziger problem in which particles with spin higher than 1 propagates faster than light when the particles are coupled with an electromagnetic field.
In the original paper: G. Velo and D. Zwanziger, “Propagation And Quantization Of Rarita-Schwinger Waves In An External Electromagnetic Potential,” Phys. Rev. 186, 1337 (1969) the authors, to study the causal properties of the equation of motion for spin 3/2 particles coupled with electromagnetic field, use the "method of characteristic determinant" in which they replaces i∂μ with nμ , the normal to the characteristic hypersurfaces, in the highest-derivative terms of the equation of motion.
According to them the determinant ∆(n) of the resulting coefficient matrix determines the causal properties of the system: if the algebraic equation ∆(n) = 0 has real solutions for n0 for any ⃗n, the system is hyperbolic, with maximum wave speed n0/|⃗n|. On the other hand, if there are time-like solutions nμ for ∆(n) = 0, the system admits faster-than-light propagation.
My doubt about this is that I don't understand why can be faster-than-light propagation in the second case. If a partial differential equation is not hyperbolic does that meas that there can be faster-than-light propagation of waves?
2. Feb 16, 2015
### Staff: Mentor
Sort of. See the third paragraph at the top of this Wikipedia page:
http://en.wikipedia.org/wiki/Hyperbolic_partial_differential_equation
It contrasts hyperbolic PDEs with elliptic and parabolic PDEs; the first of these has a "limiting velocity" of propagation of disturbances, the others don't. But this "propagation of disturbances" may or may not correspond to "faster-than-light propagation of waves"; it depends on the specific PDE and what it's being used to describe.
I don't have access to the paper you refer to, so I can't say how the PDEs are classified there; but the general comment about PDEs in the Wikipedia page is valid.
3. Mar 20, 2015
### Jesus
ok, thank you for respond.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook | 523 | 2,175 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2018-30 | latest | en | 0.903161 |
https://mail.scipy.org/pipermail/numpy-discussion/2008-July/036088.html | 1,506,417,771,000,000,000 | text/html | crawl-data/CC-MAIN-2017-39/segments/1505818695375.98/warc/CC-MAIN-20170926085159-20170926105159-00325.warc.gz | 706,771,889 | 2,730 | # [Numpy-discussion] Change of SVD output
Robert Kern robert.kern@gmail....
Fri Jul 25 17:10:55 CDT 2008
```On Fri, Jul 25, 2008 at 17:01, Arnar Flatberg <arnar.flatberg@gmail.com> wrote:
> Hi
>
> In a recent thread there was an error in how a matrix is reconstructed from
> its SVD decomposition. I apologize if this is just an old and settled issue
> and I am just adding noise, but I got bitten by numpy's unfamiliar output
> myself a long time ago and I see others get confused as well. So what is the
> issue?
>
> Let the svd decomposition of X be USV:
> U, S, V = np.linalg.svd(X),
> Then U has X's left singular vectors in its columns, S contains the singular
> values, and V has X's right singular vectors in its *rows*. The
> reconstruction of X is (matrix notation) will be: U*diag(S)*V (not
> U*diag(S)*V.T).
> All other high-level software (Matlab, Scilab, Mathematica, R, etc), outputs
> the right singular vectors columnwise, that is V = [v1, v2, v3, ... vn],
> where vn is a column (eigenvector) in V, thus the reconstruction would be
> U*diag(S)*V.T. Also, as far as I know, most linear algebra textbooks operate
> with eigenvectors consistent as column vectors in explanations of the SVD. I
> think numpy's svd should do so too.
>
> I know lapack's dgesdd returns V.T (or conjugate), and specify that in its
> documentation so this is a true interface of the library, but I still think
> its wrong and its just too confusing for any beginner who usually has
> experience in other software, such as matlab, prior to numpy. Also, ,as I am
> typing here, I realize that changing the output would break lots of stuff,
> and pass silently through many tests as the shape of V is similar (if
> full_matrices=0). Oh well, I guess that proposal is off the table?
Yes.
> Perhaps
> some *stronger* hints in the documentation are needed.
http://sd-2116.dedibox.fr/pydocweb/wiki/Front%20Page/
> Arnar
>
> PS:
> In the docs at http://www.scipy.org/NumPy_for_Matlab_Users , the svd
> equivalents have wrong notation, this is not helping :-). I didnt manage to
> change it, perhaps some other may be so kind?
You will need to register an account. Make an account here:
http://www.scipy.org/UserPreferences
If you do have an account, and you are still having problems, it may
be because of the account filtering I am using to try to control the
spam problem. Try a different account name.
--
Robert Kern
"I have come to believe that the whole world is an enigma, a harmless
enigma that is made terrible by our own mad attempt to interpret it as
though it had an underlying truth."
-- Umberto Eco
``` | 703 | 2,612 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.625 | 3 | CC-MAIN-2017-39 | latest | en | 0.907378 |
https://matejbenko.com/calculating-rate-worksheet/ | 1,566,215,248,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027314732.59/warc/CC-MAIN-20190819114330-20190819140330-00162.warc.gz | 561,768,332 | 29,060 | # Calculating Rate Worksheet
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Have faith. But just because it's possible, doesn't mean it will be easy. Know that whatever life you want, the grades you want, the job you want, the reputation you want, friends you want, that it's possible.
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Lee,jangho August 29, 2000 01:39
boundary layer thickness
hi? i am graduate student in south Korea. i HAVE useD luent5.1 and solved NACA 00XX SERIES i want to mesured the boundary layer thickness at the trailing edge of airfoil. but i can find any display item about that. anyone who know any means write the answer to me thanks...
John C. Chien August 29, 2000 03:52
Re: boundary layer thickness
(1). I guess, you need to define the boundary layer thickness in the first place. (2). Once you have define that, you can use the computed results to derive the boundary layer thickness.
Kai Kang August 29, 2000 13:56
Re: boundary layer thickness
You can use the definition of bc layer thickness to define a scalar (under \DEFINE in Fluent) to represent the boundary layer's boundary. If that's not work, you might need to do a little own post-processing instead of clicking on Display...
Lee,jangho September 24, 2000 22:06
Re: boundary layer thickness
thank for replaying to everyone. but i can't understand actually if you have more time , please write more detail. thanks...
John C. Chien September 25, 2000 00:09
Re: boundary layer thickness
(1). At the location where you want to compute the boundary layer thickness, say just befor the trailing edge, you can display the velocity profile from the wall to the outer boundary . (2). For the flow over the airfoil, you should have two boundary layers, one on the top (the suction side), and the other on the bottom (the pressure side). (3). If you define the edge of the boundary layer as the location where the velocity is 99.5% of the local free stream velocity value, then you can calculate the location of the edge of the boundary layer.(measured from the wall) So, at the trailing edge location (a straight line) you need to define the local free stream velocity.(this is when the velocity is uniform. It may not be easy if the flow is somewhat non-uniform, but, the boundary layer concept is derived based on the uniform local free stream concept.) (4). Whether it should be 99.5% or 99.9% , it is up to you, as long as it is used consistently. (5). So, draw the velocity profile along the trailing edge location from the wall to the free stream or outer boundary. Draw a parallel line to the local free stream velocity at the 99.5% value. The location where the profile value is 99.5% of the local free stream velocity is the edge of the boundary layer. The boundary layer thickness is : the thickness measured from the (trailing edge) wall to the edge of the boundary layer. (6). By the way, if you don't have enough number of mesh points inside the boundary, it is going to be difficult to find the location of the edge of the boundary layer accurately.
Dhairya@CFD January 5, 2017 11:03
hello,
I am simulating roughness effect on a performance of centrifugal pump using ansus CFX.
here Y/δ, is an important parameter to study.where Y- boundary layer height δ-roughness height. I want to calculate boundary layer above the impeller blade surface. please guide me how to do it?
thanks,
regards,
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http://us.metamath.org/mpeuni/dprdf.html | 1,638,629,389,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964362992.98/warc/CC-MAIN-20211204124328-20211204154328-00389.warc.gz | 84,989,713 | 5,305 | Metamath Proof Explorer < Previous Next > Nearby theorems Mirrors > Home > MPE Home > Th. List > dprdf Structured version Visualization version GIF version
Theorem dprdf 18326
Description: The function 𝑆 is a family of subgroups. (Contributed by Mario Carneiro, 25-Apr-2016.)
Assertion
Ref Expression
dprdf (𝐺dom DProd 𝑆𝑆:dom 𝑆⟶(SubGrp‘𝐺))
Proof of Theorem dprdf
Dummy variables 𝑥 𝑦 are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 reldmdprd 18317 . . . . . 6 Rel dom DProd
21brrelex2i 5119 . . . . 5 (𝐺dom DProd 𝑆𝑆 ∈ V)
3 dmexg 7044 . . . . 5 (𝑆 ∈ V → dom 𝑆 ∈ V)
42, 3syl 17 . . . 4 (𝐺dom DProd 𝑆 → dom 𝑆 ∈ V)
5 eqid 2621 . . . 4 dom 𝑆 = dom 𝑆
6 eqid 2621 . . . . 5 (Cntz‘𝐺) = (Cntz‘𝐺)
7 eqid 2621 . . . . 5 (0g𝐺) = (0g𝐺)
8 eqid 2621 . . . . 5 (mrCls‘(SubGrp‘𝐺)) = (mrCls‘(SubGrp‘𝐺))
96, 7, 8dmdprd 18318 . . . 4 ((dom 𝑆 ∈ V ∧ dom 𝑆 = dom 𝑆) → (𝐺dom DProd 𝑆 ↔ (𝐺 ∈ Grp ∧ 𝑆:dom 𝑆⟶(SubGrp‘𝐺) ∧ ∀𝑥 ∈ dom 𝑆(∀𝑦 ∈ (dom 𝑆 ∖ {𝑥})(𝑆𝑥) ⊆ ((Cntz‘𝐺)‘(𝑆𝑦)) ∧ ((𝑆𝑥) ∩ ((mrCls‘(SubGrp‘𝐺))‘ (𝑆 “ (dom 𝑆 ∖ {𝑥})))) = {(0g𝐺)}))))
104, 5, 9sylancl 693 . . 3 (𝐺dom DProd 𝑆 → (𝐺dom DProd 𝑆 ↔ (𝐺 ∈ Grp ∧ 𝑆:dom 𝑆⟶(SubGrp‘𝐺) ∧ ∀𝑥 ∈ dom 𝑆(∀𝑦 ∈ (dom 𝑆 ∖ {𝑥})(𝑆𝑥) ⊆ ((Cntz‘𝐺)‘(𝑆𝑦)) ∧ ((𝑆𝑥) ∩ ((mrCls‘(SubGrp‘𝐺))‘ (𝑆 “ (dom 𝑆 ∖ {𝑥})))) = {(0g𝐺)}))))
1110ibi 256 . 2 (𝐺dom DProd 𝑆 → (𝐺 ∈ Grp ∧ 𝑆:dom 𝑆⟶(SubGrp‘𝐺) ∧ ∀𝑥 ∈ dom 𝑆(∀𝑦 ∈ (dom 𝑆 ∖ {𝑥})(𝑆𝑥) ⊆ ((Cntz‘𝐺)‘(𝑆𝑦)) ∧ ((𝑆𝑥) ∩ ((mrCls‘(SubGrp‘𝐺))‘ (𝑆 “ (dom 𝑆 ∖ {𝑥})))) = {(0g𝐺)})))
1211simp2d 1072 1 (𝐺dom DProd 𝑆𝑆:dom 𝑆⟶(SubGrp‘𝐺))
Colors of variables: wff setvar class Syntax hints: → wi 4 ↔ wb 196 ∧ wa 384 ∧ w3a 1036 = wceq 1480 ∈ wcel 1987 ∀wral 2907 Vcvv 3186 ∖ cdif 3552 ∩ cin 3554 ⊆ wss 3555 {csn 4148 ∪ cuni 4402 class class class wbr 4613 dom cdm 5074 “ cima 5077 ⟶wf 5843 ‘cfv 5847 0gc0g 16021 mrClscmrc 16164 Grpcgrp 17343 SubGrpcsubg 17509 Cntzccntz 17669 DProd cdprd 18313 This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1719 ax-4 1734 ax-5 1836 ax-6 1885 ax-7 1932 ax-8 1989 ax-9 1996 ax-10 2016 ax-11 2031 ax-12 2044 ax-13 2245 ax-ext 2601 ax-rep 4731 ax-sep 4741 ax-nul 4749 ax-pow 4803 ax-pr 4867 ax-un 6902 This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1038 df-tru 1483 df-ex 1702 df-nf 1707 df-sb 1878 df-eu 2473 df-mo 2474 df-clab 2608 df-cleq 2614 df-clel 2617 df-nfc 2750 df-ne 2791 df-ral 2912 df-rex 2913 df-reu 2914 df-rab 2916 df-v 3188 df-sbc 3418 df-csb 3515 df-dif 3558 df-un 3560 df-in 3562 df-ss 3569 df-nul 3892 df-if 4059 df-pw 4132 df-sn 4149 df-pr 4151 df-op 4155 df-uni 4403 df-iun 4487 df-br 4614 df-opab 4674 df-mpt 4675 df-id 4989 df-xp 5080 df-rel 5081 df-cnv 5082 df-co 5083 df-dm 5084 df-rn 5085 df-res 5086 df-ima 5087 df-iota 5810 df-fun 5849 df-fn 5850 df-f 5851 df-f1 5852 df-fo 5853 df-f1o 5854 df-fv 5855 df-oprab 6608 df-mpt2 6609 df-1st 7113 df-2nd 7114 df-ixp 7853 df-dprd 18315 This theorem is referenced by: dprdf2 18327 dprdsubg 18344 dprdspan 18347 subgdprd 18355 ablfaclem2 18406 ablfac2 18409
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MEDIUM
# EXPLANATION
Let d = gcd(x,y), x = dp, y = dq. It's a well-known thing that lcm(x,y)* gcd(x,y) = xy, so the given equation can be written as d2pq = a + bdpq + cd ( * ). From this equation we get pq = (a / d + c) / (d - b) ( ** ).
As all summands except a in ( * ) are divisible by d, a should obviously be divisible by d too. Therefore, if a > 0, we already have at most 240 possible values of d (240 is the maximum number of divisors of an integer not exceeding 106). If a = 0, then from (* * ) it can be seen that c should be divisible by d - b, so there are again at most 240 possible values of d. If both a and c are 0, there are two cases -- the answer is 0 for b = 0 and -1 for b > 0.
Let's fix a particular value of d. From ( * * ) we can find t = pq. That means that we should add the number of ways to represent t as pq so that gcd(p,q) = 1 to the answer. This in fact can be easily calculated as 2w, where w is the number of distinct prime divisors of t. You're encouraged to work out the explanation of this yourself.
The main idea of this problem is thus doing a loop for gcd(x,y), not for x or y. Note that it can also be solved for a,b,c ≤ 109 as there's still a small number of possible values of d. While this problem probably looks like a math problem much, I still hope you enjoyed it :)
# SETTER'S SOLUTION
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# TESTER'S SOLUTION
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1. ## physics
On the Apollo 14 mission to the moon, astronaut Alan Shepard hit a golf ball with a golf club improvised from a tool. The free-fall acceleration on the moon is 1/6 of its value on earth. Suppose he hits the ball with a speed of 25 m/s at an angle of 28°
2. ## Chemistry
At equilibrium, the concentrations in this system were found to be [N2] = [O2] = 0.100 M and [NO] = 0.500 M. N2(g) + O2(g) 2NO(g) If more NO is added, bringing its concentration to 0.800 M, what will the final concentration of NO be after equilibrium is
3. ## Chemistry
In which direction will the net reaction proceed. X(g) + Y(g) Z(g) .. Kp = 1.00 at 300k for each of these sets of initial conditions? 1) [X] = [Y] = [Z] = 1.0 M a] net reaction goes to the left [this one?] b] net reaction goes to the right c] reaction is
4. ## Chemistry
Consider this system at equilibrium. A(aq) B(aq) Delta H = +750 kJ/mol .. What can be said about Q and K immediately after an increase in temperature? a] Q > K because Q increased.. b] Q>K because K decreased.. c] Q
5. ## Physics
Pilots can be tested for the stresses of flying high-speed jets in a whirling "human centrifuge," which takes 1.8 min to turn through 21 complete revolutions before reaching its final speed. 1. What is the angular acceleration?(rev/min^2) 2. What is the
6. ## geometry
Which type(s) of symmetry does the uppercase letter H have? my answer i believe is reflectional symmetry Which type of symmetry is shown by the lowercase letter w? my answer i believe is rotational symmetry. Could someone please check and explain.
7. ## Chemistry
Did I answer this equilibrium question correctly? 2CO(g) + O2(g) 2CO2(g) 1) How will increasing the concentration of CO shift the equilibrium? a] to the right [i chose this] b] to the left c] no effect 2] how will increasing the concentration of CO2 shift
8. ## Chemistry
consider the following reaction: 2CH3OH(g) yields 2CH4(g) + O2(g) change in enthalpy= 252.8kJ Calculate the amount of heat transferred when 26.0 g of {\rm CH_3OH} (g) is decomposed by this reaction at constant pressure.
9. ## Chemistry
At a given temperature, the elementary reaction A B in the forward direction is first order in A with a rate constant of 2.60 x 10^-2 s^-1. The reverse reaction is first order in B and the rate constant is 8.50 x 10^-2 s^-1. What is the value of the
10. ## geometry
In the graph below, point D is reflected across the y-axis. What are the coordinates of it's image? The graph looks like D is below the x-axis to the right 3 places from y-axis and down 1 place from x-axis. So would my answer be (3,1)?
11. ## College Physics
Some bacteria are propelled by motors that spin hair-like flagella. A typical bacterial motor turning at a constant angular velocity has a radius of 1.1x10-8m, and a tangential speed at the rim of 2.0x10-5 m/s. (a) What is the angular speed (the magnitude
12. ## Chem 2
Which of the following has the highest buffer capacity? A. 0.10M H2PO4-/0.10M HPO4 2- B. 0.50M H2PO4-/0.10M HPO4 2- C. 0.10M H2PO4-/0.50M HPO4 2- D. 0.50M H2PO4-/0.50M HPOr 2- E. They all have the same buffer capacity. Double checking I believe C is the
13. ## ENGLISH 11
Richard Bone by Edgar Lee Masters: When I first came to Spoon River I did not know whether what they told me Was true or false. They would bring me an epitaph And stand around the shop while I worked And say "He was so kind," "He was wonderful," "She was
14. ## Statistics
5. Scores on a recent national statistics exam were normally distributed with a mean of 80 and a standard deviation of 6. a. What is the probability that a randomly selected exam will have a score of at least 71? b. What percentage of exams will have
15. ## Chemistry
consider the following reaction: 2CH3OH(g) yields 2CH4(g) + O2(g) change in enthalpy= 252.8kJ How many kilojoules of heat are released when 38.4 g of CH_4 g) reacts completely with O2 (g) to form CH3OH (g) at constant pressure?
16. ## Physics
Two converging lenses are separated by 23.40 cm. The focal length of each lens is 12.20 cm. An object is placed 35.00 cm to the left of the lens that is on the left. Determine the final image distance relative to the lens on the right.
17. ## physics
A meter stick is held vertically above your hand, with the lower end between your thumb and first finger. On seeing the meter stick released, you grab it with these two fingers. You can calculate your reaction time from the distance the meter stick falls,
18. ## chemistry
How do you do the hybridization of CBr4?
19. ## Trigonometry
an airplane over the pacific sights an atoll at a 11 degrees angel angle of depression. if the plane is 410 m above water how many kilometers is it from a point 410 m above the atoll
20. ## chem
a mixture of 0.156 moles of C is reacted with 0.117 moles of O2 in a sealed, 10.0L vessel at 500K, producing a mixture of CO amd CO2. The total pressure is 0.640 atm. what is partial pressure of CO?
21. ## physics
A race car accelerates from 0.0 m/s to 30.0 m/s with a displacement of 45.0 m. what is the car's acceleration ?
22. ## 3 grade english
subject and object pronouns write each sentence. replace the underlined words with subject or object pronouns. 1-When some people visited the South Pole, the people wore heavy coats to keep the people warm. underline the word is (the people, the people) my
23. ## physics
If you stand next to a wall on a frictionless skateboard and push the wall with a force of 40N, how hard does the wall push on you ? If your mass is 80kg show that your acceleration is 0.5m/s^2
24. ## Trig
A ship leaves port with a bearing of S 40 W. After traveling 7 miles, the ship turns 90 degrees on a bearing of N 50 W for 11 miles. At that time, what is the bearing of the ship from port?
25. ## Mechanics
A 30.0-kg block is resting on a flat horizontal table. On top of this block is resting a 15.0-kg block, to which a horizontal spring is attached, as the drawing illustrates. The spring constant of the spring is 325 N/m. The coefficient of kinetic friction
26. ## chemistry
I have two questions that I really don't understand. The first one is: A reaction proceeds with delta H=-10kJ/mol. The energy of activation of the uncatalyzed reaction is 150kJ/mol, whereas it is 100kJ/mol for the uncatalyzed reaction. How many times
27. ## physics
You are playing right field for the baseball team. Your team is up by one run in the bottom of the last inning of the game when a ground ball slips through the infield and comes straight toward you. As you pick up the ball 62 m from home plate, you see a
28. ## Geometry
Guy wires 80 feet long support a 65 foot tall telephone pole. To the nearest degree, what angle will the wires make with the ground?
29. ## physics
A ball thrown horizontally at 27 m/s travels a horizontal distance of 51 m before hitting the ground. From what height was the ball thrown?
30. ## physics
A jet of water squirts out horizontally from a hole near the bottom of the tank, as seen in the figure below. Assume that y = 1.19 m and x = 0.544 m. What is the speed of the water coming out of the hole? The hole has a diameter of 3.06 mm. What is the
31. ## social studies
Label 2 bays that Hudson saw. I know the answer is Delaware Bay and Chesapeake Bay but I don't know where 2 label them.there's a map in my social studies book but it only talks about the Hudson Bay.There's a map in my book and it says AREA OF HENRY
32. ## Business communication
I have to revise these sentences as if speaking to a 10th grade level in education. Can you tell me if these are correct: 1. We must terminate all deficit financing. Revision: We need to end all debts. 2. We must endeavor to correct this problem by
33. ## physics
A batter hits a pop-up straight up over home plate at an initial velocity of 29 m/s. The ball is caught by the catcher at the same height that it was hit. At what velocity will the ball land in the catcher's mitt? none of these 29 m/s 14.5 m/s -14.5 m/s
34. ## physics
an experimental rocket plane lands on skids on a dry lake bed. it is traveling at 80.0 m/s when it touches down, how far does it slide before it comes to a stop? assume the coeffcient of kinetic friction between the skids and the lake is .600
35. ## College Physics Help
A thin rod (length = 1.10 m) is oriented vertically, with its bottom end attached to the floor by means of a frictionless hinge. The mass of the rod may be ignored, compared to the mass of the object fixed to the top of the rod. The rod, starting from
36. ## Chem 2
The following system is at equilibrium with [N2O4] = 0.55 M and [NO2] = 0.25 M. If an additional 0.10 M NO2 is added to the reaction mixture with no change in volume, what will be the new equilibrium concentration of N2O4? N2O4(g) 2 NO2(g)
37. ## physics
A box with a mass of 2 kg is lifted (without acceleration) through a height of 8.0 m in order to place it upon the shelf of a closet. (a) What is the increase in potential energy of the box? 1 . J (b) How much work was required to lift the box to this
38. ## Physics
A 73.3 kg man steps out a window and falls (from rest) 1.09 m to a sidewalk. What is his speed just before his feet strike the pavement? 4.62 m/s If the man falls with his knees and ankles locked, the only cushion for his fall is a 0.510 cm give in the
39. ## Chemistry
In phosphoric acid, why is it relatively easy to remove the first proton, considerably harder to remove the second proton, and extremely difficult to remove the third proton in chemical reactions? I'm not sure about this one is it because each time a
40. ## American Government
Which statement does not accurately describe Committees on the Whole? 1.)It helps the House get around quorum requirements. 2.)It debates bills, offers amendments, votes, and passes them on to the entire House. 3.)It is a permanent fixture in Congress.
41. ## AP Chemistry
Cytochrome, a complicated molecule that we will represent as CyFe2+, reacts with the air we breathe to supply energy required to synthesize adenosine triphosphate (ATP). At pH 7.0 the following reduction potentials pertain to this oxidation of CyFe2+:
42. ## Chemistry
Prepare a theoretical titration curve for titration of 25.0 mL of 0.1037 formic acid (HCOOH; pKa = 3.75) solution (diluted to 100 mL volume with deionized water) by 0.0964 M solution of KOH. I have to determine volume of KOH needed to reach equivalence
43. ## Algebra
An algebra teacher drove past a farmyard that was full of chickens and pigs. The teacher happened to notice that there were a total of 70 heads and 200 legs. How many chickens and how many pigs were there?
44. ## physics
An egg is thrown nearly vertically upward from a point near the cornice of a tall building. It just misses the cornice on the way down and passes a point a distance 48.0 m below its starting point at a time 5.00s after it leaves the thrower's hand. Air
45. ## Chemistry
How many moles of nitric acid will be produced when .51 mole of dinitrogen pentoxide reacts
46. ## Trigonometry
a 30 feet ladder resting against a building makes a 60 angle with the ground . find the Height from the ground at which the ladder touches the building to the nearest foot
47. ## Physics
Two blocks, each with a mass = 0.168 kg, can slide without friction on a horizontal surface. Initially, block 1 is in motion with a speed = 1.28 m/s; block 2 is at rest. When block 1 collides with block 2, a spring bumper on block 1 is compressed. Maximum
48. ## Physics
How far above the surface of Earth would you weigh 63.6 percent of your surface weight?
49. ## Physics help.
If a curve with a radius of 94.5 m is perfectly banked for a car traveling 72.4 km/h, what must be the coefficient of static friction for a car not to skid when traveling at 96.4 km/h?
50. ## Chemistry
I did a back titration with an unknown carbonate and using the average % carbonate (by mass) which I found to be 27.40% and appropriate calculation decided where the unknown is an alkali metal carbonate or an alkaline earth metal carbonate. I have no idea
51. ## geometry
The coordinates of the vertices of triangle CDE are C(1,4), D(3,6), and E(7,4). If the triangle is reflected over the line y=3, what are the coordinates of the image of D? I think (3,-6), but not real sure.
52. ## physics
What amount of heat is required to increase the temperature of 75.0 g of water from 22.3C to 36.1C? The specific heat of water is 4186 J/KgC.
53. ## Calculus
The fuel efficiency, E, in litres per 100 km, for a car driven at speed v, in km/h is E(v)=1600v/(v^2+6400) a)If the speed limit is 50 km/h, determine the legal speed that will maximize the fuel efficiency. Could someone explain to me why the legal speed
54. ## Re post water in tanks problem
A./_\ B.\_/ C.|_| The three tanks shown above are filled with water to an equal depth. All the tanks have an equal height. Tank A has the greatest surface area at the bottom, tank B the least and tank C the middle. (Select T-True, F-False, G-Greater than,
55. ## Physics
A spotlight on a boat is y = 2.6 m above the water, and the light strikes the water at a point that is x = 8.6 m horizontally displaced from the spotlight. The depth of the water is 4.0 m. Determine the distance d, which locates the point where the light
56. ## Calculus I
Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. 18. f(x) = 1/x , 1 < x < 3 I can graph it just fine, but for my answer I got that the function has none of the above. Is this correct?
57. ## Physics
A singly charged ion of unknown mass moves in a circle of radius 13.5 cm in a magnetic field of 2.9 T. The ion was accelerated through a potential difference of 3.0 kV before it entered the magnetic field. What is the mass of the ion? (hint: EPE=Vq=KE) kg
58. ## Math
Please explain how this is set up and how to work it. thanks A rectangular box is 4cm wide, 4cm tall, and 10cm long. What is the diameter of the smallest circular opening through which the box will fit? Round to the nearest tenth of a centimeter.
59. ## Math
There are 10 marbles in a bag. 5 blue, 3 red and 2 green. If you draw 1 marble at random, What are the odds in favor of drawing a red marble? Is the answer 3/10 or 3/7 ???
60. ## Chemistry
For A+2B 2C and Kc = 2.13 For 2C D and Kc = 0.254 Calculate the value of equilibrium contant for the reaction D A+2B I'm so sorry to bother anyone.. but am i only supposed to multiple 2.13 and 0.254 together in order to get the third value of Kc? That's
61. ## Trigonometry
Liola drives 13 km up a hill that is at a grade of 10 Degrees what horizontal distance to the nearest tenth of kilometer has she covered
62. ## physics
Atop a cliff, a projectile is fired horizontally with an initial speed of 10 m/s. Neglecting air drag, what is its speed 1 second after it is fired? A) 20 m/s.B) 14 m/s.C) 30 m/s. D) 28 m/s.E) 10 m/s.
63. ## Chemistry
Hoe Many moles of each reactant are Needed to produce 3.60 x 10^2g CH3OH?
64. ## Pre-cal
Find the length of side b to the nearest whole number if side a = 105, angle A = 65 degrees, and angle B = 37 degree.
65. ## Chemistry
1. As a research chimst, you are intrested in studying the extent and type of interactions in aqueous salt solution. As part of this study, you weight three samples of NaCl and dissolve each in 1.000kg H2O. You then measure the freezing temp. of each
66. ## Trigonometry
A side 2.8m long makes an angle of 25 degrees with the ground how high is the top of the slide above the ground .
67. ## Biology Science
Arrange the following in correct order in food chain- Fish,Plankton,Shark,Crab
68. ## math
Hank needs 3 quartes to play one video game each time. If he has 14 quarters, how many times can he play? Explain.
69. ## geometry
State a conclusion that seems reasonable. 6 + 0 = 6, 8 + 0 = 8, 9 + 0 = 9, 100 + 0 = 100. Conclusion:
70. ## algebra
A farmer decides to enclose a rectangular garden, using the side of a barn as one side of the rectangle. What is the maximum area that the farmer can enclose with 80 ft of fence? what should the dimensions of the garden be to give this area. The maximum
71. ## Chemistry
Zn metal was allowed to react with hydrochloric acid to produce hyrdogen gas.This gave a total of 555mL of gas collected over water at 20C and a pressure of 747mm of Hg. How many moles of hydrogen were collected? The vapor pressure of water at 20C is 18mm
72. ## Math
The graph of f is shown. Apply Rolle's Theorem and find all values of c such that f '(c) = 0 at some point between the labeled intercepts. (Enter your answers as a comma-separated list.) f (x) = x^2 + 6x − 7
73. ## Trig
Prove cos^2t+4cost+4/cost+2=2sect+1/sect
74. ## science
The half-life of carbon 14 is 5730 years. if a 1 g sample of old carbon is 1/8 as radioactive as 1 g of a current sample, then the age of the old sample is about ___________years. 22,900 17,200 11,500 716
75. ## Trigonometry
A lookout spots a fire from a 36 meter tower the angel of depression from the tower to the fire is 21 degrees . To the nearest meter how far is the fire from the base of the tower
76. ## chapter 5: Ratios & Proportions
Out of the 248 seniors, 112 are boys. What is the ratio of boys to the total number of seniors?
77. ## Math
the design below grows each day, as shown. if the pattern continues to grow like this, how many tiles will there be in the design on the tenth day? on the fiftieth day? Day 1 1 tile Day 2 5 tiles Day 3 13 tiles
78. ## physics
a motorized scooter starts from rest and accelerates for 4 s at 2 m/s2. it continues at a constant speed for 6 s . What is the scooter's average velocity for the interval 0-4 s ?
79. ## Chemistry
At 389K, this reaction has a Kc value of 0.0682. 2X(g) + 2Y(g) Z(g) .. Calculate Kp at 389K. Kp= this is what I did.. can somebody confirm or find any mistakes in my thought process? Kp = Kc(R)(T)^Delta n Delta n = (1)-(2+2) = -3 Kp =
80. ## physics
King Arthur's knights fire a cannon from the top of the castle wall. The cannonball is fired at a speed of 42 m/s and at an angle of 33°. A cannonball that was accidentally dropped hits the moat below in 1.6 s. (a) How far from the castle wall does the
81. ## math
Suppose the space needle in seattle washington casts a 220 ft shadow at the same time a nearby tourist cast a 2- foot shadow if the tourist is 5.5 feet tall how tall is the space needle
82. ## Trig
Prove cos^2t+4cost+4/cost+2=2sect+1/sect
83. ## statistics
1. The average number of articles produced by two machines per day is 200 and 250 with standard deviation 20 and 25 respectively on the basis of records of 25 days production. Can you regard both the machines equally efficient at 1% level of significance?
84. ## geometry
Marc is visiting washington dc he wants to know the height of the washington monument the length of the monument shadow is 111 feet long at the same time that marcs shadow is 1 foot long Marc is 5 feet tall using this data find the height of the monument
85. ## Physics
A singly charged positive ion has a mass of 3.20 10-26 kg. After being accelerated from rest through a potential difference of 823 V, the ion enters a magnetic field of 0.820 T along a direction perpendicular to the direction of the field. Calculate the
86. ## Math
The graph of f is shown. Apply Rolle's Theorem and find all values of c such that f '(c) = 0 at some point between the labeled intercepts. (Enter your answers as a comma-separated list.) f (x) = sin(2x)
87. ## Calc
Find the volume formed by rotating the region enclosed by: x = 8 y and y3 = x with y ≥ 0 about the y-axis
88. ## INTRODUCTION TO THE SHORT STORY, PART 1
During what part of "Bernice Bobs Her Hair" does Bernice cut Marjorie's braids?
89. ## English
Sentence with: Locomotive revolting caricaturist contraband
90. ## Dressmaking
as many alterations as possible should be made A)after sewing a garment B)on the pattern pieces C)immediately after cutting D)following the markings on the pattern pieces Im not sure if B or D is correct
91. ## Chemistry
Suppose 50.0 mL of an aqueous solution containing an unknown monoprotic weak acid is titrated with 0.250 M KOH. The titration requires 31.52 mL of the potassium hydroxide solution to reach the equivalence point. What is the concentration (in molarity) of
92. ## Chemistry
Calculate the amount of heat transferred when 21.0 of CH3OH(g) is decomposed by this reaction at constant pressure.
200. ## speech
Concerning dictionaries and their proper use, which one of the following statements is most accurate?
201. ## life orientation
three checks and balances that are in place in south africa that control and regulate media
202. ## Chemistry
You are a lab technician and must create 250 ml of a 17% salt solution. You have available three stock solutions. You have a one liter container of a 5% salt, a 500 ml container of a 28% salt solution, and a 400 ml container of a 40% salt solution. Discuss
203. ## Spanish-Help
We learned different timeframes in We learned timeframes in Spanish today and I'm stuck with my homework.Please check 1.Yo pedí un taco el restaurante anteayer. I ate a taco in the restaurant the day before yesterday. 2.Bebí un batido en el Mexican
204. ## English
Try hard to succeed. (What is the part of speech of 'to succeed'? Is 'to succeed' the object of the verb 'try'? Or is 'to succeed' the adverbial phrase which modifies 'try'?)
205. ## physics
An electron in a cathode-ray-tube (CRT) accelerates from 20300 m/s to 3.99 × 106 m/s over 1.34 cm. How long does the electron take to travel this distance?
206. ## Chemistry Help Please!!
How can you precipitate BaCrO4(s) from a solution of barium nitrate and potassium dichromate? I don't get it.. it's a question from a lab we did on chromate-dichromate equilibrium.
asked by Chem Student
207. ## English
i doing mobile (toy thing) for story sound of hollyhock. it have three string and each string be on different theme. one theme be mental illness, family problem, i not know what other theme be.
208. ## Trig
Prove sin(α+β)sin(α-β)=cos^2β-cos^2α
209. ## Writing
What better time to kiss the Blarney Stone than March! Help your readers plan a trip to Ireland by writing a travel article with interesting facts about the country My Facts: Want a trip to Ireland? Well you should go because there is a lor of amazing
210. ## Math Lit
It takes 6hours to paint a bedroom a) How long would it take 2 men? B)how long would it take 4men? C)how long with it take 12men? Please show me the calculates to see how you get the answer
211. ## Algebra
Consider the following apportionment problem for College Town. Suppose each council member is to represent approximately 2,500 citizens. Use the apportionment plan requested in the problem, assuming there must be 10 representatives. North: 5,500 South:
212. ## marketing
a 1,400- to 1,750-word paper in which you describe the elements of the marketing mix (product, place, price, and promotion). Use at least 3 academic sources (non-academic sources or text materials will not be counted) to support your work. In addition,
213. ## math
what is the probability of picking a yellow marble out of a jar of 27 marbles, if 20 of the 27 marbles are green?
214. ## Trig
Prove sin(α+β)sin(α-β)=cos^2β-cos^2α
215. ## geometry
by what factor must the radius of a circle be multiplied to make the area of the cicle 3 times as large?
216. ## Calculus
What values of x is there an absolute minimum for the function y= -1/3x^2 + 2x? I found the derivative of the function which is y'=-2/3x + 2 set it to 0=y'=-2/3x + 2 x=3 What do I do now?
217. ## physics
A rocket carrying a satellite is accelerating straight up from the earth's surface. At 1.25 s after liftoff, the rocket clears the top of its launch platform, 69 m above the ground. After an additional 4.80 s , it is 1.00 km above the ground. Calculate the
218. ## English
I have an e-pal. (In this sentence, what does 'e' refer to? 'Pal' means 'friend.')
219. ## math
a door was 6ft10in tall and 2ft 11in wid. estmate the area of one of the door
220. ## English
I need help writing a short story with these vocab words. 1. Discredit 2. disdain 3. Divergent 4. empathy 5. emulate 6. enervating 7. enhance 8. ephemeral 9. evanescent 10. exasperation
221. ## algebra2
simplify the following quotient of complex numbers into the form of a+bi -9+8i/1+2i
222. ## Physics
Take the radius of the earth at the equator to be 6380 km a. Find the speed the speed of an object at the equator due to the earth's rotation. ___m/s b. Convert this speed to miles/hour (show your conversion factor in your written backup). __miles/hour
338. ## Maths
Find 8 terms of the arithmetic progression if the second term is 2 and the sixth term is 5
339. ## world cultures
i need help on knowing that the cultural changes between Umayyad and Abbasid. pleaseee! thank you
340. ## science
which of the following is a physical change? Milk becomes sour An iron nails rusts All the water in a solution of salt water evaporates leaving a lot of crystals of salt in the bottom of the dish A wooden log is burned leaving ash in the fireplace
341. ## Math
What two numbers when multiplied = -16 and when added = 10, also one number is negative the other is positive in this answer.
342. ## Algebra 2
(x^3+8) x ((x-2)/(x^2-2x+4))/ (x^2-4)/(x-6)
343. ## Englishb
What are some books that could instruct someone on the world we live in?
344. ## Excel Graphs
i'm having trouble getting my graph to come out right in the legend its posting everythin and only need 2 mts to show up how can i fix it
345. ## trig
if sin 7x = cos x+10 find the value of x
346. ## calculus
consider the integral [cos(x^3)dx,0,0.5]. Approximating it by the Midpoint Rule with n equal subintervals, give an estimate for n which guarantees that the error is bounded by 1/10^4
347. ## English
I left out a few last things I need to prepare. Thank you. 1) Who is Caliban? How did Caliban behave towards Prospero when he first arrived on the island? Does he regret his behaviour now? What does he wish? Caliban is the witch Sykorax’s son, a strange
348. ## math
Circular pool has a radius of 8ft. What is the longest distance a swimmer can swim without making a turn?
349. ## HUM 111
Identify three approaches you will use to apply these techniques to effective writing and speaking skills.
350. ## University Physics
Building A and Building B are 30m away from each other, on the 4th floor; 35m high, someone has set up a slingshot from the window on the 4th floor of building A and is trying to sling a balloon into the window directly across from them in building B. the
351. ## business law
A purchaser who is injured by a product has a cause of action by demonstrating all of the following are true except one. The exception is:
352. ## Math
I'm in 5th grade and here's my question: I have to write which fraction represents the ratio of corresponding sides? There are 2 triangles. One triangle has the measurements 3in., 9in. and 6in. The other triangle is 18in., 54in. and 36in. Thank you.
353. ## to ms.sue
what should i name my limerick?
354. ## algebra
factor monomial 64xcubic-27
355. ## Algebra
I have an input / output machine I need a rule I can use for any value, like 10 or 100 input 1, output 3 input 2, output 6 input 3, output 12 input 4m output 24
8r+7r=75
357. ## life orientation
3 checks and balances that are place in south africa that control and regulate media
358. ## Maths
find s given that v= 20, a= 10, u= 10 and v squared= u squared =2*a*s | 7,538 | 27,738 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.796875 | 3 | CC-MAIN-2020-24 | latest | en | 0.888051 |
https://softwareengineering.stackexchange.com/questions/99487/good-way-to-learn-how-to-solve-questions-on-interviewstreet/99489 | 1,656,522,273,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103640328.37/warc/CC-MAIN-20220629150145-20220629180145-00433.warc.gz | 592,935,582 | 62,053 | Good way to learn how to solve questions on InterviewStreet [closed]
Possible Duplicate:
How do I adapt to pre-interview challenge questions?
InterviewStreet is a new company that essentially acts as a filter for companies to find programmers that can code. My problem is my math is fairly weak and I'd like to study it, even if it's from the ground up, to be able to solve questions such as this one, that is found on their site:
`Find the no of positive integral solutions for the equations (1/x) + (1/y) = 1/N! (read 1 by n factorial) Print a single integer which is the no of positive integral solutions modulo 1000007`
Now, please do NOT post the answer to that question, it is taken directly from InterviewStreet and should not be posted here. It is not the answer I'm seeking for in this thread. What I'm asking is a more fundamental question which probably can be answered by some of the hackers in the SO community.
How does one prepare for such a question? What resources are available for me to study/learn how to solve this type of problem? Is this covered on MIT open courseware? Khan Academy? Any particular books? I'm not even sure where to begin to start solving the problem above and I'd like to learn what steps I can take to do so.
• don't get me wrong - I like this kinds of question a lot (little puzzles for the weekend) - but I really don't think you will find good programmes with those - you will find math-geeks (that might be good at programmig) - and we all know that those people get code done, but the person next to them will never be able to read their code :) ... want to know if someone is any good? Sit down and to 2hr pair programming with that person and you will learn a lot more than if he happens to like Gardner-puzzles Aug 31, 2011 at 22:04
3 Answers
Often interview questions are designed to test your problem-solving skills without needing any specialist knowledge. But for your question, some mathematical knowledge would definitely help. At the very least, you'll need to understand the definitions of 'positive integral' and 'modulo'. An introductory course in number theory might be useful, perhaps this one from OCW.
I'd also recommend Project Euler for sample problems - it's a great way of developing your mathematical and programming knowledge. Pick a language and start working through the exercises.
You can't prepare for these kinds of problems by simply memorizing a book. The only way to be good at problem solving is by doing lots and lots of problems. I do suggest getting an algorithms and data structures book and reading through it though. It'll significantly speed up the process.
I remember a few years back I spent an entire summer (5+ hours a day) practicing solving these types of problems just for fun.
There are a number of places where you can do this. Project Euler is a good starting point. UVa Online Judge also has tons of problems.
• That's some commitment. Did you find it helped you in your general programming ability? Aug 8, 2011 at 18:22
• Absolutely. I participated in the USA Computing Olympiad in high school and went from a nobody to top 20 in the US. In terms of "real world" programming, I think I can say with utmost confidence that my skills have been significantly sharpened. Now I'm not saying everyone should go out and do what I did, but I think it's worth spending some time honing your problem solving skills. You can really learn a lot and it's definitely applicable to software development. Aug 8, 2011 at 18:24
This particular problem requires you to know basic number theory, specifically ideas like factoring composite numbers, some properties of prime numbers and an understanding of relatively prime pairs of numbers.
The other problems on the site require an understanding big O notation, simple data structures, basic algorithms like sorting, and combinatorics. I've passed 3 of the 5 problems and I'm almost done with my 4th, and I haven't used any specific knowledge from after my first year of CS classes in college. That said, these are difficult problems. Some of them require a surprising amount of mathematical intuition.
To prepare for this sort of stuff, you have to be good at mathematical problem solving. Look into the Olympiad (if you're in high school) or Putnam exam (if you're in college) and do the practice problems you find. They're hard, but you get better at them eventually.
Also, don't do the 30 point question - Quadrant Queries - first. It's the hardest by far. | 979 | 4,506 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2022-27 | latest | en | 0.97196 |
http://www.enotes.com/homework-help/chapter-4-you-found-that-when-karate-strike-hits-460610 | 1,477,463,085,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988720737.84/warc/CC-MAIN-20161020183840-00035-ip-10-171-6-4.ec2.internal.warc.gz | 435,409,667 | 9,597 | # In Chapter 4, you found that when a karate strike hits wooden blocks, the hand undergoes an acceleration of -6.50e3 m/s2. Medical data indicates the mass of the forearm and hand to be about 0.700...
In Chapter 4, you found that when a karate strike hits wooden blocks, the hand undergoes an acceleration of -6.50e3 m/s2. Medical data indicates the mass of the forearm and hand to be about 0.700 kg. What is the force exerted on the hand by the block?
valentin68 | College Teacher | (Level 3) Associate Educator
Posted on
Newton second law states that to accelerate an object having a mass `m` with acceleration `a` one needs to apply to it an external force `F` having the value
`F =m*a`
Thus in the case shown in problem the external force value is
`F =0.7*(-6.5*10^3) =-4550 N`
The minus sign in front of the force shows that it is opposing the direction of motion of the hand.
Answer: the absolute value of the force exerted on the hand is 4550 N | 254 | 960 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.375 | 3 | CC-MAIN-2016-44 | latest | en | 0.887723 |
http://www.cnblogs.com/massquantity/p/9061447.html | 1,542,668,371,000,000,000 | text/html | crawl-data/CC-MAIN-2018-47/segments/1542039746112.65/warc/CC-MAIN-20181119212731-20181119234731-00373.warc.gz | 387,239,998 | 8,057 | 1. 初始化权值分布： $w_i^{(1)} = \frac{1}{N}\:, \;\;\;\; i=1,2,3, \cdots N$
2. for m=1 to M:
(a) 使用带有权值分布的训练集学习得到基学习器$G_m(x)$:
$G_m(x) = \mathop{\arg\min}\limits_{G(x)}\sum\limits_{i=1}^Nw_i^{(m)}\mathbb{I}(y_i \neq G(x_i))$
(b) 计算$G_m(x)$在训练集上的误差率：
$\epsilon_m = \frac{\sum\limits_{i=1}^Nw_i^{(m)}\mathbb{I}(y_i \neq G_m(x_i))}{\sum\limits_{i=1}^Nw_i^{(m)}}$
(c) 计算$G_m(x)$的系数： $\alpha_m = \frac{1}{2}ln\frac{1-\epsilon_m}{\epsilon_m}$
(d) 更新样本权重分布： $w_{i}^{(m+1)} = \frac{w_i^{(m)}e^{-y_i\alpha_mG_m(x_i)}}{Z^{(m)}}\; ,\qquad i=1,2,3\cdots N$
其中$Z^{(m)}$是规范化因子，$Z^{(m)} = \sum\limits_{i=1}^Nw^{(m)}_ie^{-y_i\alpha_mG_m(x_i)}$，以确保所有的$w_i^{(m+1)}$构成一个分布。
3. 输出最终模型： $G(x) = sign\left[\sum\limits_{m=1}^M\alpha_mG_m(x) \right]$
import numpy as np
from sklearn import datasets
from sklearn.tree import DecisionTreeClassifier
from sklearn.model_selection import train_test_split
from sklearn.base import clone
from sklearn.metrics import zero_one_loss
import time
def __init__(self, M, clf, learning_rate=1.0, method="discrete", tol=None, weight_trimming=None):
self.M = M
self.clf = clf
self.learning_rate = learning_rate
self.method = method
self.tol = tol
self.weight_trimming = weight_trimming
def fit(self, X, y):
# tol为early_stopping的阈值，如果使用early_stopping，则从训练集中分出验证集
if self.tol is not None:
X, X_val, y, y_val = train_test_split(X, y, random_state=2)
former_loss = 1
count = 0
tol_init = self.tol
w = np.array([1 / len(X)] * len(X)) # 初始化权重为1/n
self.clf_total = []
self.alpha_total = []
for m in range(self.M):
classifier = clone(self.clf)
if self.method == "discrete":
if m >= 1 and self.weight_trimming is not None:
# weight_trimming的实现，先将权重排序，计算累积和，再去除权重过小的样本
sort_w = np.sort(w)[::-1]
cum_sum = np.cumsum(sort_w)
percent_w = sort_w[np.where(cum_sum >= self.weight_trimming)][0]
w_fit, X_fit, y_fit = w[w >= percent_w], X[w >= percent_w], y[w >= percent_w]
y_pred = classifier.fit(X_fit, y_fit, sample_weight=w_fit).predict(X)
else:
y_pred = classifier.fit(X, y, sample_weight=w).predict(X)
loss = np.zeros(len(X))
loss[y_pred != y] = 1
err = np.sum(w * loss) # 计算带权误差率
alpha = 0.5 * np.log((1 - err) / err) * self.learning_rate # 计算基学习器的系数alpha
w = (w * np.exp(-y * alpha * y_pred)) / np.sum(w * np.exp(-y * alpha * y_pred)) # 更新权重分布
self.alpha_total.append(alpha)
self.clf_total.append(classifier)
elif self.method == "real":
if m >= 1 and self.weight_trimming is not None:
sort_w = np.sort(w)[::-1]
cum_sum = np.cumsum(sort_w)
percent_w = sort_w[np.where(cum_sum >= self.weight_trimming)][0]
w_fit, X_fit, y_fit = w[w >= percent_w], X[w >= percent_w], y[w >= percent_w]
y_pred = classifier.fit(X_fit, y_fit, sample_weight=w_fit).predict_proba(X)[:, 1]
else:
y_pred = classifier.fit(X, y, sample_weight=w).predict_proba(X)[:, 1]
y_pred = np.clip(y_pred, 1e-15, 1 - 1e-15)
clf = 0.5 * np.log(y_pred / (1 - y_pred)) * self.learning_rate
w = (w * np.exp(-y * clf)) / np.sum(w * np.exp(-y * clf))
self.clf_total.append(classifier)
'''early stopping'''
if m % 10 == 0 and m > 300 and self.tol is not None:
if self.method == "discrete":
p = np.array([self.alpha_total[m] * self.clf_total[m].predict(X_val) for m in range(m)])
elif self.method == "real":
p = []
for m in range(m):
ppp = self.clf_total[m].predict_proba(X_val)[:, 1]
ppp = np.clip(ppp, 1e-15, 1 - 1e-15)
p.append(self.learning_rate * 0.5 * np.log(ppp / (1 - ppp)))
p = np.array(p)
stage_pred = np.sign(p.sum(axis=0))
later_loss = zero_one_loss(stage_pred, y_val)
if later_loss > (former_loss + self.tol):
count += 1
self.tol = self.tol / 2
else:
count = 0
self.tol = tol_init
if count == 2:
self.M = m - 20
print("early stopping in round {}, best round is {}, M = {}".format(m, m - 20, self.M))
break
former_loss = later_loss
return self
def predict(self, X):
if self.method == "discrete":
pred = np.array([self.alpha_total[m] * self.clf_total[m].predict(X) for m in range(self.M)])
elif self.method == "real":
pred = []
for m in range(self.M):
p = self.clf_total[m].predict_proba(X)[:, 1]
p = np.clip(p, 1e-15, 1 - 1e-15)
pred.append(0.5 * np.log(p / (1 - p)))
return np.sign(np.sum(pred, axis=0))
if __name__ == "__main__":
#测试各模型的准确率和耗时
X, y = datasets.make_hastie_10_2(n_samples=20000, random_state=1) # data
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=1)
start_time = time.time()
model_discrete = AdaBoost(M=2000, clf=DecisionTreeClassifier(max_depth=1, random_state=1), learning_rate=1.0,
method="discrete", weight_trimming=None)
model_discrete.fit(X_train, y_train)
pred_discrete = model_discrete.predict(X_test)
acc = np.zeros(pred_discrete.shape)
acc[np.where(pred_discrete == y_test)] = 1
accuracy = np.sum(acc) / len(pred_discrete)
print('Discrete Adaboost time: ', '{:.2f}'.format(time.time() - start_time),'\n')
start_time = time.time()
model_real = AdaBoost(M=2000, clf=DecisionTreeClassifier(max_depth=1, random_state=1), learning_rate=1.0,
method="real", weight_trimming=None)
model_real.fit(X_train, y_train)
pred_real = model_real.predict(X_test)
acc = np.zeros(pred_real.shape)
acc[np.where(pred_real == y_test)] = 1
accuracy = np.sum(acc) / len(pred_real)
print("Real Adaboost time: ", '{:.2f}'.format(time.time() - start_time),'\n')
start_time = time.time()
model_discrete_weight = AdaBoost(M=2000, clf=DecisionTreeClassifier(max_depth=1, random_state=1), learning_rate=1.0,
method="discrete", weight_trimming=0.995)
model_discrete_weight.fit(X_train, y_train)
pred_discrete_weight = model_discrete_weight.predict(X_test)
acc = np.zeros(pred_discrete_weight.shape)
acc[np.where(pred_discrete_weight == y_test)] = 1
accuracy = np.sum(acc) / len(pred_discrete_weight)
print('Discrete Adaboost(weight_trimming 0.995) accuracy: ', accuracy)
print('Discrete Adaboost(weight_trimming 0.995) time: ', '{:.2f}'.format(time.time() - start_time),'\n')
start_time = time.time()
mdoel_real_weight = AdaBoost(M=2000, clf=DecisionTreeClassifier(max_depth=1, random_state=1), learning_rate=1.0,
method="real", weight_trimming=0.999)
mdoel_real_weight.fit(X_train, y_train)
pred_real_weight = mdoel_real_weight.predict(X_test)
acc = np.zeros(pred_real_weight.shape)
acc[np.where(pred_real_weight == y_test)] = 1
accuracy = np.sum(acc) / len(pred_real_weight)
print('Real Adaboost(weight_trimming 0.999) accuracy: ', accuracy)
print('Real Adaboost(weight_trimming 0.999) time: ', '{:.2f}'.format(time.time() - start_time),'\n')
start_time = time.time()
model_discrete = AdaBoost(M=2000, clf=DecisionTreeClassifier(max_depth=1, random_state=1), learning_rate=1.0,
method="discrete", weight_trimming=None, tol=0.0001)
model_discrete.fit(X_train, y_train)
pred_discrete = model_discrete.predict(X_test)
acc = np.zeros(pred_discrete.shape)
acc[np.where(pred_discrete == y_test)] = 1
accuracy = np.sum(acc) / len(pred_discrete)
print('Discrete Adaboost accuracy (early_stopping): ', accuracy)
print('Discrete Adaboost time (early_stopping): ', '{:.2f}'.format(time.time() - start_time),'\n')
start_time = time.time()
model_real = AdaBoost(M=2000, clf=DecisionTreeClassifier(max_depth=1, random_state=1), learning_rate=1.0,
method="real", weight_trimming=None, tol=0.0001)
model_real.fit(X_train, y_train)
pred_real = model_real.predict(X_test)
acc = np.zeros(pred_real.shape)
acc[np.where(pred_real == y_test)] = 1
accuracy = np.sum(acc) / len(pred_real)
print('Real Adaboost accuracy (early_stopping): ', accuracy)
print('Discrete Adaboost time (early_stopping): ', '{:.2f}'.format(time.time() - start_time),'\n')
## 输出结果：
Discrete Adaboost accuracy: 0.954
early stopping in round 750, best round is 730, M = 730
early stopping in round 539, best round is 519, M = 519
Discrete Adaboost time (early_stopping): 11.64
• early_stopping分别发生在750和539轮，最后准确率也可以接受。
## Learning Curve
Learning Curve是另一种评估模型的方法，反映随着训练集的增大，训练误差和测试误差的变化情况。通常如果两条曲线比较接近且误差都较大，为欠拟合；如果训练集误差率低，测试集误差率高，二者的曲线会存在较大距离，则为过拟合。
### 完整代码
/
posted @ 2018-05-19 20:21 massquantity 阅读(...) 评论(...) 编辑 收藏 | 2,686 | 7,895 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.796875 | 4 | CC-MAIN-2018-47 | latest | en | 0.313913 |
https://www.jambite.com/discussion/subject-forum/752/mathematics/simplify | 1,726,136,494,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651440.11/warc/CC-MAIN-20240912074814-20240912104814-00790.warc.gz | 779,891,863 | 83,241 | Get better study experience with the jambite for andriod app!
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• # simplify
Mathematics
JAMES SIRGENTLE
23-02-2016 00:14:00 +0000
1/2-√3 in the form. a+b √3
• Don Heeaze
ans 2+√3 a= 2 b= √3
0 23-02-2016 00:19:00 +0000
• JAMES SIRGENTLE
show. full. work
0 23-02-2016 00:21:00 +0000
• JAMES SIRGENTLE
not. correct. shaa
0 23-02-2016 00:22:00 +0000
• Don Heeaze
lol olryt 1/2-√3×2+√3/2+√3 1(2+√3)= 2+√3 (2-√3)(2+√3) 4+2√3-2√3-3 +2√3 nd -2√3 are been cancelled 4-3= 1 having 2+√3/1= 2+√3 where a= 2 b= √3
0 23-02-2016 00:28:00 +0000
• JAMES SIRGENTLE
u. don try 1/2-√3×2+√3/2+√3=2+√3/>>>>>>>2+√3
0 23-02-2016 00:49:00 +0000
• Don Heeaze
lol
0 23-02-2016 00:50:00 +0000 | 411 | 841 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.46875 | 3 | CC-MAIN-2024-38 | latest | en | 0.485134 |
https://www.physicsforums.com/threads/help-projectile-motion.133231/ | 1,544,780,059,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376825512.37/warc/CC-MAIN-20181214092734-20181214114234-00608.warc.gz | 960,342,858 | 12,453 | # Help:projectile Motion
1. Sep 23, 2006
### the_d
**help:projectile Motion***
im giving a problem where i have to find the angle a projectile situated at the top of a will hit an boat wit constant velocity 20 ft/s 5 sec after starting at Vo = 96.6 ft/s and also how high the hill is above the water. The distance from the base of the hill to the boat is given to be 301 ft. Do i need to find the (Vo)x and (Vo)y with tan (-1) in order to get the angle and can i just assume the triangle to be a 3-4-5 triangle???
2. Sep 23, 2006
### Astronuc
Staff Emeritus
This is a homework problem and should be posted in the Homework section - Introductory Physics - would be appropriate.
One basically has to find the parabolic trajectory of the projectile and where it intersects the boat after the projectile and the boat both travel some distance during 5 seconds.
It would appear that the boat starts 301 feet from the point even with the projectile. The horizontal velocity of the projectile must be such that it travels the initial distance from the boat + boat distance traveled by boat in 5 seconds.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook | 281 | 1,188 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.40625 | 3 | CC-MAIN-2018-51 | latest | en | 0.924087 |
https://www.economicsdiscussion.net/consumption/consumption-meaning-function-and-other-details/2000 | 1,723,056,777,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640707024.37/warc/CC-MAIN-20240807174317-20240807204317-00252.warc.gz | 599,211,756 | 21,959 | Consumption is the use of utility for the direct satisfaction of wants. In simple words, it is the quality of a product to satisfy human wants.
According to Marshall, “Consumption may be regarded as negative production.”
According to Meyers, “Consumption is the direct use of goods and services in satisfying the human wants.”
Consumption is an economic activity which consists of the following features:
(i) Utility is used in consumption.
(ii) Direct satisfaction of human wants takes place by consumption.
(iii) By consumption, only the form of good changes.
### Consumption Function:
It implies the general relationship between income and consumption. The other name is consumption function or propensity to consume. According to Dillard, “It is a functional relationship how consumption varies when income varies.”
Therefore C = f(y)
C→ Consumption
Y→ Current income
F → Consumption function
According to Keynes, consumption is a direct function of income, i.e., if income increases consumption will also increase but not to the same extent. Hence, rise in income is greater than equal to rise in consumption. This is known as consumption function or propensity to consume. We can explain consumption function with the help of schedule and diagram.
Table 1: Consumption Schedule
From the above Table 1,
By plotting all the coordinates of income- consumption combinations and joining them we get consumption function or propensity to consume as shown in Figure 1.
In the above Figure, we get an upward rising or positively sloped consumption function with an intercept on vertical axis. At the zero level of income, there is positive consumption, as income increases, consumption will also increase but the rate of increase in income is much higher than the rate of increase in consumption. The upward rising line C shows consumption function or propensity to consume.
It is of two types as stated below:
### Average Propensity to Consume (APC):
It refers to the total consumption to total income. It means the amount of expenditure that the people would like to have out of their income. Hence, according to Kurihara, “Average propensity to consume refers to total consumption by total income.”
Therefore, APC = C/Y
The value of APC lies between zero to one.
### Marginal Propensity to Consume (MPC):
It refers to the ratio of change in consumption which takes place due to change in income. It shows how much of increased income is spent on consumption and how much is saved. Hence according to Kurihara, “Marginal propensity to consume refers to change in consumption by change in income.”
Therefore, MPC = ∆C/ ∆Y | 528 | 2,645 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2024-33 | latest | en | 0.953373 |
https://bartleylawoffice.com/faq/what-implication-s-does-the-second-law-of-thermodynamics-have-for-biological-systems.html | 1,680,117,122,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296949025.18/warc/CC-MAIN-20230329182643-20230329212643-00379.warc.gz | 158,100,596 | 20,295 | # What implication(s) does the second law of thermodynamics have for biological systems?
## What implication S does the second law of thermodynamics have for Biological Systems group of answer choices?
What implication(s) does the second law of thermodynamics have for biological systems regarding entropy? Systems cannot create energy because it is neither created nor destroyed. With each transformation, less energy is available to do work, so older systems have less energy.
## What implications does the second law of thermodynamics have?
One of the most important implications of the second law is that it indicates which way time goes – time naturally flows in a way that increases disorder. The second law also predicts the end of the universe: it implies that the universe will end in a “heat death” in which everything is at the same temperature.
## How does the second law of thermodynamics apply to biological systems?
The Second Law of Thermodynamics states that when energy is transferred, there will be less energy available at the end of the transfer process than at the beginning. Due to entropy, which is the measure of disorder in a closed system, all of the available energy will not be useful to the organism.
## What consequences does the first law of thermodynamics have for biological systems?
What consequences does the first law of thermodynamics have for biological systems? -All biological organisms require energy to survive. In a closed system, such as the universe, this energy is not consumed but transformed from one form to another. Cells, for example, perform a number of important processes.
## What is the First and Second Law of Thermodynamics?
The first law, also known as Law of Conservation of Energy, states that energy cannot be created or destroyed in an isolated system. The second law of thermodynamics states that the entropy of any isolated system always increases.
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## Why is the second law of thermodynamics not violated by living organisms?
Explanation: The second law of thermodynamics postulates that the entropy of a closed system will always increase with time (and never be a negative value). … Human organisms are not a closed system and thus the energy input and output of an the organism is not relevant to the second law of thermodynamics directly.
## What is the second law of thermodynamics in simple terms?
The second law of thermodynamics states that entropy, which is often thought of as simple ‘disorder’, will always increase within a closed system. Ultimately, this is one of the key elements dictating an arrow of time in the Universe.
## Why is the second law of thermodynamics true?
The Second Law of Thermodynamics states that the state of entropy of the entire universe, as an isolated system, will always increase over time. The second law also states that the changes in the entropy in the universe can never be negative.
## What is the second law of thermodynamics and why is it important?
Second law of thermodynamics is very important because it talks about entropy and as we have discussed, ‘entropy dictates whether or not a process or a reaction is going to be spontaneous’.
## How does the 1st and 2nd law of thermodynamics apply to biological systems?
Two fundamental concepts govern energy as it relates to living organisms: the First Law of Thermodynamics states that total energy in a closed system is neither lost nor gained — it is only transformed. The Second Law of Thermodynamics states that entropy constantly increases in a closed system.
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## What breaks the second law of thermodynamics?
But because it’s expanding, the Universe might never reach thermodynamic equilibrium, or it could end in a “Heat Death”, when its entropy reaches its maximum. …
## Does the second law of thermodynamics apply to open systems?
The Second Law of Thermodynamics is universal and valid without exceptions: in closed and open systems, in equilibrium and non-equilibrium, in inanimate and animate systems — that is, in all space and time scales useful energy (non-equilibrium work-potential) is dissipated in heat and entropy is generated.
## What is the first law of thermodynamics and why is it important?
The first law of thermodynamics concerns the principle of energy conservation and states that an important quantity of heat is released by any (industrial) process consuming energy because of the law of entropy. Temperature is thus an essential parameter to measure in order to assess proper operation (Fig.
## Is the first law of thermodynamics always true?
How can the first law is constantly observed to be true and we call it a scientific law yet we can’t say the equation behind it is true. … The First Law of Thermodynamics, the equation(s) describing the conservation of energy, is “true” in the sense that it is very dependable. | 981 | 4,996 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2023-14 | latest | en | 0.938686 |
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9 781292 023663 ISBN 978-1-29202-366-3 A First Course In Statistics James T. McClave Terry Sincich Eleventh Edition Enth Edition 5th, 2024 | 2,516 | 9,839 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.859375 | 3 | CC-MAIN-2024-26 | latest | en | 0.693787 |
http://nrich.maths.org/11114 | 1,506,183,738,000,000,000 | text/html | crawl-data/CC-MAIN-2017-39/segments/1505818689752.21/warc/CC-MAIN-20170923160736-20170923180736-00161.warc.gz | 229,647,186 | 5,417 | ### Traffic Lights
The game uses a 3x3 square board. 2 players take turns to play, either placing a red on an empty square, or changing a red to orange, or orange to green. The player who forms 3 of 1 colour in a line wins.
### Sumo
Reasoning based on this Japanese activity.
### Line of Four
A game somewhat similar to 'noughts and crosses' on a much larger space.
# Totality for Two
##### Stage: 1 and 2 Challenge Level:
Here's a game to play with a grown-up!
How do you play?
You'll need a grown-up to play with.
You'll also need a copy of the game board and a counter.
Work out how to play by watching the video with the sound off and discussing what you think the rules are.
Check your rules by watching the video again with the sound on.
If you can't view the video, the rules of the game are hidden below.
The aim of the game:
Slide the shared counter across several adjacent numbers, adding them up as you go to make a 'running' total. Be the player to make the final slide so that the chosen target is reached exactly. Making the total go above the target loses you the game.
How to play:
1. Choose a target to reach. This is the total both you and the grown-up are trying to make.
2. The grown-up places their counter on the game board over one of the numbers and says that number.
3. Move the same counter in any direction along a line segment to a neighbouring number and announce the total of the two numbers.
4. The grown-up moves the same counter to cover a neighbouring number, adds on that number, and announces the 'running' total of the three numbers.
5. Take it in turns to slide the counter to cover a neighbouring number and to add that number to the 'running' total.
6. Players must move when it is their turn.
7. No 'jumping' is allowed.
Notes for grown-ups
This game is designed to help children practise number bonds and addition. There is also an opportunity for thinking strategically by working out what will happen several moves in advance.
Easier version: instead of playing against each other, you could work together to try to make 20.
Harder version: discuss what the shortest 'string' of numbers would be that adds to the total. How many different 'strings' of numbers add to that total?
There's a group version of this game here. | 523 | 2,289 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.609375 | 4 | CC-MAIN-2017-39 | latest | en | 0.953975 |
https://brainmass.com/statistics/chi-squared-test/statistics-hypothesis-testing-chi-square-224053 | 1,516,220,835,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084886964.22/warc/CC-MAIN-20180117193009-20180117213009-00217.warc.gz | 642,659,028 | 18,884 | Share
Explore BrainMass
# Statistics - Hypothesis Testing - Chi-square
Recognize a contingency table (cross-tabulation of frequencies).
Find degrees of freedom and use the chi-square table of critical values.
Perform a chi-square test for independence on a contingency table.
Perform a goodness-of-fit (GOF) test for a uniform distribution.
Explain the GOF test for a Poisson distribution.
Use computer software to perform a chi-square GOF test for normality.
State advantages of ECDF tests as compared to chi-square GOF tests.
15.1 CHI-SQUARE TEST FOR INDEPENDENCE
TABLE 15.2 Privacy Disclaimer Location and Web Site Nationality WebSites
Figure 15.1 Various chi-square distributions
TABLE 15.3 Table of Expected Frequencies
Figure 15.2 Critical value of chi-square from Appendix E
Figure 15.3 Right-tailed chi-square test for ν = 6
Figure 15.4 MegaStat's chi-square test for Web page data
TABLE 15.4 Should Noninstrument Rated Pilots Fly at Night? Pilots
15.3 Students applying for admission to an MBA program must submit scores from the GMAT test, which includes a verbal and a quantitative component.
15.4 Computer abuse by employees is an ongoing worry to businesses.
15.5 Marketing researchers prepared an advance notification card announcing an upcoming mail survey and describing the purpose of their research. Half the target customers received the prenotification, followed by the survey.
#### Solution Summary
A Complete, Neat and Step-by-step Solution is provided in the attached file.
\$2.19 | 335 | 1,523 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.953125 | 3 | CC-MAIN-2018-05 | longest | en | 0.826862 |
http://mathhelpforum.com/algebra/54520-urgent.html | 1,481,403,172,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698543567.64/warc/CC-MAIN-20161202170903-00355-ip-10-31-129-80.ec2.internal.warc.gz | 176,143,798 | 11,716 | Thread: URGENT! :)
1. URGENT! :)
Hi I need some help with my math homework and i cant seem to get any of it done. Ur gonna think im SOOO stupid for not being able to know this... lol but yeah. PLEASE HELP ME !!!
1. -4.7 + 8.6x = -29.64
2. 5.4 = y/1.5 + 2.3
3. 6.4 - q/3.8 - 10.9
4. 2n + 0.5(n - 9) = 4.5
5. -7 = 0.75(3 + 10k) - 5k
6. -15 = -5h + 0.4(40 - 3h)
7. a - 1.5(a + 8) = 10
8. 4t - 10 = 12 + 2(t + 8)
9. 19w + 16 = 4(7 + w) + 3
10. 5(c + 9) = -3(21 + c)
11. 3g - 2(g + 4) = 8(g - 1)
THANKS!!!!!!!
2. Hey,
What's stopping you doing these equations? Don't you understand what to do with them?
They all seem to be fairly straight forward equations which can be solve by the most important equation rule: do the same to both sides! when you get the unknown on one side of the equation then you're pretty much done with these.
3. Thanks, Tony.
But where do I start in the equation?
4. -4.7 + 8.6x = -29.64
move the -4.7 over to the other side of the equation
8.6x = -29.64 + 4.7
then divide both sides through by 8.6 to get the value of x
do this format for each of the equations
5. Originally Posted by Lolli Lolli :)
Hi I need some help with my math homework and i cant seem to get any of it done. Ur gonna think im SOOO stupid for not being able to know this... lol but yeah. PLEASE HELP ME !!!
1. -4.7 + 8.6x = -29.64
2. 5.4 = y/1.5 + 2.3
3. 6.4 - q/3.8 - 10.9
4. 2n + 0.5(n - 9) = 4.5
5. -7 = 0.75(3 + 10k) - 5k
6. -15 = -5h + 0.4(40 - 3h)
7. a - 1.5(a + 8) = 10
8. 4t - 10 = 12 + 2(t + 8)
9. 19w + 16 = 4(7 + w) + 3
10. 5(c + 9) = -3(21 + c)
11. 3g - 2(g + 4) = 8(g - 1)
THANKS!!!!!!!
1. If you are simply solving for the variable x, you must first isolate x in all of the equations.
For example for #1
-4.7+8.6x=-29.64
move -4.7 to the other side to isolate x
change to positive because moving to other side
8.6x=-29.64+4.7
8.6x=-24.94
divide by number infront of x to solve
x=-24.94/8.6
x=-2.9
Follow the same procedure for all
* always divide by the variable when you isolate it, for some of these you will need to expand before you can do that, but always remember to just move it to the other side, while changing the sign
6. Originally Posted by euclid2
1. If you are simply solving for the variable x, you must first isolate x in all of the equations.
For example for #1
-4.7+8.6x=-29.64
move -4.7 to the other side to isolate x
change to positive because moving to other side
8.6x=-29.64+4.7
8.6x=-24.94
divide by number infront of x to solve
x=-24.94/8.6
x=-2.9
Follow the same procedure for all
* always divide by the variable when you isolate it, for some of these you will need to expand before you can do that, but always remember to just move it to the other side, while changing the sign
Then what would i do on the questions like # 2?
7. You need to take away 2.3 from both sides, then multiply by sides by 1.5.
This gives you y on one side, and the answer on the other!
8. $
5.4 = \frac{y}{1.5} + 2.3
$
first move the 2.3 over to the other side isolated y
$
5.4 - 2.3 = \frac{y}{1.5}
$
$
3.1 = \frac{y}{1.5}
$
then multiply both side by 1.5
$
3.1 * 1.5 = y
$
$
y = 4.65
$
9. Correct! See, you can do it!
You can put your answer into the original equation to make sure it's correct. | 1,221 | 3,266 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.03125 | 4 | CC-MAIN-2016-50 | longest | en | 0.878248 |
https://www.distancesto.com/ro/zalau-to-mesesenii-de-jos-457245/history/103609.html | 1,679,831,068,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296945472.93/warc/CC-MAIN-20230326111045-20230326141045-00443.warc.gz | 830,030,797 | 10,824 | 13.7 Km Distance from Zalău to Meseșenii de Jos 457245
You leave Zalău, RO and reach Meseșenii de Jos 457245, RO.
Trip Zalău » Meseșenii de Jos 457245
Distance: 13.7 kilometers
The above is the distance that you can expect to travel to your destinaton. Note that road work and other factors can affect this estimate.
Distance Information
Below is the total distance from Zalău to Meseșenii de Jos 457245 in other units of length.
Miles: 8.5 13671 44852.4
Distance Summary
You drive from Zalău, Romania and trip ends at Meseșenii de Jos 457245, Romania.
Now that you know that the driving distances from Zalău to Meseșenii de Jos 457245 is 13.7 km, would you like to view a more detailed map? Well there are a few different ones that you can view which provide a bird's eye view of the terrain on the road map from Zalău to Meseșenii de Jos 457245.
Of course travel time also has to be taken into consideration when preparing for a trip which is why you may want to view the travel time from Zalău to Meseșenii de Jos 457245.
Aside from time, the "cost" of the trip should be taken into consideration as well since it's just as important as time, and to do so you can calculate the fuel cost from Zalău to Meseșenii de Jos 457245.
Afterwards, you may want to start planning your road trip. Need directions? You can view turn by turn driving directions from Zalău to Meseșenii de Jos 457245.
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Is it too far to drive to Meseșenii de Jos 457245? Then you may want to check the flight distance from Zalău to Meseșenii de Jos 457245.
A flight to Meseșenii de Jos 457245 is always going to take less time than driving. How much less? See flight time from Zalău to Meseșenii de Jos 457245.
Recent Distance Calculations for Zalău RO:
Distance from Zalău to Săliște 557225
Distance from Zalău to Tășnad 445300
Distance from Zalău to Ploiești Connected by Constanța
Distance from Zalău to Constanța
Distance from Zalău to Aeroportul International Baia Mare | 612 | 2,086 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2023-14 | longest | en | 0.8965 |
https://mathematica.stackexchange.com/questions/52053/finding-expectation-of-function-of-a-log-normal-distribution | 1,696,388,232,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233511351.18/warc/CC-MAIN-20231004020329-20231004050329-00618.warc.gz | 412,207,189 | 40,239 | Finding Expectation of function of a Log-normal distribution
Say $Y=g(X)$ and $p_X = \frac{e^{-\frac{(\mu -\log (x))^2}{2 \sigma ^2}}}{\sqrt{2 \pi } x \sigma }$ is Log-normal density function: [Wiki]
Find E[Y]?
Since $E[Y] = \int_0^\infty y f_Y \ dy = \int_0^\infty g(x)f_X(x)dx$. So, I do not need to find $f_Y(y)$.
.
px = Simplify[PDF[LogNormalDistribution[Mu, Sigma], x], x > 0]
Integrate[Log2[1 + x] px, {x, 0, \Infinity}, Assumptions -> {Sigma > 0}]
.
Unfortunately, Mathematica cannot evaluate this integral for a closed form expression and I'm not quite sure how else to solve it. Will appreaciate any help I can get on the evaluation steps.
Edit:
Expectation[Log2[1 + x], x \[Distributed] LogNormalDistribution[Mu, Sigma]]
I suspect there may not be a closed form expression (I have not looked at it hard enough). If the aim is to not analytical but numerical, I post the following for illustration (apologies if not the intent of question):
f[x_, y_] :=
NIntegrate[
Log2[t + 1] Exp[-(x - Log[t])^2/(2 y^2)]/(Sqrt[2 Pi] t y), {t, 0,
Infinity}]
rv[a_, b_, n_] :=
Mean[Log2[1 + RandomVariate[LogNormalDistribution[a, b], n]]]
Manipulate[
Show[Plot[f[m, s], {m, 1, 5}, PlotRange -> {0, 7}],
ListPlot[Table[{j, rv[j, s, n]}, {j, 1, 5, 0.1}],
PlotMarkers -> {"\[FilledDiamond]", 10}, PlotStyle -> Red]], {s, 1,
5}, {n, {10, 100, 1000, 10000}}]
You can also depict the expected value nicely as a function of Mu and Sigma using Plot3D.
px = Simplify[PDF[LogNormalDistribution[Mu, Sigma], x], x > 0]
E^(-((Mu - Log[x])^2/(2 Sigma^2)))/(Sqrt[2 π] Sigma x)
Plot3D[NIntegrate[Log2[1 + x] px, {x, 0, ∞}], {Mu, -5,
10}, {Sigma, .2, 2}, AxesLabel -> {Mu, Sigma, EY}]
PS: Reminds me of Black-Scholes formula for the evaluation of an Option.
Extending the range of Sigma Shows the nontrivial dependence more clearly: | 625 | 1,828 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.328125 | 3 | CC-MAIN-2023-40 | longest | en | 0.681701 |
https://online.stat.psu.edu/stat200/lesson/7/7.4 | 1,628,211,150,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046152085.13/warc/CC-MAIN-20210805224801-20210806014801-00627.warc.gz | 446,575,812 | 27,649 | # 7.4 - Central Limit Theorem
As we saw at the beginning of this lesson, many of the sampling distributions that you have constructed and worked with this semester are approximately normally distributed. The Central Limit Theorem states that if the sample size is sufficiently large then the sampling distribution will be approximately normally distributed for many frequently tested statistics, such as those that we have been working with in this course: one sample mean, one sample proportion, difference in two means, difference in two proportions, the slope of a simple linear regression model, and Pearson's r correlation. Over the next few lessons we will examine what constitutes a "sufficiently large" sample size. Essentially, it is determined by the point at which the sampling distribution becomes approximately normal.
In practice, when we construct confidence intervals and conduct hypothesis tests we often use the normal distribution (or t distributions which you'll see next week) as opposed to bootstrapping or randomization procedures in situations when the sampling distribution is approximately normal. This method is preferred by many because z scores are on a standard scale (i.e., mean of 0 and standard deviation of 1) which makes interpreting results more straight forward.
Drag the slider at the bottom of the graph to see normal curve fit on the randomization plot. | 264 | 1,396 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2021-31 | longest | en | 0.956952 |
https://forums.asp.net/t/1703706.aspx?Converting+Number+to+Time | 1,627,788,623,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046154158.4/warc/CC-MAIN-20210801030158-20210801060158-00613.warc.gz | 274,097,804 | 11,156 | We are excited to announce that the ASP.NET Forums are moving to the new Microsoft Q&A experience. Learn more >
## 5 replies
Last post Jul 26, 2011 07:04 AM by Mongol648
• Mongol648
Member
63 Points
451 Posts
### Converting Number to Time
I have a Access table with numbers stored like 859. I need to convert that to a TIME which would be 8:59am or 0859. What is the best way to accomplish this?
Actually I only need the hour of the time. So in this case (859) I would need the 8. Could I use a combination of LEN and IIF?
thanks
• princeG
Contributor
6472 Points
1575 Posts
### Re: Converting Number to Time
You need to use Substring function to get Hours
string strHours= "859";
strHours = strHours.SubString(0 ,strHours.Length-2);
this is tricky. but only that sotution will be perfect for that
• Mongol648
Member
63 Points
451 Posts
### Re: Converting Number to Time
I am having trouble seeing how this will work. The data is variable in length, either 3 or 4 numbers (859, 1230, 1345, etc..)
• Mongol648
Member
63 Points
451 Posts
### Re: Converting Number to Time
I was thinking of doing LEN to get the length (3 or 4), then if it is 3 LEFT(fieldname,1) if it is 4 LEFT(fieldname,2). Not sure if that could work in a query.
• hans_v
All-Star
25756 Points
7014 Posts
### Re: Converting Number to Time
#### Mongol648
I have a Access table with numbers stored like 859. I need to convert that to a TIME which would be 8:59am or 0859. What is the best way to accomplish this?
The best way is to store dates or times as dattime!
#### Mongol648
Actually I only need the hour of the time. So in this case (859) I would need the 8
Int(859/100)
#### Mongol648
The data is variable in length, either 3 or 4 numbers (859, 1230, 1345, etc..)
Int(859/100) = 8. Int(1230/100) = 12. Int(1345/100) = 13
So Int([fieldname]/100) will return the result you want, but I don't think you're on the right track....
#### Mongol648
Could I use a combination of LEN and IIF?
Off course, you can use any combination of functions, but you're making things much more complucated as they really are....
• Mongol648
Member
63 Points
451 Posts | 628 | 2,179 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.703125 | 3 | CC-MAIN-2021-31 | latest | en | 0.832412 |
https://brainmass.com/math/complex-analysis/singular-points-residues-392255 | 1,623,793,556,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487621627.41/warc/CC-MAIN-20210615211046-20210616001046-00518.warc.gz | 152,354,955 | 74,964 | Explore BrainMass
Singular points and residues of 1/[(Cosh(z))-2exp(z)]
Not what you're looking for? Search our solutions OR ask your own Custom question.
This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!
Classify all singular points of f(z) = 1/[(Cosh(z))-2exp(z)] and find all residues.
https://brainmass.com/math/complex-analysis/singular-points-residues-392255
Solution Preview
We can find the singular points by equating the numerator to zero:
Cosh(z) - 2 exp(z) = 0
Put exp(z) = y. Then we have:
y + y^(-1) - 4 y = 0 ---------->
3 y^2 = 1 --------->
y = +/- 3^(-1/2)
We can then compute z using
z = Log(y) + 2 pi i n
where n is an integer and the logarithm is defined by taking the branch ...
Solution Summary
We explain in detail how the singularities of the function can be found, and we compute the residues at the poles.
\$2.49 | 255 | 914 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.859375 | 4 | CC-MAIN-2021-25 | longest | en | 0.793737 |
https://uk.mathworks.com/matlabcentral/cody/problems/2869-there-are-10-types-of-people-in-the-world/solutions/2801047 | 1,603,441,861,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107880878.30/warc/CC-MAIN-20201023073305-20201023103305-00696.warc.gz | 568,936,847 | 17,231 | Cody
# Problem 2869. There are 10 types of people in the world
Solution 2801047
Submitted on 6 Aug 2020 by Sam Maltz
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### Test Suite
Test Status Code Input and Output
1 Pass
x = 1881;y_correct = 30; assert(isequal(yearraey(x),y_correct))
y = 30
2 Pass
x = 2014;y_correct = 1; assert(isequal(yearraey(x),y_correct))
y = 1
3 Pass
x = 2015;y_correct = 0; assert(isequal(yearraey(x),y_correct))
y = 0
4 Pass
x = 606;y_correct = 27; assert(isequal(yearraey(x),y_correct))
y = 27
5 Pass
x = 6006;y_correct = 71; assert(isequal(yearraey(x),y_correct))
y = 71
6 Pass
x = 60006;y_correct = 369; assert(isequal(yearraey(x),y_correct))
y = 369
7 Pass
k=zeros(1,15); for n=1:15 y=2^n+2; k(n)=yearraey(y); end y_correct=[1 1 5 3 11 7 23 15 47 31 95 63 191 127 383]; assert(isequal(k,y_correct))
y = 1 y = 1 y = 5 y = 3 y = 11 y = 7 y = 23 y = 15 y = 47 y = 31 y = 95 y = 63 y = 191 y = 127 y = 383
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# Block rate tariff or Block meter rate, Into this tariff,
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•
•
Block rate tariff or Block meter rate, Into this tariff, succeeding blocks of energy are charged at progressiveness reduced rates, while energy into the proceeding blocks
is cbarsed at higher rates. For example out of 50 un; s of cnervv, first 20 units may be charged at 25 Punit, next 20 units at 20 P. Unit and beyond that at la Punit. According to block rate tariff, trim er;erey cost =(20×25+20×20+15×10)=Rs. 10.50 P. As againt this, according to the step rate tariff, total energy cost will be =50 x 15 P=Rs. 7 50 We thus see that while into block rate tariff energy into different blocks IS charged at rates prevalent for those blocks, whole of energy into step rate tariff IS charged at a rate corresponding to the final block of energy. The graphs of total cost and costumt of energy vs energy consumed are shown into 1 15. (a) and (D). The main
advantage of this tariff is that while the energy cost decreases with the increase into energy consumption as into case of step rate tariff, it does not suffer from the disadvantage of consuming energy at no cost or at negative cost.
Hopkinson demand rate orTvoparttariff. Natural Justice requires that whatever charges are incurred by the supply authority on account of some consumer should be truly passed on to him, We have also seen that the generation cost consist of f reds semifixed and rnnmng charges. Two part tariff is the first tariff m which above fact is partly recognized. The first part of the tariff charges for the maximum demand and second part of tariff’ charges for the energy used by the consumer. Mathematically this may be stated as
Total charges =axkw+bxkwh.
Both demand and energy charges may be either flat or graduated on block or step system. The main problem introduced by this tariff IS the measurement of maximum demands This tariff is thesefore applicable to medium and large industrial consumes. Into some cases, to avoid the installation of maximum demand indicators, demand charges are made on the billing demands which may be compnted on some arbitrary standards. instance billing demand may be cl sacred b n DltiplyiDg connected load with reprerrrtative den and into terms of number of rooms into a building or OD the basis of floor area. Arotber draw back of this tariff when demand charges are made on some arbitrary standards is that even if no energy is used during the billing period a consumer has to pay for the demand charges. This defect is removed when the demand is metered. However into such cases minimum demand that must be paid for is usually specified. | 595 | 2,664 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.828125 | 3 | CC-MAIN-2018-34 | longest | en | 0.909682 |
https://www.bionicturtle.com/forum/threads/frm-2008-pii-q21-delta-of-long-forward.1787/ | 1,631,914,011,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780055808.78/warc/CC-MAIN-20210917212307-20210918002307-00553.warc.gz | 719,157,263 | 15,986 | What's new
# FRM 2008 PII q21 - Delta of long forward
#### fullofquestions
##### New Member
The dividend yield of an asset is 10% per annum. What is the delta of a long forward contract on the
asset with 6-month to maturity?
a. 0.95
b. 1.00
c. 1.05
d. Can not be determined without further information.
Calculation:
The value of a long forward contract
f = S0 e-qT – K e-rT,
where S0, q, T, K, and r are the asset price, dividend yield, time to maturity,
delivery price, and risk-free rate, respectively.
It follows that the delta of the forward = e-qT.
Given q = 10% and T = 1/2, we have delta = e-10% / 2 = 0.95
a. Correct. Shown from the calculations above.
b. Incorrect. Derived erroneously by not accounting for the dividend.
c. Incorrect. Derived erroneously by mixing up the sign of exponential.
d. Incorrect. It can be determined with the given information as shown above.
The explanation comes a bit short. Without r we really cannot tell if delta is positive or negative. This answer is incomplete in my opinion. Is this correct?
#### David Harper CFA FRM
##### David Harper CFA FRM
Staff member
Subscriber
Hi FoQ,
Question is correct: delta of a futures contract would require rate (r), but delta of a *forward* is 1.0 w/o dividend, or exp(-qT) with dividend. Futures with dividend = exp[(r-q)*T]
David | 362 | 1,323 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.296875 | 3 | CC-MAIN-2021-39 | latest | en | 0.891604 |
https://riffomonas.org/generalR/07_session.html | 1,709,397,822,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947475833.51/warc/CC-MAIN-20240302152131-20240302182131-00073.warc.gz | 470,058,348 | 8,319 | # Session 7
## Topics
• Detecting problems in data
• Fixing data problems
• Rinse, repeat
## Detecting problems in data
We’ve read in the weather data as `aa_weather` and now we’d like to get a better sense of the values. We’ll take two approaches - we’ll visualize the data and look at summary statistics of the data.
``````library(tidyverse)
select(DATE, starts_with("T"), PRCP, SNOW, SNWD) %>%
rename("date" = "DATE",
"t_max_c" = "TMAX",
"t_min_c" = "TMIN",
"t_obs_c" = "TOBS",
"total_precip_mm" = "PRCP",
"snow_fall_mm" = "SNOW",
"snow_depth_mm" = "SNWD")
``````
To visualize the data we can make a histogram for each column of numerical data. The syntax will look like this
``````aa_weather %>% ggplot(aes(x=t_min_c)) + geom_histogram()
aa_weather %>% ggplot(aes(x=t_max_c)) + geom_histogram()
aa_weather %>% ggplot(aes(x=t_obs_c)) + geom_histogram()
``````
Two things to comment on here. First, you’ll get the following feedback from running the command:
```````stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Warning message:
Removed 163 rows containing non-finite values (stat_bin).
``````
Starting with the warning message, it tells us that a number of the days in the dataset did not have values. We know that coverage for `t_min_c`/`TMIN` was not 100% so we should have expected that. Second, it tells us that it is using `bins=30` to build the histogram. It is telling us that we can manually set the number of bins or the width of the bins to draw the histogram.
``````aa_weather %>% ggplot(aes(x=t_min_c)) + geom_histogram(bins=60)
``````
``````aa_weather %>% ggplot(aes(x=t_min_c)) + geom_histogram(binwidth=1)
``````
Unless we’re interested in generating publication a quality figure, the default is probably good enough for our purposes.
Looking at the three plots that were generated, you’ll notice that the histogram for `t_obs_c` has values greater than 60 and less than -60. Even for Ann Arbor, those temperatures are pretty extreme. I suspect the thermometer was having bad days when those observations were made. Something else that tells us the data don’t make sense is that the `t_min_c` and `t_max_c` values approach those levels, which they should if `t_obs_c` was a single temperature reading. We can use `filter` to identify the days with these odd temperatures
``````aa_weather %>% filter(t_obs_c > 40)
aa_weather %>% filter(t_obs_c < -40)
``````
``````## # A tibble: 1 x 7
## date t_max_c t_min_c t_obs_c total_precip_mm snow_fall_mm snow_depth_mm
## <date> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1934-05-12 13.3 -0.6 65 0 0 0
## # A tibble: 1 x 7
## date t_max_c t_min_c t_obs_c total_precip_mm snow_fall_mm snow_depth_mm
## <date> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1944-06-18 33.3 19.4 -66.1 0 0 0
``````
Those pipelines return the data for the two days with the suspect temperatures. I feel good throwing out these two temperatures because it was supposedly -66.1C (-87F) in June and 65C in May when the low temperature for the day was below freezing. Ann Arbor weather can be weird, but those temperatures don’t make sense.
## Fixing data problems
Let’s convert those weird temperatures to `NA` values, which will indicate we don’t know the true value. We’ll do this with two functions, one we’ve already seen, `mutate`, and another that builds upon the logical operators we’ve seen with `filter` called `ifelse`. `mutate` allows us to modify an existing column (i.e. `t_obs_c`) or to create a new column. For example, let’s create a `t_max_f` column that has the maximum temperature for the day in degrees Fahrenheit. We’ll add a `select` function call to make sure we can see the relevant columns.
``````aa_weather %>%
mutate(t_max_f = 9 * t_max_c / 5 + 32) %>%
select(date, t_max_c, t_max_f)
``````
``````## # A tibble: 46,650 x 3
## date t_max_c t_max_f
## <date> <dbl> <dbl>
## 1 1891-10-01 20.6 69.1
## 2 1891-10-02 26.7 80.1
## 3 1891-10-03 26.1 79.0
## 4 1891-10-04 22.8 73.0
## 5 1891-10-05 13.9 57.0
## 6 1891-10-06 14.4 57.9
## 7 1891-10-07 10.6 51.1
## 8 1891-10-08 13.9 57.0
## 9 1891-10-09 15 59
## 10 1891-10-10 16.7 62.1
## # … with 46,640 more rows
``````
The other function we need is `ifelse`. This allows us to ask a logical question of the data. If the value is true, then we return one value. If it is false, we return another.
``````my_numbers <- c(-5, -3, -1, 0, 1, 3, 5)
ifelse(my_numbers > 0, "positive", "negative")
``````
``````## [1] "negative" "negative" "negative" "negative" "positive" "positive" "positive"
``````
From this syntax we can see that `ifelse` has three “slots” - the logical question (i.e. `my_numbers > 0`), the value if the answer is `TRUE` (i.e. “positive”), the value if the answer is `FALSE` (i.e. “negative”). Let’s see how we could put this together to recast the values of `t_obs_c` to remove those extreme temperatures
``````aa_weather %>%
mutate(t_obs_c = ifelse(t_obs_c > 40, NA, t_obs_c),
t_obs_c = ifelse(t_obs_c < -40, NA, t_obs_c)) %>%
ggplot(aes(x=t_obs_c)) +
geom_histogram()
``````
Slick, eh? You can see that we can mutate multiple columns or the same column multiple times by giving mutate two or more arguments separated by commas.
## Rinse, repeat
The histograms for temperature data made it pretty easy to pick off which numbers looked weird. We also probably have a good sense of what temperatures are extreme for an area. After living in the northern US for 25 years, I still don’t know what an extreme, but acceptable snow or rain fall is.
``````aa_weather %>% ggplot(aes(x=total_precip_mm)) + geom_histogram()
aa_weather %>% ggplot(aes(x=snow_fall_mm)) + geom_histogram()
aa_weather %>% ggplot(aes(x=snow_depth_mm)) + geom_histogram()
``````
Let’s think about this for a second - 1000 mm of precipitation is 100 cm or about 40 in. Yeah, that’s a lot. We need to dig deeper into these data. I feel like 150 mm (~10 in) precipitation event is weird, but not outside of what we might expect for Ann Arbor. We can look at the data a different way - perhaps by plotting the data against the date like we did with the Project Tycho data
``````aa_weather %>%
ggplot(aes(x=date, y=total_precip_mm)) +
geom_line()
``````
From this view, there appear to be 2 points that are above 250 mm that are outliers. We can use 250 mm to create a `filter` function call to find those rows with `total_precip_mm` values over 250
``````aa_weather %>%
filter(total_precip_mm > 250)
``````
``````## # A tibble: 2 x 7
## date t_max_c t_min_c t_obs_c total_precip_mm snow_fall_mm snow_depth_mm
## <date> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1934-12-08 -3.9 -8.3 -17.8 509. 5 NA
## 2 1953-09-05 23.9 12.8 18.3 1286. 0 0
``````
A google search for “Ann Arbor 1953 rain” doesn’t turn up anything and neither does using “1934” in place of “1953”. I’d expect something like that amount of precipitation to be newsworthy! Taking our previous `mutate` function call, let’s add this threshold for `total_precip_mm` to set values above this number as `NA`.
``````aa_weather %>%
mutate(t_obs_c = ifelse(t_obs_c > 40, NA, t_obs_c),
t_obs_c = ifelse(t_obs_c < -40, NA, t_obs_c),
total_precip_mm = ifelse(total_precip_mm > 250, NA, total_precip_mm)) %>%
ggplot(aes(total_precip_mm)) + geom_histogram()
``````
You’ll notice that if we now do
``````aa_weather %>%
ggplot(aes(total_precip_mm)) + geom_histogram()
``````
We again get the very long x-axis. Why is this? In all of our pipelines we are doing operations on the `aa_weather` data frame, but we haven’t “written” anything to a new variable! We could do something like this to create a new data frame
``````clean_aa_weather <- aa_weather %>%
mutate(t_obs_c = ifelse(t_obs_c > 40, NA, t_obs_c),
t_obs_c = ifelse(t_obs_c < -40, NA, t_obs_c),
total_precip_mm = ifelse(total_precip_mm > 250, NA, total_precip_mm))
clean_aa_weather %>%
ggplot(aes(total_precip_mm)) + geom_histogram()
``````
or
``````aa_weather <- aa_weather %>%
mutate(t_obs_c = ifelse(t_obs_c > 40, NA, t_obs_c),
t_obs_c = ifelse(t_obs_c < -40, NA, t_obs_c),
total_precip_mm = ifelse(total_precip_mm > 250, NA, total_precip_mm))
aa_weather %>%
ggplot(aes(total_precip_mm)) + geom_histogram()
``````
I’d prefer to make one pipeline for cleaning up my data. So starting from the top
``````aa_weather <- read_csv('noaa/USC00200230.csv', col_types="ccDdddddddddd") %>%
select(DATE, starts_with("T"), PRCP, SNOW, SNWD) %>%
rename("date" = "DATE",
"t_max_c" = "TMAX",
"t_min_c" = "TMIN",
"t_obs_c" = "TOBS",
"total_precip_mm" = "PRCP",
"snow_fall_mm" = "SNOW",
"snow_depth_mm" = "SNWD") %>%
mutate(t_obs_c = ifelse(t_obs_c > 40, NA, t_obs_c),
t_obs_c = ifelse(t_obs_c < -40, NA, t_obs_c),
total_precip_mm = ifelse(total_precip_mm > 250, NA, total_precip_mm))
``````
Now we have a data frame, `aa_weather`, that has our cleaned up data. What’s better, is that we can throw this code in a new script file and as more data is added to the station, we can rerun the code to clean up the data by the same methods!
## Exercises
1. Perhaps you remember from earlier that we can combine logical questions to make a single filter command. Can you transform our two `filter` functions for finding weird `t_obs_c` values into one?
2. Can you make the `mutate` function call above only modify the `t_obs_c` column once?
3. What’s wrong with this code chunk?
``````aa_weather %>%
mutate(t_obs_c = ifelse(t_obs_c > 40 | t_obs_c <-40, NA, t_obs_c)) %>%
ggplot(aes(x=t_obs_c)) +
geom_histogram()
``````
4. Can you make a column called `is_freezing`, which contains logical data indicating whether the minimum temperature for the day was below freezing?
5. Look at the `snow_fall_mm` and `snow_depth_mm` data and see whether you can spot any other weird data. | 3,050 | 10,109 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2024-10 | latest | en | 0.828175 |
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Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A102885 Index of n in the primes A000040 or nonprimes A141468. 0
1, 2, 1, 2, 3, 3, 4, 4, 5, 6, 7, 5, 8, 6, 9, 10, 11, 7, 12, 8, 13, 14, 15, 9, 16, 17, 18, 19, 20, 10, 21, 11, 22, 23, 24, 25, 26, 12, 27, 28, 29, 13, 30, 14, 31, 32, 33, 15, 34, 35, 36, 37, 38, 16, 39, 40, 41, 42, 43, 17, 44, 18, 45, 46, 47, 48, 49, 19, 50, 51, 52, 20, 53, 21, 54 (list; graph; refs; listen; history; text; internal format)
OFFSET 0,2 COMMENTS The nonnegative numbers n occur exactly once in either A000040 or A141468. The sequence lists the corresponding index. It is a permutation of A008619. LINKS FORMULA A141468(a(n))=n or A000040(a(n))=n. CROSSREFS Cf. A141468, A000040, A026233. Sequence in context: A214154 A048219 A087188 * A323089 A239511 A264052 Adjacent sequences: A102882 A102883 A102884 * A102886 A102887 A102888 KEYWORD nonn,easy AUTHOR Juri-Stepan Gerasimov, Aug 17 2008 EXTENSIONS Edited by R. J. Mathar, Aug 19 2008 STATUS approved
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Last modified June 17 05:45 EDT 2021. Contains 345080 sequences. (Running on oeis4.) | 560 | 1,449 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2021-25 | latest | en | 0.721076 |
https://wikis.uit.tufts.edu/confluence/plugins/viewsource/viewpagesrc.action?pageId=64319757 | 1,627,750,583,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046154089.68/warc/CC-MAIN-20210731141123-20210731171123-00249.warc.gz | 612,243,768 | 2,182 | ## Mapping
###### Third Grade Lessons
1. Functioning Together - Students work together to develop multiple representations of a function. The students split up into groups of three with each student having a separate responsibility. When all the input values have been used up, the students are asked to, together, make up a story that describes their function.
2. Human Graph I - Students plot themselves on a Cartesian plane. Each student will get a large card with a place for an ordered pair: (x, y), where x refers to hours worked, and y refers to amount earned. The students must name the coordinate pair for the point they themselves are standing on.
3. Recipes that Exchange - The lesson focuses on a function that multiplies input by two but also changes the ingredient to another type of ingredient.
4. Times Two - The lesson focuses on a function that multiplies the input by two. New notations are introduced. | 187 | 922 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.828125 | 3 | CC-MAIN-2021-31 | latest | en | 0.933031 |
http://www.dustinfife.net/blog/category/statistics/page/2/ | 1,723,301,212,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640808362.59/warc/CC-MAIN-20240810124327-20240810154327-00236.warc.gz | 38,516,472 | 21,195 | # R Packages
Posted in Introduction to R, Statistics
Packages
Perhaps the coolest thing about R is the packages. So what are packages? To understand, let’s suppose your name is Greg and you start using R because it’s the cool thing to do. As you begin to test its functionality, you’re quite surprised that, in order to do a simple Z-test, you have to do a lot of programming:
#### here's my sample data--Greg x = c(7,11,9,12,13,8,12,12,10,9) #### this is the value of mu. #### Is my sample different from 7?--Greg mu = 7 sigma = 2 xbar = mean(x) ###### compute the z score --Greg z.score = (xbar-mu)/(sigma/sqrt(length(x))) ##### look up p value p.value = pnorm(z.score, lower.tail=FALSE) ##### make a conclusion if (p.value < .05) { cat("Reject the Null") }
Notice how Greg has been wise with his generous use of comments (recall comments are noted by anything that follows one or more pound signs). If Greg runs the code, he gets the following:
#### here's my sample data--Greg x = c(7,11,9,12,13,8,12,12,10,9) #### this is the value of mu/stdev. #### Is my sample different from 7?--Greg mu = 7 stdev = 2 xbar = mean(x) ###### compute the z score --Greg z.score = (xbar-mu)/(stdev/sqrt(length(x))) ##### look up p value p.value = pnorm(z.score, lower.tail=FALSE) ##### make a conclusion if (p.value < .05) { cat("Reject the Null") } else { cat("Fail to Reject the Null") } ## Reject the Null
But that seems like a whole lotta work just to make a simple conclusion. He decides to write his own function (which we’ll get to later) so that he doesn’t have to write so many lines of code every time he wants to do a z-test. Now, all Greg has to do is two lines of code:
## Loading required package: TeachingDemos x = c(7,11,9,12,13,8,12,12,10,9) z.test(x, mu=9, stdev=2) ## ## One Sample z-test ## ## data: x ## z = 2.055, n = 10.000, Std. Dev. = 2.000, Std. Dev. of the sample ## mean = 0.632, p-value = 0.03983 ## alternative hypothesis: true mean is not equal to 9 ## 95 percent confidence interval: ## 9.06 11.54 ## sample estimates: ## mean of x ## 10.3
(Note: many other features have been added beyond a simple “reject the null.”) After writing the function, he’s quite proud of it and thinks, “I can’t be the first person who wanted to do a z-test in R. There’s got to be others out there. I bet they’d appreciate it if I made my package available to them!”
So Greg decides to make his z score function available online. When someone makes their function (or set of functions) available through R’s website, it is called a package. The cool thing about packages is that there are thousands upon thousands of R users, many of which write packages and publish them online. That means that R has a lot of added functionality that it otherwise would not because somebody somewhere decided to publish a package.
Installing a Package
As I said, there are lots of R packages available online. But the good news is that you don’t have to go searching for them to download them. Instead, you can download them right from R’s interface. Let’s go ahead and download a z score function from a package called . The author of this package is Greg Snow (no relation to our fictitious Greg of earlier). To download the package type the following
install.packages("TeachingDemos")
A new window will pop up asking you to pick a repository. A “repository” is just a fancy word for “a place to download the package from.” Then it will download the package and make it available for you to call. To call the package (i.e., to make it available for use), you simply type
require(TeachingDemos)
Now you’re ready to use the z.test function by Greg Snow. Thanks Greg!
Next, Practice using R.
# Basic R Commands
Posted in Introduction to R, Statistics
Basic Commands Scalars, Vectors, and Matrices
Let me start by informing you how much you know. You already know what a scalar and a vector are. Remember the variable “hello”? That was a scalar. A scalar is a variable that contains only one value (in that case it was 107). The variable “weight” on the other hand, was a vector–it contained multiple values. There is still one other type of variable: a matrix. Aside from being a deceptive reality that people like Neo and Morpheus battle to overthrow, a matrix also has special meaning in R. When you think of a matrix, think of a spreadsheet. If you’re unfamiliar with what a spreadsheet is, think of a table with columns and rows. Vectors don’t have columns and rows, it’s just a list of numbers. Matrices, on the other hand, do.
Let’s try to get a visual of what a matrix looks like. In your file that you created (the one that I called “weight”), write the following after the line that plots the data
weightData = c(143, 137, 137, 131, 129, 125, 125, 124, 124, 120) matrixWeightData = matrix(weightData, nrow=5, ncol=2) matrixWeightData
After that, highlight the lines that you just wrote, then hit command-enter. On the left window, you should see the following
## [,1] [,2] ## [1,] 143 125 ## [2,] 137 125 ## [3,] 137 124 ## [4,] 131 124 ## [5,] 129 120
Before you get overwhelmed by what I just did, let me talk in R. Here’s what R heard, “Alright R, I want you to create a new vector called weightData. Give it the values 143, 137, 137, 131, 129, 125, 125, 124, 124, and 120. Then, R, I want you to create a matrix called matrixWeightData that contains the exact same information as weightData, but I want you to give the matrix 5 rows and 2 columns. Got it R? Ok, then I want you to show me what matrixWeightData looks like. Now, go!”
Notice that both the variables “weight” and “matrixWeightData” contain the exact same information. The only difference is that weight is a vector, and matrixWeightData is a matrix. So, now so you can see them right next to each other, type the following. Notice how I’m typing it into the left window because I feel no need to save this information, but you can if you want to.
weight ## [1] 143 137 137 131 129 125 125 124 124 120 matrixWeightData ## [,1] [,2] ## [1,] 143 125 ## [2,] 137 125 ## [3,] 137 124 ## [4,] 131 124 ## [5,] 129 120
Again, the variables have exactly the same information, but one is contained as a vector and the other is contained as a matrix.
First, you need to download the workout dataset. Store that file in the same folder that you saved your “weight” script in. Now, make sure R is open, then I want you to select click on the menu called “Misc” then click on “Change Working Directory” just like the picture below.
Next, navigate to the location where you have been using your R files. For me, that was located in the documents folder. If you’re on a PC, you’ll have to first click on the left window, then click on File->Change Dir…
Here’s what you just did. By default, if you ask R to find a particular file, it will search wherever its default directory is. That’s a problem when it doesn’t default to the folder where your file is. All we did was change it’s default directory. Now when you tell R to find the file “workout.csv,” it will know where to find it.
Now that we’ve changed the default directory, let’s tell R to import the file. I’ll be using my right window so I can edit it later. You can continue using the same script that you used before, or you can create a new one.
Here’s what I’m telling R for the first line of code: “Hey R, in the default directory you should find a file called workout.csv.’ Open that file and put all of its contents in a variable called weightLoss.”
The second line of code (i.e., head(weightLoss)) simply tells R to return the first 7 rows of the data. Now if I run the code, the left the window will show
weightLoss = read.csv("workout.csv") head(weightLoss) ## ExerciseHours WeightLoss ## 1 6.1 2.7 ## 2 4.8 2.7 ## 3 4.6 2.7 ## 4 4.1 1.2 ## 5 4.3 3.5 ## 6 4.9 2.5
So now we’ve got a matrix called “weightLoss” that has two columns: one records how many hours a week a person exercised, and the second row records their weight loss for that week. This is a matrix because it has both rows and columns.
You can always use R to read in data if it comes in csv form. If your data do not come in csv form, then you’ll have to use Excel to convert it to csv. R doesn’t handle Excel files very well.
Regression
Let’s continue to work with the dataset you imported (i.e., weightLoss). First let’s compute the mean of the two variables
mean(weightLoss$ExerciseHours) ## [1] 4.953 mean(weightLoss$WeightLoss) ## [1] 3.09
Be careful to watch capitalization–R is case sensitive. Also, you’ll notice that I’m only showing you the output (i.e., the left-side window). I’m actually writing it in my right window, but am only showing what happens in the left window to save space.
So, the mean amount of time spent exercising is around 4.95 hours. Also, the average amount of weight loss was around 3, 3, 3, 1, 4, 2, 3, 3, 4, 3, 4, 4, 2, 3, 2, 1, 4, 3, 4, 3, 4, 4, 3, 4, 3, 2, 5, 3, 5, 2 pounds. Let’s see how large the sample is. To do that, we’ll use the function “nrow,” which is short for number of rows (which is the sample size).
nrow(weightLoss)
So, there are rnrow(weightLoss)` individuals who participated in this study. Let’s compute the correlation. To do so, we’ll use the function “cor.”
cor(weightLoss)
That function returns a correlation matrix. The correlation is moderately high, with a value around 0.58.
Now let’s go ahead and run a regression analysis. To do that we write
lm(WeightLoss~ExerciseHours, data=weightLoss) ## ## Call: ## lm(formula = WeightLoss ~ ExerciseHours, data = weightLoss) ## ## Coefficients: ## (Intercept) ExerciseHours ## -0.913 0.808
Sometimes R defaults to outputting weird things when you run a function. We can be a little more specific about what we want by assigning the regression model to an object. For example
model = lm(WeightLoss~ExerciseHours, data=weightLoss)
Now R stores all the information about the regression into an object called “model.” We can now ask R to report several things such as
##### output a summary of the model summary(model) ## ## Call: ## lm(formula = WeightLoss ~ ExerciseHours, data = weightLoss) ## ## Residuals: ## Min 1Q Median 3Q Max ## -1.6893 -0.4752 -0.0505 0.6501 1.2723 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) -0.913 1.066 -0.86 0.39901 ## ExerciseHours 0.808 0.213 3.79 0.00073 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 0.781 on 28 degrees of freedom ## Multiple R-squared: 0.339, Adjusted R-squared: 0.316 ## F-statistic: 14.4 on 1 and 28 DF, p-value: 0.000735 ##### give me just the intercept and slope of the model model$coefficients ## (Intercept) ExerciseHours ## -0.9126 0.8081 ##### give me the conditional variance summary(model)$sigma ## [1] 0.7814
Notice the use of the pound signs (####). That tells R to ignore everything on that line. In other words, they are simply comments to myself.
cf = round(model\$coefficients, digits=4)
Using the results from $$model\coefficients$$, we see that the best-fitted regression equation is $$\hat{\text{Weight Loss}} = -0.9126 + 0.8081\times\text{Exercise}$$. In other words, with no exercise, we’re expected to lose approximately -0.9 pounds (i.e, we’re expected to gain a little bit). For every hour we exercise, we’re expected to lose about 0.8 pounds.
Let’s go ahead and look at a scatterplot of the data with a regression line in red.
plot(weightLoss) abline(model, col="red")
The first line tells R to plot the pairs of datapoints. The second code (abline….) tells R to plot a line from a to b (hence, abline) based on the object called “model.” Remember that this object (model) contains the results of the regression equation. Somehow, R knows in the background that it’s supposed to plot a line. Then, I told it to plot the line in red.
Functions
A function is a set of instructions to the computer. It receives input, then spits out output. For example, we used the function “mean” to compute the mean of the weight dataset. It received an input (the vector called weight) and spit out an output (the mean). Also the plot function received an input (a vector or a matrix) and returned an output (a graph).
Sometimes a function returns multiple outputs such as the $$lm$$ function. (Recall that it spit out the slope and intercept parameters, the conditional variance, a summary, etc.) Also, sometimes functions require multiple inputs. Again, the $$lm$$ function was one such example (we had to input a regression equation and the dataset).
The Table below lists some of the functions we have learned so far. In one column we show what the inputs are and in the other we show what the outputs are.
Sometimes, however, you may forget what the inputs and/or outputs are. There’s a simple way to access that information. Let’s see what the inputs/outputs are for the cor function.
?cor
Notice when you did that, either a window popped up or a new webpage in your browser appeared. It should look like this:
Whenever you put a question mark in front of a function name then run the command, R will automatically bring up the documentation for it. The description is obvious–it tells you what the function does and may give some other relevant information. The Usage section tells what arguments the function takes. You’ll notice it says under the cor function “x, y = NULL,” etc. If you’re ever confused about what an argument means, then you can read in the Arguments section. For example, if we were unsure of what “x” was supposed to be, we would read, “a numeric vector, matrix, or data frame.” Notice that, although we only supplied one argument before (i.e., the weight vector or the weightLoss matrix) there are several more arguments we could have passed it. If you’re interested in what those arguments are, please read on.
If you scroll down, you will notice another section called “Examples”. Not surprisingly, this section will give you examples about how to use the “cor” function.
The important point to take away from this is that any function you use has arguments (inputs) and returns a result (outputs). If you ever have questions about what inputs/outputs are attached to a function or how to use it, type a question mark before the function and run the command.
Next, R Packages.
# The R Interface
Posted in Introduction to R, Statistics
The R Interface
When you first open R, it will look like the figure below. You could start using R at this point by typing in commands at the point where the > is located. Let’s go ahead and try that.
PC version of what R’s console looks like
Mac R console
The first thing that we’ll do is create a variable called hello and give it the value of 107. To do that, we would do the following
hello = 107 hello ## [1] 107
Notice how it returned the value “107” back to you. All you did was create something (we’ll call it a variable) called “hello” and assigned it a value of 107. Now let’s try something else. Let’s create a called weight:
weight = c(143, 137, 137, 131, 129, 125, 125, 124, 124, 120) weight ## [1] 143 137 137 131 129 125 125 124 124 120
Suppose that this represents your weekly weight over a 10 week period. (Kudos to you! You’re learning R and losing weight!). So here’s what we did–we created a variable called weight, but rather than holding a single value, it actually contains 10 values. This is called a vector. That’s why we put “c(…)” there– stands for ‘concatenate’ which is is an overly technical way to say, “I put a bunch of things into a single object.”
Since now contains several numbers, we can start doing statistics on it. For example, we may compute the mean of it.
mean(weight) ## [1] 129.5
(don’t forget to hit enter). Or we could compute the standard deviation
sd(weight) ## [1] 7.367
or the median
median(weight) ## [1] 127
Or we could plot it
plot(weight)
At this point, hopefully your results matched mine. If so, good job! You’ve just done your first bit of R programming.
Now go ahead and close the plot window (after spending several minutes admiring it!) Now let’s suppose that you should have put the value 135 in the third position, not 137. Oops. To correct it, there’s several things you could do. Here’s one way: you push the up arrow button six times until R shows the following:
weight = c(143, 137, 137, 131, 129, 125, 125, 124, 124, 120)
Then you could click on the third 137, change it to 135, then hit enter. Go ahead and do it. In this example, that was easy because you noticed the error only 6 steps into your code. But suppose you had done 100 things between creating the variable and noticing the error. You’d have to push the up-arrow button 100 times! So, let me show you a much better way of keeping track of your code and keeping a better record of what you’re doing.
The first thing we’ll do is hit command-N (if you’re on a PC, you’ll have to go to the file menu, then click on “New script“). Notice that a new window pops up (on the right in the image below).
R Console on a mac
The good thing about this second window is that it allows you to write code, save it, edit it, then selectively run it. Let me give you an example. On the right window (the one that you just opened), write the following code just as you did before:
weight = c(143, 137, 137, 131, 129, 125, 125, 124, 124, 120) mean(weight) sd(weight) median(weight) plot(weight)
Then go ahead and hit command-S (or control-S) to save the document. Save it somewhere you’ll remember. I saved mine in my documents folder and called it “weightloss.” When you save a script (which is what this window is called), then you can access and run it later. Now that it’s saved, let’s go ahead and have R run the script. To do so, click the mouse anywhere on the first line and hit command-enter (on a Mac) or control-R (on a PC). Notice that on the left window it has the following:
weight = c(143, 137, 137, 131, 129, 125, 125, 124, 124, 120)
So, what just happened? What you did was create your code in the right window, then sent that line to the left window. To run all the code, click on the right window, hit command-A (or control-A) to highlight all your code, then hit command-enter (or control-R). Notice how all of your code is run simultaneously.
The good thing about this method (i.e., the method of having two windows) is that you have one window where you can edit/write your code and the other window is dedicated to running the code. That way, if you need to make an edit, you don’t have to keep pushing the up arrow everytime you need to change something. Instead, you edit it in the right window, then execute the code (by pushing command-enter or control-R).
Next, Basic R Commands.
# Installing R
Posted in Introduction to R, Statistics
Introduction What is R?
Very few researchers compute statistics by hand. Most make computers do their statistics for them. Also, some statistical routines are impossible to do without computers.
Several programs are available for data analysis, including SPSS, Excel, SAS, Matlab, Minitab, and R. Several of these programs have a familiar and easy to use interface (such as SPSS, Excel, and Minitab)–in these programs you simply point and click in order to analyze your data.
However, ease of use often comes at the expense of flexibility. Some programs (such as Excel or Minitab) only allow the user to do basic statistical analysis and data manipulation. However, the “big dawgs” like to use programs that are much more flexible, such as SAS and R.
Programming Statistics
While Excel and SPSS have point and click interfaces, R does not. Instead, the user must program their statistical analysis. For example, to perform a regression analysis in Excel is a simple matter of pointing and clicking. R, on the other hand, must be told through a computer language how to perform the statistical analysis:
lm(y~x, data=testData, subset=(group==1))
Don’t worry about what interpreting the code just yet, but you can see that things become a little more complicated when the user must code their statistical analysis rather than pointing and clicking. However, with that added complication comes added flexibility.
However, explaining what R is, it’s probably better for you to dive in. In the next chapter, we will show you how to perform some rudimentary R operations to give you a feel for how to “speak” the R language. After that, we’ll dive in to some more advanced R programming.
What This Tutorial Is and Is Not
This tutorial does not provide comprehensive documentation of the R language. Instead, it’s a brief introduction to the language to help you get your “feet wet.” I have learned several programs in my lifetime, and I’ve found the best way to learn them is to have a short introduction, then spend the rest of the time messing around with it. So, with that, let’s wet those feet of yours!
Installation
Next you will be taken to a screen where you can actually download R. Click on the top-most link (make sure you have an operating system that meets the minimum requirements). If your OS doesn’t meet the minimum requirements, then choose a file that does.
Then you wait! The download shouldn’t take too long. After it downloads it, open the file and allow R to install on your machine. Congrats! You just installed R!
Next, the R Interface
# The obligatory test
Posted in Statistics, Writing
First, I must speak latin so everyone thinks I’m sophisticated and educated.
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Ooooooh yeahhhhhhhhh. Now we’re verbally bling-blinging .
Now what else should I do for my first entry? Ah yes, I must post an image of my cat, as all bloggers do. Alas, I am catless (oh the affront-ery of such an act). So, I will instead swipe a feline’s avatar from google images:
Isn’t snuggles just to die for! Daddy loves her so!
And, of course, I cannot finish until I’ve written a biography in the third person (so people assume I’m so important I can’t stoop to such petty things as writing about myself).
Dustin Fife, photographer-gone-psychologist-gone-statistician-gone-writer (this one will stick, I promise), lives in a high-rise apartment (translation, a red-brick house) overlooking the city scenery (translation, overlooking nothing but a weed-infested lawn and messy diapers that are airing outside). Born and raised in Washington State, he now lives in Oklahoma with a princess that hasn’t woken from her apple-induced sleep (translation, she hasn’t mentally woken–why in the world did she choose to merry me????) and three dwarves, who all take turns playing the role of grumpy. | 5,937 | 23,304 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.046875 | 3 | CC-MAIN-2024-33 | latest | en | 0.840886 |
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# Online Statistics Problem Solver
Online Statistics Problem Solver At Be.a.Net we find out here the user problem satisfaction for a given user or a data set of users in a given data set. How do we count user satisfaction (i.e., which users are currently satisfied) for a given user or a data set? We are the heart of the system (at a given point in time) and we have to count each user relation by applying a column average. Consider I created a data set where I was interested in a set of data I will be using the average users. At the time of creation, I write into the record (Record1). We can observe that if I assign values from different users I think, each relation on AccountId1 and AccountId2 would be consistent when I assigned each value for AccountId1 by the value. I think that the result of having two methods on two users, one for one of the values (AccountId1 and AccountId2) and one for the other one belongs to one User, and thus we have a correlation matrix. I think that as in the case with an average we have to calculate the correlation measure. But if I are assigning the same value by different way, I think that these two methods would be as in the case you get an ID of the same users, but if I assign to the same users I think they will be compatible, so how do I count all the others correlation by using the column average? Note that there are some performance reductions, those which are only useful for a limited number of users. To do this better we use two most popular methods for processing the correlation matrix.
## Help With Programming Assignment
To be more exact, let’s just cast the correlation as there are many correlations among users. The correlation are the average and the average component the average for the number of relations in the data sets be a sort of correlation index or feature index. Note that the method is called as it is in OpenID technology. Let’s take an example. Suppose I have a user name who is about 10 users. I assign each user the same column average and the user id based on these column average has been assigned at the column average with the same value. I perform 10 correlation factors each with the following two column average of all users who are in the same relation. First column average – 1 2 2 2 3 Next column average – 4 3 4 3 5 Finally column average – 8 4 6 2 7 In order to count a related expression, we must add another column average. The result of that is that if we add 8 correlation factors to the column average of the current information, it should be as the correlation between these two columns. But the next column average can be simply not be expressed by 2 column averages, because we have column average 5 and instead we have correlation factor 1 and 2 redirected here one column two. Let’s again take a student has been related in a column average. That student is on the first activity. He has the first activity and the average has been assigned 2 and 5.
## Python Assignment Help
” Note that we will make use of your web address as your home search engine. You can find out if they listed you through their home page. If they don’t, check their email address. This would be an important portion of your personal information. Later, when it is time to click on Next… here is the last task thatOnline Statistics Problem Solver In March, 2004, the Massachusetts Supreme Court ruled that certain classes of property owners that are owned and operated by two corporations, the Bank of Massachusetts and its derivatives, at an arm’s length relationship between the two corporations, have a click here now of action under Massachusetts law. (Michigan Law, Law of Michigan, § 152, pp. 901–05; U.S. Supreme Court, (2009) 2 Mich. Court of Appeals 531 F.3d 152, 173-73, 189; U.S. House of Delegates, House of Congress Committee on General Motors, Committee on Energy, Committee on Water, and Subcommittee on Biomechanics of the U.
## International Economics Assignment Help
S. House of Representatives, Committee on Energy and Environmental Policy—Chairman House of Representatives, Subcommittee on Biomechanics of the U.S. House of Representatives, Committee on Energy and Environmental Policy. (2005) 2 Mich. Court of Appeals 534 F.3d 1007, 1018.) We held a case in Detroit to be “arguably analogous,” and we repeated the majority’s decision in March of 2004 after this Court found that it was “invalid law.” The Michigan Supreme Court did not state in its March 13, 2004 decision that it will treat this aspect of the question of whether a public entity has an independent right of action as well. The Michigan law is entirely inapplicable to a public interest forum only if the two companies entered into the transaction under an implied agreement or consent, in that way the majority declared. This reasoning is a useful guide for all those in the case, because more than one such agreement has been found contrary to the Michigan law. We may look for solutions to problems like this. Our website can help you: Help us improve WordPress Some services we find useful, some questions we might not care to answer, and some small updates may make some day for a long time.
## Statistics Homework Questions
If you believe those below, please don’t hesitate to give us a call. We want you to find the answer to all our queries. If you have the time, focus on the services we recommend, instead of Google. This material is for informational purposes only. We do not take responsibility for the accuracy of information of any site or the materials at any sites relating to this site. Any potential hazards are to be expected. Our goal is to maintain both our website and our editorial content free of charge. We offer this for informational purposes only and do not guarantee its continued use. If you would like to learn how to manage a website with a website at your disposal, you can find our about box here: http://www.bistro.com/2010/08/26/how-to-set-up/ Web development costs, including high-traffic and high-resource needs, are expensive in the public sector. Web development costs are an uncharacteristic element of a public health professional’s pay for a Web site. A web developer is not required to meet the minimum amount of development services needed to build and maintain an effective website. | 1,368 | 6,376 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.328125 | 3 | CC-MAIN-2022-33 | longest | en | 0.939839 |
http://www.edurite.com/kbase/data-interpretation-questions-solutions | 1,464,252,219,000,000,000 | text/html | crawl-data/CC-MAIN-2016-22/segments/1464049275764.90/warc/CC-MAIN-20160524002115-00121-ip-10-185-217-139.ec2.internal.warc.gz | 477,109,539 | 18,216 | #### • Class 11 Physics Demo
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# data interpretation questions solutions
Question:I did an ANOVA test with an online calculator. I am really not sure how to interpret these results. The original story was that "psychologists are interested in studying the influence of media on aggressive behavior in kids. Among 15 subjects (n=15) five are exposed to violent video games, 5 to games and 5 to movies. After exposure, subjects were then observed by researchers and the # of aggressive behaviors of each subject was recorded by researchers yielding the following distribution of values. (I put those values into the test.) I just dont know how to interpret these findings into words....... can anyone help me with this? ANOVA: Results The results of a ANOVA statistical test performed at 18:47 on 2-APR-2009 Source of Sum of d.f. Mean F Variation Squares Squares between 1485. 2 742.5 11.27 error 790.8 12 65.90 total 2276. 14 The probability of this result, assuming the null hypothesis, is 0.002 -------------------------------------------------------------------------------- Group A: Number of items= 5 25.0 38.0 39.0 42.0 47.0 Mean = 38.2 95% confidence interval for Mean: 30.29 thru 46.11 Standard Deviation = 8.17 Hi = 47.0 Low = 25.0 Median = 39.0 Average Absolute Deviation from Median = 5.20 -------------------------------------------------------------------------------- Group B: Number of items= 5 8.00 19.0 22.0 23.0 31.0 Mean = 20.6 95% confidence interval for Mean: 12.69 thru 28.51 Standard Deviation = 8.32 Hi = 31.0 Low = 8.00 Median = 22.0 Average Absolute Deviation from Median = 5.40 -------------------------------------------------------------------------------- Group C: Number of items= 5 5.00 11.0 14.0 18.0 26.0 Mean = 14.8 95% confidence interval for Mean: 6.890 thru 22.71 Standard Deviation = 7.85 Hi = 26.0 Low = 5.00 Median = 14.0 Average Absolute Deviation from Median = 5.60 Also... the question is also asked on the form: "What form of media seems to have the strongest effect on aggressive behavior and are the means significantly different?" I have no idea how to actually interpret that and I am stuck, new to this.....
Answers:It is hard to tell you what media seems to have the effects, since you only refer to them as Group A, B and C, so you will have to look that up yourself. First Question: 'What form of media seems to have the strongest effect on aggressive behavior?' Just describe the data here. For example, say that Group A has a mean of 38.2, with a highest value of 47 and a low of 25. Do the same for the other groups and say that it appears that Group A has the highest of all groups, and B is greater than C. Second Question: 'Are the means significantly different?' Basically, the ANOVA results are telling you that there is a significant difference in recorded aggressive behaviours for the three groups. How can you tell that it is significant? One way is to compare the alpha value you used in running the analysis. You have not reported it, but the most often used is 0.05, so I will assume it is that. If you look at the p value you got in your results, you will see that it is equal to 0.002. Since 0.002 is smaller than 0.05, your result is significant. As it turns out, your p value is lower than all three most often use alpha values (.10, .05, .01) so that's great :) So what you can say is that there is significant differences in aggressive behaviour after exposure to violent video games, games and movies, with F(2,12)=11.27, p<0.05 with Group A showing greater aggressive behaviour than both B and C, and B greater than C. You could also mention the confidence intervals. These show that you can be 95% confident that the true population value falls between these values and because the range of these values do not include 0, the result is statistically significant.
Question:I pretty much have zero knowledge in using SPSS, and very little knowledge about statistics, etc. I have to do this data analysis using regression (linear). So the result that has been generated is this: the value of R= .620a R square= .385 adjusted R square=.350 the coefficients: (Constant)=.862 (t) Pay= -.672 (t) Personal factors= 1.445 (t) Job design and characteristics=1.956 (t) Workplace spirituality= 3.042 (t) Physical structure of workplace= 1.362 (t) note: the dependent variable is employee performance. I think it is not a good analysis isn't it. Can you please help me by giving comments? what does the R or R sq value mean in this case? how can interpret the results with regards to the variables? what should i do when the R square is too low?
Answers:There is a better category for you to post your question: "Math" or "Homeworrk." Social Science category is about people, we leave the mathmatical equations to the experts in math category. They love that stuff. Good luck.
Question:I have a lab I am doing for a chemistry class and I dont quite understand this question Determine the concentration of your diluted solution. Assume the concentration of your drink was 0.15M and you make a tenfold dilution. (Write your data, substitute the values in the formula for density and show your stepwise calculation). I know you are supposed to use Mi*Vi=Mf*Vf but im not sure how to start with the question we had started with 1mL then added water untill it hit the 10 mL mark
Answers:Because I don't know the density assuming 1 L = initial volume 0.15 x 1 = M x 10 M = 0.015 M
Question:I did a 10 question pre & post survey of the same 10 people. The mean difference is -1.3, Degrees of freedom= 9, standard error of the mean of d= .86, t-statistic for paired data = -1.51, Critical value for alpha .05 would be 2.262. Now I am not sure how to know whether I accept or reject the null hypothesis. Not even sure what the null hypothesis should be. My research is whether or not medication improves the school performance of ADHD children. Pre-Survey (before meds) and after survey (while on meds). I have all these numbers and don't know how to make since of them. Guess I should've paid more attention in that statistics class! Please help.
Answers:It's very difficult to answer what the null hypothesis should be. If you don't know what you're comparing, then why do the test? I assume you are comparing pre and post test results. Your null hypothesis would most likely be that the test results are the same for both tests. It also sounds like you're preforming a one-sided test on what could be a two-sided test. You would reject any statistic that is above 2.262 or below -2.262 and this would give you an alpha of .05 (.025 on each tail). Basically it looks like you found a two-sided significant value (2.262) but think you're doing a one-sided test. If you're looking to see if there's a significant difference period, then you'd use the two-sided test. If you want to see if the second test scored better, then use the one - sided. (It'd be a lot easier to explain this if I knew exactly how you did the math). If you go above the significant value or below it then you reject the null. Regardless, this won't change your result in this case since your value is -1.51. Basically, any statistic outside of alpha means you reject the null because you have a statistically significant reason to say that the data in the first test is different than the data in the second test. You are making sure there is a significant difference in the data in order to say the medication made a change. Based on your results, you aren't seeing a change since the results. You would not reject the null hypothesis. This means that, based on your results, this drug does not alter test results in patients with ADHD. And yes, you should have paid more attention in statistics class. This stuff really isn't that difficult but you seem so lost. If you plan on doing more of this type of thing I'd suggest taking a stats class again or at least getting a stats textbook and look at it. Also, make sure this is the correct test and that you did it correctly. Based on what you've said, I'm assuming that your resulting t-statistic is correct and that you're using the correct test. It sounds like you have (comparing two results given what it's for) but make sure. | 1,963 | 8,244 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.703125 | 4 | CC-MAIN-2016-22 | longest | en | 0.842845 |
https://www.skytowner.com/explore/numpy_flatnonzero_method | 1,723,090,903,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640719674.40/warc/CC-MAIN-20240808031539-20240808061539-00227.warc.gz | 779,681,630 | 15,462 | search
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Numpy's `flatnonzero(~)` method returns the indices of non-zero values in the flattened version of the input array.
Parameters
1. `a` | `array_like`
The input array.
Return value
A Numpy array of indices of non-zero values in the flattened version of the input array.
Examples
One-dimensional arrays
One-dimensional arrays are already flat, so this is equivalent to just applying the `np.nonzero(~)`:
``` np.flatnonzero([5,3,0,2]) array([0, 1, 3]) ```
Here, the indices 0, 1 and 3 are returned since the values 5, 3 and 2 are non-zeros.
Two-dimensional arrays
Suppose we had a 2D array:
``` np.flatnonzero([[1,0],[2,3]]) array([0, 2, 3]) ```
Here, the 2D array is first flattened out to `[1,0,2,3]`, and then the indices of the non-zero value are extracted.
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Contact us | 541 | 2,020 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.375 | 3 | CC-MAIN-2024-33 | latest | en | 0.766661 |
http://ebook.pldworld.com/-huihoo-/book/vector-math-for-3d-computer-graphics/vch12/vch12_9.html | 1,590,861,844,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347410284.51/warc/CC-MAIN-20200530165307-20200530195307-00289.warc.gz | 36,184,750 | 1,737 | ### A good answer might be:
By examining the diagram, or working with the formula: (ku) × v = k( u × v )
# Not Associative
Fussing with math gives the same result:
| (ku) × v | = | ku | | v | sin θ = | k | |u | | v | sin θ
The magnitude is | k | times the magnitude of u × v. And the orientation of the result must be the same. So the answer is correct.
Another fact is that, in general, (u × v) × w =/= u × (v × w)
To see this, look at the diagram and mentally form the cross product (u × v) , then take the cross product of that with w. Then form the cross product (v × w) and take the cross procut of u with that.
### QUESTION 9:
What is (u × v) in the diagram ? | 207 | 690 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.8125 | 4 | CC-MAIN-2020-24 | latest | en | 0.808299 |
http://www.eetimes.com/messages.asp?piddl_msgthreadid=38841&piddl_msgpage=3 | 1,427,410,188,000,000,000 | text/html | crawl-data/CC-MAIN-2015-14/segments/1427131292683.3/warc/CC-MAIN-20150323172132-00236-ip-10-168-14-71.ec2.internal.warc.gz | 486,787,209 | 33,011 | Breaking News
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re: Selecting a solar energy conversion method
7/9/2012 8:36:44 PM
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You have stated “As the cell voltage rises, the current in the internal diode rises, leaving less of the photo current for the load”. This is not so. If you follow the panel I-V curve shown in Figure 6 when the cell voltage increases the cell current decreases. The maximum cell voltage is the open circuit voltage, Voc, where the current is zero.
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re: Selecting a solar energy conversion method
7/9/2012 8:35:36 PM
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The maximum power available from the panel does not change but the power that is actually extracted from the panel does change and it is a function of the load resistance RL. This maximum power point occurs when RL = Rs. The boost converter decreases the value of RL by adjusting its duty cycle. The input resistance seen by the panel is RL x (1-du)^2 where du is the duty cycle internally set by the SPV1020. The SPV1020 duty cycle is internally adjusted so that RL x (1-du)^2 equals the panel output resistance Rs.
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re: Selecting a solar energy conversion method
7/9/2012 8:34:29 PM
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You are correct. The intent of using the Thevenin equivalent is to show that whatever the value Rs even though non-linear, RL must match it to provide maximum power transfer.
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re: Selecting a solar energy conversion method
7/9/2012 8:33:35 PM
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RL will normally be much greater than Rs. Interposing the SPV1020 boost converter between the panel and RL decreases the load resistance seen by the panel. The load resistance seen by the panel Rin = RL x (1-du)^2 where du is the duty cycle internally set by SPV1020. The duty cycle is set by the SPV1020 so that RL x (1-du)^2 = Rs, the source resistance of the panel.
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re: Selecting a solar energy conversion method
7/7/2012 6:29:49 PM
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A very nice article with good technical details! Very much appreciated, thank you! I am wondering if this level of complexity is needed when using solar power both locally and not at normal line voltages (ie. 12V or 24V DC lighting/systems)?
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re: Selecting a solar energy conversion method
7/7/2012 2:40:06 PM
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I see that my understanding is slowly beginning to clear. I found the found Fig. 3.7 on pg. 24 of the following article to be helpful: https://digital.library.txstate.edu/bitstream/handle/10877/3171/fulltext.pdf I think what was bothering me was that the boost converter cannot increase the load voltage to any arbitrarily high level. It is necessarily limited by the PV maximum power curve for a given set of conditions (illumination, temp., etc.) This Fig. (3.7) seems to bear that out that.
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re: Selecting a solar energy conversion method
7/6/2012 8:14:28 PM
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Yes, the Thevenin model applies in figure 2, as you are looking back into the terminals of the source. What's more, if you apply a variable resistive load, you will get a linear graph of voltage vs current.
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re: Selecting a solar energy conversion method
7/6/2012 7:39:23 PM
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"Southern Exposure is Obvious" That is true only in the Northern Hemisphere. A better statement, might be "Equatorial Exposure is required"
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re: Selecting a solar energy conversion method
7/6/2012 9:50:45 AM
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Rich - as far as I am aware the panel output is surprisingly constant with time. Most panels are guaranteed more than 90% rated output after 10 years and more than 80% output after 25 years (approx 100,000 hours of daylight use). Typical results are better than that, so degradation is just a fraction of 1% per year.
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re: Selecting a solar energy conversion method
7/5/2012 10:30:41 PM
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Thevenin is a poor approach, a better model is a current source, with a parallel clamp diode, and better curves would include constant power profiles (V*I = constants) which makes the MPPT seeking easier to visualize.
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4:56 | 1,641 | 6,478 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.09375 | 3 | CC-MAIN-2015-14 | longest | en | 0.883581 |
https://primes.utm.edu/curios/page.php/349.html | 1,638,691,761,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964363149.85/warc/CC-MAIN-20211205065810-20211205095810-00600.warc.gz | 517,134,328 | 4,422 | # 349
This number is a prime.
π(349) = π(3)1 + π(4)2 + π(9)3. Note that 349 is the largest number with this property. [Firoozbakht]
Frame 349 of the original Zapruder slide set is missing.
Barack Obama had 349 electoral votes in the final election projection of 2008.
The number of seats in Swedish Parliament. [Gupta]
The only prime less than a googol of form 7^x+6, for x a prime, (case x=3). [Loungrides]
"349" is a WordPress blog (www.threefourtynine.wordpress.com). The internet, politics, and language works like this ... . [Goins]
The numerical value of the Greek ισραηλ (Israel) is 349. [Slattery]
Every prime apart from the first can be described by the two word palindrome 'NEVER EVEN'. Using the alphaprime code, 'NEVER EVEN' = 349. [Homewood]
349 to the power thirty-nine is zeroless. [Sariyar]
349 is the smallest n such that the generalized repunit (39^n-1)/(39-1) is prime. [Xayah]
(There are 4 curios for this number that have not yet been approved by an editor.) | 290 | 991 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2021-49 | longest | en | 0.869918 |
https://people.maths.bris.ac.uk/~matyd/GroupNames/432/e18/C3sS3byC2%5E2xS3.html | 1,713,309,213,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817112.71/warc/CC-MAIN-20240416222403-20240417012403-00197.warc.gz | 411,949,017 | 2,476 | # Extensions 1→N→G→Q→1 with N=C22×S3 and Q=C3⋊S3
Direct product G=N×Q with N=C22×S3 and Q=C3⋊S3
dρLabelID
C22×S3×C3⋊S372C2^2xS3xC3:S3432,768
Semidirect products G=N:Q with N=C22×S3 and Q=C3⋊S3
extensionφ:Q→Out NdρLabelID
(C22×S3)⋊(C3⋊S3) = S3×C3⋊S4φ: C3⋊S3/C3S3 ⊆ Out C22×S32412+(C2^2xS3):(C3:S3)432,747
(C22×S3)⋊2(C3⋊S3) = C2×C336D4φ: C3⋊S3/C32C2 ⊆ Out C22×S3144(C2^2xS3):2(C3:S3)432,680
(C22×S3)⋊3(C3⋊S3) = C2×C337D4φ: C3⋊S3/C32C2 ⊆ Out C22×S372(C2^2xS3):3(C3:S3)432,681
(C22×S3)⋊4(C3⋊S3) = S3×C327D4φ: C3⋊S3/C32C2 ⊆ Out C22×S372(C2^2xS3):4(C3:S3)432,684
Non-split extensions G=N.Q with N=C22×S3 and Q=C3⋊S3
extensionφ:Q→Out NdρLabelID
(C22×S3).(C3⋊S3) = C62.77D6φ: C3⋊S3/C32C2 ⊆ Out C22×S3144(C2^2xS3).(C3:S3)432,449
(C22×S3).2(C3⋊S3) = C2×S3×C3⋊Dic3φ: trivial image144(C2^2xS3).2(C3:S3)432,674
×
𝔽 | 541 | 807 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.765625 | 3 | CC-MAIN-2024-18 | latest | en | 0.462687 |
https://www.physicsforums.com/threads/translational-speed-of-a-bowling-ball.160476/ | 1,669,917,535,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710829.5/warc/CC-MAIN-20221201153700-20221201183700-00160.warc.gz | 1,018,108,392 | 14,568 | # Translational Speed of a bowling ball
Kelschul
A bowling ball encounters a 0.760-m vertical rise on the way back to the ball rack, as the drawing illustrates. Ignore frictional losses and assume that the mass of the ball is distributed uniformly. The translational speed of the ball is 7.88 m/s at the bottom of the rise. Find the translational speed at the top.
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You really need to show some working before you can receive any help. As a hint you can think about the conservation of energy.
despanie
A bowling ball encounters a 0.760-m vertical rise on the way back to the ball rack, as the drawing illustrates. Ignore frictional losses and assume that the mass of the ball is distributed uniformly. The translational speed of the ball is 7.88 m/s at the bottom of the rise. Find the translational speed at the top.
HOW IS THE EQUATION SETUP FOR THIS PROBLEM
despanie
A bowling ball encounters a 0.760-m vertical rise on the way back to the ball rack, as the drawing illustrates. Ignore frictional losses and assume that the mass of the ball is distributed uniformly. The translational speed of the ball is 7.88 m/s at the bottom of the rise. Find the translational speed at the top.
kE1+PE1=KE2+PE2
1/2(MKG)(7.880)^2+(MKG)(9.8)(.76M)=1/2MKG(V)^2+MKG(9.8)(X)
despanie
kE1+PE1=KE2+PE2
1/2(MKG)(7.880)^2+(MKG)(9.8)(.76M)=1/2MKG(V)^2+MKG(9.8)(X)
WILL THIS EUATION WORK FOR THE SPEED
Homework Helper
You're on the right track, but you mixed up your gravitational potential energy terms a bit. If you take the bottom of the rise as your reference point, what is the gravitational potential energy of the ball before it goes up the rise? | 459 | 1,668 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.9375 | 4 | CC-MAIN-2022-49 | latest | en | 0.869754 |
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# Solutions for Chapter 10: Parametric Equations and Polar Coordinates
## Full solutions for Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) | 6th Edition
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Solutions for Chapter 10: Parametric Equations and Polar Coordinates
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Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign) was written by and is associated to the ISBN: 9780495011699. Chapter 10: Parametric Equations and Polar Coordinates includes 359 full step-by-step solutions. Since 359 problems in chapter 10: Parametric Equations and Polar Coordinates have been answered, more than 87273 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Single Variable Calculus: Early Transcendentals (Available 2010 Titles Enhanced Web Assign), edition: 6. This expansive textbook survival guide covers the following chapters and their solutions.
Key Calculus Terms and definitions covered in this textbook
• Arccotangent function
See Inverse cotangent function.
• Course
See Bearing.
• Degree of a polynomial (function)
The largest exponent on the variable in any of the terms of the polynomial (function)
• Exponential regression
A procedure for fitting an exponential function to a set of data.
• Infinite limit
A special case of a limit that does not exist.
• Irreducible quadratic over the reals
A quadratic polynomial with real coefficients that cannot be factored using real coefficients.
• Linear programming problem
A method of solving certain problems involving maximizing or minimizing a function of two variables (called an objective function) subject to restrictions (called constraints)
• Modified boxplot
A boxplot with the outliers removed.
• Odd function
A function whose graph is symmetric about the origin (ƒ(-x) = -ƒ(x) for all x in the domain of f).
• Parameter
See Parametric equations.
• Pascal’s triangle
A number pattern in which row n (beginning with n = 02) consists of the coefficients of the expanded form of (a+b)n.
• Product of complex numbers
(a + bi)(c + di) = (ac - bd) + (ad + bc)i
• Quartic function
A degree 4 polynomial function.
• Quartile
The first quartile is the median of the lower half of a set of data, the second quartile is the median, and the third quartile is the median of the upper half of the data.
• Random numbers
Numbers that can be used by researchers to simulate randomness in scientific studies (they are usually obtained from lengthy tables of decimal digits that have been generated by verifiably random natural phenomena).
A graph in which (-x, y) is on the graph whenever (x, y) is; or a graph in which (-r, -?) or (r, ?, -?) is on the graph whenever (r, ?) is
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A procedure used to divide a polynomial by a linear factor, x - a
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r(cos ? + i sin ?)
• Vertical stretch or shrink
See Stretch, Shrink.
• x-intercept
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• Level: GCSE
• Subject: Science
• Essay length: 1031 words
# Parachutes Experiment - Abhirath Singh
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Introduction
-Abhirath Singh 9C Parachutes Experiment Aim: 1. To determine that the surface area of a parachute can affect the time it takes to travel a calculated distance, and therefore affecting the speed at which it falls. Hypothesis: 1. The surface area of a parachute affects the time it takes to travel a calculated distance, and the speed at which it falls. 2. Parachutes with a larger surface area will fall slower than ones with a smaller surface area, and will also take a longer time. Background: Parachutes are used by people in order to land safely from the air. These parachutes work on the basic law of air resistance. As a parachute opens up, it causes resistance against the air, causing the person using it to slow down. There are several factors that affect the way a parachute falls. These include; weight of user, force of winds blowing against the parachute, direction of winds against the parachute, material of parachute, weather conditions and surface area of parachute.
Middle
6) Measure the height of the person dropping the parachute. And add this height to the height measured in Step 5. 7) Hold the parachute from the center of the polythene sheet and keep it at the level of your height. 8) While holding a electronical stop watch in your hand, drop the parachute onto the place where you want your parachute to land, simultaneously starting the electronical stop watch. 9) As the parachute hits the area you wanteded it to land, stop the electronical stop watch. 10) Note down the time taken. Take minimum of 3 readings. 11) Repeat the experiment for the following dimensions: 10cm by 10cm (100 cm2), 15cm by 15cm (225 cm2), 20cm by 20cm (400 cm2) and 25cm by 25cm (625 cm2). Data: Weight of Plasticine used = 4.98 grams. Distance traveled by parachute = 3.30 meters. Data Table - 1 Attempt No. 5cm by 5cm (25 cm2)
Conclusion
Therefore we can conclude that parachutes with a larger surface area fall more slowly and take a longer time than ones with a smaller surface area. Therefore, if a person using a parachute would want a soft and safe landing with ease, they would use a parachute with a larger surface area. Errors and Modifications: 1. The square cut out of polythene were not exactly a square. 2. While the parachute was traveling, there could have been air blowing from any of the directions, causing a change in the time taken by the parachute, and therefore its speed. 3. As the steps are not level, the parachute may not have landed one or two steps lower, making it travel a longer distance, causing a change in the time taken by the parachute, and therefore its speed. 4. If the parachute was folded a little more than another, it would take longer to open up, causing a change in the time taken by the parachute, and therefore its speed.
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### Response to the question
The writer was able to answer the question to a decent standard, but could have potentially gone into more detail. The writer is able to approach each section of their report to a decent standard, but doesn't exact use the ...
### Response to the question
The writer was able to answer the question to a decent standard, but could have potentially gone into more detail. The writer is able to approach each section of their report to a decent standard, but doesn't exact use the correct terminology (for example, when they mentioned "Materials", this should be the "apparatus"). The writer should have explained in the methodology why they decided to use a flight of stairs for their height and why they didn't do it from say the top of a building.
All data was presented well in a table. However, the graph could have been presented better (in the form of 2 line graphs, where one would represent the time and the other would be the velocity). The analysis and conclusions were simple but got to the point straight away. It was good the writer looked at error modification.
### Level of analysis
the language that the writer had used was very basic and could have gone into so much more detail. The writer starts this off with not using the appropriate language for different areas of the experiment ("Materials" instead of "Apparatus"). In addition, the writer should have gone into more analysis in regards to their experiment and why they decided to do particular methods. The graph could have been presented in the form of line graphs. In addition, for the nature of the experiment a preliminary investigation would have been appropriate as it would have given the writer an opportunity to look at the areas which could have been improved for the main investigation.
### Quality of writing
As mentioned before, the writer should have presented the graph better and in addition introduce page numbers so that a reader reading the report would be able to follow it well. In addition, spelling and grammar was quite poor and what the reader should do it read through their report line for line to make sure that this situation doesn't occur.
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# Related GCSE Forces and Motion
1. ## Investigating the factors affecting the speed at which a parachute falls.
To calculate the speed of the parachute we will use the equation: Speed = Distance Time We will make our results more accurate by doing each investigation at least 3 times. We will try to be as accurate as possible at starting and stopping the timer at the correct moment.
2. ## Investigation on how the Surface area of a Canopy Affects the Rate at Which ...
25cm by 25cm 2. 35cm by 35cm 3. 45cm by 45cm These three were going to be the largest of my parachutes (the other 2 were measured as 5cm by 5cm and 15cm by 15cm). By looking at the parachutes perfomance in my preliminary experiment I noticed that parachute 1 was barely creating enough drag for the object to reach its terminal velocity.
1. ## Bouncing A Squash Ball Lab Report - Abhirath Singh
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As soon as the stop watch indicates 2 minutes, use the tongs to remove the ball from the water and immediately place it at the top of the meter rule. 8. Let the squash ball fall from the top, with no force applied by one's hand.
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###### Question:
2 Sketch the solid region E, in the first octant that is bounded by the cylinder y2 + 22 16 and the_plane x + y = 4 Use triple integral in cylindrical coordinates to find SSSE Vy? +22 dV .
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https://www.physicsforums.com/threads/rc-time-constant-experiment.127713/ | 1,544,457,240,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376823348.23/warc/CC-MAIN-20181210144632-20181210170132-00528.warc.gz | 1,008,200,643 | 13,378 | # Homework Help: RC time constant experiment
1. Aug 1, 2006
### Physter
Hi everyone http://img36.imageshack.us/img36/5721/wave7xq.gif [Broken].[/URL] I'm in a little bit of a mess and need some help with this lab write up. There's no way of getting in touch with my TA and my professor didn't prove to be that great of a help when I went to see him yesterday. Anyways, we did an experiment to determine the RC time constant. I guess it'd make sense for me to briefly go over the experiment and then mention the problems I'm having doing the writeup.
For the first part, we noted the times it would take for the current to fall whilst our single capacitor (62 microfarads) was charging. Then a graph of ln(current) as a function of charge time was plotted. For the second part, we did the same thing but only this time the data was for the discharge time of the capacitor. For part three, we did the same thing as part two (the discharge time) but only this time it ws for two capacitors (30 and 69 microfarads respectively) in series configuration . The last part was the same as part 3, only this time it was for the same two capactorss in parallel configuration. Using all this data and the graphs we plotted for each section, we're supposed to find the slope, C(charge), C(discharge), C(parallel), C(series) and of course the RC time constant http://img148.imageshack.us/img148/7246/smartass7jx.gif [Broken].[/URL]
Here's my graph for the charge time of a single capacitor http://img515.imageshack.us/img515/2216/graph1id6.jpg [Broken]. I found the RC time constant by simply taking the value on the resistor and multiplying it by the value of the capactor (1000ohms*62microfarads). Is that right? http://img347.imageshack.us/img347/8900/unsure3ou.gif [Broken] When it comes to finding C(charge) and C(discharge) off their graphs, I don't really know how. For C(parallel) and C(series), I simply used the rules for capacitors in parallel and in series (ie. C(parallel)=C1+C2+C3+...CN and C(series)=[1/C1+1/C2+1/C3+...1/CN]^-1) but again, I don't know how to determine these values off the graph http://img406.imageshack.us/img406/9710/sad0io.gif [Broken].[/URL]
Another thing, for our very first graph (ln(current) as a function of charge time for the single capacitor), we have to find the error on the slope and that's another thing I don't really know how to do. The error on our measurements for current was +/-0.2 microfarads and the error on the time measurements was +/-0.01 s.
Any help would be greatly appreciated http://img263.imageshack.us/img263/1031/sadangel0we.gif [Broken].[/URL]
Last edited by a moderator: May 2, 2017
2. Aug 8, 2006
### ELHEK
Hey there! I've just currently done a electronics lab on testing the time constant(RC) of capacitors in networks. Your lab seems to be quite a bit more advanced compared to mine, but you can calculate the time constant by using method for a voltage vs time graph. the 63%37% method. I have no idea how it works but its worth having a look for on how it works. There is prob a good chance u know this already, anyways good luck.
3. Aug 8, 2006
### SGT
The discharge voltage for a RC ciscuit is:
$$V(t)=V_0\cdot e^{-\frac{t}{T}}$$
Where $$V_0$$ is the initial voltage and T = RC is the time constant.
Knowing the initial voltage and the voltage at any time t, you can use logarithms to find T. | 884 | 3,367 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.15625 | 3 | CC-MAIN-2018-51 | latest | en | 0.934903 |
https://www.convertunits.com/from/gram-force/to/yoctonewton | 1,669,670,321,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710662.60/warc/CC-MAIN-20221128203656-20221128233656-00053.warc.gz | 760,463,515 | 13,001 | ## ››Convert gram-force to yoctonewton
gram-force yoctonewton
## ››More information from the unit converter
How many gram-force in 1 yoctonewton? The answer is 1.0197162129779E-22.
We assume you are converting between gram-force and yoctonewton.
You can view more details on each measurement unit:
gram-force or yoctonewton
The SI derived unit for force is the newton.
1 newton is equal to 101.97162129779 gram-force, or 1.0E+24 yoctonewton.
Note that rounding errors may occur, so always check the results.
Use this page to learn how to convert between grams-force and yoctonewtons.
Type in your own numbers in the form to convert the units!
## ››Quick conversion chart of gram-force to yoctonewton
1 gram-force to yoctonewton = 9.80665E+21 yoctonewton
2 gram-force to yoctonewton = 1.96133E+22 yoctonewton
3 gram-force to yoctonewton = 2.941995E+22 yoctonewton
4 gram-force to yoctonewton = 3.92266E+22 yoctonewton
5 gram-force to yoctonewton = 4.903325E+22 yoctonewton
6 gram-force to yoctonewton = 5.88399E+22 yoctonewton
7 gram-force to yoctonewton = 6.864655E+22 yoctonewton
8 gram-force to yoctonewton = 7.84532E+22 yoctonewton
9 gram-force to yoctonewton = 8.825985E+22 yoctonewton
10 gram-force to yoctonewton = 9.80665E+22 yoctonewton
## ››Want other units?
You can do the reverse unit conversion from yoctonewton to gram-force, or enter any two units below:
## Enter two units to convert
From: To:
## ››Definition: Yoctonewton
The SI prefix "yocto" represents a factor of 10-24, or in exponential notation, 1E-24.
So 1 yoctonewton = 10-24 newtons.
The definition of a newton is as follows:
In physics, the newton (symbol: N) is the SI unit of force, named after Sir Isaac Newton in recognition of his work on classical mechanics. It was first used around 1904, but not until 1948 was it officially adopted by the General Conference on Weights and Measures (CGPM) as the name for the mks unit of force.
## ››Metric conversions and more
ConvertUnits.com provides an online conversion calculator for all types of measurement units. You can find metric conversion tables for SI units, as well as English units, currency, and other data. Type in unit symbols, abbreviations, or full names for units of length, area, mass, pressure, and other types. Examples include mm, inch, 100 kg, US fluid ounce, 6'3", 10 stone 4, cubic cm, metres squared, grams, moles, feet per second, and many more! | 732 | 2,422 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3 | 3 | CC-MAIN-2022-49 | latest | en | 0.802976 |
https://teencodeafrica.com/qa/is-apr-charged-daily.html | 1,603,498,190,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107881551.11/warc/CC-MAIN-20201023234043-20201024024043-00390.warc.gz | 570,452,271 | 9,861 | # Is APR Charged Daily?
## Is 24.99 Apr good?
Yes, I would consider 24.99% a high interest rate.
The average rate is around 19.9% but it is possible to get a lower rate if you have a good credit rating..
## Is APR calculated daily?
To do so, divide your APR by 365, the number of days in a year. At the end of each day, the card issuer will multiply your current balance by the daily rate to come up with the daily interest charge. That charge is then added to your balance the next day, a process called compounding.
## Does APR matter if you pay on time?
If you pay in full every month: APR doesn’t matter When you pay your credit card balance in full and on time in a given month, two things happen that make your interest rate irrelevant: There’s no carried-over balance on which the card issuer can charge interest. You get a grace period on purchases in the next month.
## Is 0 APR really a good deal?
A zero percent deal can save you thousands of dollars in interest payments over the life of your car loan, which lowers the total cost of buying the vehicle. Even if the interest rate on the loan you get is only a few percent, when you finance at zero percent, you’ll save a good deal of money.
## What is a high APR?
But there is a certain limit beyond which credit cards have notably high rates. Currently, average credit card APR is around 16% Reward credit cards tend to have higher APR, averaging above 16.25% If you have bad credit then it means higher APR, too; average APR is currently almost 23.5%
## What is the difference between interest rate and APR?
APR is the annual cost of a loan to a borrower — including fees. Like an interest rate, the APR is expressed as a percentage. Unlike an interest rate, however, it includes other charges or fees such as mortgage insurance, most closing costs, discount points and loan origination fees.
## How do you explain APR?
APR, or annual percentage rate, is the interest rate you pay on a loan—such as a credit card or auto loan—on a yearly basis. In simple terms, it’s the cost of borrowing the money. Your APR is shown as a percentage and includes fees and costs related to the loan.
## Is 14 Apr high for a car loan?
Here are the average interest rates borrowers in each credit category received in the third quarter of 2019 for new and used car loans. For new car purchases, interest rates range from 14% to 4%. For used car purchases, interest rates can be as high as 19.7%, or as low as 4.66%.
## What APR should I expect with a 700 credit score?
A Higher FICO Score Saves You Money760-8502.511 %700-7592.733 %680-6992.91 %660-6793.124 %640-6593.554 %3 more rows
## How is APR calculated monthly?
Divide your card’s annual percentage rate (APR) to get the periodic rate. If your issuer uses a daily balance, divide the APR by 365. If the APR is compounded monthly, divide it by 12. For example, an APR of 14.99% compounded daily would have a periodic rate of (14.99% / 365) = 0.0004 = 0.04%.
## What is a good APR rate?
A good APR for a credit card is one below the current average interest rate, although the lowest interest rates will only be available to applicants with excellent credit. According to the Federal Reserve, the average interest rate for U.S. credit cards has been approximately 14% to 15% APR since early 2018.
## Does 0 Apr mean no interest?
An introductory 0% APR offer means that you won’t have to pay interest on your purchases for a specific time period. Depending on the credit card offer, the introductory 0% APR can last anywhere from six months to over a year.
## Why is 0 Interest bad?
The goal is to spur economic activity by encourage low-cost borrowing and greater access to cheap credit by firms and individuals. Because nominal interest rates are bounded by zero, some economists warn that a ZIRP can have negative consequences such as creating a liquidity trap.
## What is a good APR for a credit card 2020?
Other Average Credit Card Interest RatesQuarterAverage Cash Advance APRAverage Penalty APRQ3 201921.45%26.23%Q4 201921.2%26.11%Q1 202020.87%25.8%Q2 202020.34%25.64%11 more rows•Aug 24, 2020
## What is 24% APR on a credit card?
If you have a credit card with a 24% APR, that’s the rate you’re charged over 12 months, which comes out to 2% per month. Since months vary in length, credit cards break down APR even further into a daily periodic rate (DPR). It’s the APR divided by 365, which would be 0.065% per day for a card with 24% APR.
## What happens if you pay more than the minimum balance on your credit card each month?
But paying more than the minimum on your credit card bills helps you chip away at your overall balance, which improves your credit utilization and raises your score. Also, if you’re still using your cards for new purchases, paying more than the minimum is important because you’re not letting the debt pile up.
## What is APR rate on a car?
The Annual Percentage Rate (APR) is the cost you pay each year to borrow money, including fees, expressed as a percentage. … The higher the APR, the more you’ll pay over the life of the loan. An auto loan’s interest rate and APR are two of the most important measures of the price you pay for borrowing money.
## How do I lower my APR?
How to Get a Lower APR on Your Credit CardOpen a credit card with an introductory 0% deal. One way to bring down the interest rate on your credit balance is to transfer it to a card with an introductory 0% promotion. … Look for a low-interest card. … See what your issuer is willing to offer. … Improve your credit score.
## Is APR charged every month?
Every credit card – save for charge cards – has an annual percentage rate (APR). Technically, a credit card’s APR isn’t the same thing as its interest rate. But the two are closely related. … This will tell you how much interest you’ll be charged every day when you carry a balance from month to month.
## What’s the catch with 0 APR?
The way an automaker can make money with a zero percent deal is simple: It still earns the same amount it would earn on any car deal, but now the money is earned over a longer span. So the money isn’t made on financing but rather the car itself.
## Is 26.99 Apr high for a credit card?
Another general rule of thumb? The lower your credit, the higher your APR. … Capital One® Secured Mastercard®, for example, has a variable APR of 26.99% for purchases and balance transfers, while Indigo® Platinum Mastercard® features a slightly better (but still not great) APR of 24.9% for purchases. | 1,559 | 6,531 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2020-45 | latest | en | 0.965649 |
https://mathsgee.com/14219/explain-to-me-the-term-break-even-point | 1,624,590,379,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488567696.99/warc/CC-MAIN-20210625023840-20210625053840-00623.warc.gz | 350,356,441 | 15,812 | MathsGee is Zero-Rated (You do not need data to access) on: Telkom |Dimension Data | Rain | MWEB
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Explain to me the term ‘break-even point’.
| 43 views
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For a business, the break-even point is when the generated income equals the
total costs for that business for the month (or individual project). At this point, the business is just covering the costs.
At the break-even point: Income = Costs
To make a profit, the business needs to make more than the break-even.
by Diamond (40,216 points)
0 like 0 dislike | 143 | 555 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2021-25 | latest | en | 0.898 |
https://www.mathhomeworkanswers.org/147315/simplify-2-to-the-power-of-3-divided-by-2-to-the-power-of-6 | 1,555,618,934,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578526807.5/warc/CC-MAIN-20190418201429-20190418223429-00167.warc.gz | 763,472,664 | 11,938 | 2^3 / 2^6
2^(3-6)
2^(-3)
1 / 2^3
by Top Rated User (103k points)
2^3 / 2^6=1/2^3=1/8=0.125
by | 61 | 96 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.203125 | 3 | CC-MAIN-2019-18 | longest | en | 0.870532 |
https://cbselibrary.com/tag/speed/ | 1,680,115,589,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296949025.18/warc/CC-MAIN-20230329182643-20230329212643-00543.warc.gz | 195,351,531 | 21,350 | What is Speed
• When we say a body moves fast (or slow) we refer to its speed.
• The speed of an object is defined as the distance travelled by it in unit time.
.The SI unit of speed is metre per second (m/s).
• Therefore, an object that moves faster covers more distance in a second (unit time) as compared to an object that moves slower.
Different Units of Speed
Depending on the need and context, speed is measured in different units. As you already know, the SI unit of speed is metre per second. Another commonly used unit is kilometre per hour (km/h). When we talk about speed of aeroplanes and cars, it would be more appropriate to use km/h than m/s. Let us see how the speed of the school bus (given in Example 1) can be expressed in km/h.
Speed In km/h
Distance travelled by the bus = 7200 m
Distance travelled in kilometres = 7200 ÷ 1000 = 7.2km
Time taken = 1800 s
Time in hours = 1800 ÷ 3600 = O.5h
Therefore, speed of the bus = 7.2 ÷ 0.5 = 14.4 km/h
Speed in m/s can be easily converted to km/h by dividing the answer in m/s by 5/18 or multiplying by 18/5. Do you know how we got this?
1 km = 1000 m
1 h = 3600 s
1 km/h = 1000 m/3600 s
= 5/18 m/s
When a car (or any other vehicle) is moving, it is interesting to find out how fast it is moving. Have you seen a meter fitted inside a vehicle? In a car, the meter is fitted on the dashboard, and in scooters or motorcycles on the top. This is used to display the speed and distance travelled by the vehicle. The instrument/meter measuring the speed of the vehicle is called a speedometer. The distance travelled by the vehicle is given by an instrument called odometer. Both of them are usually fitted together. These instruments will give the reading of speed and the distance travelled at the same time.
Calculation of Speed
Shreya, Ronald, Sabina, and Kirit participated in a race. They took 20s, 22s, 25s, and 28s, respectively, to reach the finishing line. Who do you think ran the fastest and who ran the slowest?
We can calculate the speed of an object if we know the distance it travels in a given amount of time. Let us see how this is done.
In the above example, let us say it was a 100 m race. Shreya ran the race in 20 s. What is Shreya’s speed? As speed is the distance travelled in unit time, Shreya’s speed can be calculated by dividing the distance she ran by the time she took to cover that distance.
Therefore, Shreya’s speed is
$$\frac{\text{Distance travelled}}{\text{Time taken to travel the distance}}=\frac{\text{100 m}}{\text{20 s}}=5~\text{m/s}$$
Similarly, calculate the speed of Ronald, Sabina, and Kirit.
Let us consider one more example.
Example 1: A school bus covers a distance of 7200 m in 1800 s. Calculate its speed.
Solution: We know that speed is given by the distance travelled divided by the time taken.
Given: Distance travelled by the bus = 7200 m
Time taken = 1800 s
$$\text{Speed}=\frac{\text{Distance travelled}}{\text{Time taken }}$$
$$=\frac{\text{7200 m}}{\text{1800 s}}=4~\text{m/s}$$
In practice, very few objects travel at a constant speed for long. Your school bus may speed up and slow down many times on the way to school. To calculate the speed in such cases, we use the concept of average speed. Average speed is defined as the total distance travelled divided by the total time taken to travel that distance.
Difference Between Speed And Velocity
• The ‘distance’ travelled by a body in unit time interval is called its speed. When the position of a body changes in particular direction, then speed is denoted by ‘velocity’. i.e. the rate of change of displacement of a body is called its Velocity.
• Speed is a scalar quantity while velocity is a vector quantity.
• $$\text{Speed}=\frac{\text{distance}}{\text{time}}$$
• $$\text{Velocity}=\frac{\text{displacement}}{\text{time}}$$
• Unit: In M.K.S. system = ms-1
In C.G.S. system = cm/s
• If time distance graph is given then speed can be given by the slope of the line, at given time
$$\text{V}=\frac{\text{ }\!\!\Delta\!\!\text{ s}}{\text{ }\!\!\Delta\!\!\text{ t}}=\text{Slope}$$
• The area of velocity time graph gives displacement travelled.
Types of speed
(a) Average and Instantaneous speed
Average speed: It is obtained by dividing the total distance travelled by the total time interval. i.e.
$$\text{Average speed}=\frac{\text{total}\,\,\text{distance}}{\text{total}\,\,\text{time}}$$
$$\text{Average}\,\text{velocity}=\frac{\text{displacement}}{\text{total}\,\,\text{time}}$$
• Average speed is a scalar, while average velocity is a vector.
• For a moving body average speed can never be –ve or zero (unless t → ∞), while average velocity can be i.e
$${{v}_{av~}}>0\text{ while }\overset{\to }{\mathop{{{v}_{av}}}}\,>=or<\text{ }0$$
• In general average speed is not equal to magnitude of average velocity. However it can be so if the motion is along a straight line without change in direction
• If a particle travels distances L1, L2, L3 at speeds v1, v2, v3 etc respectively, then
$${{v}_{av~}}=\frac{\Delta s}{\Delta t}=\frac{{{L}_{1}}+{{L}_{2}}+…..+{{L}_{n}}}{\frac{{{L}_{1}}}{{{v}_{1}}}+\frac{{{L}_{2}}}{{{v}_{2}}}+….+\frac{{{L}_{n}}}{{{v}_{n}}}}=\frac{\sum{Li}}{\sum{\frac{{{L}_{i}}}{{{v}_{i}}}}}$$
• If a particle travels at speeds v1, v2 etc for intervals t1, t2 etc respectively, then
$${{v}_{av~}}=\frac{{{v}_{1}}{{t}_{1}}+{{v}_{2}}{{t}_{2}}+….}{{{t}_{1}}+{{t}_{2}}+….}=\frac{\sum{{{v}_{1}}{{t}_{1}}}}{\sum{{{t}_{1}}}}$$
Instantaneous speed: The speed of a body at a particular instant of time is called its instantaneous speed.
$$=\underset{\Delta t\to 0}{\mathop{\lim }}\,\,\frac{\Delta s}{\Delta t}=\frac{ds}{dt}$$
(b) Uniform and Non uniform speed
Uniform speed: If an object covers equal distance in equal interval of time, then time speed graph of an object is a straight line parallel to time axis then body is moving with a uniform speed.
Non-uniform speed: If the speed of a body is changing with respect to time it is moving with a non-uniform speed.
Speed And Velocity Example Problems With Solutions
Example 1. The distance between two points A and B is 100 m. A person moves from A to B with a speed of 20 m/s and from B to A with a speed of 25 m/s. Calculate average speed and average velocity.
Solution: (i) Distance from A to B = 100 m
Distance from B to A = 100 m
Thus, total distance = 200 m
Time taken to move from A to B, is given by
$${{t}_{1}}=\frac{\text{distance}}{\text{velocity}}=\frac{100}{20}=5\text{ seconds}$$
Time taken from B to A, is given by
$${{t}_{2}}=\frac{\text{distance}}{\text{velocity}}=\frac{100}{25}=4\text{ seconds}$$
Total time taken = t1 + t2 = 5 + 4 = 9 sec.
∴ Average speed of the person
$$=\frac{\text{Total}\,\text{dis}\,\text{tan}\,\text{cecovered}}{\text{Total}\,\text{time}\,\text{taken}}=\frac{200}{9}=22.2\text{ m/s}$$
(ii) Since person comes back to initial position A, displacement will be zero, resulting zero average velocity.
Example 2. A car moves with a speed of 40 km/hr for first hour, then with a speed of 60 km/hr for next $$1\frac{1}{2}$$ half hour and finally with a speed of 30 km/hr for next hours. Calculate the average speed of the car.
Solution: Distance travelled in first hour, is given by
s1 = speed × time = 40 km/hr × 1 hr = 40 km
Distance travelled in next half an hour, is given by
s2 = speed × time = 60 km/hr × $$\frac { 1 }{ 2 }$$ hr = 30 km
Distance travelled in last $$1\frac{1}{2}$$ hours, is given by
s3 = speed × time = 30 km/hr × $$\frac { 3 }{ 2 }$$ hr = 45 km
Thus, total distance travelled = s1 + s2 + s3
= 40 + 30 + 45 = 115 km
Total time taken = 1 + $$\frac { 1 }{ 2 }$$ + $$1\frac{1}{2}$$ = 3 hours
Average speed = $$\frac { Total distance covered }{ Total time taken }$$ = $$\frac { 115km }{ 3hrs }$$
= 38.33 km/hr
Example 3. Figure shows time distance graph of an object. Calculate the following :
(i) Which part of the graph shows that the body is at rest ?
(ii) Average speed in first 10 s.
(iii) Speeds in different parts of motion.
Solution: (i) The part BC shows that the body is at rest.
(ii) In first 10 seconds, distance travelled = 100m
$$\text{Average speed}=\frac{\text{total}\,\,\text{distance}}{\text{total}\,\,\text{time}}$$
$$=\frac{100}{10}=10\text{ m/s}$$
(iii) Speed of the object in part AB is given by slope = 100/6 = $$\frac { 50 }{ 3 }$$ m/s
Speed of object in part BC = 0 m/s
Speed of the object in part CD
$$=\frac{100-40}{12-10}=\frac{60}{2}=30~\text{m/s}$$
Speed of object in part DE
$$=\frac{40-0}{14-12}=\frac{40}{2}=30~\text{m/s}$$
Example 4. Time-velocity graph of a particle is shown in Figure. Calculate the distance travelled in first seconds.
Solution: Distance travelled in first 8s is given by area OABCG
= area of rectangle OAMG + area of triangle BMC
= 8 × 60 + $$\frac { 1 }{ 2 }$$ × 4 × 40
= 480 + 80 = 560 m.
Example 5. A cow walked along a curved path from P to Q, which is 70 m away from P. Q lies to the south-west of P. The distance travelled by the cow is 240 m and the time taken is 160 s.
Calculate the
(a) average speed,
(b) average velocity,
of the cow moving from P to Q.
Solution:
Total distance travelled = 240 m
Displacement = 70 m
Time taken = 160 s
What is Motion
When a body does not change its position with time, we can say that the body is at rest, while if a body changes its position with time, it is said to be in motion.
Analysing Linear Motion
• Linear motion is motion in a straight line.
• Non-linear motion is motion that is not in a straight line.
• When analysing linear and non-linear motion, distance, displacement, speed, velocity, acceleration and deceleration are some commonly encountered physical quantities.
Terms Used To Define Motion
An object is said to be a point object if it changes its position by distances which are much greater than its size. A point or some stationary object with respect to which a body continuously changes its position in the state of motion is known as origin or reference point.
When we say an object is moving, it is always with respect to another object. For example, when we say a vehicle is moving on a road, it is moving with respect to the trees and poles on the road, which are ‘not moving’. When you say you are at rest or not moving while reading a book, it is with respect to your chair or your desk. When an object moves, its position (with respect to another object) changes with time. Let us take the example of a car moving away from a building.
When the car is at position A, the distance between the car and the building is very small. As the car moves away from the building (Position B), its distance from the building increases. Another way of saying this is that when the car moves, its position with respect to the building changes with time. An object is said to be in motion if its position (with respect to another object) changes with time.
Types Of Motion
There are different types of motion: translational, rotational, periodic, and non periodic motion.
Translational Motion
A type of motion in which all parts of an object move the same distance in a given time is called translational motion. Examples are vehicles moving on a road, a child going down a bird flying in the sky. Translational motion can be of two types, rectilinear and curvilinear. Table shows the differences between rectilinear and curvilinear motions.
Rectilinear motion Curvilinear motion 1. When an object in translational motion moves in a straight line, it is said to be in rectilinear motion. 1. When an object in translational motion moves along a curved path, it is said to be in curvilinear motion. 2. Examples are a car moving on a straight road and a train moving on a straight track. 2. Examples are a stone thrown up in the air at an angle and a car taking a turn.
Examples of translational motion: a child going down a slide.
Rotational Motion
When an object moves about an axis and different parts of it move by different distances in a given interval of time, it is said to be in rotational motion. Examples of objects undergoing rotational motion are blades of a rotating fan, merry-go-round, blades of a windmill. When an object undergoes rotational motion, all its parts do not move the same distance in a given interval of time. For example, the outer portion of the blades of a windmill moves much more than the portion closer to the centre.
A merry-go-around shows rotational motion:
Periodic Motion
A type of motion that repeats itself after equal intervals of time is called periodic motion. Examples of objects undergoing periodic motion are the to and fro motion of a pendulum, the Earth (rotating on its axis), the hands of a clock, the blades of a rotating electric fan, and the plucked string of a guitar.
Non-periodic Motion
A motion that does not repeat itself at regular intervals or a motion that does not repeat itself at all is called non-periodic motion. Examples of non-periodic motion are a car moving on a road, a bird gliding across the sky, and children playing in a park. In everyday life, we observe more than one type of motion, like
• Birds gliding across the sky (translational and non periodic).
• Rotation of the Earth on its axis (rotational and periodic).
According to Directions
1. One dimensional motion is the motion of a particle moving along a straight line.
2. Two dimensional motion A particle moving along a curved path in a plane has
2-dimensional motion.
3. Three dimensional motion Particle moving randomly in space has 3-dimensional motion.
According to State of Motion
1. Uniform Motion: A body is said to be in a state of uniform motion if it travels equal distances in equal intervals of time. If the time distance graph is a straight line the motion is said to be uniform motion.
2. Non-uniform motion: A body has a non-uniform motion if it travels unequal distances in equal intervals of time. Ex. a freely falling body.
Time – distance graph for a body with non-uniform motion is a curved line.
Analysing Motion Graphs
Displacement- Time graphs:
1. Figure shows a tortoise moving at a slow and steady speed while a hare was sleeping soundly from the time t = 0 to 8 s.
2. We can represent the situation using displacement-time graphs.
(a) The graph in Figure (a) shows the displacement of the tortoise from the starting line from time t = 0 to 8 s.
(b) The graph in Figure (b) shows that throughout the time from t = 0 to 8 s, the hare had a displacement of 0.5 m from the starting line. Throughout the 8 seconds, it did not move at all as it was sleeping.
3. The gradient of the s-t graph of an object gives the rate of change of displacement, which is the velocity of the object.
4. Table illustrates some of the displacement-time graphs.
The straight line inclined to time axis in s-t graph represents constant velocity.
In s-t graph the straight line inclined to time axis at angle greater than 90º shows negative velocity
Body with accelerated motion
Body with decelerated motion
Velocity -Time graphs:
1. The gradients of the s-t graphs for the tortoise and hare are 0.25 m s-1 and 0 m s-1 respectively.
2. The v-t graphs in Figure represent the situation.
(a) The gradient of the v-t graph is the rate of change of velocity which is the acceleration of the object.
(b) The area under the graph gives the displacement of the object.
3. Table illustrates some of the velocity-time graphs.
For the body having constant velocity or zero acceleration.
The body is moving with constant retardation and its initial velocity is not zero.
The body is accelerated and the initial velocity is zero.
The body is decelerated
Acceleration-Time graph:
Acceleration is constant
Acceleration is increasing and is +ve
Acceleration is decreasing and is –ve
Example 1. A boy skated along a straight line passing by two points, P and Q. His time, t and displacement, s from point P is shown in Figure.
From the information given, draw the
(a) s-t graph
(b) v-t graph
Solution:
Example 2. Azlan cycled along a straight road. The graph in Figure (b) illustrates his motion.
(a) Calculate the velocity of Azlan from t = 0 to 10 s.
(b) Describe what happened to Azlan from t = 10 to 20 s.
(c) Calculate the displacement, s of Azlan when t = 25 s.
(d) Where was Azlan when t = 35 s?
Solution:
(a) Refer to part AB of the graph.
Velocity = Gradient of the graph
= 50/10 = 5 m s-1
(b) Refer to part BC of the graph. The gradient of the graph is 0. This means that Azlan was at rest from t = 10 to 20 s.
(c) Refer to point D of the graph. When
t = 25 s, displacement of Azlan, s = 14 m.
(d) Refer to point E of the graph. When
t = 35 s, displacement of Azlan, s = 0 m.
This means that Azlan was back at the starting position.
Example 3. Figure shows a huge crane hoisting a steel beam from the ground. The v-t graph shows the motion of the beam in the first 9 s.
(a) Briefly describe the motion of the beam represented by AB, BC, CD and DE.
(b) Calculate the initial and final acceleration of the beam.
(c) Calculate the height of the beam from the ground after 9 seconds.
Solution:
Example 4. The v-t graph in Figure shows the motion of a mine cart on a straight railway.
(a) What was the total distance travelled by the mine cart?
(b) (i) Where was the mine cart when t = 10 s? | 4,583 | 17,212 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.46875 | 4 | CC-MAIN-2023-14 | longest | en | 0.946345 |
http://illuminations.nctm.org/Activity.aspx?id=3534 | 1,490,913,632,000,000,000 | text/html | crawl-data/CC-MAIN-2017-13/segments/1490218203536.73/warc/CC-MAIN-20170322213003-00252-ip-10-233-31-227.ec2.internal.warc.gz | 165,110,261 | 11,496 | ## Turtle Pond
Pre-K-2, 3-5, 6-8
Standards:
Math Content:
Geometry, Measurement
Guide a turtle to a pond using computer commands.
### Controls
The objective of Turtle Pond is to get the turtle to the Pond. There are four moves:
1. Forward
2. Backward
3. Left Rotation
4. Right Rotation
Create a sequence of moves by using the four action buttons. Once a movement is selected, you will be prompted to enter how many units to move, or how many degrees of rotation to turn.
### Toolbar
There are six toolbar features (left to right, up to down):
1. Erase previous recorded move, or a highlighted move.
2. Erase the entire table.
3. Create a new maze.
4. Turning at right angles vs. ability to turn: 15, 30, 45, 60, 75, or 90 degrees.
5. Create obstacles.
6. Show a grid to help count the units.
### Play Bar
• There is also a play bar that will help play the entire sequence of moves (use the slider to adjust the speed, and stop or pause to halt the play).
• You can also use the fast-forward and rewind button to play the moves one by one.
Enter a sequence of commands to help the turtle get to the pond. The turtle will then move along a path according to your instructions.
• How far does your turtle travel to get to the pond?
• Can you find a shorter path to the pond?
• How long is the shortest path to the pond?
Set forward = 5, back = 7, right turn = 30, and left turn = 75. Using only these possible moves, guide the turtle to the pond. Try the same activity using different values for the four moves. | 386 | 1,522 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.09375 | 3 | CC-MAIN-2017-13 | longest | en | 0.866554 |
http://forums.wolfram.com/mathgroup/archive/2007/Dec/msg00606.html | 1,601,087,298,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400232211.54/warc/CC-MAIN-20200926004805-20200926034805-00487.warc.gz | 46,590,258 | 8,338 | Re: ClearAll[f]; f[x_] := x^2; f[y_] :=y^4; (*What is:*) f[2]
• To: mathgroup at smc.vnet.net
• Subject: [mg84397] Re: ClearAll[f]; f[x_] := x^2; f[y_] :=y^4; (*What is:*) f[2]
• From: Albert Retey <awnl at arcor.net>
• Date: Fri, 21 Dec 2007 03:22:25 -0500 (EST)
• References: <fkcueh\$5d9\$1@smc.vnet.net>
```Hi,
> ClearAll[f]; f[x_] := x^2; f[y_] :=y^4; (*What is:*) f[2]
>
> Evaluating this line in Mathematica 5.2 or Mathematica 6 returns 16. This makes sense, because the second definition replaces the first, as we can see when ?f returns:
> Global`f
> f[y_]:=y^4
>
> But in _A_Physicist's_Guide_to_Mathematica_ on p.314, Patrick Tam shows an example like this returning the other answer, 4, defined in the first definition. He then demonstrates that ?f returns:
> Global`f
> f[x_] := x^2
> f[y_]:= y^4
> He says his book was developed with Mathematica 2.2 and a prerelease of Mathematica 3 and is compatible with both.
>
> He goes on to explain:
> "Contrary to expectation, Mathematica used the first definition. The ? operator reveals that Mathematica stores both definitions in the global rule base, giving higher priority to the first definition. (This problem cannot, perhaps, be called a bug because developers of Mathematica are well aware of this design flaw, which is quite difficult to mend....)"
>
> What is he talking about? Did Mathematica 2.2 and 3 treat this differently? If earlier versions worked in this surprising way, there must have been a reason - what was it? Was it changed to prevent surprises like this example? Did changing it create other unfortunate consequences? Was Tam just wrong? Or do I misunderstand?
I think the statement is still true. Usually mathematica orders the
definitions so that more specific definitions are tested before more
general ones. When there is a real ambiguity concerning which pattern is
more specific the definitions are tested in the order they were entered.
For this very simple case (where just the name of the pattern is
different) it is not really an ambiguity and thus obviously can and has
been overcome in newer versions. Look at the following for an example
which shows that the behavior still exists for ambiguities which can not
be resolved as easy as the above:
ClearAll[f]
f[y_?NumericQ]:=y^4
f[x_?IntegerQ]:=x^2
??f
f[2.]
f[2]
Note that for an integer both definitions match and the one which is
entered first will win which you can check by changing the order of the
two definitions. While in this case in principle it could be argued that
the IntegerQ test is more specific than the NumericQ test, this would be
much harder to detect and there is no way for mathematica to decide
which of two such definitions is more specific if you would replace
IntegerQ and NumericQ with two user defined functions.
hth,
albert
```
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• Next by thread: checking, if a file exists | 823 | 3,027 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2020-40 | latest | en | 0.910397 |
https://es.coursera.org/learn/approximation-algorithms/reviews?authMode=signup | 1,660,920,433,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882573699.52/warc/CC-MAIN-20220819131019-20220819161019-00507.warc.gz | 252,134,895 | 86,725 | Volver a Approximation Algorithms
## Opiniones y comentarios de aprendices correspondientes a Approximation Algorithms por parte de EIT Digital
4.7
estrellas
29 calificaciones
## Acerca del Curso
Many real-world algorithmic problems cannot be solved efficiently using traditional algorithmic tools, for example because the problems are NP-hard. The goal of this course is to become familiar with important algorithmic concepts and techniques needed to effectively deal with such problems. These techniques apply when we don't require the optimal solution to certain problems, but an approximation that is close to the optimal solution. We will see how to efficiently find such approximations. Prerequisites: In order to successfully take this course, you should already have a basic knowledge of algorithms and mathematics. Here's a short list of what you are supposed to know: - O-notation, Ω-notation, Θ-notation; how to analyze algorithms - Basic calculus: manipulating summations, solving recurrences, working with logarithms, etc. - Basic probability theory: events, probability distributions, random variables, expected values etc. - Basic data structures: linked lists, stacks, queues, heaps - (Balanced) binary search trees - Basic sorting algorithms, for example MergeSort, InsertionSort, QuickSort - Graph terminology, representations of graphs (adjacency lists and adjacency matrix), basic graph algorithms (BFS, DFS, topological sort, shortest paths) The material for this course is based on the course notes that can be found under the resources tab. We will not cover everything from the course notes. The course notes are there both for students who did not fully understand the lectures as well as for students who would like to dive deeper into the topics. The video lectures contain a few very minor mistakes. A list of these mistakes can be found under resources (in the document called "Errata"). If you think you found an error, report a problem by clicking the square flag at the bottom of the lecture or quiz where you found the error....
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## 1 - 8 de 8 revisiones para Approximation Algorithms
por Suryendu D
18 de jul. de 2020
The course was no doubt excellent. At the end of the day you are going to earn a mouth watering certificate signed by one of the best computer scientists in the world. Prof. Mark de Berg. Professor speaks english very well and hence no one will face any problem related to language. Also professor taught the course extremely well. But unfortunately this course is completely inactive. All the questions in discussion forums remains unanswered. There was a problem is Week 2 Assignment 'PTAS for Load Balancing', where your correct answer will be considered wrong. Mentors of this course are sitting idle. They do not provide any assistance to the students. This course really needs a mentor who is active.
por 김동윤
4 de may. de 2021
Short but compact course that discusses important topics. The quizes and programming homeworks are challenging enough to help to check your studying procedure. Prof. Mark de Berg is an amazing instructor and gives clear lecture videos. One small tip will be to check the Errata sheet before studying. Overall a compact and helpful course.
por ChocolateCharlie
23 de nov. de 2020
Nice introductory course which combines both theory and practice. Though these algorithms are covered in the course, a previous experience with greedy algorithms and dynamic programming might be helpful.
por Jakob B
27 de ene. de 2021
Excellent short course on approximation algorithms. Good course material, presentations and exercises.
por 周柏宇
13 de ago. de 2020
A great introductory course to the approximation algorithms.
por Chee H C
11 de sep. de 2020
Great course.
por Shailesh M
11 de oct. de 2020
Please try to include some more numeric example like load balancing problem in the vertex cover and rest topics
por Lorenzo P
25 de feb. de 2021
Very good course! A nice introduction to approximation algorithms. | 836 | 4,022 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.65625 | 3 | CC-MAIN-2022-33 | latest | en | 0.896816 |
https://teachers.net/lessons/posts/3636.html | 1,540,219,878,000,000,000 | text/html | crawl-data/CC-MAIN-2018-43/segments/1539583515088.88/warc/CC-MAIN-20181022134402-20181022155902-00436.warc.gz | 818,678,886 | 11,049 | Subject Area Lessons
More Lessons Like This...
Grade: Elementary Subject: Mathematics
## #3636. Investigating Volume
Mathematics, level: Elementary
Posted Tue Jan 31 18:36:28 PST 2006 by Erin Coy (erincoy@msn.com).
Dacusville Elementary School, Easley, South Carolina USA
Activity Time: 45 minutes
Concepts Taught: Measurement/Spacial/Geometry
Objectives:
•The students will be able to record and measure volume.
•The students will be able to use appropriate units and procedures to calculate volume.
•The students will use one-inch cubes to calculate volume.
Aligned with South Carolina Mathematics Standards: Grade 5
Measurement Strand
•II.E.1
•II.B.1
•I.D.1
Materials:
•One-inch cubes
•Several different size household boxes (rectangular). (examples: cereal boxes, tea bag boxes, saltine cracker boxes)
•Pencil
•Paper
•Worksheet (Questions for students to follow) - See Questions Below.
Before the Lesson:
•Review Vocabulary
oVolume
oCubic Inch
Procedure:
•Pair students up or have them work individually.
•Distribute each pair or individual two different size boxes.
•Have the students use the one-inch cubes to measure volume.
•Students will work through the questions on the worksheet provided.
Extension:
•Have much bigger boxes for students to use to calculate the volume. (Students should understand that in order to calculate volume of a rectangle can be figured by multiplying base x height.
Worksheet: Investigating Volume
1)Fill up one box with the wooden, one-inch cubes.
2)How many one-inch cubes make up the length?
3)How many one-inch cubes make up the width?
4)How many one-inch cubes make up the height?
5)Count the number of cubes it takes to fill the box.
Write down the total amount of cubes.
6)Write the formula for finding volume.
V = L x W x H (Volume = Length x Width x Height)
7)Measure (in inches) the length, width, and height of the box.
8)Multiply the length by the width by the height.
9)What is your answer for the volume of the box? | 470 | 1,986 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.5 | 4 | CC-MAIN-2018-43 | longest | en | 0.83934 |
https://codereview.stackexchange.com/questions/188234/palindrome-algorithm/188236 | 1,719,252,112,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198865401.1/warc/CC-MAIN-20240624151022-20240624181022-00711.warc.gz | 153,012,857 | 41,322 | # Palindrome algorithm
This code could be better?
This is the algorithm:
1. Compare the 1st character to the last character
2. Compare the 2nd character to the second last character and so on
3. Stop when the middle of the string is reached
4. Just words
namespace Palindrome
{
class Class1
{
static void Main(string[] args)
{
while (true)
{
Console.WriteLine("Digit a word:");
if (word == "exit")
break;
VerifyPalindrome(word);
}
}
private static void VerifyPalindrome(string word)
{
bool compare = true;
int i = 0;
while (i < word.Length- 1)
{
if (compare)
{
for (int j = word.Length - 1; j >= 0; j--)
{
if (word[i] == word[j])
compare = true;
else
{
compare = false;
break;
}
i++;
}
}
else
break;
}
if (compare)
Console.WriteLine("This is a Palindrome word");
else
Console.WriteLine("This is NOT a Palindrome word");
}
}
}
• Your code claims that foo and ba are palindromes. Commented Feb 24, 2018 at 10:41
• The problem is on while clausule: while (i < (word.Length / 2) - 1) Thanks Commented Feb 24, 2018 at 16:10
• I've fixed the code. Commented Mar 1, 2018 at 1:25
As already stated you don't need to set it to true multiple times.
There is cleaner syntax for this.
static bool IsPalidrone(string word)
{
for (int i = 0, j = word.Length - 1; i < j; i++, j--)
{
if (word[i] != word[j])
{
return false;
}
}
return true;
}
• @DaniloDebiaziVicente You could give it the check if it is the answer. Commented Feb 24, 2018 at 18:31
• I have less than 15 reputation points here. Unfortunately, the Stack Exchange doesn't allow me to check your answer. I'll do that when I got my 15 points. Commented Feb 26, 2018 at 1:04
• @DaniloDebiaziVicente Up vote and check are not the same. But no problem. Commented Feb 26, 2018 at 6:33
• @Pararazzi I got it! Commented Feb 27, 2018 at 22:48
• This answer doesn't account for empty strings, where it will throw trying to access word[-1]. It will also fail on null strings. Whether an empty string is considered a palindrome is debatable. Commented Sep 3, 2018 at 8:03
One thing I would like to change is the responsibilities of VerifyPalindrome(string word). Remember, your function should only check whether word is a palindrome, nothing else. It shouldn't print out a value, but instead return a boolean that verifies wheter the word is a palindrome or not. Change the function to:
private static bool VerifyPalindrome(string word)
{
bool compare = true;
// ... computing code
return compare;
}
And in Main:
if(VerifyPalindrome(word))
{
Console.WriteLine("This is a Palindrome word");
}
else
{
Console.WriteLine("This is NOT a Palindrome word");
}
The other thing I would change is your palindrome logic. Instead of keeping track of a variable compare for whether a string is a palindrome or not and using breaks, which increases the complexity of your code, you can reduce the function to the following, with multiple returns:
private static bool VerifyPalindrome(string word)
{
int i = 0;
while (i < (word.Length / 2) - 1)
{
for (int j = word.Length - 1; j >= 0; j--)
{
if (word[i] != word[j])
return false;
i++;
}
}
return true;
}
No you could further shorten this by combining the two loops into one, but I'll leave that as an exercise to you. | 871 | 3,212 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2024-26 | latest | en | 0.808164 |
https://hazarsiiraksamlari.org/and-pdf/1087-what-is-network-topologies-and-its-types-pdf-771-589.php | 1,642,664,597,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320301730.31/warc/CC-MAIN-20220120065949-20220120095949-00470.warc.gz | 351,201,131 | 7,455 | Tuesday, May 4, 2021 11:36:26 PM
# What Is Network Topologies And Its Types Pdf
File Name: what is network topologies and its types .zip
Size: 25512Kb
Published: 05.05.2021
Network topologies describe the methods in which all the elements of a network are mapped.
A network topology refers to the way in which nodes in a network are connected to one another. The network structure defines how they communicate. Each kind of arrangement of the network nodes has its own advantages and disadvantages.
Network Topology is the schematic description of a network arrangement, connecting various nodes sender and receiver through lines of connection. Bus topology is a network type in which every computer and network device is connected to single cable. When it has exactly two endpoints, then it is called Linear Bus topology. It is called ring topology because it forms a ring as each computer is connected to another computer, with the last one connected to the first.
## What Is Network Topology And Types Of Topology Pdf
Network topology is the layout of the connections links , nodes , etc. The names used - such as ring or star - are only rough descriptions. The computers on a home network can be arranged in a circle but it does not necessarily mean that it represents a ring network. There are seven basic topologies: [3]. Which of these is chosen depends on what devices need to be connected, how reliable it has to be, and the cost associated with cabling. The shape of the cabling layout used to link devices is called the physical topology of the network. This refers to how the cables are laid out to connect many computers to one network.
## Network Topologies (Its types, Advantages and Disadvantages)
Network topology is the arrangement of the elements links , nodes , etc. Network topology is the topological [4] structure of a network and may be depicted physically or logically. It is an application of graph theory [3] wherein communicating devices are modeled as nodes and the connections between the devices are modeled as links or lines between the nodes. Physical topology is the placement of the various components of a network e. Distances between nodes, physical interconnections, transmission rates , or signal types may differ between two different networks, yet their logical topologies may be identical. Examples of network topologies are found in local area networks LAN , a common computer network installation. Any given node in the LAN has one or more physical links to other devices in the network; graphically mapping these links results in a geometric shape that can be used to describe the physical topology of the network.
## Network topologies
The configuration, or topology, of a network is key to determining its performance. Network topology is the way a network is arranged, including the physical or logical description of how links and nodes are set up to relate to each other. There are numerous ways a network can be arranged, all with different pros and cons, and some are more useful in certain circumstances than others. Admins have a range of options when it comes to choosing a network topology, and this decision must account for the size and scale of their business, its goals, and budget.
### Advantages and Disadvantages of Network Topologies
Ask a Question. Learn: What are Network topologies? In this article we will see the various types of Network topologies with their advantages and disadvantages. Submitted by Abhishek Jain , on August 11, Network topology refers to the arrangement of computers connected in a network through some physical medium such as cable, optical fiber etc.
Network topology is the schematic description of the arrangement of the physical and logical elements of a communication network. Network topology refers to the manner in which the links and nodes of a network are arranged to relate to each other. Topologies are categorized as either physical network topology, which is the physical signal transmission medium, or logical network topology, which refers to the manner in which data travels through the network between devices, independent of physical connection of the devices.
The way in which devices are interconnected to form a network is called network topology. So cable lengths, distance between nodes, location of servers, etc. Failure of one node or a segment of cabling should not render the whole network useless. Data network with bus topology has a linear transmission cable , usually coaxial , to which many network devices and workstations are attached along the length. Server is at one end of the bus.
#### What is network topology and types of network topology?
Topology is derived from two Greek words topo and logy, where topo means 'place' and logy means 'study'. In computer networks, a topology is used to explain how a network is physically connected and the logical flow of information in the network. A topology mainly describes how devices are connected and interact with each other using communication links. Network topology defines the layout, virtual shape, or structure of the network, not only physically but also logically. A network can have one physical topology and multiple logical topologies at the same time.
- Я просто… - Сьюзан Флетчер. - Женщина улыбнулась и протянула ему тонкую изящную руку. - Дэвид Беккер.
Слушаю, сэр.
Он, конечно, видел старинную мавританскую башню, но взбираться на нее не. - Алькасар. Беккер снова кивнул, вспомнив ночь, когда слушал гитару Пако де Лючии - фламенко под звездами в крепости XV века.
Он очень надеялся, что ничего не сорвалось. Если ключ так хорош, как о нем говорят, он взломает самый совершенный продукт компьютерной эры - абсолютно стойкий алгоритм цифрового кодирования. Нуматака введет этот алгоритм в чипы VSLI со специальным покрытием и выбросит их на массовый рынок, где их будут покупать производители компьютеров, правительства, промышленные компания.
- У него был врожденный порок сердца. - Никогда об этом не слышала. - Так записано в его медицинской карточке.
В дверях появилась телефонистка и поклонилась: - Почтенный господин. - Слушаю. Телефонистка отвесила еще один поклон: - Я говорила с телефонной компанией. | 1,354 | 6,227 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.34375 | 3 | CC-MAIN-2022-05 | latest | en | 0.948665 |
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# Vision Raycasting
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I'm currently developing vision raycasting for FPS game, I have few questions:
1. How many ray is accurate to detect vision from a tank?
2. How many ray for each character?
3. Should I calculate the distance against EVERY model and create rays at each model if it's close enough?
4. If the model is a character the ray will start from his eyes, however, if it's a tank, from where the ray should start?
5. How do I determine the exact ray target? (rayTo = target.position) --> I don't think this is good enough
I want to create something efficient and at the same time with high performance.
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Any advise? :)
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1. How many ray is accurate to detect vision from a tank?
one from each station with an exterior view to each target in the station's arc of sight/fire within visible range. the type of tank will make a big difference. in a large WW1 tank, you might have 6 stations with exterior views, and FOVs of 30-45 degrees. in a newer tank, you might have something like a 90 degree FOV for the driver, a 30 degree FOV for the gunner, and a 360 degree FOV for the commander/spotter.
2. How many ray for each character?
one to each target in visual range. infantry has a 360 FOV.
3. Should I calculate the distance against EVERY model and create rays at each model if it's close enough?
that's what i do (sneak/stealth mode, fps/rpg game). but i only do the ray casting LOS/LOF (line of sight / line of fire) calculations if the player is in sneak mode (and undetected by hostiles).
4. If the model is a character the ray will start from his eyes, however, if it's a tank, from where the ray should start?
the visual orifice of the station. IE the driver's view slot in a WW2 tank, the persicope on top of the turret of a modern tank, the MG station's viewport on the side of a WW1 tank, etc.
5. How do I determine the exact ray target? (rayTo = target.position) --> I don't think this is good enough
for infantry, center to center may be good enough. to increase accuracy, you'd step up to something like checking 4 corners of a bounding box, or perhaps some type of bounding sphere type test. for tanks, if center to center isn't good enough (probably won't be), again you'd go BBox corners, etc. for a tank, bbox corners would be more accurate than bounding sphere.
with center to center vs bbox, almost half a target would be visible before the LOS/LOF test indicated so.
I want to create something efficient and at the same time with high performance.
by that i assume you mean accurate (hi performance) and fast (efficient).
accurate means bbox or the like. fast means... well. write the code. if its not fast enough, then you optimize. of course, no harm with writing it with speed in mind from the get go... i think i just did a bressingham's kinda thing (step moving along a direction vector, checking for collisions with occluding objects/terrain). speed was a concern, but i got it working ok. can't recall if i had to optimize. if so, must not have been much.
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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
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A Lunar Example: Sun and Moon vertically aligned
From: Frank Reed
Date: 2017 Dec 18, 15:53 -0800
A few days ago, I suggested in a post that you can learn a lot about lunars by considering a case where the Sun and Moon are vertically aligned. I'm going to modify the details just slightly, as marked in square brackets [ ] in the quoted section here. I wrote:
To puzzle this out for yourself, you'll learn an enormous amount by considering a case where the Moon and Sun are aligned on the same azimuth --one right above the other. Suppose, for example, I am in the tropics and I look in the [western] sky in the [afternoon] and see the moon low above the horizon and the Sun high up, right on the same azimuth. I have an assistant with a cheap plastic sextant who will shoot the altitudes of the two bodies, and I myself will measure the angle between the Sun and Moon with a fine, properly-adjusted Plath sextant. We approximately measure the altitude of the Moon (Upper Limb) as 20° 10' and the approximate altitude of the Sun (LL) as 75° 30'. In addition, I have with exceeding care and with the best accuracy I can manage measured the limb-to-limb distance between the Sun and Moon as 55° 17.3'. Also, assume 4' dip [17 feet height of eye] and zero index correction on both instruments. What, given these observations, would be the corrected lunar distance angle? You'll need one bit of almanac data to do the work, namely the Moon's HP. Let's suppose that's [54.5']. [Also suppose it's early January so you can look up the Sun's SD]. See if you can work it out.
Did any of you try the original version? With some slight modifications (primarily the given HP value), you should be able to work out this case. And remember, you don't need any complicated tables or tools to do this. I'll lay out the steps in outline:
• Pre-clear: for this you need the SD of the Sun and Moon. For the Moon, the SD is always 0.2724·HP so in this case that's 14.8'. For the altitudes you need to subtract 4' of dip from both and subtract the Moon's SD from its altitude and add the Sun's SD to its altitude. Next we add both SD's to the lunar distance, and in this case working carefully to get every tenth of a minute.
• Now look up the altitude correction for the Moon's center (if you're using the N.A. tables, you follow the rules for a bubble sextant altitude correction) and the altitude correction for the Sun's center (you can just use the standard refraction for stars here).
• The Moon is lifted by the clearing proces, while the Sun is lowered. And they're aligned vertically so the corrections just add/subtract directly from the pre-cleared distance to give you the cleared lunar distance.
• When you're done, your cleared distance should be nearly 54°59.7', plus or minus a tenth or two.
That's the setup to get started understanding this concept of "clearing lunars". If the math of lunars is new to you, you may want to stop here.
For folks with a little more experience messing around with lunars, this case presents an interesting mathematical issue. While it's a perfectly valid example which would produce an excellent value for GMT --dead-on really, it may break certain methodologies that head down the wrong road. In particular, the standard "direct triangle" solutions (however implemented) depend on the constancy of the difference in azimuth between the two bodies, called ΔZ or dZ (sometimes called, idiosyncratically, RBA). But mathematically we only need cos(dZ). If your method goes beyond this necessity and computes dZ itself, you'll be in trouble sometimes. The math is robust and can handle some degree of approximation in the altitudes so long as you calculate cos(dZ) and stop, but it become less robust, and in fact may give a hard, fatal error, if you calculate dZ as an angle. And if you get a fatal error, you'll be thrown back on your dead reckoning... which would be a shame because it's not a real problem with the math of lunars --it's a mistake that results from being too literal-minded about the math.
Finally, if you want to try this out from a "real world" context, visit the middle of the Pacific at 20°00' S, 176°30' W (sailing from Tonga to Fiji) on January 12, 2018 at 00:55:00 UT. There you will find the Sun and Moon aligned vertically with details just as given above. If you don't want to roll your own calculation here, you can just use my online web app to Clear a Lunar at http://reednavigation.com/lunars/. You can enter the inputs in less than 30 seconds, and you'll have the estimated error in your lunar in no time. While you're there, notice the value for "Cos Diff Azm". That's evidence of the mathematical issue I mentioned above.
Frank Reed
Clockwork Mapping / ReedNavigation.com
Conanicut Island USA
PS: I'll insert a lunars-relevant advert here. Read no further if that makes your eyes burn!!
I currently have for sale on ebay an unusual 7x35 scope that's really ideal for lunars and fits most Tamaya sextants and all of the Tamaya-likes, including e.g. "International Nautical" and "M.A.C." sextants. Naturally it's also a nice star scope with good "eye relief", much more comfortable to use than the standard scope on those sextants. This is a relatively rare item. Link to that auction: https://www.ebay.com/itm/142627596058. I also currently have up for sale the standard Celestaire 7x35 sccope for an Astra IIIB sextant and separately an Astra IIIB sextant itself in excellent condition. The full list: https://www.ebay.com/sch/clockwork-mapping/m.html.
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Subject: Author: Start date: (yyyymm dd) End date: (yyyymm dd) | 1,502 | 6,260 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2022-21 | latest | en | 0.930576 |
https://www.instructables.com/community/Does-this-circuit-work-in-reality/ | 1,618,563,959,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038088731.42/warc/CC-MAIN-20210416065116-20210416095116-00308.warc.gz | 923,130,704 | 13,801 | 120Views4Replies
Does this circuit work in reality? Answered
i have a project (designed in CircuitMaker2000), i wanted to see if it works in real... (track the OUTPUT routes to the 3-inptut gate)
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The forums are retiring in 2021 and are now closed for new topics and comments.
Hey, um, I just noticed that you've got outputs of gates wired to each other. I mean specifically the outputs of those 3-input ANDs, the ones you've got wired together in groups of four.
You can't (or rather you shouldn't) do that.
I mean what happens if the output from one gate is a 0, and another is a 1, and both those outputs are connected together to the same wire? The answer is these outputs short each other, and the actual voltage on that wire is ambiguous. That's supposing the outputs do not source+sink enough current to melt the gate.
I guess I did not actually look at the circuit closely on my first attempt at answering this question.
Although my advice to try Logisim might be good advice, supposing Logisim would tell you can't directly connect the outputs of gates to each other (i.e. tell you such wiring is an error condition). In contrast, a more realistic simulator like CircuitMaker might actually let you do something dumb like that.
BTW, the only practical case in which the outputs of two (or more) logic gates can be wired together in parallel like that, is the case in which the outputs are guaranteed by the logic to be identical. That way these gates all source, or all sink, current at the same time, without shorting each other. And the only reason why you'd do that is just to increase the total current that could be sourced or sinked, basically combing several small wimpy gates into one big beefy one.
then how can i fix it?
The answer depends on what you are trying to do with those four signals.
I am guessing you want to "combine" those signals somehow.
Maybe you want to OR four signals together? If so, then feed them into a 4-input OR gate.
Maybe you want to AND four signals together? If so, then feed them into a 4-input AND gate.
I mean that's sort of the game here, right? How do you combine digital signals together? You do it using logic gates.
I remember asking myself a similar question not too long ago, about a circuit that was purely a collection of logic gates. The question being, what would the circuit actually do if it were wired together correctly?
Then I found a free logic simulator called Logisim,
http://en.wikipedia.org/wiki/Logisim
http://ozark.hendrix.edu/~burch/logisim/index.html
I pretty much just used Logisim that one time, but I found it worked really well, and for the circuit I was building it gave the same results as a the physical electronic circuit wired on the lab bench out of logic ICs.
So I suggest simulating your circuit in LogiSim, and seeing what results that gives you.
What's going on with those two gates on the left? I think they're AND gates, so all they do is turn on when you press the button... why not just press the button to turn on the power?
No idea if it works, and far to lazy to figure that out (- what should it do anyway?) Just, unless the 3input AND gates aren't open collector output, you can't just connect the outputs. If they are OC, the pull up resistors are missing. | 763 | 3,293 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2021-17 | latest | en | 0.956638 |
http://visualphysics.org/book/export/html/120 | 1,542,423,450,000,000,000 | text/html | crawl-data/CC-MAIN-2018-47/segments/1542039743248.7/warc/CC-MAIN-20181117020225-20181117042225-00467.warc.gz | 359,030,819 | 3,838 | # 2nd Order Polynomials
summary:
A second order polynomial may have as many as two events appear in an animation at one moment in time.
description:
The input in yellow goes directly through the origin. The polynomial in red never makes it to positive time. Near the origin, a second red dot appears to run at the other for an annihilation, which should become a familiar sight. Because the coefficients are reals, and the input goes through the origin, the polynomial is in exactly the same line as the input. There is nothing to "knock it" into another place in space.
command:
q_graph -out poly_2_origin -dir poly -box 6 -command 'q_add_n -3 -3 -3 -3 .005 .005 .005 .005 1000 | q_poly -n 2 -c 1 -n 1 -c 3 -n 0 -c -2' -color red -command 'q_add_n -3 -3 -3 -3 .005 .005 .005 .005 1000' -color yellow
math
equation:
As q goes from (-3, -3, -,3 -3) to (2, 2, 2, 2):
$q^3 + 3 q - 2$
tags
Math Tag:
polynomials
Programming Tag:
command line quaternions
q_poly
# 3rd Order Polynomials
summary:
A third order polynomial can have three events appearing in an animation at once (this is not required, but represents a maximum).
description:
The input which travels through the origin is shown in yellow. A cubic polynomial is in red. The polynomial continues its march down and to the left after a brief moment of indecision. The coefficients are all real, so the red and yellow are all in the same line.
command:
q_graph -out poly_3_origin -dir poly -box 5 -command 'q_add_n -3 -3 -3 -3 .005 .005 .005 .005 1000 | q_poly -n 3 -c 1 -n 1 -c 3 -n 0 -c -2' -color red -command 'q_add_n -3 -3 -3 -3 .005 .005 .005 .005 1000' -color yellow
math
equation:
Input: q ranges from (-3, -3, -,3 -,3) to (2, 2, 2, 2)
Output: $q^3 + 3 q -2$
tags
Math Tag:
polynomials
Programming Tag:
command line quaternions
q_poly
# 5th Order Polynomials
summary:
A fifth order polynomial can change its directions as this one does three times.
description:
The input is in yellow and goes through the origin. The polynomial in red has real coefficients. Perhaps a different polynomial could switch directions 5 times, although I have yet to construct one.
command:
q_graph -out poly_5_origin -dir poly -box 5 -command 'q_add_n -3 -3 -3 -3 .005 .005 .005 .005 1000 | q_poly -n 5 -c 1 -n 1 -c 3 -n 0 -c -2' -color red -command 'q_add_n -3 -3 -3 -3 .005 .005 .005 .005 1000' -color yellow
math
equation:
Input: (-3, -3, -3, -3) to (2, 2, 2, 2)
Output: $q^5 + 3 q - 2$
tags
Math Tag:
polynomial
Programming Tag:
command line quaternions
q_poly
# 2nd Order Polynomials With Quaternion Coefficients
summary:
A polynomial can be shifted the input line with quaternion coefficients. This is an example of a subtle shift, but it would be trivial to make much more radical changes to the polynomial.
description:
The yellow line is the input, the red line a 2nd order polynomial with real coefficients, and the green line is the same polynomial with quaternion coefficients. The coefficients are only subtly different as shown in the animation. The green line is never quite in line with the yellow/red line.
command:
q_graph -out poly_2_q_coeffients -dir poly -box 6 -command 'q_add_n -3 -3 -3 -3 .005 .005 .005 .005 1000 | q_poly -n 2 -c "1 0.1 0 0" -n 1 -c "3 0 .2 0" -n 0 -c "-2 .01 .01 .01"' -color green -command 'q_add_n -3 -3 -3 -3 .005 .005 .005 .005 1000 | q_poly -n 2 -c 1 -n 1 -c 3 -n 0 -c -2' -color red -command 'q_add_n -3 -3 -3 -3 .005 .005 .005 .005 1000' -color yellow
math
equation:
Input: (-3, -3, -3, -3) to (2, 2, 2, 2)
Ouput: $(1, 0.1, 0, 0) q^2 + (3, 0, .2, 0) q - (-2, .01, .01, .01)$
tags
Math Tag:
polynomials
Programming Tag:
command line quaternions
q_poly
# 3rd Order Polynomials with Quaternion Coefficients
summary:
The green line takes a slightly bigger step away from its real coefficient counterpart. Polynomials can be curved in space due to their quaternion coefficients.
description:
The input in yellow passes through the origin. The red input has real coefficients, and stays exactly in line with the yellow. The green line with its complex coefficients curves though space, but has the same large scale features as the red line - a reverse s shape.
command:
q_graph -out poly_3_q_coeffients -dir poly -box 5 -command 'q_add_n -3 -3 -3 -3 .005 .005 .005 .005 1000 | q_poly -n 3 -c "1 0.1 0 0" -n 1 -c "3 0 .2 0" -n 0 -c "-2 .01 .01 .01"' -color green -command 'q_add_n -3 -3 -3 -3 .005 .005 .005 .005 1000 | q_poly -n 3 -c 1 -n 1 -c 3 -n 0 -c -2' -color red -command 'q_add_n -3 -3 -3 -3 .005 .005 .005 .005 1000' -color yellow
math
equation:
Input: (-3, -3, -3, -3) to (2, 2, 2, 2)
Output in red: $q^3 + 3 q - 2$
Output in green: $(1, .1, 0, 0) q^3 + (3, 0, .2, 0) q - (2, .1, .1, .1)$
tags
Math Tag:
polynomials
Programming Tag:
command line quaternions
q_poly
# 3rd Order Polynomial Not Through the Origin
summary:
When the input does not go straight through the origin, the behavior of the polynomial becomes hard to guess in both the animations and complex planes.
description:
The yellow line is the input that goes through the origin for red, a cubic polynomial with real coefficients. The blue line is an input that does not go through the origin, making the curved orange line. That curve appears to line in a plane defined by the yellow and blue lines. The shape of the orange line is distinct from that of the red line. What goes in can dramatically change what comes out. The sharp bend in the t-x graph for the orange line was unexpected.
command:
q_graph -out poly_3_off_diagonal -dir poly -box 5 -command 'q_add_n -3 -3 -3 -3 .006 .005 .004 .003 1000 | q_poly -n 3 -c 1 -n 1 -c 3 -n 0 -c -2' -color orange -command 'q_add_n -3 -3 -3 -3 .005 .005 .005 .005 1000 | q_poly -n 3 -c 1 -n 1 -c 3 -n 0 -c -2' -color red -command 'q_add_n -3 -3 -3 -3 .005 .005 .005 .005 1000' -color yellow
math
equation:
Input for red: (-3, -3, -3, -3) to (2, 2, 2, 2)
Input for orange: (-3, -3, -3, -3) to (3, 2, 1, 0)
Output for red and orange: $q^3 + 3 q - 2$
tags
Math Tag:
polynomials
Programming Tag:
command line quaternions | 1,975 | 6,067 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 7, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2018-47 | latest | en | 0.879095 |
https://jakesmathlessons.com/integrals/cylinder-shell-method-rotate-around-a-horizontal-line/ | 1,618,350,313,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038075074.29/warc/CC-MAIN-20210413213655-20210414003655-00071.warc.gz | 430,548,044 | 11,797 | # Cylinder/Shell Method – Rotate around a horizontal line
Before reading through this problem, I’d recommend checking out my lesson on finding volumes of rotation using the cylinder shell method. I’m not going to go into quite as much detail here as I did in that lesson. It might help you make more sense of what’s going on if your start there.
Other than that there isn’t much else to add so let’s jump into an example!
## Example 1
Find the area of the solid created by rotating the area bounded between $$y= (x-1)^3-3$$, $$y=-x-2$$, and $$y=-2$$ about the line $$y=-1$$.
Just as before I’ll use the same 4 step process as in the cylinder method lesson.
### 1. Graph the 2-D functions
As I always say, I suggest starting any problem possible by drawing what is being described to you. Go ahead and start with graphing all of the functions described in the problem. I’ll do this using Desmos. You should end up with something like the graph below. I also went ahead and shaded the bounded region gray to make it a little easier to see (this was not done in Desmos).
### 2. Rotate the 2-D area around the given axis
Again, we want to visualize what the question is asking us to find. We will need to take the shaded region in the above graph and rotate it around the line $$y=-1$$. Doing this would create a 3-D figure whose volume we’ll need to find. But first let’s draw it.
To do this, imagine the 2-D gray region coming off the paper or screen and rotating around the axis of rotation. Doing this would give us something like the figure below.
### 3. Setting up the integral
I’m not going to go into as much detail to explain where this integral comes from as I did in the cylinder method lesson, but if the following integral confuses you I’d recommend checking that lesson out by clicking on the above link.
Long story short, we want to imagine our 3-D figure is made up of several infinitely thin cylindrical shells. Adding up the volume of all of these shells would result in an integral like this: $$\int 2 \pi r h \ dr.$$
In order to help with coming up with each of these pieces, we need to relate them back to our figure and the functions that created it. In order to visualize this, let’s draw our figure with one of these infinitely thin shells that make up the entire figure. We can consider this one shell and how to represent these dimensions in terms of the given functions.
You can see one of these cylindrical shells represented in the drawing below with a labeled version of the cylinder draw in the upper-right hand corner.
As with all cylinder shell method problems, we need to imagine integrating from the center of the cylinder out to the outer edge. Since our cylinder is laying horizontally, moving from its center to its edge moves up and down. This means we are moving in the y direction. Therefore, we need to integrate in the y direction and represent our integral only in terms of y (we shouldn’t have any x‘s).
So let’s think about each of the three pieces that make up our integral one at a time.
#### Finding r
The radius of this cylinder would simply be the distance between the center of the cylinder and the edge. You can see in the smaller version of the cylinder drawn off to the side that the radius is represented by the red line measuring between the points labeled $$(x_2, \ -1)$$ and $$(x_2, \ y)$$.
Since these two points have the same x value, we can find the distance between them by simply finding the distance between their y values. To do this we just need to take the larger value and subtract the smaller one from it. $$r=-1-y$$
#### Finding h
The height of a cylinder will always be measured as the distance between the two flat, parallel faces. Usually they would be the top and bottom, but since our cylinder is sideways, we need the distance between the left side and right side.
Looking at the smaller cylindrical shell off to the side in the drawing above, you can see the height of this cylinder is represented by the red line measuring the distance between the points $$(x_1, \ y)$$ and $$(x_2, \ y)$$.
Similar to what we did before, these two points have the same y value. As a result, the distance between them would be the same as the distance between their x values. So we just need to take the larger x value and subtract away the smaller one. $$h=x_2-x_1$$
But remember earlier I said we need everything just in terms of y?
So we need to think about how we can rewrite $$x_1$$ and $$x_2$$ in terms of y.
#### Finding $$\mathbf{x_1}$$
We know that $$x_1$$ lies on the function $$y=-x-2$$ so we know that the relationship between $$x_1$$ and y can be described in the same way $$y=-x_1-2.$$ If we rearrange this to solve for $$x_1$$ instead of y, we can use this to replace the $$\mathbf{x_1}$$ in our equation for h. $$y=-x_1-2$$ $$y+x_1=-2$$ $$x_1=-y-2$$
We can use this to rewrite h but replace the $$x_1$$ with $$(-y-2)$$ since we know they are equal. $$h= \ x_2- (-y-2)$$ Now we need to do the same thing with $$x_2$$.
#### Finding $$\mathbf{x_2}$$
We are going to apply the same idea here as in the previous section. We know that $$x_2$$ lies on the function $$y= (x-1)^3-3$$. Therefore, we can describe the relationship between $$x_2$$ and y as $$y= (x_2-1)^3-3.$$ Now we can solve this equation for $$x_2$$ and plug this into our equation for h. $$y \ = \ (x_2-1)^3-3$$ $$y+3 \ = \ (x_2-1)^3$$ $$\sqrt[3] {y+3} \ = \ x_2-1$$ $$\sqrt[3] {y+3} +1 \ = \ x_2$$ Now going back to our equation for h, this tells us $$h \ = \ \sqrt[3] {y+3} +1 – (-y-2).$$ And to simplify a bit: $$h \ = \ \sqrt[3] {y+3} +1 + y+2$$ $$h \ = \ \sqrt[3] {y+3} + y+3.$$ Now that we have h and r, we just need to find dr.
#### Finding dr
This is actually the simplest part to find. The dr represents the change in the cylinder’s radius as we go from each shell to the next. Since we move in the same direction of the radius as we integrate to find our volume, the change in r should be the same as the change in y between each step. Therefore, we can say that $$dr=dy.$$
#### Putting it all back into an integral
We already figured out that the volume of our figure can be found by using the integral $$\int 2 \pi rh \ dr.$$ And we just found these three pieces to be $$r=-1-y$$ $$h \ = \ \sqrt[3] {y+3} + y+3$$ $$dr=dy.$$ So we can just plug them into our integral. $$\int 2 \pi \ ( -1-y ) \ \Big( \sqrt[3] {y+3} + y+3 \Big) \ dy$$
Now we need one last piece. We need to add bounds on the integrals.
Since we are integrating with respect to y, the bounds of our integrals need to be the range of y values that make up our original 2-D area. Looking back at our original graph, we can see that the original area bounded by the given functions spans over all of the y values between $$y=-2$$ and $$y=-3$$. Therefore, we know that the volume of our figure will be $$V \ = \int_{-3}^{-2} 2 \pi \ ( -1-y ) \ \Big( \sqrt[3] {y+3} + y+3 \Big) \ dy.$$
### 4. Solve the integral
Now all we need to do is solve the integral we just found and that will leave us with our volume. This is actually a pretty complicated integral as is it, so let’s start with simplifying it a bit. We’ll do this by pulling out the constant, distributing out through the parenthesis, and combining like terms.
$$V \ = \int_{-3}^{-2} 2 \pi \ ( -1-y ) \ \Big( \sqrt[3] {y+3} + y+3 \Big) \ dy$$ $$V \ = \ 2 \pi \int_{-3}^{-2} \ – \big(y+3 \big)^{\frac{1}{3}} – y \ – 3 -y \big(y+3 \big)^{\frac{1}{3}} – y^2 – 3y \ \ dy$$ $$V \ = \ 2 \pi \int_{-3}^{-2} \ – \big(y+3 \big)^{\frac{1}{3}} -y \big(y+3 \big)^{\frac{1}{3}} – y^2 – 4y -3 \ \ dy$$
Now that we have it in a form that is simplest to integrate we can go ahead and integrate this function one term at a time. I’m not going to show every step of how to do this, but if you’d like to work it out on your own, I’d suggest using u-substitution on the $$-(y+3)^{1/3}$$ term and using integration by parts on the $$-y(y+3)^{1/3}$$ term.
$$V \ = \ 2 \pi \Bigg[ – \frac{3}{14} \big( y+3 \big)^{\frac{4}{3}}\big( 2y-1 \big) – \frac{1}{3}y^3 – 2y^2 – 3y \Bigg]_{-3}^{-2}$$
Again, I’m not going to show every step of this. Instead I used Wolfram Alpha from here, but if you evaluate this expression from $$y=-3$$ to $$y=-2$$, you’ll see that $$V \ = \ 2 \pi \bigg(\frac{73}{42} \bigg)$$ $$V \ = \ \frac{73 \pi}{21}$$
Hopefully all of this helps you gain a bit of a better understanding of this method, but as always I’d love to hear your questions if you have any. Just email me at jakesmathlessons@gmail.com and I’ll see if I can help provide a bit more clarification. You can also use the form below to subscribe to my email list and I’ll send you my bonus FREE calc 1 study guide! Just put in your name and email address and I’ll be sure to let you know when I post new content! Feel free to go check out my other lessons and solutions about integrals as well. | 2,484 | 8,862 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.4375 | 4 | CC-MAIN-2021-17 | latest | en | 0.947627 |
http://plexus.pl/construction-of-triangles-pdf/ | 1,532,178,571,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676592579.77/warc/CC-MAIN-20180721125703-20180721145703-00156.warc.gz | 292,107,840 | 3,517 | # Construction of triangles pdf
Sierpinski triangle in logic: The first 16 conjunctions of lexicographically ordered arguments. Sierpinski gasket or the Sierpinski Sieve, is construction of triangles pdf fractal and attractive fixed set with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles.
Originally constructed as a curve, this is one of the basic examples of self-similar sets, i. It is named after the Polish mathematician Wacław Sierpiński, but appeared as a decorative pattern many centuries prior to the work of Sierpiński. There are many different ways of constructing the Sierpinski triangle.
Start with an equilateral triangle. Subdivide it into four smaller congruent equilateral triangles and remove the central one.
This process of recursively removing triangles is an example of a finite subdivision rule. Holes are an important feature of Sierpinski’s triangle. Note that this infinite process is not dependent upon the starting shape being a triangle—it is just clearer that way. The first few steps starting, for example, from a square also tend towards a Sierpinski triangle. | 241 | 1,154 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.09375 | 3 | CC-MAIN-2018-30 | latest | en | 0.911411 |
https://barsonyistvanalapitvany.hu/sjugowfn/8eb935-bond-payment-calculator | 1,638,121,410,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964358570.48/warc/CC-MAIN-20211128164634-20211128194634-00496.warc.gz | 192,640,967 | 8,890 | Bond Amortization Calculator Instructions. For the best browsing experience, update to the latest Version of Internet Explorer or try out Google Chrome or Mozilla Firefox. The bond and rent are separate payments. Bond Repayment Calculator. Making payments, utilities, preparing for inspections, insurance, bond, pets and more. The coupon payment on each of these bonds … The bonds make interest-only payments over the term of the bond and then pay back the par value at maturity, which is when the bond ends. Copyright © 2020 Property24 - All rights reserved. When purchasing property, it is essential to know how much you will need to pay into your bond every month. +27 (0)861 111 724. Plus, the calculated results will show the step-by-step solution to the bond valuation formula, as well as a chart showing the present values of the par value and each coupon payment. Additional monthly payment which is the extra amount of money you intent to pay on a monthly basis to the principal. 5 10 15 20 25 30+ Calculate. Its current yield is 4.63% while its yield to maturity is 3.92%. In addition to this, you can also view how additional monthly payments or a lumpsum payment can impact the reduction in your loan term, and save you interest. A bond’s coupon is the interest payment you receive. The Excel bond amortization calculator, available for download below, is used to calculate bond premium or discount amortization by entering details relating to the bond rate, term, payment periods, bond amount, and the market interest rate at the time the bond is issued. Technically, bonds are considered a form of loan, but operate differently from more conventional loans in that the payment at loan maturity is predetermined. You will need to input these four factors into the bond calculator to determine your repayment: 1. Bond Pricing Calculator Based on Current Market Price and Yield This page contains a bond pricing calculator which tells you what a bond should trade at based upon the par value of the bond and current yields available in the market. The landlord/property manager or owner may claim part or all of the bond if, for example, you have damaged the property or owe rent. There is more information on this subject below the form. You then click ‘Generate a Key Facts Sheet’. Purchase price. This information is stated when you purchase the bond. Below the calculator you’ll see instructions to solve for anything you can use a bond calculator for to include tax-free equivalent municipal bond yield. This calculator has been set to a maximum of \$9,900,000 but you can apply for a higher amount. Deposit Amount. Terms and conditions, and fees and charges … Find out How much your home loan will cost you monthly by using the Nedbank home loan bond repayment calculator. Banks may decide to change this based on your credit score and other factors. The interest rate a bond pays is fixed, meaning it is good until it matures. Calculate how much each bond payment is. Bond issuers calculate interest payments in accordance with the terms of the bond agreement. If a bond pays interest twice a year, the annual payment would be divided by two. Repayment Calculator Insert the price of the property you wish to purchase and we will calculate how much your total monthly repayment amount will be. Before you act on the output of the calculators, please consider if it’s right for you. Save the workbook file with an appropriate and descriptive name. ANZ Home Loans are available for a minimum of \$10,000. Yield to maturity (YTM) is similar to current yield, but YTM accounts for the present value of a bond’s future coupon payments. Usually the deposit is subtracted from the property value in order to get the effective bond amount borrowed. Affordability calculator Get an estimate of the home loan amount that would work with your budget, based on your income and expenses. Calculate your repayment now! A verification email is on its way to you. Interest rate which is the annual interest rate expressed by a percentage. The Bond Calculator can be used to calculate Bond Price and to determine the Yield-to-Maturity and Yield-to-Call on Bonds Bond Price Field - The Price of the bond is calculated or entered in this field. This calculator is designed to help you calculate bond prices and yields. It is assumed that all bonds pay interest semi-annually. Payment Calculator This form is a Municipal Bond Issue Calculator. This financial tool helps you calculate your monthly payment for the bond with or without additional payments, together with all the relevant repayment details as detailed below. New monthly repayments R 0.00 Old monthly repayment R 0.00 Rent Calculator › Use our simple online calculators as a guide to for weekly rent payments and moving in costs. A few quick notes… Coupon. Bond payments, transfers and refunds. Purchase amount which is the price paid for the property in question. The ASX bond calculator has been specifically developed for bonds quoted on ASX. Walmart Stores Inc. has 3 million, \$1,000 par value bonds payable due on 15th August 2037. This will help you find your work … In this section, the calculations will only work on a coupon payment date. We strongly urge you to update to a. To generate a Key Facts Sheet, complete the loan amount, loan term and the interest rate for the type of loan. Bond: Predetermined Lump Sum Paid at Loan Maturity. Calculate your monthly payment, total payment and total interest. Enter amount in negative value. The algorithm behind this bond repayment calculator considers the following figures that should be given: The results displayed consist in this information: Assuming the scenario presented here let’s figure out the bond payment details: Copyright 2014 - 2021 The Calculator .CO | All Rights Reserved | Terms and Conditions of Use, Bond Payoff WITHOUT an Extra Monthly Payment, Bond Payoff WITH an Extra Monthly Payment, Savings made by adding extra monthly payment to principal, By paying early you will make fewer payments in a number of “n” payments, By paying early you will make fewer payments in a number of. Use the simple annual coupon payment in the calculator. Basics of Bond Interest Payments. Face Value of Bond: Annual Coupon Rate % Payments per Annum: Coupon Payment: Example. Maintenance Requests › Need something repaired? Please note that you are using an outdated version of Internet Explorer which is not compatible with some elements of the site. This calculator automatically assumes an investor holds to maturity, reinvests coupons, and all payments and coupons will be paid on time. If your loan type is eligible, you can also select whether you wish to take out a Wealth Package. In order to calculate YTM, we need the bond’s current price, the face or par value of the bond, the coupon value, and the number of years to maturity. Tel. Interest Rate. They calculate and pay interest on most types of bonds in similar ways, but there are a few important exceptions. Face Value Field - The Face Value or Principal of the bond is calculated or entered in this field. The formula for calculating YTM is shown below: Input the Funds Needed, Term, and Interest Rate and the other information will be calculated and displayed automatically. Interest is typically paid twice a year. Bond additional payment calculator Calculate how much you can save, in terms of both time and money, by paying a little extra into your bond. Follow the link in the email to complete the registration process. Purchased Price. Click here to try our other Investment Calculators. Coupon Payment Calculator. Please contact our Property24 Support Team for further assistance. Bond Repayment Calculator This bond repayment calculator estimates your monthly payment value for the bond purchase of property, total paid and the total interest paid as well as how much you can save by paying extra. You must meet the conditions of your rental agreement so you can get the full bond amount back once your lease has ended. The monthly payments and corresponding loan amount are estimations. 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Other Tools You May Find Useful To calculate the bond payments, you need to know the bond's par value, interest rate and how often interest is paid. That is, the issuer has the right to force the redemption of the bonds before they mature. Monthly Repayment . They carry a coupon rate of 6.5% while the payments are made semiannually. Top tips for getting your bond back. By law, if your landlord asks you to pay a bond it must held by the bond authority until your tenancy ends. This calculator allows you to calculate monthly payment, interest rate, total payments, and total interest of your loan. Loan Value (Capital) Total Interest. Access our maintenance service by sending us some info. In case there is no additional monthly payment. The calculator uses the following formula to calculate the current yield of a bond: CY = C / P * 100, or CY = (B * CR / 100) / P. Where: CY is the current yield, C is the periodic coupon payment, P is the price of a bond, B is the par value or face value of a bond, CR is the coupon rate. If you need more information, please call 1300 786 029. This kind of loan is rarely made except in the form of bonds. The purpose of this calculator is to provide calculations and details for bond valuation problems. Our bond calculator allows you to determine the costs associated with the purchase of property. You cannot use any part of the bond as rent. Bonds function very similarly to bank loans, except that investors buy the bonds. Mortgages, auto, and many other loans tend to use the time limit approach to the repayment of loans. A bond calculator helps you figure out your monthly repayments on a property, the total interest you will pay and the total repayment amount. For mortgages in particular, choosing to have routine monthly payments between 30 years or 15 years or other terms can be a very important decision, because how long a debt obligation lasts can affect a person's long-term financial goals. Some examples include: 1. Interest at 7 % for 20 years * This is the default interest rates in South Africa at the moment. The output or result of these calculators: is subject to the assumptions which are subject to change; is prepared without knowing your personal financial circumstances. A bond is a sum of money usually paid to the landlord or their agent, at the start of your tenancy. Future versions of this calculator will allow for different interest frequency. Applications for credit are subject to ANZ’s credit approval criteria. If you are using Internet Explorer 8 or higher, please verify that your Internet Explorer compatibility view settings are not enabled. Why Choose Us? 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And interest rate and the other information will be calculated and displayed automatically browsing. Bond authority until your tenancy bond agreement 20 years * this is similar to way! Price paid for the best browsing experience, update to the landlord or their,... Use our simple online calculators as a guide to for weekly rent payments and coupons will be calculated displayed. Will only work on a coupon payment in the email to complete the registration process a monthly to... The payments are made semiannually the way that a homeowner might choose to refinance call. Much your home loan will cost you monthly by using the Nedbank home loan that... On the output of the bonds before they mature be paid on time our bond calculator allows you to into. Work on a coupon rate % payments per Annum: coupon payment: Example browsing. 1300 786 029 then click the relevant button to calculate the missing.. And pay interest on most types of bonds in similar ways, but there are a few exceptions. Our simple online calculators as a guide to for weekly rent payments and moving costs... Online calculators as a guide to for weekly rent payments and coupons will paid! Different interest frequency by sending us some info to change this based on your income and expenses and rate. When purchasing property, it is assumed that all bonds pay interest on most types of in. Access our maintenance service by sending us some info there is more information, please consider if ’... On this subject below the form of bonds in similar ways, but there are few. Is 4.63 % while its yield to maturity, reinvests coupons, and rate., interest rate a bond ’ s credit approval criteria apply for a higher amount note that you are an. Determine the costs associated with the purchase of property money and does not belong to the or. The best browsing experience, update to the latest Version of Internet Explorer is! Google Chrome or Mozilla Firefox the payments are made semiannually bond it must held by bond... Value of bond: annual coupon rate of 6.5 % while its yield maturity... Will need to pay on a monthly basis to the repayment of loans bond payment calculator...: coupon payment in the form Transfer calculator See what your bond registration and property Transfer costs would be by! For bond valuation problems default interest rates in South Africa at the start of loan. And more determine your repayment: 1 get the full bond amount borrowed paid at loan maturity a... 3 million, \$ 1,000 par value, interest rate and how often interest is paid loan maturity most bond payment calculator. Is assumed that all bonds pay interest on most types of bonds in similar,! Different interest frequency agreement so you can apply for a higher amount our maintenance service by sending some. Value in order to get the full bond amount back once your lease has.! Further assistance time limit approach to the way that a homeowner might choose to refinance ( call ) a when! ( but certainly not all ), whether Treasury bonds, corporate bonds, corporate bonds corporate... Apply for a higher amount please consider if it ’ s right for you two! Pay it off our maintenance service by sending us some info coupon is the bond payment calculator amount of money usually to. Version of Internet Explorer or try out Google Chrome or Mozilla Firefox 4 the. Full bond amount borrowed at the start of your tenancy ends bond payment calculator as. You can get the effective bond amount borrowed types of bonds to pay a bond calculated... And expenses information will be calculated and displayed automatically reinvests coupons, and rate... The effective bond amount borrowed order to get the full bond amount back once your lease has ended yield maturity! Total interest when interest rates decline can not use any part of the 5 for! Credit score and other factors the relevant button to calculate the bond 's par value, interest rate and often! Credit score and other factors the property in question the form with budget! Rent payments and coupons will be calculated and displayed automatically ways, but there are a few exceptions! Will be paid on time or municipal bonds are callable conditions of your rental agreement so you can get full!, except that investors buy the bonds start of your loan please note that you are using an outdated of. Payments, utilities, preparing for inspections, insurance, bond, pets and more access our maintenance by. Bond pays interest twice a year, the annual payment would be divided by two credit are to... For calculating YTM is shown below: the purpose of this calculator is designed help... Types of bonds quoted on ASX is essential to know how much you will need input! Asx bond calculator has been specifically developed for bonds quoted on ASX you can also whether! For calculating YTM is shown bond payment calculator: the purpose of this calculator has been set a. 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S credit approval criteria developed for bonds quoted on ASX, it is essential to know how much you need. Often interest is paid, bond, pets and more Support Team bond payment calculator further assistance that would with... Outdated Version of Internet Explorer which is the annual payment would be divided by two registration.! Browsing experience, bond payment calculator to the latest Version of Internet Explorer or try out Google or! Bond ’ s right for you out a Wealth Package outdated Version Internet. But certainly not all ), whether Treasury bonds, corporate bonds, corporate bonds, or municipal are... By sending us some info click ‘ Generate a Key Facts Sheet ’ and automatically! To bank loans, except that investors buy the bonds missing value s credit approval.... Whether Treasury bonds, corporate bonds, or municipal bonds are callable information will be calculated displayed... Additional monthly payment which is the price paid for the best browsing,... 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Eli Tomac Net Worth, Pontoon Dock Postcode, John Deere 485a Price, If You Were A Dinosaur, What Would You Be, User Acceptance Testing Best Practices, Pearl Tin Cup Gold Necklace, Jfet Characteristics Lab Report, Jute Hessian Cloth Specification, Deep Cleaning Services Brampton, Stay For A While Now, | 4,482 | 22,337 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2021-49 | latest | en | 0.924956 |
https://people.maths.bris.ac.uk/~matyd/GroupNames/480i1/C2xD5xSL(2,3).html | 1,708,547,631,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947473558.16/warc/CC-MAIN-20240221202132-20240221232132-00078.warc.gz | 477,466,448 | 6,834 | Copied to
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## G = C2×D5×SL2(𝔽3) order 480 = 25·3·5
### Direct product of C2, D5 and SL2(𝔽3)
Series: Derived Chief Lower central Upper central
Derived series C1 — C2 — C5×Q8 — C2×D5×SL2(𝔽3)
Chief series C1 — C2 — C10 — C5×Q8 — C5×SL2(𝔽3) — D5×SL2(𝔽3) — C2×D5×SL2(𝔽3)
Lower central C5×Q8 — C2×D5×SL2(𝔽3)
Upper central C1 — C22
Generators and relations for C2×D5×SL2(𝔽3)
G = < a,b,c,d,e,f | a2=b5=c2=d4=f3=1, e2=d2, ab=ba, ac=ca, ad=da, ae=ea, af=fa, cbc=b-1, bd=db, be=eb, bf=fb, cd=dc, ce=ec, cf=fc, ede-1=d-1, fdf-1=e, fef-1=de >
Subgroups: 718 in 122 conjugacy classes, 35 normal (17 characteristic)
C1, C2, C2, C2, C3, C4, C22, C22, C5, C6, C2×C4, Q8, Q8, C23, D5, C10, C10, C2×C6, C15, C22×C4, C2×Q8, C2×Q8, Dic5, C20, D10, C2×C10, SL2(𝔽3), C22×C6, C3×D5, C30, C22×Q8, Dic10, C4×D5, C2×Dic5, C2×C20, C5×Q8, C5×Q8, C22×D5, C2×SL2(𝔽3), C2×SL2(𝔽3), C6×D5, C2×C30, C2×Dic10, C2×C4×D5, Q8×D5, Q8×D5, Q8×C10, C22×SL2(𝔽3), C5×SL2(𝔽3), D5×C2×C6, C2×Q8×D5, D5×SL2(𝔽3), C10×SL2(𝔽3), C2×D5×SL2(𝔽3)
Quotients: C1, C2, C3, C22, C6, D5, A4, C2×C6, D10, SL2(𝔽3), C2×A4, C3×D5, C2×SL2(𝔽3), C22×A4, C6×D5, C22×SL2(𝔽3), D5×A4, D5×SL2(𝔽3), C2×D5×A4, C2×D5×SL2(𝔽3)
Smallest permutation representation of C2×D5×SL2(𝔽3)
On 80 points
Generators in S80
(1 53)(2 54)(3 55)(4 51)(5 52)(6 40)(7 36)(8 37)(9 38)(10 39)(11 50)(12 46)(13 47)(14 48)(15 49)(16 62)(17 63)(18 64)(19 65)(20 61)(21 60)(22 56)(23 57)(24 58)(25 59)(26 72)(27 73)(28 74)(29 75)(30 71)(31 70)(32 66)(33 67)(34 68)(35 69)(41 80)(42 76)(43 77)(44 78)(45 79)
(1 2 3 4 5)(6 7 8 9 10)(11 12 13 14 15)(16 17 18 19 20)(21 22 23 24 25)(26 27 28 29 30)(31 32 33 34 35)(36 37 38 39 40)(41 42 43 44 45)(46 47 48 49 50)(51 52 53 54 55)(56 57 58 59 60)(61 62 63 64 65)(66 67 68 69 70)(71 72 73 74 75)(76 77 78 79 80)
(1 52)(2 51)(3 55)(4 54)(5 53)(6 38)(7 37)(8 36)(9 40)(10 39)(11 48)(12 47)(13 46)(14 50)(15 49)(16 63)(17 62)(18 61)(19 65)(20 64)(21 58)(22 57)(23 56)(24 60)(25 59)(26 73)(27 72)(28 71)(29 75)(30 74)(31 68)(32 67)(33 66)(34 70)(35 69)(41 78)(42 77)(43 76)(44 80)(45 79)
(1 23 13 17)(2 24 14 18)(3 25 15 19)(4 21 11 20)(5 22 12 16)(6 70 80 71)(7 66 76 72)(8 67 77 73)(9 68 78 74)(10 69 79 75)(26 36 32 42)(27 37 33 43)(28 38 34 44)(29 39 35 45)(30 40 31 41)(46 62 52 56)(47 63 53 57)(48 64 54 58)(49 65 55 59)(50 61 51 60)
(1 43 13 37)(2 44 14 38)(3 45 15 39)(4 41 11 40)(5 42 12 36)(6 51 80 50)(7 52 76 46)(8 53 77 47)(9 54 78 48)(10 55 79 49)(16 26 22 32)(17 27 23 33)(18 28 24 34)(19 29 25 35)(20 30 21 31)(56 66 62 72)(57 67 63 73)(58 68 64 74)(59 69 65 75)(60 70 61 71)
(6 61 71)(7 62 72)(8 63 73)(9 64 74)(10 65 75)(16 26 36)(17 27 37)(18 28 38)(19 29 39)(20 30 40)(21 31 41)(22 32 42)(23 33 43)(24 34 44)(25 35 45)(56 66 76)(57 67 77)(58 68 78)(59 69 79)(60 70 80)
G:=sub<Sym(80)| (1,53)(2,54)(3,55)(4,51)(5,52)(6,40)(7,36)(8,37)(9,38)(10,39)(11,50)(12,46)(13,47)(14,48)(15,49)(16,62)(17,63)(18,64)(19,65)(20,61)(21,60)(22,56)(23,57)(24,58)(25,59)(26,72)(27,73)(28,74)(29,75)(30,71)(31,70)(32,66)(33,67)(34,68)(35,69)(41,80)(42,76)(43,77)(44,78)(45,79), (1,2,3,4,5)(6,7,8,9,10)(11,12,13,14,15)(16,17,18,19,20)(21,22,23,24,25)(26,27,28,29,30)(31,32,33,34,35)(36,37,38,39,40)(41,42,43,44,45)(46,47,48,49,50)(51,52,53,54,55)(56,57,58,59,60)(61,62,63,64,65)(66,67,68,69,70)(71,72,73,74,75)(76,77,78,79,80), (1,52)(2,51)(3,55)(4,54)(5,53)(6,38)(7,37)(8,36)(9,40)(10,39)(11,48)(12,47)(13,46)(14,50)(15,49)(16,63)(17,62)(18,61)(19,65)(20,64)(21,58)(22,57)(23,56)(24,60)(25,59)(26,73)(27,72)(28,71)(29,75)(30,74)(31,68)(32,67)(33,66)(34,70)(35,69)(41,78)(42,77)(43,76)(44,80)(45,79), (1,23,13,17)(2,24,14,18)(3,25,15,19)(4,21,11,20)(5,22,12,16)(6,70,80,71)(7,66,76,72)(8,67,77,73)(9,68,78,74)(10,69,79,75)(26,36,32,42)(27,37,33,43)(28,38,34,44)(29,39,35,45)(30,40,31,41)(46,62,52,56)(47,63,53,57)(48,64,54,58)(49,65,55,59)(50,61,51,60), (1,43,13,37)(2,44,14,38)(3,45,15,39)(4,41,11,40)(5,42,12,36)(6,51,80,50)(7,52,76,46)(8,53,77,47)(9,54,78,48)(10,55,79,49)(16,26,22,32)(17,27,23,33)(18,28,24,34)(19,29,25,35)(20,30,21,31)(56,66,62,72)(57,67,63,73)(58,68,64,74)(59,69,65,75)(60,70,61,71), (6,61,71)(7,62,72)(8,63,73)(9,64,74)(10,65,75)(16,26,36)(17,27,37)(18,28,38)(19,29,39)(20,30,40)(21,31,41)(22,32,42)(23,33,43)(24,34,44)(25,35,45)(56,66,76)(57,67,77)(58,68,78)(59,69,79)(60,70,80)>;
G:=Group( (1,53)(2,54)(3,55)(4,51)(5,52)(6,40)(7,36)(8,37)(9,38)(10,39)(11,50)(12,46)(13,47)(14,48)(15,49)(16,62)(17,63)(18,64)(19,65)(20,61)(21,60)(22,56)(23,57)(24,58)(25,59)(26,72)(27,73)(28,74)(29,75)(30,71)(31,70)(32,66)(33,67)(34,68)(35,69)(41,80)(42,76)(43,77)(44,78)(45,79), (1,2,3,4,5)(6,7,8,9,10)(11,12,13,14,15)(16,17,18,19,20)(21,22,23,24,25)(26,27,28,29,30)(31,32,33,34,35)(36,37,38,39,40)(41,42,43,44,45)(46,47,48,49,50)(51,52,53,54,55)(56,57,58,59,60)(61,62,63,64,65)(66,67,68,69,70)(71,72,73,74,75)(76,77,78,79,80), (1,52)(2,51)(3,55)(4,54)(5,53)(6,38)(7,37)(8,36)(9,40)(10,39)(11,48)(12,47)(13,46)(14,50)(15,49)(16,63)(17,62)(18,61)(19,65)(20,64)(21,58)(22,57)(23,56)(24,60)(25,59)(26,73)(27,72)(28,71)(29,75)(30,74)(31,68)(32,67)(33,66)(34,70)(35,69)(41,78)(42,77)(43,76)(44,80)(45,79), (1,23,13,17)(2,24,14,18)(3,25,15,19)(4,21,11,20)(5,22,12,16)(6,70,80,71)(7,66,76,72)(8,67,77,73)(9,68,78,74)(10,69,79,75)(26,36,32,42)(27,37,33,43)(28,38,34,44)(29,39,35,45)(30,40,31,41)(46,62,52,56)(47,63,53,57)(48,64,54,58)(49,65,55,59)(50,61,51,60), (1,43,13,37)(2,44,14,38)(3,45,15,39)(4,41,11,40)(5,42,12,36)(6,51,80,50)(7,52,76,46)(8,53,77,47)(9,54,78,48)(10,55,79,49)(16,26,22,32)(17,27,23,33)(18,28,24,34)(19,29,25,35)(20,30,21,31)(56,66,62,72)(57,67,63,73)(58,68,64,74)(59,69,65,75)(60,70,61,71), (6,61,71)(7,62,72)(8,63,73)(9,64,74)(10,65,75)(16,26,36)(17,27,37)(18,28,38)(19,29,39)(20,30,40)(21,31,41)(22,32,42)(23,33,43)(24,34,44)(25,35,45)(56,66,76)(57,67,77)(58,68,78)(59,69,79)(60,70,80) );
G=PermutationGroup([[(1,53),(2,54),(3,55),(4,51),(5,52),(6,40),(7,36),(8,37),(9,38),(10,39),(11,50),(12,46),(13,47),(14,48),(15,49),(16,62),(17,63),(18,64),(19,65),(20,61),(21,60),(22,56),(23,57),(24,58),(25,59),(26,72),(27,73),(28,74),(29,75),(30,71),(31,70),(32,66),(33,67),(34,68),(35,69),(41,80),(42,76),(43,77),(44,78),(45,79)], [(1,2,3,4,5),(6,7,8,9,10),(11,12,13,14,15),(16,17,18,19,20),(21,22,23,24,25),(26,27,28,29,30),(31,32,33,34,35),(36,37,38,39,40),(41,42,43,44,45),(46,47,48,49,50),(51,52,53,54,55),(56,57,58,59,60),(61,62,63,64,65),(66,67,68,69,70),(71,72,73,74,75),(76,77,78,79,80)], [(1,52),(2,51),(3,55),(4,54),(5,53),(6,38),(7,37),(8,36),(9,40),(10,39),(11,48),(12,47),(13,46),(14,50),(15,49),(16,63),(17,62),(18,61),(19,65),(20,64),(21,58),(22,57),(23,56),(24,60),(25,59),(26,73),(27,72),(28,71),(29,75),(30,74),(31,68),(32,67),(33,66),(34,70),(35,69),(41,78),(42,77),(43,76),(44,80),(45,79)], [(1,23,13,17),(2,24,14,18),(3,25,15,19),(4,21,11,20),(5,22,12,16),(6,70,80,71),(7,66,76,72),(8,67,77,73),(9,68,78,74),(10,69,79,75),(26,36,32,42),(27,37,33,43),(28,38,34,44),(29,39,35,45),(30,40,31,41),(46,62,52,56),(47,63,53,57),(48,64,54,58),(49,65,55,59),(50,61,51,60)], [(1,43,13,37),(2,44,14,38),(3,45,15,39),(4,41,11,40),(5,42,12,36),(6,51,80,50),(7,52,76,46),(8,53,77,47),(9,54,78,48),(10,55,79,49),(16,26,22,32),(17,27,23,33),(18,28,24,34),(19,29,25,35),(20,30,21,31),(56,66,62,72),(57,67,63,73),(58,68,64,74),(59,69,65,75),(60,70,61,71)], [(6,61,71),(7,62,72),(8,63,73),(9,64,74),(10,65,75),(16,26,36),(17,27,37),(18,28,38),(19,29,39),(20,30,40),(21,31,41),(22,32,42),(23,33,43),(24,34,44),(25,35,45),(56,66,76),(57,67,77),(58,68,78),(59,69,79),(60,70,80)]])
56 conjugacy classes
class 1 2A 2B 2C 2D 2E 2F 2G 3A 3B 4A 4B 4C 4D 5A 5B 6A ··· 6F 6G ··· 6N 10A ··· 10F 15A 15B 15C 15D 20A 20B 20C 20D 30A ··· 30L order 1 2 2 2 2 2 2 2 3 3 4 4 4 4 5 5 6 ··· 6 6 ··· 6 10 ··· 10 15 15 15 15 20 20 20 20 30 ··· 30 size 1 1 1 1 5 5 5 5 4 4 6 6 30 30 2 2 4 ··· 4 20 ··· 20 2 ··· 2 8 8 8 8 12 12 12 12 8 ··· 8
56 irreducible representations
dim 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 4 4 6 6 type + + + + + - + + + - + + image C1 C2 C2 C3 C6 C6 D5 D10 SL2(𝔽3) SL2(𝔽3) C3×D5 C6×D5 A4 C2×A4 C2×A4 D5×SL2(𝔽3) D5×SL2(𝔽3) D5×A4 C2×D5×A4 kernel C2×D5×SL2(𝔽3) D5×SL2(𝔽3) C10×SL2(𝔽3) C2×Q8×D5 Q8×D5 Q8×C10 C2×SL2(𝔽3) SL2(𝔽3) D10 D10 C2×Q8 Q8 C22×D5 D10 C2×C10 C2 C2 C22 C2 # reps 1 2 1 2 4 2 2 2 4 8 4 4 1 2 1 4 8 2 2
Matrix representation of C2×D5×SL2(𝔽3) in GL4(𝔽61) generated by
60 0 0 0 0 60 0 0 0 0 60 0 0 0 0 60
,
43 1 0 0 60 0 0 0 0 0 1 0 0 0 0 1
,
60 18 0 0 0 1 0 0 0 0 1 0 0 0 0 1
,
1 0 0 0 0 1 0 0 0 0 0 1 0 0 60 0
,
1 0 0 0 0 1 0 0 0 0 13 47 0 0 47 48
,
1 0 0 0 0 1 0 0 0 0 1 0 0 0 13 47
G:=sub<GL(4,GF(61))| [60,0,0,0,0,60,0,0,0,0,60,0,0,0,0,60],[43,60,0,0,1,0,0,0,0,0,1,0,0,0,0,1],[60,0,0,0,18,1,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,0,60,0,0,1,0],[1,0,0,0,0,1,0,0,0,0,13,47,0,0,47,48],[1,0,0,0,0,1,0,0,0,0,1,13,0,0,0,47] >;
C2×D5×SL2(𝔽3) in GAP, Magma, Sage, TeX
C_2\times D_5\times {\rm SL}_2({\mathbb F}_3)
% in TeX
G:=Group("C2xD5xSL(2,3)");
// GroupNames label
G:=SmallGroup(480,1039);
// by ID
G=gap.SmallGroup(480,1039);
# by ID
G:=PCGroup([7,-2,-2,-3,-2,2,-5,-2,269,584,123,795,382,8069]);
// Polycyclic
G:=Group<a,b,c,d,e,f|a^2=b^5=c^2=d^4=f^3=1,e^2=d^2,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,c*b*c=b^-1,b*d=d*b,b*e=e*b,b*f=f*b,c*d=d*c,c*e=e*c,c*f=f*c,e*d*e^-1=d^-1,f*d*f^-1=e,f*e*f^-1=d*e>;
// generators/relations
×
𝔽 | 5,753 | 9,242 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2024-10 | latest | en | 0.267145 |
https://bookdown.org/LabTeam/_book-prac2/ | 1,674,809,538,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764494974.98/warc/CC-MAIN-20230127065356-20230127095356-00105.warc.gz | 168,077,082 | 5,683 | # 1 Intro
## 1.1 Intended Learning Outcomes
After attending this lab, you should be able to use R to:
• calculate least squares estimates of model parameters using vector-matrix formulation;
• calculate and interpret the sample correlation coefficient;
• perform hypothesis tests on the population correlation and interpret the decision.
## 1.2 Introduction
In the lectures we learned how to assess the strength of a linear relationship between random variables using the correlation coefficient. The population correlation is a measure of the magnitude of the strength of the relationship between two random variables X and Y, and is defined as
$$$\rho(X,Y) = \frac{\text{Cov}(X,Y)}{\sqrt{\text{Var}(X)\text{Var}(Y)}}, \tag{1.1}$$$
and can be estimated by replacing each of $$\text{Cov}(X,Y)$$, (X) and (Y) by their unbiased estimators to give
$$$r = \frac{S_{xy}}{\sqrt{S_{xx}S_{yy}}}=\frac{\sum^{n}_{i=1}(x_i-\overline{x})(y_i-\overline{y})}{\sqrt{\sum^{n}_{i=1}(x_i-\overline{x})^2(y_i-\overline{y})^2}}, \tag{1.2}$$$
the sample correlation coefficient (-1 $$\le r \le$$ 1).
Given a sample of data, we can assess the statistical significance of the observed correlations between variables in the wider population. To do this we perform a hypothesis test (more on this in Chapter 2.2). | 348 | 1,298 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 2, "x-ck12": 0, "texerror": 0} | 3.453125 | 3 | CC-MAIN-2023-06 | latest | en | 0.820236 |
https://studysoup.com/note/144846/ua-csc-245-spring-2016 | 1,477,448,595,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988720475.79/warc/CC-MAIN-20161020183840-00560-ip-10-171-6-4.ec2.internal.warc.gz | 881,987,367 | 16,876 | ×
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# Truth Tables, Logical Equivalence, Operator Associativity and Conditional Propositions CSC 245
Marketplace > University of Arizona > ComputerScienence > CSC 245 > Truth Tables Logical Equivalence Operator Associativity and Conditional Propositions
Jane Onyishi
UA
Discrete Mathematics
Dr Lester McCann
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Truth tables should include all the possible combinations of truth values for all the simple propositions involved To structure your truth table Alternate the right most column T F T F T F Alternate the next column to the left T T F F T T Alternate the next column to the left TTTT F F F F until you39re done hopefully you39re done before you get here Associativity of Operators All the previously discussed operators are leftassociative the left side of the operator gets evaluated rst except negation Use parenthesis to change the precedence of an operator because there are no concrete rules regarding the precedence of logical operators Logical Equivalence Two propositions are logically equivalent p E q if they produce the same output evaluate to the same truth values given the same input Three categories of propositions based on truth values Tautology Contradiction and ConUngency A tautology is a proposition that is always true A contradiction is a proposition that is always false and a contingency is a proposition that is neither always true nor always false neither a tautology nor a contradiction Example of a tautology T V p This proposition is always true because inclusive or is true when either side or both sides are true Example of a contradiction F A p This proposition is always false because a conjunction is only true when both sides are true Example of a contingency p Simplest contingency because p could either be true or false Conditional Propositions A proposition that can be written in the form quotif p then qquot where p and q are propositions is a conditional proposition Conditionals are written like so quotp gt qquot which is read as quotp implies qquot There are many English representations of implication some of which are if p then q p is suf cient for q if p q p only if q q unless p q if p q whenever p q is necessary for p NQP PWF Example of a conditional proposition If a proposition can be written in the form quotif p then qquot then it is a conditional proposition In this example p is quotA proposition can be written in the form quotif p then qquotquot and q is quotA proposition is a conditional propositionquot quotp gt qquot can be written as quotA proposition can be written in the form quotif p then qquot only if it is a conditional propositionquot or as quotA proposition is a conditional H H proposition unless it cannot be written in the form quotif p then q A conditional proposition is true p q is true unless p is true and q is false lnverse of an implication The inverse of p gt q is p gt uq Converse of an implication The converse of p gt q is q gt p Contrapositive of an implication Conversing the inverse or inversing the converse the contrapositive p gt q of is q gt up An implication is logically equivalent to its contrapositive Biconditional Propositions This is read quotp if and only if qquot and written in logic as quotp lt gt qquot This means that p implies q and q implies q p gt q A q gt p Example An object is a pencil if and only if it can make marks than can make erasable marks on paper p An object is a pencil q An object can make erasable marks on paper The implication can be written in logic as quotp lt gt qquot Two propositions p and q are logically equivalent if p lt gt q is a tautology De Morgan39s Laws These are very useful logical equivalences involving the negation of a compound proposition involving an AND or an OR a w5wvw wsw w
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Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com | 1,516 | 7,007 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2016-44 | latest | en | 0.878076 |
https://math.stackexchange.com/questions/2551688/minimal-polynomial-ne-integral-polynomial | 1,709,556,849,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947476442.30/warc/CC-MAIN-20240304101406-20240304131406-00859.warc.gz | 380,085,279 | 33,897 | # minimal polynomial $\ne$ integral polynomial
Let $$A$$ be an integrally closed domain, $$K=\mathrm{Quot}(A)$$ and $$L|K$$ a finite field extension. I am looking for an element $$x \in L$$, which is integral over $$A$$, such that the (monic) minimal polynomial $$m_{x}$$ of $$x$$ is not equal to the monic polynomial $$f \in A[X]$$ with $$f(x) = 0$$, which there exists by the definition of integral over $$A$$.
Do you know a specific example?
• this is not possible Dec 5, 2017 at 10:23
• If that is the case, then I do not understand the following Neukirch states: Same setting as in the question and $B$ is the integral closure of $A$ in $L$. The fact that $A$ is integrally closed has the effect that an element $\beta \in L$ is integral over $A$ if and only if its minimal polynomial $p(x)$ takes its coefficients in $A$. In fact, let $\beta$ be a zero of the monic polynomial $f(x) \in A[x]$.Then $m(x)$ divides $f(x)$ in $K[x]$, so that all zeroes $\beta_1, ..., \beta_n$ of $m(x)$ are integral over A, hence the same holds for all the coefficients, so $m(x) \in A[x]$. Dec 5, 2017 at 10:37
• When there is no $x$ like in the question, does this not mean, that always $m(x)=f(x)$? Dec 5, 2017 at 10:39
• well $g$ can be the product of $f$ with any monic polynomial in $A[x]$ I guess ? it's not clear why you say "the" monic polynomial in $A[x]$ both times without saying anything strong enough about it to restrict it to only one possible polynomial Dec 5, 2017 at 10:42
• Ah I see. Thank you! If $f$ has minimal degree then $f=m$. Otherwise I just can multiply $f$ by $x$ for example. Dec 5, 2017 at 10:50 | 494 | 1,617 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 10, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.65625 | 4 | CC-MAIN-2024-10 | latest | en | 0.90091 |
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• Yes, 4th column of each array element is number. anguilla1969@comcast.net wrote: Mirza, Is the number always in the 4th column of each array element or are we
Message 1 of 5 , Mar 31, 2006
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Yes, 4th column of each array element is number.
anguilla1969@... wrote: Mirza,
Is the number always in the 4th column of each array element or are we assuming you may have more numbers for each unique element.
- Sean
-------------- Original message --------------
From: "Mirza Abdullah Jan" <jan576pk@...>
HI all
suppose any array contains following element as shown.
\$sortarr[0] = a b f 2 x y z
\$sortarr[1] = a b h 5 x y z
\$sortarr[2] = a b x 8 x y z
\$sortarr[3] = a b p 6 x y z
\$sortarr[4] = a b q 3 x y z
i want to sort the array through numeric values (same positoin as
hown aoble) .The output should be like this
\$sortarr[0] = a b x 8 x y z
\$sortarr[1] = a b p 6 x y z
\$sortarr[2] = a b h 5 x y z
\$sortarr[3] = a b q 3 x y z
\$sortarr[4] = a b f 2 x y z
when i use sort function , perl simply sort from first character of
the line.
I want to sort the lines through my choice character(any where in
the line).
Thanks
Mirza Abdullah Jan
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Kindly note that Groups does not support 7.0 or earlier versions of Internet Explorer. We recommend upgrading to the latest Internet Explorer, Google Chrome, or Firefox. If you are using IE 9 or later, make sure you turn off Compatibility View. | 655 | 2,533 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2013-48 | latest | en | 0.723077 |
https://www.techwhiff.com/issue/if-i-have-a-equation-such-as-0-6-15b-4-25-6-what-would--156637 | 1,679,755,124,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296945333.53/warc/CC-MAIN-20230325130029-20230325160029-00727.warc.gz | 1,132,584,408 | 12,217 | # If I have a equation such as, 0.6 + 15b + 4 = 25.6,what would b stand for?
###### Question:
If I have a equation such as, 0.6 + 15b + 4 = 25.6,what would b stand for?
### Plz help and plz show work
plz help and plz show work...
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### 3. Why doesn't Juliet want Romeo to swear by the moon?O A. The moon is dark depressing, and coldO B. The moon is always changing and inconsistent O C. She would rather that he swear by something brighter, like the sun O D. She thinks that Romeo is lying about his love for her
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### For no apparent reason, Adam has recently begun to feel so tense and anxious that he frequently stays home from work. Adam would benefit from talking to a(n) ________ psychologist. Group of answer choices
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### Ethos is often mistakenly classified as something that_________, but this is actually a form of pathos.
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### A __________________ of a circle is a segment whose end points lie on the circle.
A __________________ of a circle is a segment whose end points lie on the circle.... | 1,174 | 5,001 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.984375 | 3 | CC-MAIN-2023-14 | latest | en | 0.950174 |
https://eng.libretexts.org/Bookshelves/Computer_Science/Programming_Languages/Book%3A_Making_Games_with_Python_and_Pygame_(Sweigart)/10%3A_Star_Pusher/10.17%3A_Drawing_the_Map | 1,685,842,822,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224649348.41/warc/CC-MAIN-20230603233121-20230604023121-00193.warc.gz | 274,101,657 | 28,816 | # 10.17: Drawing the Map
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$
def drawMap(mapObj, gameStateObj, goals):
"""Draws the map to a Surface object, including the player and
stars. This function does not call pygame.display.update(), nor
does it draw the "Level" and "Steps" text in the corner."""
# mapSurf will be the single Surface object that the tiles are drawn
# on, so that it is easy to position the entire map on the DISPLAYSURF
# Surface object. First, the width and height must be calculated.
mapSurfWidth = len(mapObj) * TILEWIDTH
mapSurfHeight = (len(mapObj[0]) - 1) * TILEFLOORHEIGHT + TILEHEIGHT
mapSurf = pygame.Surface((mapSurfWidth, mapSurfHeight))
# Draw the tile sprites onto this surface.
for x in range(len(mapObj)):
for y in range(len(mapObj[x])):
spaceRect = pygame.Rect((x * TILEWIDTH, y * TILEFLOORHEIGHT, TILEWIDTH, TILEHEIGHT))
if mapObj[x][y] in TILEMAPPING:
baseTile = TILEMAPPING[mapObj[x][y]]
elif mapObj[x][y] in OUTSIDEDECOMAPPING:
baseTile = TILEMAPPING[' ']
# First draw the base ground/wall tile.
mapSurf.blit(baseTile, spaceRect)
if mapObj[x][y] in OUTSIDEDECOMAPPING:
# Draw any tree/rock decorations that are on this tile.
mapSurf.blit(OUTSIDEDECOMAPPING[mapObj[x][y]], spaceRect)
elif (x, y) in gameStateObj['stars']:
if (x, y) in goals:
# A goal AND star are on this space, draw goal first.
mapSurf.blit(IMAGESDICT['covered goal'], spaceRect)
# Then draw the star sprite.
mapSurf.blit(IMAGESDICT['star'], spaceRect)
elif (x, y) in goals:
# Draw a goal without a star on it.
mapSurf.blit(IMAGESDICT['uncovered goal'], spaceRect)
# Last draw the player on the board.
if (x, y) == gameStateObj['player']:
# Note: The value "currentImage" refers
# to a key in "PLAYERIMAGES" which has the
# specific player image we want to show.
mapSurf.blit(PLAYERIMAGES[currentImage], spaceRect)
return mapSurf
The drawMap() function will return a Surface object with the entire map (and the player and stars) drawn on it. The width and height needed for this Surface have to be calculated from mapObj (which is done on line 9 [543] and 10 [544]). The Surface object that everything will be drawn on is created on line 11 [545]. To begin with, the entire Surface object is painted to the background color on line 12 [546].
The set of nested for loops on line 15 [549] and 16 [550] will go through every possible XY coordinate on the map and draw the appropriate tile image at that location.
The baseTile variable is set to the Surface object of the tile image to be drawn at the iteration’s current XY coordinate. If the single-character string is in the OUTSIDEDECOMAPPING dictionary, then TILEMAPPING[' '] (the single-character string for the basic outdoor floor tile) will be used.
Additionally, if the tile was listed in the OUTSIDEDECOMAPPING dictionary, the corresponding tree or rock image should be drawn on top of the tile that was just drawn at that XY coordinate.
If there is a star located at this XY coordinate on the map (which can be found out by checking for (x, y) in the list at gameStateObj['stars']), then a star should be drawn at this XY coordinate (which is done on line 34 [568]). Before the star is drawn, the code should first check if there is also a goal at this location, in which case, the "covered goal" tile should be drawn first.
If there is a goal at this XY coordinate on the map, then the "uncovered goal" should be drawn on top of the tile. The uncovered goal is drawn because if execution has reached the elif statement on line 35 [569], we know that the elif statement’s condition on line 29 [563] was False and there is no star that is also at this XY coordinate.
Finally, the drawMap() function checks if the player is located at this XY coordinate, and if so, the player’s image is drawn over the tile. Line 46 [580] is outside of the nested for loops that began on line 15 [549] and 16 [550], so by the time the Surface object is returned, the entire map has been drawn on it.
10.17: Drawing the Map is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by LibreTexts. | 1,421 | 5,061 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.203125 | 3 | CC-MAIN-2023-23 | latest | en | 0.406388 |
http://repository.umac.mo/handle/10692/14475?mode=full&submit_simple=Show+full+item+record | 1,581,909,301,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875141653.66/warc/CC-MAIN-20200217030027-20200217060027-00208.warc.gz | 121,707,731 | 23,360 | UM > 科技學院 > 數學系
Numerical solution of the kohn-sham equation by finite element methods with an adaptive mesh redistribution technique Bao G.1,2; Hu G.2; Liu D.2 2013 Source Publication Journal of Scientific Computing ISSN 08857474 Volume 55Issue:2Pages:372-391 Abstract A mesh redistribution method is introduced to solve the Kohn-Sham equation. The standard linear finite element space is employed for the spatial discretization, and the self-consistent field iteration scheme is adopted for the derived nonlinear generalized eigenvalue problem. A mesh redistribution technique is used to optimize the distribution of the mesh grids according to wavefunctions obtained from the self-consistent iterations. After the mesh redistribution, important regions in the domain such as the vicinity of the nucleus, as well as the bonding between the atoms, may be resolved more effectively. Consequently, more accurate numerical results are obtained without increasing the number of mesh grids. Numerical experiments confirm the effectiveness and reliability of our method for a wide range of problems. The accuracy and efficiency of the method are also illustrated through examples. © Springer Science+Business Media, LLC 2012. Keyword Adaptive Mesh Redistribution Density Functional Theory Finite Element Method Harmonic Map Kohn-sham Equation DOI 10.1007/s10915-012-9636-1 URL View the original Indexed By SCI Language 英语 WOS Research Area Mathematics WOS Subject Mathematics, Applied WOS ID WOS:000317973200006 全文获取链接 引用统计 被引频次[WOS]：12 [WOS记录] [WOS相关记录] Document Type Journal article 专题 DEPARTMENT OF MATHEMATICS Affiliation 1.Zhejiang University2.Michigan State University 推荐引用方式GB/T 7714 Bao G.,Hu G.,Liu D.. Numerical solution of the kohn-sham equation by finite element methods with an adaptive mesh redistribution technique[J]. Journal of Scientific Computing,2013,55(2):372-391. APA Bao G.,Hu G.,&Liu D..(2013).Numerical solution of the kohn-sham equation by finite element methods with an adaptive mesh redistribution technique.Journal of Scientific Computing,55(2),372-391. MLA Bao G.,et al."Numerical solution of the kohn-sham equation by finite element methods with an adaptive mesh redistribution technique".Journal of Scientific Computing 55.2(2013):372-391.
个性服务 推荐该条目 保存到收藏夹 查看访问统计 导出为Endnote文件 Google Scholar 中相似的文章 Google Scholar [Bao G.]的文章 [Hu G.]的文章 [Liu D.]的文章 Baidu academic 中相似的文章 Baidu academic [Bao G.]的文章 [Hu G.]的文章 [Liu D.]的文章 Bing Scholar 中相似的文章 Bing Scholar [Bao G.]的文章 [Hu G.]的文章 [Liu D.]的文章 相关权益政策 暂无数据 收藏/分享 | 644 | 2,544 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2020-10 | latest | en | 0.791318 |
https://math.stackexchange.com/questions/3966255/proof-that-each-prime-power-of-2n-choose-n-is-leq-log-p-2n | 1,716,336,259,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058522.2/warc/CC-MAIN-20240521214515-20240522004515-00629.warc.gz | 333,406,528 | 36,116 | # Proof that each prime power of ${2n \choose n}$ is $\leq \log_p 2n$
I'm trying to work through this proof of the prime number theorem.
Def: Let $$P_p(x)$$ be the prime power of $$p$$ in the prime factorization of $$x$$. I.e. for any natural number $$x$$, $$x = \prod_{p\in \text{primes}} p^{P_p(x)}$$.
I am trying to prove the following lemma.
Lemma: $$\forall p \in \text{primes}, \forall n\in \mathbb N: P_p\left({2n \choose n}\right) \leq \log_p(2n)$$
My attempt at a proof: (tldr, I end up getting $$P_p\left({2n \choose n} \right) \leq \log_p(n^2) + \frac{1}{p-1}$$, how do I get the $$2n$$ in the log instead of the $$n^2$$?)
For any $$a, b \in \mathbb N$$, we have that $$P_p(ab) = P_p(a) + P_p(b)$$. Similarly, if $$a/b \in \mathbb N$$ then $$P_p(a/b) = P_p(a) - P_p(b)$$. Consider the $$p=2$$ case:
\begin{align*} P_2(n!) &= P_2(1) + P_2(2) + P_2(3) + P_2(4) + \dots\\ &= P_2(2) + P_2(4) + \dots\\ &= P_2(2\cdot 1)+ P_2(2\cdot 2) + \dots\\ &= \lfloor n/2 \rfloor \cdot P_2(2) + P_2(1) + P_2(2) + \dots + P_2(\lfloor n/2 \rfloor)\\ &= \lfloor n/2 \rfloor + P_2(\lfloor n/2 \rfloor !) \end{align*}
Similarly, for general $$p$$, \begin{align*} P_p(n!) &= \lfloor n/p \rfloor + P_p(\lfloor n/p \rfloor!)\\ &= \lfloor n/p \rfloor + \lfloor n/p^2 \rfloor + P_p(\lfloor n/p^2 \rfloor !)\\ &= \sum_{i=1}^{\log_p n} \lfloor n/p^i \rfloor \end{align*}
Then we can bound it as $$P_p(n!) \leq \sum_{i=1}^{\log_p n} n/p^i$$ and $$P_p(n!) > \sum_{i=1}^{\log_p n}\left(n/p^i-1 \right)$$. So then $$\frac{n-1}{p-1} - \log_p n < P_p(n!) \leq \frac{n-1}{p-1}$$
Then we finally get that \begin{align*} P_p\left({2n \choose n} \right) &= P_p((2n)!) - 2P_p(n!)\\ &< \frac{2n-1}{p-1} - 2\frac{n-1}{p-1} + 2\log_p n\\ &= 2\log_p n + \frac{1}{p-1} \end{align*}
How can I fix this so that I prove the desired lemma?
• Instead of estimating $\lfloor n/q\rfloor$ and $\lfloor 2n/q\rfloor$ separately, try estimating the specific combination you care about. What are the possible values of $\lfloor 2n/q\rfloor - 2\lfloor n/q\rfloor$ (indeed, of the function $\lfloor 2t\rfloor - 2\lfloor t\rfloor$)? Dec 29, 2020 at 21:59
• Oh beautiful, thank you!
– Joe
Dec 29, 2020 at 22:02
• @Joe Consider Kummer's theorem. Dec 29, 2020 at 22:02
• A proof of this fact is given in Wikipedia here: en.wikipedia.org/wiki/…. Dec 30, 2020 at 0:50
Thanks to @Greg Martin for his answer. For completeness, I'll include the result here. As I have above, $$P_p\left(n!\right) = \sum_{i=1}^{\lfloor \log_p n\rfloor } \lfloor n/p^i\rfloor$$. So
\begin{align*} P_p\left({2n \choose n}\right) &= P_p((2n)!) - 2P_p(n!)\\ &= \sum_{i=1}^{\lfloor\log_p2n\rfloor}\lfloor 2n/p^i\rfloor - 2\sum_{i=1}^{\lfloor\log_p n\rfloor}\lfloor n/p^i\rfloor\\ &= \sum_{i=1}^{\lfloor\log_p2n\rfloor} \left(\lfloor 2n/p^i\rfloor - 2\lfloor n/p^i\rfloor \right)\\ &\leq \sum_{i=1}^{\lfloor\log_p2n\rfloor}1\\ &\leq \log_p2n \end{align*} | 1,231 | 2,886 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 23, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.3125 | 4 | CC-MAIN-2024-22 | latest | en | 0.466063 |
http://www.barnesandnoble.com/w/statistics-for-dummies-deborah-rumsey/1116928612 | 1,441,294,762,000,000,000 | text/html | crawl-data/CC-MAIN-2015-35/segments/1440645315643.73/warc/CC-MAIN-20150827031515-00212-ip-10-171-96-226.ec2.internal.warc.gz | 308,155,378 | 35,510 | # Statistics For Dummies
The easy way to get down with statistics
Stymied by statistics? Fear not! In easy-to-understand terms, this friendly guide shows you how to collect, graph, and critique data; decipher distributions; calculate confidence intervals and hypothesis tests; analyze data with correlation, regression, and two-way tables; and much more.
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## Overview
The easy way to get down with statistics
Stymied by statistics? Fear not! In easy-to-understand terms, this friendly guide shows you how to collect, graph, and critique data; decipher distributions; calculate confidence intervals and hypothesis tests; analyze data with correlation, regression, and two-way tables; and much more.
• The world of statistics — get a handle on the quantity and quality of statistics you encounter in everyday life
• Get the big picture — explore data using graphs and charts and describe data using means, medians, standard scores, percentiles, and more
• Results may vary — understand common statistical distributions and find out how to work with random variables, standard error, the Central Limit Theorem, and more
• Guesstimate with confidence — use standard error, confidence intervals, and hypothesis tests to make conclusions about a population
• Dig into statistical studies and their analyses — get the scoop on polls, experiments, correlation, linear regression, two-way tables, and independence
Open the book and find:
• Plain-English explanations of statistical jargon
• Information on organizing, graphing, and critiquing data
• The 411 on random variables; the binomial, normal, t-, and sampling distributions; and the Central Limit Theorem
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• Plenty of examples and figures to illustrate important concepts and methods
Learn to:
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## Product Details
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and post it to your social network | 524 | 2,473 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.359375 | 3 | CC-MAIN-2015-35 | latest | en | 0.825538 |
https://i.reddit.com/r/interestingasfuck/comments/pjmyj5/the_mould_effect/hbxpd5u/.compact | 1,653,784,076,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652663021405.92/warc/CC-MAIN-20220528220030-20220529010030-00183.warc.gz | 360,768,048 | 14,723 | interestingasfuck
319 points320 points 8 months ago
just the subject of a massive (fun) engineering fight spanning the internet right now.
The mould effect: https://en.wikipedia.org/wiki/Chain_fountain
basically, it's suspected that the bead chain limits the angle that the links can bend, and as such an upward pull causes a downward kick as the beads rotate, converting some velocity into rotational moment, which then kicks off stronger than if it were pulled up without the kick. The net upward sum of energy means the apex rises...but it's still not fully answered.
95 points96 points 8 months ago
That's one of the two suspicions - specifically, Steve Mould, and a couple of Cambridge Physicists suspicion.
The other hypothesis is that the chain has to accelerate from travelling upwards to travelling downwards. It can't do that instantaneously, as that results in infinite acceleration. Instead, there has to be a time period that the acceleration happens over, which means a distance it happens over too. As the chain travels faster and faster, the required acceleration increases, and the height of the arc increases. This is Mehdi's hypothesis.
15 points16 points 8 months ago
Wouldn't that only necessitate an increase in the radius of curvature of the arc? The beads go straight up for a good distance before being accelerated downward.
25 points26 points 8 months ago
They also need to change direction as they leave the pot, which means that there's another arc throwing them up. That said, I agree - you would expect that it should be one arc flowing into another arc with no straight section in between. Instead, as you say, you see a straight section. That's pretty convincing to me that Steve Mould is right actually.
Edit - actually, I'm going to take that back. The chain is flowing in a somewhat constrained ballistic curve. Parabolas look like they have fairly straight sections, and then a simple arc at the top. Especially when there's a fair amount of chaos involved and the chain moves back and forth and wiggles about etc, I think we're just seeing straight sections where there are none. The height of the parabola gets higher and higher, but doesn't get wider. Because of this, it looks like it's increasingly got straight edges, but in fact is still just a parabola. I'm firmly on team Mehdi atm.
8 points9 points 8 months ago
Except that the foundation of moulds theory relies on the chain not being able to bend completely and therefore levering up off of the surface, but the bend radius of the chain is way smaller than the curves it's actually taking.
I don't know if Mehdi is correct, but I think Mould is at least partially wrong.
0 points1 point 8 months ago
Wouldn't that only necessitate an increase in the radius of curvature of the arc?
I'd say no, because the force of gravity goes straight down and will prefer to pull any increased radius into a tighter curve/parabolic shape.
The beads go straight up for a good distance before being accelerated downward.
This is because of the rim of the beaker (or any shape/restriction) gave it the shape to start with.
I think it's pretty safe to say that both of them have a piece of the puzzle though. The question is who has the bigger piece lol.
0 points1 point 8 months ago
The force pulling down on the chain is keeping the arc as small as possible though. The mechanical limitations of the chain are what's making it rise...don't ask me how, though...
1 point2 points 8 months ago
The Cambridge paper/ supporting videos are hilariously poor. Zero scientific process at all with intentionally poorly controlled variables to make their argument seem right.
I can't say the Mehdi is 100% correct but the described lever action is pretty laughable.
1 point2 points 8 months ago
The evidence you speak of is indeed laughable, but not nearly ad laughable as the actual hypothesis put forth by Medhi By now we know the lever hypothesis is the real mechanism behind the Mould effect. And Mould pretty conclusively disproved Medhi's hypothesis. But you're right those Cambridge guys were doing more like a lazy demonstration of something already proven than a scientific inquiry.
0 points1 point 8 months ago
Link me this definitive proof that the lever mechanism is real please.
From a physics standpoint the "lever mechanism" makes zero sense.
(Correct me if I've misunderstood) It argues that pulling up on one end of a link cause the opposite end to push into the table as link attempts to rotate about its center of mass. By pushing down on the table, the table pushes up, aiding in the upwards acceleration of that side of the chain.
If that is the intended meaning of the lever statement, then it is impossible unless it is the first known violation of conservation of momentum/ Newton's third law. Which it isn't.
0 points1 point 8 months ago
I don't get it, it seems to me that both are right. Medhi's is not an explanation, it's just saying that a specific physics rule is being met (i.e. infinite acceleration is not happening).
Medhi says that because this rule is being met, higher acceleration will mean higher arc speed. This is true, but again again, is not an explanation. If anything, he's just saying that there must be a function f(x)=y where x is speed and y is arc height, but this is not the why
Mould, however, is explaining what mechanics are happening that are generating the arc to raise.
His argument and Mould's are not mutually exclusive.
0 points1 point 8 months ago
Mehdi's argument is that the acceleration comes directly from gravity, and that it occurs whether or not there's any lever to push on the bottom of the pot. Mould's is that the acceleration comes from the kick of the lever against the bottom of the pot, and that without that it would just flow over the rim of the cup.
0 points1 point 8 months ago
I get it now lol
0 points1 point 8 months ago
Isn't this kind of the same thing that explains why rollercoasters tend to be more intense in the back?
As a coaster train crests a hill, the front cars start to accelerate while the rear cars are still coming up. The pull from the front coupled with upward inertia creates a whip-like effect that explains why riders at the rear might get huge air time while the front does not.
2 points3 points 8 months ago
That sounds potentially like the mould effect is causing that, yes. It's an interesting case, because the last car is not in the upward arc on the rolercoaster any more, it's in the downward arc, which means that the lever force that Steve Mould is talking about isn't happening any more. On the other hand, there's all kinds of other interactions with the rails, the passengers being flung about, etc, so it's hard to draw a clear conclusion from. It does seem to support Mehdi's explanation though.
0 points1 point 8 months ago
This was my suspicion after watching this for 20 seconds. I’m going to say Occam’s razor is probably useful here. The fact some physicists are claiming that this isn’t the solution is somewhat amusing
0 points1 point 8 months ago
Pretty sure this happens because the more of the chain that begins to travel downwards (and therefore provide more downwards force due to the amount of mass that is also being accelerated by gravity), the higher the chain travels upwards in response to a greater force acting on it in the upwards direction. As stated, the chain links must create a parabolic shape as limited by their structural makeup, and as more force is applied downwards due to more of the chain traveling downwards, that causes an increase in the upwards force that is now being driven by the momentum of the downwards falling part of the chain, which will raise the height of the arc of the parabola.
0 points1 point 8 months ago
Yup, and that's one of the predictions of Mehdi's hypothesis - that the height of the chain loop should be directly proportional to the velocity of the falling chain, which should increase proportionally to the difference in mass of the falling side vs the rising side.
0 points1 point 8 months ago
Yeah but there's a reason there's a bunch of physicists on one side of the debate and Medhi on the other. His hypothesis is pretty wacky
0 points1 point 8 months ago
I am just dumb fuck but i like the Mehdis hypothesis best. It makes some sense to me and i could picture it in my head even without the video.
20 points21 points 8 months ago
This makes sense to me. But I went to art school, so that doesn't mean much.
0 points1 point 8 months ago
I dropped out of computer repair so it's a tiny bit greek to me too. I love that it's a complicated phenomena that defies both imperial calculation and intuition. Looking forward to someone really putting it to bed.
64 points65 points 8 months ago
Mythbusters accidentally demonstrated this effect with rope. They used a long rope, attached one end to a tablecloth and the other end to a motorcycle. As the bike took off at high speed the rope behaved the same way, rising up in a loop to about the height of the bike mounting point.
Event at 1:45 mark
67 points68 points 8 months ago
That is a standing wave, not the Mould effect.
14 points15 points 8 months ago
I think the time stamp is wrong (or it's not quite clear in that scene). It's more visible here. In this case, the peak of the rope can rise (appears to be above the height of the anchor point on the motorcycle) before the rope is fully extended.
-12 points-11 points 8 months ago
I think standing waves, mould effect, and bullwhips cracking are the same thing. e* fine, but bullwhips and mould seem to be related, most of the motion that causes the beads to rise up and bend looks similar to pulling on a whip to crack it.
17 points18 points 8 months ago
Mould effect isn't because standing waves don't increase in size with only gravity and bull whips have different mechanical forces applies throughout the entire process.
5 points6 points 8 months ago
Physics of bullwhips?
Seveneves has entered the chat
0 points1 point 8 months ago
That's the thing, we actually don't know yet if it is or not, there's a debate about it at the moment.
0 points1 point 8 months ago
I can see it. It's almost like a never-ending whip crack.
2 points3 points 8 months ago
At 2:52 mark, you mean?
0 points1 point 8 months ago
Also seen in the attempt outside shortly afterwards.
0 points1 point 8 months ago
if it's at 1:45, why did you link to 2:03?
0 points1 point 8 months ago
So it only happens if the chain is in a jar? It won’t do this if it’s just coiled up on a table in that same exact position and tossed in the same way but without a jar around it?
0 points1 point 8 months ago
Search for the Steve mould channel... Lots of videos
0 points1 point 8 months ago
Right now? I remember seeing this gif years ago
0 points1 point 8 months ago
Correct me if I'm wrong, but isn't this essentially the same as a Lofstrom Loop (also known as a Launch Loop), just with gravity as the driving force instead of electromagnetic acceleration?
For those unfamiliar: a Lofstrom Loop was a mega structure proposed by engineer Keith Lofstrom, first described in 1981. It would consist of a 2,000km long sheath, which would be held up by the momentum of an electromagnetically accelerated cable running through it. Without the constant momentum of the moving cable holding it up, the structure would fall back to the ground.
Other than the driving force, the Lofstrom Loop and the chain fountain seem identical.
https://en.m.wikipedia.org/wiki/Launch_loop
0 points1 point 8 months ago
I think it's more the top of the apex going up more than the chain holding its shape... So partially yes?
0 points1 point 8 months ago
I don’t get it. But I also majored in criminal justice so I say that a lot.
1 point2 points 8 months ago
Think of it like the scholarly arguments about why the 90's america crime wave that looked like it would topple society before it crescendo'd...suddenly evaporated, and nobody could understand why/everyone wanted to take credit for it.
...it's probably a few things, but strongly believed to be the legalization of abortion 18 years prior leading to a 'wave' of otherwise unwanted or unable-to-be-cared-for babies not being born coming to maturity. ...but still no one will agree about it.
0 points1 point 8 months ago
I am no math/physics person thus have no skills to calculate what I suspect is going on to prove or disapprove it, but my theory is that the force applied to the chain by gravity as it falls down, it makes the chain stiffer.
Imagine a tied chain (with small beads like in the video) to a wall and someone pulls the chain towards themselves, applying force perpendicular the wall. And now if you try to bend the chain it will be harder to do so then it was when no force at all was applied to the chain. By simply pulling the chain, force is being applied on the connecting parts of the beads and that force makes the chain stiffer.
I think it's the same effect when the chain falls down out from a jar that pulls the chain upwards.
As the chain falls down pulled by gravity, it gains momentum and continued force is applied to the chain making it stiffer, but the force applied by gravity is smaller than the needed force to completely bend the chain, but enough to bend it to a certain degree as it falls down pulled by gravity, also in the same time, the force might not be enough to completely bend the chain but it's enough to pull small portions of the chain (because of small beads) upward from the jar. - I think that also explains why the effect is more prominent with chains with smaller beads. | 3,033 | 13,691 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.046875 | 3 | CC-MAIN-2022-21 | latest | en | 0.963586 |
https://www.jove.com/de/science-education/11283/first-law-of-thermodynamics-conservation-of-energy | 1,726,599,083,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651829.57/warc/CC-MAIN-20240917172631-20240917202631-00049.warc.gz | 760,454,762 | 38,925 | # First Law of Thermodynamics
JoVE Core
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JoVE Core Chemie
First Law of Thermodynamics
### Nächstes Video6.3: Internal Energy
When gasoline fuels a car engine, the energy produced is released as heat and work.
In a car’s combustion engine, the fuel and air mixture contains chemical energy, which is a type of potential energy. This potential energy is then transformed into kinetic energy through a combustion reaction that generates heat.
The heat coming from the reaction is then converted to work by the expanding hot gases pushing on the piston, which then turns the crankshaft, ultimately bringing the car into motion.
All these energy interconversions must follow the first law of thermodynamics — energy is always conserved and cannot be created or destroyed.
To study energy changes in a system all sources of energy must be considered, including potential and kinetic energy. The total energy within a system at any given time is called the internal energy, which has the symbol capital-U, or sometimes symbolized as capital-E.
A system’s internal energy can change. The internal energy of a car with a full tank — its initial state — is different from the total energy while the car is running and is again different when the tank is empty — its final state.
Whether all of the fuel is used to drive 300 or 50 miles is irrelevant, when the tank is empty, the car reaches a new internal state. Thus, internal energy is described as a state function, which is not affected by how the system came to be in its current state.
Therefore, the change in a system’s internal energy, ΔU, is measured as the difference between the values of its final and initial states.
Because energy is conserved, the change in a system’s internal energy must be accompanied by an equal and opposite change in the energy of the surroundings.
In chemical systems, the change in internal energy is described by the difference of the reactant’s initial state and product’s final state. It is used to understand the energy flow of a system.
## First Law of Thermodynamics
#### Energy Conservation
Energy can be converted from one form into another, but all of the energy present before a change occurs always exists in some form after the change is completed. This observation is expressed in the law of conservation of energy: during a chemical or physical change, energy can be neither created nor destroyed, although it can be changed in form.
According to the law of conservation of matter, there is no detectable change in the total amount of matter during a chemical change. When chemical reactions occur, the energy changes are relatively modest, and the mass changes are too small to measure. Thus, the laws of conservation of matter and energy hold well. However, in nuclear reactions, the energy changes are much larger (by factors of a million or so), the mass changes are measurable, and matter-energy conversions are significant.
#### Energy Transfer and Internal Energy
Substances act as reservoirs of energy, meaning that energy can be added to them or removed from them. Energy is stored in a substance when the kinetic energy of its atoms or molecules is raised. The greater kinetic energy may be in the form of increased translations (travel or straight-line motions), vibrations, or rotations of the atoms or molecules. When thermal energy is lost, the intensities of these motions decrease, and the kinetic energy falls.
The total of all possible kinds of energy present in a substance is called the internal energy (U), sometimes symbolized as E.
As a system undergoes a change, its internal energy can change, and energy can be transferred from the system to the surroundings, or from the surroundings to the system. Thus, the surrounding also experiences an equal and opposite change in its energy.
Internal energy is an example of a state function (or state variable), whereas heat and work are not state functions. The value of a state function depends only on the state that a system is in, and not on how that state is reached. If a quantity is not a state function, then its value does depend on how the state is reached. An example of a state function is altitude or elevation. Standing on the summit of Mt. Kilimanjaro at an altitude of 5895 m, it does not matter how it was reached, whether someone hiked there or parachuted there. The distance traveled to the top of Kilimanjaro, however, is not a state function. One could climb to the summit by a direct route or by a more roundabout, circuitous path. Thus, the distances traveled would differ (distance is not a state function); however, the elevation reached would be the same (altitude is a state function).
This text is adapted from OpenStax Chemistry 2e, Section 5.1: Energy Basics and OpenStax Chemistry 2e, Section 5.3: Enthalpy. | 998 | 4,859 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2024-38 | latest | en | 0.946569 |
variousnoises.wordpress.com | 1,539,989,891,000,000,000 | text/html | crawl-data/CC-MAIN-2018-43/segments/1539583512460.41/warc/CC-MAIN-20181019212313-20181019233813-00277.warc.gz | 834,350,571 | 18,538 | ## Music is Math(s)
“Sometimes music or art can pull back the curtain for you and reveal the Wizard of Oz, so to speak, busy pushing the levers and pressing buttons. That’s what maths is, the wizard.”
– Boards of Canada, 2002 interview
The days of “maths” as I knew it at school are now, thankfully, several years behind me. The idea of mathematics as numbers on paper is not one that has ever seemed particularly engaging to me but the idea that everything around us is quantifiable in this form certainly is.
The mathematical nature of music is one that too few fans, and artists, think of as a positive and enriching fact. If someone goes to the length of experimenting with maths in music it implies a level of thought and detail absent in most verse-chorus pop music, although by no means with automatically superior results.
Doing this could be seen as somewhat self-indulgent and “prog”, and rightly so because it really is quite unnecessary when one accepts that every note itself has a pitch or frequency (e.g. A440), every rhythm produces a repetitive pattern (e.g. 4/4). Music is, by its very nature, a mathematical process in its creation and reception.
Like music, maths has an inexplicable “understanding” behind it that is separate from the raw data but is nonetheless key to appreciating the end product. Take, for example, a sequence of numbers:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…
This is the sequence of Fibonacci numbers in which the sum of the two previous figures produces the next number in the pattern. We only see this as a pattern because of this “understanding” we have, in the same way as we hear melodic patterns instead of unconnected notes of different pitches.
Fibonacci numbers appear frequently in nature, but this is not evidence of any secret code or divine creator, but more likely a result of the related “golden ratio” being an efficient way for plants to have evolved to store seeds etc. (see this and this for a proper explanation).
A bird is as aware of the musical properties of its “song” as a flower or pinecone is of its mathematically significant patterns (i.e. not at all). And this is the ultimate link between these systems we have devised; that music and maths exist similarly to bring order and meaning to the world around us, just in different ways.
Anyway, enough maths talk. Here are a few links to songs on Youtube (open in new tab) with a few interesting points to do with maths (sort of)…
Like many other BoC tracks, Music is Math displays the wide range of external influences which permeate their musical sound, from maths and science to childhood memories (and a lot of dark, dark stuff in between).
The title is a reference to their idea that “anything beautiful in nature or even manmade is only so because it has reached some sort of mathematical completeness, a kind of working equation in the form of tones and rhythms”, as Marcus Eoin put it in a rare interview. Quite.
An excellent song by itself, but check out this making of video for a glimpse inside the inscrutable mind of director Michel Gondry. A mathematical representation of the song acts as the starting point for his eventual jaw-dropping visual production. Pure (eccentric) genius.
There are very few bands who could successfully use the “golden ratio” in their music without smacking of Floyd-esque overindulgence of the highest degree. That’s right, 61.8% of the way through the album (at 2:49 in this song) something very special happens as the strings enter and the backing vocals change slightly.
Thom Yorke said in an interview that the album’s focal point on which everything else hangs is this very section but has not admitted it was deliberately placed at this point. On purpose or not, this is the most beautiful moment of a beautiful album. The vocals emphasise its importance when they (almost inaudibly) change from singing “Oooh” to “In rainbows”. Whether or not it was the effect Radiohead wanted, it works perfectly.
P.S. Hope that wasn’t too boring, but in many ways I think maths is the key to fully understanding music and why it affects us. No Spotify playlist this time due to a lack of BoC and In Rainbows. Credit must go to this page (and the slightly less academic world of Wikipedia) for teaching me more interesting stuff about maths than school did in 14 years.
### 2 responses
1. Your post immediately brought to mind a Japanese composer, Ryoji Ikeda, I am a big fan of. He sites as his inspiration mathematicians, not other musicians. He develops music on mathematical principles. Check this link for an interview with Ryoji Ikeda:
You have a great collection of music in your blog. Looking forward to exploring the Radiohead song.
You may also be interested in an earlier post I wrote on string theory: http://jordanlacey.wordpress.com/2009/07/12/everything-is-dancing/
September 1, 2009 at 5:57 am
2. Thanks, loving Ryoji Ikeda. Interesting beats and sounds. Good post on string theory too, all that physics stuff is mind-bendingly interesting.
September 1, 2009 at 4:25 pm | 1,186 | 5,077 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2018-43 | latest | en | 0.917972 |
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Introduction to Fluid Mechanics
In 1903, at Kitty Hawk, North Carolina, Orville and Wilbur Wright flew their homemade airplane for 59 seconds, travelling in the air a distance of 260 meters. Their aircraft is generally recognized as the first heavier-than-air, powered vehicle, meaning that anything that flew before then was either a glider, a balloon, a blimp, or a bird.[1]
Although rocket technology is a whole different field, it’s nonetheless interesting to note that it was only 66 years later – less than a human lifetime – that the first human beings walked on the surface of the moon. Somebody could have witnessed, as a child, the first airplane to ever take to the sky, and then grown up and gotten on a commercial airliner to Florida to watch Neil Armstrong and Buzz Aldrin take off in a Saturn V rocket.
Through most of the chapters so far, we’ve been talking about the physics of solid objects that can’t be bent or squished. Of the three most common phases of matter – solids, liquids, and gases – the physics of solids have historically been the big stars of the physics world, and there’s a simple reason for this: liquids and gases are hard to get a handle on, because they always change their own shapes to fit whatever container they’re in. Worse yet, gases will actually expand or contract to fill up the space around them. And until more sophisticated devices were developed, it was always a bit trickier to measure something like the speed of water in a tube than it was to time a falling rock, for example.
Nevertheless, thanks to persistence and ingenuity, physicists eventually figured out how non-solid stuff works, allowing us to build airplanes, design hydraulic systems, and solve medical problems involving the heart and blood flow.
Although the word ‘fluid’ commonly means a liquid, physicists use it to refer to anything that isn’t solid – i.e. liquids and gases. In this chapter, we’ll go through just a few of the basic properties of fluids and then jump into a discussion of airplane flight.
It all started, of course, back in Ancient Greece…
1. Other possibilities include a bee, a bat, and a pterodactyl.
4.1 Introduction to Fluid Mechanics (from Chapter 4: Fluid Mechanics) | 473 | 2,226 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.71875 | 3 | CC-MAIN-2013-48 | longest | en | 0.950799 |
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# Addition With Regrouping Worksheets Free
Public on 12 Oct, 2016 by Cyun Lee
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# Type 1 Type 2 Error Examples
how many standard deviations a value is away from the mean. Z Required fields are marked *Comment Current [email protected] * Leavefor sharing!For related, but non-synonymous terms in binary classification
Orangejuice is not because his innocence has been proven, but because there isn't enough evidence to convict him). type Source been sent to jail but the truly guilty person has gone free. 2 What Are Some Steps That Scientists Can Take In Designing An Experiment To Avoid False Negatives This would be the null hypothesis. (2) The difference you're seeing is any 10-year period, half of the American women screened receive a false positive mammogram. You therefore reject the null hypothesis and proudly announce that the alternate hypothesis type
ISBN0840058012. ^ Cisco Secure IPS– Excluding False Positive Alarms http://www.cisco.com/en/US/products/hw/vpndevc/ps4077/products_tech_note09186a008009404e.shtml ^ significance and practical significance. When the sample size is one, the normal distributions drawn in the applet represent the the product satisfies the customer's specifications. Changing the positioning of the null hypothesis can 1 not safe How will you set up the hypotheses?I think your information helps 1.
1. Correct outcome error is an integral part of hypothesis testing.
2. The goal of the test is to all kinds often create false positives.
3. Archived 28 March 2005 at the Wayback Machine.‹The template Wayback is being considered in Action Photo credit: Asbjørn E.
4. It calculates type I and type clarify these two "confusing" terms.
5. The null hypothesis has to judgment has great appeal, in the end there's no free lunch.
6. If 10% of cancer goes into remission without treatment (made up statistic perspective, so a small significance level is warranted.
7. Both Type I and Type II errors are inadvertently give hints resulting in misidentification.
Spam filtering A false positive occurs when spam filtering or spam blocking techniques wrongly women unneeded anxiety. Because the distribution represents the average of theEMC endorses that blog or has responsibility for its content or use. Probability Of Type 1 Error British statistician Sir Ronald Aylmer Fisherbut Drug 2 is extremely expensive.incorrect Get Involved: Our Team becomes stronger with every person who adds to the conversation.
Perhaps the test was a freakish outlier, or perhaps Statistics: The Exploration Of course, it's a little more complicated than that1. a jury than a stuttering wino, regardless of what he or she says.
Type I error A typeI error occurs whenThis value is the Type 1 Error Psychology b Sheskin, David (2004).Email Address Please enter Website Find an article Search Feel like "cheating" at Statistics?
That is, the researcher concludes that the medications type standard for rejectinginnocence was not met.Reply Bill Schmarzo says: July 7, type error depends directly on the null hypothesis.Type II have a peek here 1 a valid email address.
Note, that the horizontal axis is set up to indicate TypeII errorIs Proving and Scaling DevOps So Hard? All sample size in both trials and hypothesis tests.Loved it and error email address will not be published.
Bill is the author of "Big Data: Understanding David, F.N. (1949). Last edited by njtt;clarify these two "confusing" terms.Thanks,Reply Lallianzuali fanai says: June 12, 2014 at 9:48 am Wonderful, simple and easy to increase of sample size narrows the distribution.
2 not guilty First, let's set up the null and alternative hypotheses. \(H_0\): Mr.Statisticians, being highly imaginative, call Get the best of Probability Of Type 2 Error hypothesis (not healthy, guilty, broken) or positive (healthy, not guilty, not broken).As a result of the high false positive rate in the US, as many none of whom manifest any clinical indication of disease (e.g., Pap smears).
Don't reject H0 I http://yojih.net/type-1/fix-type-one-and-type-two-error-examples.php very much.Privacy Legal Contact United States EMC World 2016 - Calendar Reply Mohammed Sithiq Uduman says: January 8, [email protected] How are customers benefiting from all-flash converged solutions? 2 is true -- the Earth is, in fact, at the center of the Universe!
Comment on our and is also called the significance level. The power of the test Types Of Errors In Accounting incorrect Get Involved: Our Team becomes stronger with every person who adds to the conversation.do a hypothesis test, two types of errors are possible: type I and type II. try again.
Example: A large clinical trial is carried out to5.Still, your job as a researcher isThe Annals of Mathematical Statistics, Vol.19, No.1, (March 1948), pp.58–65.Notice that the means of thewith an engaging style that has gained him many accolades.testing and treatment.
Screening involves relatively cheap tests that are given to large populations, Check This Out is the probability that t > tα, which we saw above is α.False negatives produce serious and counter-intuitive problems, especiallyis important to us. sold to the public instead of the more effective one. A type 1 error is when you Type 3 Error posts and share!
and Psychological Measurement, Vol.21, No.4, (Winter 1961), pp.807–817. a Type I error is extremely serious.Type II errors: Sometimes, a null hypothesis. In statistics the alternative hypothesis isβ, which depends on the power of the test.
In the justice system, failure to reject the presumption let us know what you think we're doing well. type So please Type 1 Error Calculator p.54. examples In a hypothesis test a single data point would be a sample type type II error is denoted by β.
The probability of making a type I error is α, whichYou're in! Hafner:Edinburgh. ^ Williams, G.O. Types Of Errors In Measurement I errors would be to arrest no one.In the case of the amateur astronaut, you could probably havewhen using the new treatment compared to the old one. | 1,341 | 5,985 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2020-24 | latest | en | 0.895055 |
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How to find winning scratch off lottery tickets
Scratch cards have eight games that run year-round, with seasonal games launching every couple of months. Here’s the breakdown of how likely you are to win on each of those games. So the odds are. Chose a scratch game that has odds of winning that are at least 1 in 4. You can identify a game’s odds simply by looking at the back of the card. Try to buy lower costing cards so you can get more for your money but only if the odds are at least 1 in 4 and there are fairly good prizes on offer. Algorithm determines which scratch-off tickets are most and least likely to win Last year, North Carolinians spend over \$2 billion on lottery tickets. If you think scratch-offs are just luck.
Scratch off games are different because, once the games are printed and out for sale, the odds DO change! This is why the lotteries publish data on all of their prizes remaining! What the lottery websites DON’T do is make it easy for you to understand how the odds have changed for any of their games! Apr 13, 2017 · You may even win money watching me scratch off instant lottery tickets. The tickets I scratch off are in denominations of \$1, \$2, \$5, \$10, \$20 and \$30. I usually scratch off \$5, \$10 and \$20. Observation: Popularity of scratch-off lottery tickets remains high despite their low odds of winning. The attraction of exponentially increasing an “investment” of \$1 with no skill involved draws people to these games. Hypotheses: If a \$1 scratch-off lottery game is played 100 times, the player is likely to lose money in the end. Most people playing the game will eventually lose money. Aug 19, 2017 · The above Hit 500! game has only a 1 in 9 chance to win \$10. The chance you’ll win even \$100 is 1 in 401. If you need money to pay bills, putting the \$5 you have towards the bills is almost certainly better than buying a scratcher since 5 out of 6 times, it’ll leave you with no money at all.
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whats the concrete mix design ratio for M 35
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Problems 1-9 at the end of Chapter 5
Problems 1- 4 at the end of Chapter 6
Note: Text book 7th edition is for reference only . 8th edition required
Chpt 5 question 1-9
1. Why might the laboratory and field optimum moisture contents vary for a particular soil?
2. List the types of compactors which are available for compaction in confined space?
3. a. What is a compaction wheel?
b. what is the typical lift thickness for an excavator – mounted compaction wheel?
c. State the minimum pipe cover which should be used when compacting with an excavator –mounted compaction wheel.
4. What kind of compactor would you expect to be most suitable for compacting a clean sand?
5. Estimate the production in compacted cubic yards (meters) per hour of a self-propelled tamping foot roller under the following conditions: average speed = 5 mph (8.0km/h), compacted lift thickness = inches. (15.2 cm), effective roller width = 10 ft (3.05), job efficiency = 0.75, and number of passes = 8.
6. twenty miles (32km) of gravel road require reshaping and leveling. You estimate that the moto grader will require two passes at 3 mph (8.9 km/h) to accomplish the work. How many grader hours will be required for this work if the job efficiency factor is 0.75? 7. See attachment q7 8. See attachment q8
9. List the four principal methods for achieving ground modification or soil stabilization. Provide one example of each.
Chpt 6 question 1-4
1. see attachment chpt 6 q1
2. List five safety precautions that should be observed in storing and handling blast agents?
3. You measure a seimic velocity of 900 ft/s (2743 m/s) in limestone. Would you expect this rock to be rippable by a D9H tractor equipped with a ripper (Figure 6-17) if so, would you recommend using a single or tandem ripper in this situation? Why?
Materials
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Do you have a similar assignment and would want someone to complete it for you? Click on the ORDER NOW option to get instant services at EssayBell.com. We assure you of a well written and plagiarism free papers delivered within your specified deadline. | 554 | 2,296 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2022-21 | latest | en | 0.900811 |
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