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 |
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https://googology.wikia.org/wiki/Quattuortrigintillion?oldid=232770 | 1,585,645,249,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585370500426.22/warc/CC-MAIN-20200331084941-20200331114941-00303.warc.gz | 461,279,069 | 29,823 | ## FANDOM
10,421 Pages
A quattuortrigintillion is equal to $$10^{105}$$.[1]
In the long scale which is commonly used in France and Germany, $$10^{105}$$ is called septendecilliard.
Sbiis Saibian gave the name googolcrowd, referring to the value of this number.[2]
10105 is also called kumuda.[3]
## Decimal expansion
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
## Approximations
Notation Lower bound Upper bound
Scientific notation $$1\times10^{105}$$
Arrow notation $$10\uparrow105$$
Steinhaus-Moser Notation 59[3] 60[3]
Copy notation 9[105] 10[53]
Taro's multivariable Ackermann function A(3,345) A(3,346)
Pound-Star Notation #*(11,7,10,8,5,8)*11 #*(7,4,5,5,7,7,3)*9
BEAF {10,105}
Hyper-E notation E105
Bashicu matrix system (0)(0)(0)(0)(0)[1910] (0)(0)(0)(0)(0)[1911]
Hyperfactorial array notation 72! 73!
Fast-growing hierarchy $$f_2(340)$$ $$f_2(341)$$
Hardy hierarchy $$H_{\omega^2}(340)$$ $$H_{\omega^2}(341)$$
Slow-growing hierarchy $$g_{\omega^{\omega^2+5}}(10)$$
## List of prefixed numbers derived from trigintillion
Name Short scale Long scale
untrigintillion 1096 10186
duotrigintillion 1099 10192
tretrigintillion 10102 10198
quattuortrigintillion 10105 10204
quintrigintillion 10108 10210
sextrigintillion 10111 10216
septentrigintillion 10114 10222
octotrigintillion 10117 10228
novemtrigintillion 10120 10234
## Sources
-minutia group
n-ary numbers with multipliers
Eyelash mite group: eyelash mite-speck · eyelash mite-crumb · eyelash mite-chunk · (binary/ternary/octal)eyelash mite · eyelash mite-bunch · eyelash mite-crowd · eyelash mite-swarm
Dust mite group: dust mite-speck · dust mite-crumb · dust mite-chunk · (binary/ternary/octal)dust mite · dust mite-bunch · dust mite-crowd · dust mite-swarm
Cheese mite group: cheese mite-speck · cheese mite-crumb · cheese mite-chunk · (binary/ternary/octal)cheese mite · cheese mite-bunch · cheese mite-crowd · cheese mite-swarm
Clover mite group: clover mite-speck · clover mite-crumb · clover mite-chunk · (binary/ternary/octal)clover mite · clover mite-bunch · clover mite-crowd · clover mite-swarm
Pipsqueak group: (binary/ternary/octal)pipsqueak
Little squeaker group: (binary/ternary/octal)little squeaker
Small fry group: (binary/ternary/octal)small fry
Guppy group: (binary/ternary/octal)guppyspeck · (binary/ternary/octal)guppycrumb · (binary/ternary/octal)guppychunk · (ternary/quaternary/quinary/duodecimal/hexadecimal/vigesimal/sexagesimal)guppy(bit/byte)
Minnow group: (binary/ternary/octal)minnowspeck · (binary/ternary/octal)minnowcrumb · (binary/ternary/octal)minnowchunk · (ternary)minnow(bit/byte)
Goby group: (binary/ternary/octal)gobyspeck · (binary/ternary/octal)gobycrumb · (binary/ternary/octal)gobychunk · (ternary)goby(bit/byte) | 1,025 | 2,829 | {"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} | 2.71875 | 3 | CC-MAIN-2020-16 | latest | en | 0.543677 |
http://slideplayer.com/slide/3276489/ | 1,521,720,766,000,000,000 | text/html | crawl-data/CC-MAIN-2018-13/segments/1521257647883.57/warc/CC-MAIN-20180322112241-20180322132241-00337.warc.gz | 276,808,705 | 24,963 | Presentation is loading. Please wait.
# Non-orthogonal regressors: concepts and consequences
## Presentation on theme: "Non-orthogonal regressors: concepts and consequences"— Presentation transcript:
Non-orthogonal regressors: concepts and consequences
overview Problem of non-orthogonal regressors
Concepts: orthogonality and uncorrelatedness SPM (1st level): covariance matrix detrending how to deal with correlated regressors Example
design matrix regressors Scan number Each column in your design matrix represents 1) events of interest or 2) a measure that may confound your results. Column = regressor The optimal linear combination of all these columns attempts to explain as much variance in your dependent variable (the BOLD signal) as possible
= + + error 1 2 x1 x2 e Time BOLD signal
Source: spm course 2010, Stephan
The beta’s are estimated on a voxel-by-voxel basis
high beta means regressor explains much of BOLD signal’s variance (i.e. strongly covaries with signal)
Problem of non-orthogonal regressors
Y total variance in BOLD signal
Orthogonal regressors
Y X2 = + X1 total variance in BOLD signal X1 X2 every regressor explains unique part of the variance in the BOLD signal
Orthogonal regressors
Y X2 = + X1 total variance in BOLD signal X1 X2 There is only 1 optimal linear combination of both regressors to explain as much variance as possible. Assigned beta’s will be as large as possible, stats using these beta’s will have optimal power
non-orthogonal regressors
Y X1 X2 = + Regressor 1 & 2 are not orthogonal. Part of the explained variance can be accounted for by both regressors and is assigned to neither. Therefore, betas for both regressors will be suboptimal
Entirely non-orthogonal
X1 X2 total variance in BOLD signal regressor 2 regressor 1 = + Betas can’t be estimated. Variance can not be assigned to one or the other
“It is always simpler to have orthogonal regressors and therefore designs.“
(spm course 2010)
orthogonality Regressors can be seen as vectors in n-dimensional space, where n = number of scans. Suppose now n = 2 r1 r2 1 2 2 1 1 2 r1 r2
orthogonality Two vectors are orthogonal if raw vectors have
inner product == 0 angle between vectors == 90° cosine of angle == 0 Inner product: r1 • r2 = (1 * 2) + (2 * 1) = 4 θ = acos(4 / (|r1| * |r2|) = about 35 degrees 1 2 r1 r2 35
orthogonality Orthogonalizing one vector wrt another: it matters which vector you choose! (Gram-Schmidt orthogonalization) Orthogonalize r1 wrt r2: u1 = r1 – projr2(r1) u1 = [1 2] – (r1 • r2)/(r2 • r2) u1 = [ ] Inner product: u1 • r2 = (-0.6 * 2) + (1.2 * 1) = 0 1 2 r1 r2 u1
orthogonality & uncorrelatedness
An aside on these two concepts Orthogonal is defined as: X’Y = 0 (inner product of two raw vectors = 0) Uncorrelated is defined as: (X – mean(X))’(Y – mean(Y)) = 0 (inner product of two detrended vectors = 0) Vectors can be orthogonal while being correlated, and vice versa!
Orthogonal because: Inner product 1*5 + -5*1 + 3*1 + -1*3 = 0
please read Rodgers et al. (1984) Linearly independent, orthogonal and uncorrelated variables. The American Statistician, 38: Will be in the FAM folder as well Orthogonal because: Inner product 1*5 + -5*1 + 3*1 + -1*3 = 0 Inner product van orthogonal example geven, laten zien dat ongecorreleerd is. Figuur laten zien waar vectoren orthogonal zijn, en na detrending gecorreleerd zijn. Laat switchen van vectoren zien
Orthogonal, but correlated! 3.75 6.75 -5.25 -0.25
please read Rodgers et al. (1984) Linearly independent, orthogonal and uncorrelated variables. The American Statistician, 38: Will be in the FAM folder as well Detrend: Mean(X) = -0.5 Mean(Y) = 2.5 X_det Y_det ================== Mean(X_det) = 0 Mean(Y_det) = 0 Inner product: 5 Orthogonal, but correlated! 3.75 6.75 -5.25 -0.25 Inner product van orthogonal example geven, laten zien dat ongecorreleerd is. Figuur laten zien waar vectoren orthogonal zijn, en na detrending gecorreleerd zijn. Laat switchen van vectoren zien
r1_det r2_det r1 r2 1.2 1 r1 detrend r2 1 2
orthogonality & uncorrelatedness
Q: So should my regressors be uncorrelated or orthogonal? A: When building your SPM.mat (i.e. running your jobfile) all regressors are detrended (except the grand mean scaling regressor). This is why orthogonal and uncorrelated are both used when talking about regressors update: it is unclear whether all regressors are detrended when building an SPM.mat. This seems to be the case, but recent SPM mailing list activity suggests detrending might not take place in versions newer than SPM99. Donders batch? Include from Guillaume stating this is not the case since SPM99 Explain people talk about orthogonal in the case of uncorrelatedness, and I will do so from now on as well “effectively there has been a change between SPM99 and SPM2 such that regressors were mean-centered in SPM99 but they are not any more (this is regressed out by the constant term anyway).” Link
Your regressors correlate
Despite scrupulous design, your regressors likely still correlate to some extent This causes beta estimates to be lower than they could be You can see correlations using review SPM.mat Design design orthogonality
For detrended data, the cosine of the angle (black = 1, white = 0) between two regressors is the same as the correlation r ! orthogonal vectors cos(90) = 0 r = 0 r2 = 0 correlated vector cos(81) = r = r2 = r2 indicates how much variance is common between the two vectors (2.56% in this example). Note: -1 ≤ r ≤ 1 and 0 ≤ r2 ≤ 1
Correlated regressors: variance from single regressor to shared
Correlated regressors: variance from single regressor to shared
t-test uses beta, determined by amount of variance explained by single regressor.
Correlated regressors: variance from single regressor to shared
t-test uses beta, determined by amount of variance explained by single regressor. Large shared variance: low statistical power
Correlated regressors: variance from single regressor to shared
t-test uses beta, determined by amount of variance explained by single regressor. Large shared variance: low statistical power Not necessarily a problem if you do not intend to test these two regressors! Movement regressor 1 Movement regressor 2
How to deal with correlated regressors?
Strong correlations between regressors are not necessarily a problem. What is relevant is correlation between contrasts of interest relative to the rest of the design matrix Example: lights on vs lights off. If movement regressors correlate with these conditions (contrast of interest not orthogonal to rest of design matrix), there is a problem. If nuisance regressors only correlate with each other, no problem! Grand mean scaling is not centered around 0 (i.e. not detrended), these correlations are not informative
But what about the fact that SPM book says that correlation between contrast and rest of design matrix matters (and not all regressors of interest vs each other and versus movement regressors? A: it is a problem assuming you will test all of your regressors of interest. Then all contrasts will not be orthogonal to the rest of the design matrix
How to deal with correlations between contrast and rest of design matrix?
Orthogonalize regressor A wrt regressor B: all shared variance will now be assigned to B.
orthogonality 1 2 r1 r2
total variance in BOLD signal
orthogonality r1 r2 total variance in BOLD signal regressor 1 regressor 2 1 2
How to deal with correlations between contrast and rest of design matrix?
Orthogonalize regressor A wrt regressor B: all shared variance will now be assigned to B. Only permissible given a priori reason to do this: hardly ever the case
How to deal with correlations between contrast and rest of design matrix?
do an F-test to test overall significance of your model. For example, to see if adding a regressor will significantly improve your model. Shared variance is taken along to determine significance then. In the case where a number of regressors represent the same manipulation (e.g. switch activity, convolved with different hrfs) you can serially orthogonalize the regressors before estimating betas.
Example how not to do it:
2 types of trials: gain and loss Voon et al. (2010) Mechanisms underlying dopamine-mediated reward bias in compulsive behaviors. Neuron
Example how not to do it:
4 regressors: Gain predicted outcome Positive prediction error (gain trials) Loss predicted outcome Negative prediction error (loss trials) Highly correlated! Highly correlated! Highly correlated because they simply are, ESPECIALLY when no jitter is introduced Voon et al. (2010) Mechanisms underlying dopamine-mediated reward bias in compulsive behaviors. Neuron
Example how not to do it:
Performed 6 separate analyses (GLMs) Shared variance is attributed to single regressor in all GLMs Amazing! Similar patterns of activation! Voon et al. (2010) Mechanisms underlying dopamine-mediated reward bias in compulsive behaviors. Neuron
Take home messages If regressors correlate, explained variance in your BOLD signal will be assigned to neither, which reduces power on t-tests If you orthogonalize regressor A with respect to regressor B, values of A will be changed and A will have equal uniquely explained variance. B, the unchanged variable, will come to explain all variance shared by A and B. However, don’t do this unless you have a valid reason. Orthogonality and uncorrelatedness are only the same thing if your data is centered around 0 (detrended, spm_detrend) SPM does (NOT?) detrend your regressors the moment you go from job.mat to SPM.mat
Interesting reads Combines SPM book and Rik Henson’s own attempt at explaining design efficiency and the issue of correlated regressors. Rodgers et al. (1984) Linearly independent, orthogonal and uncorrelated variables. The American Statistician, 38: 15-minute read that describes three basic concepts in statistics/algebra
regressors
x y x y -3 3 3 6 0 -6 6 -3 3 3 9 6 Same vectors, but detrended:
-3 3 0 -6 3 3 Raw vectors: x y 3 6 6 -3 9 6 Inner product: 54 Non-orthogonal inner product: uncorrelated But! Include example here where raw vectors are orthogonal, but after detrending (which is what spm does) the vectors are correlated.
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# Hypothesis testing problems in SPSS.
Not what you're looking for?
Automobile insurance is much more expensive for teenage drivers than for older drivers. To justify this cost difference, insurance companies claim that younger drivers are much more likely to be involved in costly accidents. To test this claim, a researcher obtains information about registered drivers from the department of motor vehicles and selects a sample of n = 300 accident reports from the police department. The motor vehicle department reports the percentage of registered drivers in each age category as follows: 16% are under 20; 28% are 20 to 29 years old, and 56% are age 30 or older. The number of accident reports for each age group is as follows:
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68 92 140
Do the date indicate that the distribution of accidents for the three age groups is significantl different from the distribution of drivers? Test with a = .05.
Do all steps in hypothesis testing
_______________________________________________________________
Mulvihill, Obuseh, and Caldwell(2008) conducted a survey evaluating healthcare providers' perception of a new state childrens insurance program. One question asked the providers whether they viewed the reimbursement from the new insurance as higher,lower, or the same as private insurance. another question assessed the providers overall satisfaction with the new insurance. The following table presents observed frequencies similar to the study results
Satisfied Not Satisfied
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Same or More Reimbursement 42 18 60
________________________________
88 72
Do the results indicate that the providers' satisfaction of the new program is related to their perception of the reimbursement rates? Test with alpha= .05
Do all steps in hypothesis testing
##### Solution Summary
Step by step method for computing test statistic is given in the answer.
##### Solution Preview
Automobile insurance is much more expensive for teenage drivers than for older drivers. To justify this cost difference, insurance companies claim that younger drivers are much more likely to be involved in costly accidents. To test this claim, a researcher obtains information about registered drivers from the department of motor vehicles and selects a sample of n = 300 accident reports from the police department. The motor vehicle department reports the percentage of registered drivers in each age category as follows: 16% are under 20; 28% are 20 to 29 years old, and 56% are age 30 or older. The number of accident reports for each age group is as follows:
Under Age 20 Age 20 to 29 Age 30 and over
68 92 140
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##### Measures of Central Tendency
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How to find the image under the reflection in the y-axis: formula, example, and its solution.
## Formula
The image of a point (x, y)
under the reflection in the y-axis is
(-x, y).
To find the image,
change the sign of the x value.
## Example
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The image of B(5, 4) is,
change the sign of the x value,
B'(-5, 4).
The image of C(3, -2) is,
change the sign of the x value,
C'(-3, -2).
ABC has vertices
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A'B'C' has vertices
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Use these vertices
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[Crypto 198points] A Lost Cause
Written by: Disha Name Credits: Shray
Pirate Keith loves cryptography and has protected his treasure with a very annoying caesar shift. He has witten “CGULKVIPFRGDOOCSJTRRVMORCQDZG” on his treasure chest and has left a piece of paper with the following message: “every subsequent letter is shifted one less than the previous.” Knowing this, can you unlock Pirate Keith’s treasure chest?
Following the explanation of the challenge, I wrote a brute force decryption program as shown below.
def keithshift(s, n):
r = ""
for c in s:
r += chr((ord(c) - ord("A") + n) % 26 + ord("A"))
n = (n + 1) % 26
return r
s = "CGULKVIPFRGDOOCSJTRRVMORCQDZG"
for i in range(26):
print(keithshift(s, i))
The output of the program included a readable sentence GLASSESAREUSEFULDONOTLOSETHEM. My teammate yoshiking found the correct flag format: hsctf{glassesareusefuldonotlosethem}.
CHWOOAOWNAQOABQHZKJKPHKOAPDAI
DIXPPBPXOBRPBCRIALKLQILPBQEBJ
EJYQQCQYPCSQCDSJBMLMRJMQCRFCK
FKZRRDRZQDTRDETKCNMNSKNRDSGDL
GLASSESAREUSEFULDONOTLOSETHEM <----
HMBTTFTBSFVTFGVMEPOPUMPTFUIFN
INCUUGUCTGWUGHWNFQPQVNQUGVJGO
JODVVHVDUHXVHIXOGRQRWORVHWKHP
KPEWWIWEVIYWIJYPHSRSXPSWIXLIQ
LQFXXJXFWJZXJKZQITSTYQTXJYMJR
MRGYYKYGXKAYKLARJUTUZRUYKZNKS
NSHZZLZHYLBZLMBSKVUVASVZLAOLT
OTIAAMAIZMCAMNCTLWVWBTWAMBPMU
PUJBBNBJANDBNODUMXWXCUXBNCQNV
QVKCCOCKBOECOPEVNYXYDVYCODROW
RWLDDPDLCPFDPQFWOZYZEWZDPESPX
SXMEEQEMDQGEQRGXPAZAFXAEQFTQY
TYNFFRFNERHFRSHYQBABGYBFRGURZ
UZOGGSGOFSIGSTIZRCBCHZCGSHVSA
WBQIIUIQHUKIUVKBTEDEJBEIUJXUC
XCRJJVJRIVLJVWLCUFEFKCFJVKYVD
YDSKKWKSJWMKWXMDVGFGLDGKWLZWE
ZETLLXLTKXNLXYNEWHGHMEHLXMAXF
AFUMMYMULYOMYZOFXIHINFIMYNBYG
BGVNNZNVMZPNZAPGYJIJOGJNZOCZH
[Crypto 316points]Really Secure Algorithm
Written by: cppio
I heard about RSA, so I took a go at implementing it.
We were given n, e, and c in RSA. When I factorized n by factordb.com, it turned out that n is square of some prime p.
n = 263267198123727104271550205341958556303174876064032565857792727663848160746900434003334094378461840454433227578735680279553650400052510227283214433685655389241738968354222022240447121539162931116186488081274412377377863765060659624492965287622808692749117314129201849562443565726131685574812838404826685772784018356022327187718875291322282817197153362298286311745185044256353269081114504160345675620425507611498834298188117790948858958927324322729589237022927318641658527526339949064156992164883005731437748282518738478979873117409239854040895815331355928887403604759009882738848259473325879750260720986636810762489517585226347851473734040531823667025962249586099400648241100437388872231055432689235806576775408121773865595903729724074502829922897576209606754695074134609
e = 65537
c = 63730750663034420186054203696069279764587723426304400672168802689236894414173435574483861036285304923175308990970626739416195244195549995430401827434818046984872271300851807150225874311165602381589988405416304964847452307525883351225541615576599793984531868515708574409281711313769662949003103013799762173274319885217020434609677019589956037159254692138098542595148862209162217974360672409463898048108702225525424962923062427384889851578644031591358064552906800570492514371562100724091169894418230725012261656940082835040737854122792213175137748786146901908965502442703781479786905292956846018910885453170712237452652785768243138215686333746130607279614237568018186440315574405008206846139370637386144872550749882260458201528561992116159466686768832642982965722508678847
In such a case, Euler's totient function is given as *1. Thus, we just have to decrypt it.
from Crypto.Util.number import *
p = 16225510719965861964299051658340559066224635411075742500953901749924501886090804067406052688894869028683583501052917637552385089084807531319036985272636554557876754514524927502408114799014949174520357440885167280739363628642463479075654764698947461583766215118582826142179234382923872619079721726020446020581078274482268162477580369246821166693123724514271177264591824616458410293414647
assert p * p == n
phi = p * (p - 1)
d = inverse(e, phi)
m = pow(c, d, n)
print(m)
print(bytes.fromhex(hex(m)[2:]))
The flag was hsctf{square_number_time}.
[Reversal 180points] A Byte
Written by: ItzSomebody
Just one byte makes all the difference.
We were given a 64bit ELF executable. It takes one command line argument and determines if the given text is equal to the correct one. By disassembling it, I found the correct length was 35. Since it transformed the given text and compared it to magic text irbugzv1v^x1t^jo1v^e5^v@2^9i3c@138|, I tried giving irbugzv1v^x1t^jo1v^e5^v@2^9i3c@138|. Then it converted to hsctf{w0w_y0u_kn0w_d4_wA3_8h2bA029}. It seemed the flag.
Written by: ItzSomebody
Description: Keith made a cool license-checking program but he forgot the flag he used to create the key! To make matters worse, he lost the source code and stripped the binary for his license-generator program. Can you help Keith recover his flag? All he knows is:
• The license key is 4-EZF2M-7O5F4-V9P7O-EVFDP-E4VDO-O
• He put his name (in the form of 'k3ith') as the first part of the flag
• There are 3 underscores
• The flag is in the format hsctf{}
• The flag doesn't have random character sequences (you should be able to read the entire flag easily).
• The flag only contains lowercase English letters and numbers.
• The generator might produce the same keys for different inputs because Keith was too lazy to write the algorithm properly.
We were given a license generator. It took the text and generated the corresponding license. By the observation, it turned out that the binary converted one byte to byte and the conversion had regularity. For example, o is converted to A, p -> B, q -> C, and r -> D. Using this characteristic and hint given at the description, we could get the flag byte by byte. The flag was hsctf{k3ith_m4k3s_tr4sh_r3}. We needed to note that both 3 and } are converted to O.
[Reversal 295points] DaHeck
Written by: ItzSomebody
Unicode? ...da heck?
We were given the following program written in Java. It converted the given text byte by byte. So we could determine correct input by brute-forcing.
public class DaHeck {
private static boolean check_flag(String s) {
char[] cs = s.toCharArray();
char[] daheck = new char[cs.length];
int n = cs.length ^ daheck.length;
char[] heck = "001002939948347799120432047441372907443274204020958757273".toCharArray();
while (true) {
try {
if (heck[n] - cs[n % cs.length] < 0) daheck[n] = (char) (heck[n] - cs[n % cs.length] % 128);
else daheck[n] = (char) (heck[n] - cs[n % cs.length] % 255);
n++;
} catch (Throwable t) {
break;
}
}
return "\uffc8\uffbd\uffce\uffbc\uffca\uffb7\uffc5\uffcb\u0005\uffc5\uffd5\uffc1\uffff\uffc1\uffd8\uffd1\uffc4\uffcb\u0010\uffd3\uffc4\u0001\uffbf\uffbf\uffd1\uffc0\uffc5\uffbb\uffd5\uffbe\u0003\uffca\uffff\uffda\uffc3\u0007\uffc2\u0001\uffd4\uffc0\u0004\uffbe\uffff\uffbe\uffc1\ufffd\uffb5".equals(new String(daheck));
}
public static void main(String... args) {
if (args.length != 1) {
System.out.println(":thonk:");
System.exit(1);
}
if (check_flag(args[0])) System.out.println("Huh. How'd you know?");
else System.out.println("Da heck? No.");
}
}
I wrote the following solve function. The correct input was hsctf{th4t_w4s_fun!_l3ts_try_s0m3_m0r3_r3v3rs3}.
public static void solve() {
char[] daheck = "\uffc8\uffbd\uffce\uffbc\uffca\uffb7\uffc5\uffcb\u0005\uffc5\uffd5\uffc1\uffff\uffc1\uffd8\uffd1\uffc4\uffcb\u0010\uffd3\uffc4\u0001\uffbf\uffbf\uffd1\uffc0\uffc5\uffbb\uffd5\uffbe\u0003\uffca\uffff\uffda\uffc3\u0007\uffc2\u0001\uffd4\uffc0\u0004\uffbe\uffff\uffbe\uffc1\ufffd\uffb5".toCharArray();
char[] heck = "001002939948347799120432047441372907443274204020958757273".toCharArray();
for (int i = 0; i < daheck.length; i++) {
for (int c = 0; c < 256; c++) {
if (heck[i] - c < 0 && daheck[i] == (char) (heck[i] - c % 128)) {
System.out.print((char)c);
break;
} else if (daheck[i] == (char) (heck[i] - c % 255) ) {
System.out.print((char)c);
break;
}
}
}
}
[Reversal 375points]I Thought Trig Was Really Easy
Written by: v1sanjay
After finishing a hard lesson in geometry class, Keith decided that he wanted to put your understanding of trig and python to the test. Can you solve his challenge?
We were given the following script. It seems a bit difficult to read.
import math
def nice_math(x, y):
return round(x + y*math.cos(math.pi * x))
lots_of_nums = lambda n,a:(lambda r:[*r,n-sum(r)])(range(n//a-a//2,n//a+a//2+a%2))
def get_number(char):
return ord(char) - 96
inp = input("Enter the text: ")
out = []
for i in range(0, len(inp)):
for j in lots_of_nums(nice_math(get_number(inp[i]), len(inp) - i), i + 1):
out.append(nice_math(j, i + 1))
ans = [-25, 1, 10, 7, 4, 7, 2, 9, 3, 8, 1, 10,
3, -1, -8, 3, -6, 5, -4, 7, -5, 8, -3,
10, -1, 12, 10, 7, -6, 9, -4, 11, -2,
13, -2, -11, 6, -9, 8, -7, 10, -5, 12,
1, -12, 7, -10, 9, -8, 11, -6, 13, -4,
11, 6, -13, 8, -11, 10, -9, 12, -7, 14,
-5, 22, -16, 7, -14, 9, -12, 11, -10, 13,
-8, 15, -6, -2, 2, -21, 4, -19, 6, -17, 8,
-15, 10, -13, 12, -11, 5]
if (out == ans):
print("That is correct! Flag: hsctf{" + inp + "}")
else:
print("Nope sorry, try again!")
The lots_of_nums function takes two numbers n and a and creates the numerical array whose size equals to a+1. So we could divide the array ans into corresponding to each input character. As array for first character has a length of 2, the first two elements of ans (i.e. [-25, 1]) correspond. For the second character, ans[2:5] corresponds.
From the avobe, we could determine the correct input byte by byte.
import math
def nice_math(x, y):
return round(x + y * math.cos(math.pi * x))
lots_of_nums = lambda n, a: (lambda r: [*r, n - sum(r)])(
range(n // a - a // 2, n // a + a // 2 + a % 2)
)
def get_number(char):
return ord(char) - 96
# inp = input("Enter the text: ")
ans = [-25, 1, 10, 7, 4, 7, 2, 9, 3, 8, 1, 10,
3, -1, -8, 3, -6, 5, -4, 7, -5, 8, -3,
10, -1, 12, 10, 7, -6, 9, -4, 11, -2,
13, -2, -11, 6, -9, 8, -7, 10, -5, 12,
1, -12, 7, -10, 9, -8, 11, -6, 13, -4,
11, 6, -13, 8, -11, 10, -9, 12, -7, 14,
-5, 22, -16, 7, -14, 9, -12, 11, -10, 13,
-8, 15, -6, -2, 2, -21, 4, -19, 6, -17, 8,
-15, 10, -13, 12, -11, 5]
def get_len(n):
res = 0
for i in range(n + 1):
res += i + 2
return res
for n in range(12):
inp = "A" * 12
for ic in range(0x20, 0x7F):
inp = inp[:n] + chr(ic) + inp[n + 1 :]
out = []
for i in range(0, len(inp)):
for j in lots_of_nums(nice_math(get_number(inp[i]), len(inp) - i), i + 1):
out.append(nice_math(j, i + 1))
assert len(out) == len(ans)
p1 = get_len(n - 1)
p2 = get_len(n)
if out[p1:p2] == ans[p1:p2]:
print(chr(ic))
break
The solver script outputs :hyperthonk: and flag is hsctf{:hyperthonk:}.
Written by: Ptomerty
Help! I got this new lock for Christmas, but I've forgotten the first two values. I know the last value is hsctfissocoolwow. I also managed to grab a copy of their secret key generator. Can you help me out?
Note: submit the first two combo values separated by a space in hex format.
We were given the generator.py
#!/usr/bin/env python2
ch = '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ!\"#\$%&\'()*+,-./:;<=>?@[\\]^_{|}~ '
s = [SECRET_1, SECRET_2]
# TOP SECRET: DO NOT LEAK
def o(x,k):
return x<<k
def m(a):
return a&0xffffffffffffffff
def next():
b = m(s[0]+s[1])
h()
return m(b)
def p(k, x):
return x>>(64-k)
def x(b, a):
return a^b
def oro(a, b):
return a|b
def h():
s1 = m(x(s[0],s[1]))
s[0] = m(x(oro(o(s[0],55),p(55,s[0])),x(s1,(o(s1,14)))))
s[1] = m(oro(o(s1,36),p(36,s1)))
# Helper methods
def bin2chr(data):
result = ''
while data:
char = data & 0xff
result += chr(char)
data >>= 8
return result
def isp(d):
if all(c in ch for c in d):
return d
else:
return d.encode('hex')
# throw away first value for additional randomness
next()
next()
COMBO_NUM_1 = isp(bin2chr(next())) + isp(bin2chr(next()))
COMBO_NUM_2 = isp(bin2chr(next())) + isp(bin2chr(next()))
COMBO_NUM_3 = isp(bin2chr(next())) + isp(bin2chr(next()))
print "Thanks! Your numbers are: "
print COMBO_NUM_1
print COMBO_NUM_2
print COMBO_NUM_3
The function next is the core of this challenge. It works as shown below.
def next(x, y):
xx = RotateLeft(x, 55) ^ ((x ^ y) ^ ((x ^ y) << 14))
yy = RotateLeft(x ^ y, 36)
return xx & 0xFFFFFFFFFFFFFFFF, yy & 0xFFFFFFFFFFFFFFFF
As we know that the last x2, y2 (let x2, y2 = next(x, y) ) have a constraint that bin2chr(x2 + y2) == 'ocoolwow' and previous one (i.e. x and y) has bin2chr(x + y) == 'hsctfiss' as its constraint. Using this fact, I managed to get x and y with z3.
from z3 import *
def chr2bin(s):
data = 0
for c in s:
data <<= 8
data += ord(c)
return data
def next(x, y):
xx = RotateLeft(x, 55) ^ ((x ^ y) ^ ((x ^ y) << 14))
yy = RotateLeft(x ^ y, 36)
return xx & 0xFFFFFFFFFFFFFFFF, yy & 0xFFFFFFFFFFFFFFFF
X, Y = BitVecs("x y", 64)
s = Solver()
X2, Y2 = next(X, Y)
r = s.check()
print(r)
if r != sat:
exit()
m = s.model()
x = m[X].as_long()
y = m[Y].as_long()
print([x, y])
Also, one more previous pair (u, v) could get by the following script.
U, V = BitVecs("u v", 64)
s = Solver()
X2, Y2 = next(U, V)
r = s.check()
if r != sat:
exit()
m = s.model()
u = m[U].as_long()
v = m[V].as_long()
print([u, v])
By repeating this several times, I could get the first pair (SECRET_1, SECRET_2). It was s = [7294543424534665732, 16423178736247365903] and generator.py outputted the combo e06f76cd556604f0f21c34f1519d2fd2 73c8535ab0f954b5ad1cbab7abc18309 hsctfissocoolwow.
from z3 import *
def chr2bin(s):
data = 0
for c in s:
data <<= 8
data += ord(c)
return data
def next(x, y):
xx = RotateLeft(x, 55) ^ ((x ^ y) ^ ((x ^ y) << 14))
yy = RotateLeft(x ^ y, 36)
return xx & 0xFFFFFFFFFFFFFFFF, yy & 0xFFFFFFFFFFFFFFFF
X, Y = BitVecs("x y", 64)
s = Solver()
X2, Y2 = next(X, Y)
r = s.check()
print(r)
if r != sat:
exit()
m = s.model()
x = m[X].as_long()
y = m[Y].as_long()
print([x, y])
for i in range(6):
X, Y = BitVecs("x y", 64)
s = Solver()
X2, Y2 = next(X, Y)
` | 5,153 | 14,278 | {"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} | 2.75 | 3 | CC-MAIN-2024-26 | latest | en | 0.794905 |
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a = 1, b = 2, c = 0, 0.8, 1
In geometry, a spiric section, sometimes called a spiric of Perseus, is a quartic plane curve defined by equations of the form
${\displaystyle (x^{2}+y^{2})^{2}=dx^{2}+ey^{2}+f.\,}$
Equivalently, spiric sections can be defined as bicircular quartic curves that are symmetric with respect to the x and y-axes. Spiric sections are included in the family of toric sections and include the family of hippopedes and the family of Cassini ovals. The name is from σπειρα meaning torus in ancient Greek.
A spiric section is sometimes defined as the curve of intersection of a torus and a plane parallel to its rotational symmetry axis. However, this definition does not include all of the curves given by the previous definition unless imaginary planes are allowed.
Spiric sections were first described by the ancient Greek geometer Perseus in roughly 150 BC, and are assumed to be the first toric sections to be described.
## Equations
Start with the usual equation for the torus:
${\displaystyle (x^{2}+y^{2}+z^{2}+b^{2}-a^{2})^{2}=4b^{2}(x^{2}+y^{2}).\,}$
Interchanging y and z so that the axis of revolution is now on the xy-plane, and setting z=c to find the curve of intersection gives
${\displaystyle (x^{2}+y^{2}-a^{2}+b^{2}+c^{2})^{2}=4b^{2}(x^{2}+c^{2}).\,}$
In this formula, the torus is formed by rotating a circle of radius a with its center following another circle of radius b (not necessarily larger than a, self-intersection is permitted). The parameter c is the distance from the intersecting plane to the axis of revolution. There are no spiric sections with c > b + a, since there is no intersection; the plane is too far away from the torus to intersect it.
Expanding the equation gives the form seen in the definition
${\displaystyle (x^{2}+y^{2})^{2}=dx^{2}+ey^{2}+f\,}$
where
${\displaystyle d=2(a^{2}+b^{2}-c^{2}),\ e=2(a^{2}-b^{2}-c^{2}),\ f=-(a+b+c)(a+b-c)(a-b+c)(a-b-c).\,}$
In polar coordinates this becomes
${\displaystyle (r^{2}-a^{2}+b^{2}+c^{2})^{2}=4b^{2}(r^{2}\cos ^{2}\theta +c^{2})\,}$
or
${\displaystyle r^{4}=dr^{2}\cos ^{2}\theta +er^{2}\sin ^{2}\theta +f.\,}$
## Examples of spiric sections
Examples include the hippopede and the Cassini oval and their relatives, such as the lemniscate of Bernoulli. The Cassini oval has the remarkable property that the product of distances to two foci are constant. For comparison, the sum is constant in ellipses, the difference is constant in hyperbolae and the ratio is constant in circles.
## References
Original courtesy of Wikipedia: http://en.wikipedia.org/wiki/Spiric_section — Please support Wikipedia.
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Copyright © 2009-2016 Digparty. All rights reserved. | 990 | 3,605 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 7, "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} | 3.953125 | 4 | CC-MAIN-2016-30 | latest | en | 0.908042 |
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Unformatted text preview: C.4 Solutions Last updated June 16, 2010 Video solutions at http://www.theinfiniteactuary.com/?page=exams&id=144 1 . D (600) = F n (600)- F * (600) = 3 4- F (600)- F (100) 1- F (100) = 3 4- ( 6 7 ) 2- ( 1 2 ) 2 1- ( 1 2 ) 2 = . 104 2 . Because of the truncation, we want F * (600) = P[ X ≤ 600 | X > 100] = F (600)- F (100) 1- F (100) = ( 6 7 ) 2- ( 1 2 ) 2 1- ( 1 2 ) 2 = . 646 3 . The x-coordinate is the smoothed empirical percentile (and in particular doesn’t need to be adjusted for the deductible), which is 3 / (4 + 1) = . 6 4 . D (100) = F n (100)- F * (100) so since 0 > D (100) we have F * (100) > F n (100), which means that the fitted model places greates weight than the observed between 0 and 100. < D (200)- D (100) = [ F n (200)- F n (100)]- [ F * (200)- F * (100)], so F * (200)- F * (100) < F n (200)- F n (100) and the fitted model places less weight than the observed between 100 and 200. Finally, 0 > D (300)- D (200) so F * (300)- F * (200) > F n (300)- F n (200) and the fitted model places more weight than the observed from 200 to 300. THis gives us D as our answer. 5 . By the definition of a p- p plot, s is the smoothed empirical percentile so s = 4 / (7 + 1) = 0 . 5 while t = F (3 , 000). Meanwhile, D (3 , 000) = F n (3 , 000)- F (3 , 000) = (4 / 7)- F (3 , 000) so ( s- t )- D (3 , 000) = 1 2- F (3 , 000)- 4 7- F (3 , 000) =- . 07 c 2010 The Infinite Actuary, LLC C.4 Solutions 6 . Our hypothesized density is that of a Pareto with θ = 1 and α = 4 and there is no truncation so F * ( x ) = F ( x ) = 1- (1+ x )- 4 . Our standard Kolmogorov-Smirnov table is then x F * ( x ) F n ( x- ) F n ( x ) max difference . 1 . 317 . . 2 . 317 . 2 . 518 . 2 . 4 . 318 . 5 . 802 . 4 . 6 . 402 . 7 . 880 . 6 . 8 . 280 1 . 3 . 964 . 8 1 . . 164 The maximum value in the right hand column is our answer of . 402 7 . We are estimating the mean using the method of moments, so ˆ θ = ¯ X = 100. Note that this will reduce our critical values, but that isn’t asked. There is no truncation, so F * ( x ) = F ( x ) = 1- e- x/ 100 and we obtain x F * ( x ) F n ( x- ) F n ( x ) max difference 29 . 25 . . 2 . 25 64 . 47 . 2 . 4 . 27 90 . 59 . 4 . 6 . 19 135 . 74 . 6 . 8 . 14 182 . 83 . 8 1 . . 17 The max in the right hand column is . 27 8 . With no truncation, F * ( x ) = F ( x ) = 1- (1 + x )- 4 and so x F * ( x ) F n ( x- ) F n ( x ) max difference . 2 . 517 . . 2 . 517 . 7 . 880 . 2 . 4 . 680 . 9 . 923 . 4 . 6 . 523 1 . 1 . 949 . 6 . 8 . 349 1 . 3 . 964 . 8 1 . . 164 The max in the right hand column is our test statistic of 0 . 680. For our critical values, we plug into the formula they gave us. The 0.025 critical value is 0.66, which is less than our test statistic, and the 0.010 critical value is 0.72, which is c 2010 The Infinite Actuary, LLC C.4 Solutions above out test statistic, so we reject at the 0.025 level and do not at the 0.010 level, giving an answer of D 9 . We have truncation at 10. To find....
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## This note was uploaded on 07/16/2011 for the course STATS 141 taught by Professor Rahul during the Spring '11 term at Drake University .
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Solutions to Additional Problems - C.4 Solutions Last...
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Ask a homework question - tutors are online | 1,343 | 3,746 | {"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} | 4.34375 | 4 | CC-MAIN-2017-17 | longest | en | 0.851773 |
https://www.antonfoto4k.pl/37646_crushing_calculation_of_reduction_ratio.html | 1,632,255,973,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780057227.73/warc/CC-MAIN-20210921191451-20210921221451-00270.warc.gz | 688,521,192 | 9,682 | #### crushing calculation of reduction ratio
Calculation of reduction ratio in roll crusher
Calculation of reduction ratio in roll crusher Products. As a leading global manufacturer of crushing, grinding and mining equipments, we offer advanced, reasonable solutions for any size-reduction requirements including, Calculation of reduction ratio in roll crusher, quarry, aggregate, and different kinds of minerals.
Size Reduction Ratio Of Crusher
Crusher size reduction ratio. Crusher size reduction ratio measurement and evaluation from the crushing process and crushing effect on the number of common calculation method jaw crusher size reduction ratio there are three 1, with a maximum particle size of the material before crushing ratio of product to calculate the maximum size after.
Reduction ratio | Article about reduction ratio by The ...
Looking for reduction ratio? Find out information about reduction ratio. Ratio of feed size to product size for a mill operation; measured by lump and sieve sizes. In stone crushing, the ratio of the maximum dimension of stone... Explanation of reduction ratio
How Is Reduction Ratio Of Hammer Mill Calculated
The hammer crusher size reduction ratio is 20 to 1. reduction ratio mill. reduction ratio mill Calculation of the Total Reduction Ratio in WAAS Jul 29, 2013To calculate the reduction in traffic (the total reduction ratio), use this formula: In this example, the calculation is 1 (210596/1189172) = .82290535 or 82.291%. 1일 전 Reduction
about impact mining mill reduction ratio calculatio
Reduction Ratio Of Ball Mill. generally, every crusher machine is not the same, here are several common crusher size reduction ratio the impact crusher size reduction ratio is 20 to 1he vertical shaft impact crusher size reduction ratio is 4-8 to 1he vertical roller mill size reduction ratio is 2-2to 1he hammer crusher size reduction ...
Rock Crushing Rule of Thumb - Mineral Processing & Metallurgy
Metallurgical Content Crusher Selection Crusher Design Crusher InstallationCrusher CostsThe Crusher's Rock BreakersArea of Application Here is a list of Rules of Thumb often used in Rock Crushing and around Crushers: Crusher Selection For a hard rock mine application below 600 tonnes/hour, select a jaw as the primary crusher. Over 1,000 tph, select a gyratory crusher. Between these ...
Jaw Crusher - ScienceDirect
Jan 01, 2016· The crusher feed rate can increase to maintain the same crushing rate. Taggart expressed the relationship between crusher capacity and reduction ratio in terms of a reduction ton or tonne, Q R defined as (4.22) Q R = Q T ⋅ R 80 where Q T is the capacity in terms of actual tonnage crushed per hour. The quantity of feed actually crushed is ...
jaw crusher reduction ratios - sirvall.cz
The reduction ratio of jaw crusher is 3:1 to 5:1. working principle of jaw crusher shown below in Figure 1 and the single and double toggle Chat Now Crushing of coal and calculation of size reduction
how to get machine reduction ratio
Calculate the reduction ratio.Get price mineral processing laboratory manual - vssut.Crushing of ore in the jaw crusher, and determination of reduction ratio and verifiion of rittingers law of crushing.13-15.Calculate the reduction ratio.Get price design of a crushing system that improves the - …
standard cone crusher reduction ratio
Crusher Size Reduction Ratio Calculation Method. Crusher Size Reduction Ratio Calculation Method Crusher size reduction ratio is the ratio of raw material particle size and particle size of crushing Crusher size reduction ratio is the ratio of raw material particle size and particle size of crushingCalculated method are the following
Reduction Ratio Calculation Jaw Crusher Reduction Ratio
About impact crusher reduction ratio calculatio. Crushing of coal and calculation of size reduction efficiency feb 25 2015 one of modes of size reduction impact sharp instantaneous impact crusher the reduction ratio and efficiency of roll crusher is very low get quote reduction ratio calculat...
crushing calculation of reduction ratio
big reduction ratio high crushing efficiency stone jaw crusher. Calculation of reduction ratio in crushing [image: (13553)] Crushing Equipment The selection of the right crushing equipment is influenced by many factors some of which are upstream of the crushing plant (e.g. blasting pattern and mining method) and others which are downstream of the crushing plant (e.g. mill and grinding circuit ...
What affects cone crusher performance? — Mining ...
These are the two main causes of sub-optimal crushing performance, but losses in the reduction ratio can also be caused by selecting the wrong mantle or by having a poor chamber profile or design. Surprisingly, selecting the wrong alloy has no effect when it comes to the reduction ratio (although this will affect the life of wearable parts in ...
size reduction grinding crushing - marktbewerkinginict.nl
Crusher Size Reduction Ratio Calculation Method. Crusher Size Reduction Ratio Calculation Method. Crusher size reduction ratio is the ratio of raw material particle size and particle size of crushing. Crusher size reduction ratio is the ratio of raw material particle size and particle size of crushing.Calculated method are the following . Chat ...
Crusher Size Reduction Ratio Calculation Method
Crusher Size Reduction Ratio Calculation Method. Crusher size reduction ratio is the ratio of raw material particle size and particle size of crushing. Crusher size reduction ratio is the ratio of raw material particle size and particle size of crushing.Calculated method are the following:
Soybean Crush Reference Guide - CME Group
calculation is referred to as the Gross Processing Margin (GPM) or "Crush." To Calculate the Crush or GPM [(Price of Soybean Meal (\$/short ton) x .022) + Price of Soybean Oil (¢/lb) x 11] – Price of Soybeans (\$/bu.) Typically, crushing activity is expanded or reduced to …
Reduction Ratio Of Crusher - mobile-hundeschule-hamm.de
Crusher Reduction Ratio I have mentioned the fact that, as the % of voids in the crushing chamber decreases, the production of fines by attrition increases. This is like saying that, as the Crusher Reduction Ratio in any given crusher is increased, the % of fines in the product will increase, even though the discharge setting remains unchanged.
AMIT 135: Lesson 5 Crushing – Mining Mill Operator Training
Calculation of reduction ratio in crushing [image: (135-5-3)] Crushing Equipment The selection of the right crushing equipment is influenced by many factors some of which are upstream of the crushing plant (e.g. blasting pattern and mining method) and others which are downstream of the crushing plant (e.g. mill and grinding circuit selection).
reduction ratio calculation crusher
Reduction Ratio Of Hammer Mill For Stone Crushing. Crusher size reduction ratio calculation method. generally every crusher machine is not the same here are several common crusher size reduction ratio the impact crusher size reduction ratio is 20 to 1 the vertical shaft impact crusher size reduction ratio is 4-8 to 1 the vertical roller mill size reduction ratio is 2-25 to 1 the ...
Crushing of coal and calculation of size reduction efficiency.
Feb 25, 2015· Roll Crusher • The reduction ratio and efficiency of roll crusher is very low. • The main advantage associated with roll crushers is small proportion of fines produced and more uniform size of product crushed, than the other crushers. • Low capacity • Low reduction ratio = F/P • Sensitive to top size 2/25/2015 6:58:05 AM 38 39.
calculate the effiaciancy of a crusher
Crushing of coal and calculation of size reduction efficiency. 25-2-2015Roll Crusher • The reduction ratio and efficiency of roll crusher is very low. • The main advantage associated with roll crushers is small proportion of fines produced and more uniform size of product crushed, than the other crushers.
reduction ratio crusher
High Reduction Ratio Crusher 911Metallurgist. 10″ x 16″ High Reduction Ratio Jaw Crusher 911MPEJC400 Jaw Crushers for Coarse Primary Crushing and Mid Range Primary Crushing This 35 TPH jaw crusher is equipped with a 20 HP motor and a 7″ X 14″ jaw cavity that will produce a discharge crushed product of under 10mm. Read More
power calculation of double roll crusher - ME Mining Machinery
They can be used in coal, salt, coke, glass, and trona operations, among others. Triple Roll Crushers combine a Single Roll Crusher with a Double Roll Crusher to form a crusher that is capable of achieving a 6:1 reduction ratio in the primary stage and a 4:1 reduction in the secondary stage while producing a cubicle product at high capacity.
jaw crusher reduction ratio
how to calculate reduction ratio of jaw crusher. ratio jaw crusher high reduction ratio crusher 911metallurgistjaw crushers for coarse primary crushing and mid range primary crushing this 3 5 tph jaw crusher is equipped with a 20 hp motor and a 7 x 14 jaw cavity that will produce a discharge crushed product of under ratio jaw crusher reduction ratio for crushers newest crusher.
Reduction Ratio - an overview | ScienceDirect Topics
In any crushing operation, the raw material flow rate and the reduction ratio (ratio of feed size to product size) have obvious influences on the wear of crushing equipment. However, the hardness and fracture toughness of the rocks being crushed are unavoidable parameters in allowing for the wear of crushing …
(PDF) SIZE REDUCTION BY CRUSHING METHODS
All crushers have a limited reduction ratio m eaning that size reduction will take place in stages. 3.2 Operation stages: The operating stages in minerals process ing have remained the same for ...
reduction ratio for cone crusher pdf
reduction ratio for cone crusher pdf - De Balans. HPT Hydraulic Cone Crusher. product description The Hydraulic Cone Crusher is widely used in highly automatic crushing line which has strict requirements for the fineness of the end products and crushing ratio.The machine is widely used for secondary and fine crushing in the fields of mining building materials metallurgy and so on.
Crusher Reduction Ratio - Mineral Processing & Metallurgy
What is the impact of the Crusher Reduction Ratio on crusher performance.
Cone Crushers | McLanahan
A general rule of thumb for applying Cone Crushers is the reduction ratio. A crusher with coarse style liners would typically have a 6:1 reduction ratio. Thus, with a 3⁄4" closed side setting, the maximum feed would be 6 x 3⁄4 or 4.5 inches. Reduction ratios of 8:1 may be possible in certain coarse crushing … | 2,164 | 10,628 | {"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} | 2.84375 | 3 | CC-MAIN-2021-39 | latest | en | 0.88395 |
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# Among the more effective kinds of publicity that publishers
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Among the more effective kinds of publicity that publishers [#permalink]
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29 May 2006, 22:53
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Among the more effective kinds of publicity that publishers can get for a new book is to have excerpts of it published in a high-circulation magazine soon before the book is published. The benefits of such excerption include not only a sure increase in sales but also a fee paid by the magazine to the book’s publisher.
Which of the following conclusions is best supported by the information above?
(A) The number of people for whom seeing an excerpt of a book in a magazine provides an adequate substitute for reading the whole book is smaller than the number for whom the excerpt stimulates a desire to read the book.
(B) Because the financial advantage of excerpting a new book in a magazine usually accrues to the book’s publisher, magazine editors are unwilling to publish excerpts from new books.
(C) In calculating the total number of copies that a book has sold, publishers include sales of copies of magazines that featured an excerpt of the book.
(D) The effectiveness of having excerpts of a book published in a magazine, measured in terms of increased sales of a book, is proportional to the circulation of the magazine in which the excerpts are published.
(E) Books that are suitable for excerpting in high-circulation magazines sell more copies than books that are not suitable for excerpting.
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29 May 2006, 23:05
I'll pick A.
The passage states that sales increases due to the publication of excerpts in magazines.
So we can conclude that people who purchase books due to this are more than people who actually don't.
Hence A follows.
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29 May 2006, 23:20
I am also inclined towards A though the statement re "fee paid by the magazine to the book’s publisher" is confusing as to what role does it play in this conclusion ?
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30 May 2006, 03:59
A for me.
The author mentions that such a strategy will increase the sales of the book as well as get money from magazines.
A safely concludes that more people are interested in buying the books after reading the excerpts than the number of people not interested.
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30 May 2006, 04:07
(A) The number of people for whom seeing an excerpt of a book in a magazine provides an adequate substitute for reading the whole book is smaller than the number for whom the excerpt stimulates a desire to read the book.
(B) Not important. The magazine editor's reluctance does not have a significant impact on the conclusion.
(C) Irrelevant
(D) We're already told it's effective, so we do not need to debate whether the magazine is highly circulated or not.
(E) Not important
A is the best choice. If a great number of people have a strong desire to read the book after going through the excerpt, then the conclusion that publishing an excerpt in magazines will result in an increase in sales is true.
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30 May 2006, 05:37
d comes close, but A has the KO
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30 May 2006, 05:41
gmatmba wrote:
d comes close, but A has the KO
KO?
BTW, I can sense your very strong verbal skills So please be around and share with us your profound verbal explanations
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15 Among the more effective kinds of publicity 15 22 Jul 2013, 19:06
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1 Among the more effective kinds of publicity that publishers 13 23 Mar 2009, 06:35
1 Among the more effective kinds of publicity that publishers 13 08 Aug 2008, 11:35
Among the more effective kinds of publicity that publishers 6 21 Jan 2007, 23:29
Display posts from previous: Sort by | 1,333 | 5,230 | {"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} | 2.84375 | 3 | CC-MAIN-2016-18 | longest | en | 0.926145 |
https://www.dataunitconverter.com/mebibit-per-second-to-megabyte-per-minute/10 | 1,709,408,332,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947475897.53/warc/CC-MAIN-20240302184020-20240302214020-00352.warc.gz | 715,358,262 | 16,440 | # Mibps to MB/Min - 10 Mibps to MB/Min Conversion
expand_more
Input Mebibits per Second (Mibps) - and press Enter.
Mibps
Sec
Min
Hr
Day
Sec
Min
Hr
Day
S = Second, M = Minute, H = Hour, D = Day
label_important RESULT sentiment_satisfied_alt
10 Mibps =78.6432 MB/Min
( Equal to 7.86432E+1 MB/Min )
content_copy
Calculated as → 10 x 10242 ÷ (8x10002) x 60 smart_display Show Stepsexpand_more
Below chart table shows the amount of data that can be transferred at a constant speed of 10 Mibps in various time frames.
Transfer RateAmount of Data can be transferred
@ 10 Mibpsin 1 Second1.31072 Megabytes
in 1 Minute78.6432 Megabytes
in 1 Hour4,718.592 Megabytes
in 1 Day113,246.208 Megabytes
## Mebibits per Second (Mibps) to Megabytes per Minute (MB/Min) Conversion - Formula & Steps
The Mibps to MB/Min Calculator Tool provides a convenient solution for effortlessly converting data rates from Mebibits per Second (Mibps) to Megabytes per Minute (MB/Min). Let's delve into a thorough analysis of the formula and steps involved.
Outlined below is a comprehensive overview of the key attributes associated with both the source (Mebibit) and target (Megabyte) data units.
Source Data Unit Target Data Unit
Equal to 1024^2 bits
(Binary Unit)
Equal to 1000^2 bytes
(Decimal Unit)
The conversion from Data per Second to Minute can be calculated as below.
x 60
x 60
x 24
Data
per
Second
Data
per
Minute
Data
per
Hour
Data
per
Day
÷ 60
÷ 60
÷ 24
The formula for converting the Mebibits per Second (Mibps) to Megabytes per Minute (MB/Min) can be expressed as follows:
diamond CONVERSION FORMULA MB/Min = Mibps x 10242 ÷ (8x10002) x 60
Now, let's apply the aforementioned formula and explore the manual conversion process from Mebibits per Second (Mibps) to Megabytes per Minute (MB/Min). To streamline the calculation further, we can simplify the formula for added convenience.
FORMULA
Megabytes per Minute = Mebibits per Second x 10242 ÷ (8x10002) x 60
STEP 1
Megabytes per Minute = Mebibits per Second x (1024x1024) ÷ (8x1000x1000) x 60
STEP 2
Megabytes per Minute = Mebibits per Second x 1048576 ÷ 8000000 x 60
STEP 3
Megabytes per Minute = Mebibits per Second x 0.131072 x 60
STEP 4
Megabytes per Minute = Mebibits per Second x 7.86432
By applying the previously mentioned formula and steps, the conversion from 10 Mebibits per Second (Mibps) to Megabytes per Minute (MB/Min) can be processed as outlined below.
1. = 10 x 10242 ÷ (8x10002) x 60
2. = 10 x (1024x1024) ÷ (8x1000x1000) x 60
3. = 10 x 1048576 ÷ 8000000 x 60
4. = 10 x 0.131072 x 60
5. = 10 x 7.86432
6. = 78.6432
7. i.e. 10 Mibps is equal to 78.6432 MB/Min.
Note : Result rounded off to 40 decimal positions.
You can employ the formula and steps mentioned above to convert Mebibits per Second to Megabytes per Minute using any of the programming language such as Java, Python, or Powershell.
### Unit Definitions
#### What is Mebibit ?
A Mebibit (Mib or Mibit) is a binary unit of digital information that is equal to 1,048,576 bits and is defined by the International Electro technical Commission(IEC). The prefix 'mebi' is derived from the binary number system and it is used to distinguish it from the decimal-based 'megabit' (Mb). It is widely used in the field of computing as it more accurately represents the amount of data storage and data transfer in computer systems.
arrow_downward
#### What is Megabyte ?
A Megabyte (MB) is a decimal unit of digital information that is equal to 1,000,000 bytes (or 8,000,000 bits) and commonly used to express the size of a file or the amount of memory used by a program. It is also used to express data transfer speeds and in the context of data storage and memory, the binary-based unit of mebibyte (MiB) is used instead.
## Excel Formula to convert from Mebibits per Second (Mibps) to Megabytes per Minute (MB/Min)
Apply the formula as shown below to convert from 10 Mebibits per Second (Mibps) to Megabytes per Minute (MB/Min).
A B C
1 Mebibits per Second (Mibps) Megabytes per Minute (MB/Min)
2 10 =A2 * 0.131072 * 60
3
If you want to perform bulk conversion locally in your system, then download and make use of above Excel template.
## Python Code for Mebibits per Second (Mibps) to Megabytes per Minute (MB/Min) Conversion
You can use below code to convert any value in Mebibits per Second (Mibps) to Mebibits per Second (Mibps) in Python.
mebibitsperSecond = int(input("Enter Mebibits per Second: "))
megabytesperMinute = mebibitsperSecond * (1024*1024) / (8*1000*1000) * 60
print("{} Mebibits per Second = {} Megabytes per Minute".format(mebibitsperSecond,megabytesperMinute))
The first line of code will prompt the user to enter the Mebibits per Second (Mibps) as an input. The value of Megabytes per Minute (MB/Min) is calculated on the next line, and the code in third line will display the result.
## Similar Conversions & Calculators
All below conversions basically referring to the same calculation. | 1,447 | 4,956 | {"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} | 3.0625 | 3 | CC-MAIN-2024-10 | latest | en | 0.759762 |
https://www.whatnumberis.net/190-roman-numeral/ | 1,722,773,746,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640398413.11/warc/CC-MAIN-20240804102507-20240804132507-00476.warc.gz | 823,975,656 | 3,205 | # What number is 190 in Roman numerals?
Your question is: what is the number 190 in Roman numerals? Learn how to convert the normal number 190 into a correct translation of the Roman numeral.
The normal number 190 is identical to the Roman numeral CXC
CXC = 190
### How to convert 190 to Roman numerals?
To convert the number 190 into Roman numerals, the translation involves dividing the number into place values (units, tens, hundreds, thousands), like this:
Place valueNumberRoman numbers
Conversion100 + 90C + XC
Hundreds100C
Dozens90XC
## How do you write 190 in Roman numerals?
To write the number 190 as Roman numerals correctly, combine the normal converted numbers. Higher numbers should always precede the lower numbers to provide you with the correct written translation, as shown in the table above.
100+90 = (CXC) = 190
191 in Roman Numerals
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http://reference.wolfram.com/language/tutorial/DSolveExamplesOfDAEs.html | 1,534,656,242,000,000,000 | text/html | crawl-data/CC-MAIN-2018-34/segments/1534221214702.96/warc/CC-MAIN-20180819051423-20180819071423-00709.warc.gz | 350,711,519 | 10,856 | # Examples of DAEs
This is a simple homogeneous DAE with constant coefficients.
In[1]:=
This finds the general solution. It has only one arbitrary constant because the second equation in the system specifies the relationship between x[t] and y[t].
In[2]:=
Out[2]=
This verifies the solution.
In[3]:=
Out[3]=
Here is an inhomogeneous system derived from the previous example.
In[4]:=
The general solution is composed of the general solution to the corresponding homogeneous system and a particular solution to the inhomogeneous equation.
In[5]:=
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This solves an initial value problem for the previous equation.
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Here is a plot of the solution and the constraint (algebraic) condition.
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In this DAE, the inhomogeneous part is quite general.
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Note that there are no degrees of freedom in the solution (that is, there are no arbitrary constants) because z[t] is given algebraically, and thus x[t] and y[t] can be determined uniquely from z[t] using differentiation.
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In this example, the algebraic constraint is present only implicitly: all three equations contain derivatives of the unknown functions.
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The Jacobian with respect to the derivatives of the unknown functions is singular, so that it is not possible to solve for them.
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The differential-algebraic character of this problem is clear from the smaller number of arbitrary constants (two rather than three) in the general solution.
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Systems of equations with higher-order derivatives are solved by reducing them to first-order systems.
Here is the general solution to a homogeneous DAE of order two with constant coefficients.
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This inhomogeneous system of ODEs is based on the previous example.
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Here is an initial value problem for the previous system of equations.
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Here is a plot of the solution.
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Finally, here is a system with a third-order ODE. Since the coefficients are exact quantities, the computation takes some time.
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The symbolic solution of DAEs that are nonlinear or have non-constant coefficients is a difficult problem. Such systems can often be solved numerically with the Wolfram Language function NDSolve. | 638 | 2,483 | {"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} | 3.578125 | 4 | CC-MAIN-2018-34 | latest | en | 0.870683 |
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1 THE TRINGLE ND ITS PROPERTIES 113 The Triangle and its Properties Chapter INTRODUCTION triangle, you have seen, is a simple closed curve made of three line segments. It has three vertices, three sides and three angles. Here is BC (Fig 6.1). It has Sides: B, BC, C Fig 6.1 ngles: BC, BC, BC Vertices:, B, C The side opposite to the vertex is BC. Can you name the angle opposite to the side B? You know how to classify triangles based on the (i) sides (ii) angles. (i) Based on Sides: Scalene, Isosceles and Equilateral triangles. (ii) Based on ngles: cute-angled, Obtuse-angled and Right-angled triangles. Make paper-cut models of the above triangular shapes. Compare your models with those of your friends and discuss about them. TRY THESE 1. Write the six elements (i.e., the 3 sides and the 3 angles) of BC. 2. Write the: (i) Side opposite to the vertex Q of PQR (ii) ngle opposite to the side LM of LMN (iii) Vertex opposite to the side RT of RST 3. Look at Fig 6.2 and classify each of the triangles according to its (a) Sides (b) ngles
2 114 MTHEMTICS P L 10cm 8cm 7cm Q 6cm (ii) R M 7cm (iii) N Fig 6.2 Now, let us try to explore something more about triangles. 6.2 MEDINS OF TRINGLE Given a line segment, you know how to find its perpendicular bisector by paper folding. Cut out a triangle BC from a piece of paper (Fig 6.3). Consider any one of its sides, say, BC. By paper-folding, locate the perpendicular bisector of BC. The folded crease meets BC at D, its mid-point. Join D. B D C B D C Fig 6.3 The line segment D, joining the mid-point of BC to its opposite vertex is called a median of the triangle. Consider the sides B and C and find two more medians of the triangle. median connects a vertex of a triangle to the mid-point of the opposite side. THINK, DISCUSS ND WRITE 1. How many medians can a triangle have? 2. Does a median lie wholly in the interior of the triangle? (If you think that this is not true, draw a figure to show such a case).
3 THE TRINGLE ND ITS PROPERTIES LTITUDES OF TRINGLE Make a triangular shaped cardboard BC. Place it upright, on a table. How tall is the triangle? The height is the distance from B C vertex (in the Fig 6.4) to the base BC. From to BC you can think of many line segments (see the next Fig 6.5). Which among them will represent its height? The height is given by the line segment that starts from, comes straight down to BC, and is perpendicular to BC. Fig 6.4 This line segment L is an altitude of the triangle. n altitude has one end point at a vertex of the triangle and the other on the line containing the opposite side. Through each vertex, an altitude can be drawn. B L Fig 6.5 C THINK, DISCUSS ND WRITE 1. How many altitudes can a triangle have? 2. Draw rough sketches of altitudes from to BC for the following triangles (Fig 6.6): B C B C B C cute-angled Right-angled Obtuse-angled (i) (ii) (iii) Fig Will an altitude always lie in the interior of a triangle? If you think that this need not be true, draw a rough sketch to show such a case. 4. Can you think of a triangle in which two altitudes of the triangle are two of its sides? 5. Can the altitude and median be same for a triangle? (Hint: For Q.No. 4 and 5, investigate by drawing the altitudes for every type of triangle). DO THIS Take several cut-outs of (i) an equilateral triangle (ii) an isosceles triangle and (iii) a scalene triangle. Find their altitudes and medians. Do you find anything special about them? Discuss it with your friends.
4 116 MTHEMTICS EXERCISE In PQR, D is the mid-point of QR. P PM is. PD is. Is QM = MR? 2. Draw rough sketches for the following: (a) In BC, BE is a median. Q M D R (b) In PQR, PQ and PR are altitudes of the triangle. (c) In XYZ, YL is an altitude in the exterior of the triangle. 3. Verify by drawing a diagram if the median and altitude of an isosceles triangle can be same. 6.4 EXTERIOR NGLE OF TRINGLE ND ITS PROPERTY DO THIS 1. Draw a triangle BC and produce one of its sides, say BC as shown in Fig 6.7. Observe the angle CD formed at the point C. This angle lies in the exterior of BC. We call it an exterior angle of the BC formed at vertex C. Clearly BC is an adjacent angle to CD. The Fig 6.7 remaining two angles of the triangle namely and B are called the two interior opposite angles or the two remote interior angles of CD. Now cut out (or make trace copies of) and B and place them adjacent to each other as shown in Fig 6.8. Do these two pieces together entirely cover CD? Can you say that m CD = m + m B? 2. s done earlier, draw a triangle BC and form an exterior angle CD. Now take a protractor and measure CD, and B. Find the sum + B and compare it with the measure of CD. Do you observe that CD is equal (or nearly equal, if there is an error in measurement) to + B? Fig 6.8
5 THE TRINGLE ND ITS PROPERTIES 117 You may repeat the above two activities by drawing some more triangles along with their exterior angles. Every time, you will find that the exterior angle of a triangle is equal to the sum of its two interior opposite angles. logical step-by-step argument can further confirm this fact. n exterior angle of a triangle is equal to the sum of its interior opposite angles. Given Consider BC. CD is an exterior angle. To Show: m CD = m + m B Through C draw CE, parallel to B. Justification Steps Reasons Fig 6.9 (a) 1 = x B CE and C is a transversal. Therefore, alternate angles should be equal. (b) 2 = y B CE and BD is a transversal. Therefore, corresponding angles should be equal. (c) = x + y (d) Now, x + y = m CD From Fig 6.9 Hence, = CD The above relation between an exterior angle and its two interior opposite angles is referred to as the Exterior ngle Property of a triangle. THINK, DISCUSS ND WRITE 1. Exterior angles can be formed for a triangle in many ways. Three of them are shown here (Fig 6.10) Fig 6.10 There are three more ways of getting exterior angles. Try to produce those rough sketches. 2. re the exterior angles formed at each vertex of a triangle equal? 3. What can you say about the sum of an exterior angle of a triangle and its adjacent interior angle?
6 118 MTHEMTICS EXMPLE 1 Find angle x in Fig SOLUTION Sum of interior opposite angles = Exterior angle or 50 + x =110 or x = 60 Fig 6.11 THINK, DISCUSS ND WRITE 1. What can you say about each of the interior opposite angles, when the exterior angle is (i) a right angle? (ii) an obtuse angle? (iii) an acute angle? 2. Can the exterior angle of a triangle be a straight angle? TRY THESE Fig n exterior angle of a triangle is of measure 70º and one of its interior opposite angles is of measure 25º. Find the measure of the other interior opposite angle. 2. The two interior opposite angles of an exterior angle of a triangle are 60º and 80º. Find the measure of the exterior angle. 3. Is something wrong in this diagram (Fig 6.12)? Comment. EXERCISE Find the value of the unknown exterior angle x in the following diagrams:
7 THE TRINGLE ND ITS PROPERTIES Find the value of the unknown interior angle x in the following figures: 6.5 NGLE SUM PROPERTY OF TRINGLE There is a remarkable property connecting the three angles of a triangle. You are going to see this through the following four activities. 1. Draw a triangle. Cut on the three angles. Rearrange them as shown in Fig 6.13 (i), (ii). The three angles now constitute one angle. This angle is a straight angle and so has measure 180. (i) (ii) Fig 6.13 Thus, the sum of the measures of the three angles of a triangle is The same fact you can observe in a different way also. Take three copies of any triangle, say BC (Fig 6.14). Fig 6.14
8 120 MTHEMTICS rrange them as in Fig What do you observe about ? (Do you also see the exterior angle property?) Fig Take a piece of paper and cut out a triangle, say, BC (Fig 6.16). Make the altitude M by folding BC such that it passes through. Fold now the three corners such that all the three vertices, B and C touch at M. B C B M M (i) (ii) (iii) Fig 6.16 You find that all the three angles form together a straight angle. This again shows that the sum of the measures of the three angles of a triangle is Draw any three triangles, say BC, PQR and XYZ in your notebook. Use your protractor and measure each of the angles of these triangles. Tabulate your results Name of Measures of ngles Sum of the Measures of the three ngles BC m = m B = m C = m + m B + m C = PQR m P = m Q = m R = m P + m Q + m R = XYZ m X = m Y = m Z = m X + m Y + m Z = llowing marginal errors in measurement, you will find that the last column always gives 180 (or nearly 180 ). When perfect precision is possible, this will also show that the sum of the measures of the three angles of a triangle is 180. You are now ready to give a formal justification of your assertion through logical argument. Statement The total measure of the three angles of a triangle is 180. To justify this let us use the exterior angle property of a triangle. Fig 6.17 C
9 THE TRINGLE ND ITS PROPERTIES 121 Given 1, 2, 3 are angles of BC (Fig 6.17). 4 is the exterior angle when BC is extended to D. Justification = 4 (by exterior angle property) = (adding 3 to both the sides) But 4 and 3 form a linear pair so it is 180. Therefore, = 180. Let us see how we can use this property in a number of ways. EXMPLE 2 In the given figure (Fig 6.18) find m P. P SOLUTION By angle sum property of a triangle, m P = 180 Therefore m P = = = 81 Q Fig 6.18 R EXERCISE Find the value of the unknown x in the following diagrams: 2. Find the values of the unknowns x and y in the following diagrams:
10 122 MTHEMTICS TRY THESE 1. Two angles of a triangle are 30º and 80º. Find the third angle. 2. One of the angles of a triangle is 80º and the other two angles are equal. Find the measure of each of the equal angles. 3. The three angles of a triangle are in the ratio 1:2:1. Find all the angles of the triangle. Classify the triangle in two different ways. THINK, DISCUSS ND WRITE 1. Can you have a triangle with two right angles? 2. Can you have a triangle with two obtuse angles? 3. Can you have a triangle with two acute angles? 4. Can you have a triangle with all the three angles greater than 60º? 5. Can you have a triangle with all the three angles equal to 60º? 6. Can you have a triangle with all the three angles less than 60º? 6.6 TWO SPECIL TRINGLES : EQUILTERL ND ISOSCELES triangle in which all the three sides are of equal lengths is called an equilateral triangle. Take two copies of an equilateral triangle BC (Fig 6.19). Keep one of them fixed. Place the second triangle on it. It fits exactly into the first. Turn it round in any way and still they fit with one another exactly. re you able to see that when the three sides of a triangle have equal lengths then the three angles are also of the same size? We conclude that in an equilateral triangle: (i) all sides have same length. (ii) each angle has measure 60. B C (i) (ii) Fig 6.19
11 THE TRINGLE ND ITS PROPERTIES 123 triangle in which two sides are of equal lengths is called an isosceles triangle. Fig 6.20 From a piece of paper cut out an isosceles triangle XYZ, with XY=XZ (Fig 6.20). Fold it such that Z lies on Y. The line XM through X is now the axis of symmetry (which you will read in Chapter 14). You find that Y and Z fit on each other exactly. XY and XZ are called equal sides; YZ is called the base; Y and Z are called base angles and these are also equal. Thus, in an isosceles triangle: (i) two sides have same length. (ii) base angles opposite to the equal sides are equal. TRY THESE 1. Find angle x in each figure:
12 124 MTHEMTICS 2. Find angles x and y in each figure. Fig SUM OF THE LENGTHS OF TWO SIDES OF TRINGLE 1. Mark three non-collinear spots, B and C in your playground. Using lime powder mark the paths B, BC and C. sk your friend to start from and reach C, walking along one or more of these paths. She can, for example, walk first along B and then along BC to reach C; or she can walk straight along C. She will naturally prefer the direct path C. If she takes the other path ( B and then BC ), she will have to walk more. In other words, B + BC > C (i) Similarly, if one were to start from B and go to, he or she will not take the route BC and C but will prefer B This is because BC + C > B (ii) By a similar argument, you find that C + B > BC (iii) These observations suggest that the sum of the lengths of any two sides of a triangle is greater than the third side. 2. Collect fifteen small sticks (or strips) of different lengths, say, 6 cm, 7 cm, 8 cm, 9 cm,..., 20 cm. Take any three of these sticks and try to form a triangle. Repeat this by choosing different combinations of three sticks. Suppose you first choose two sticks of length 6 cm and 12 cm. Your third stick has to be of length more than 12 6 = 6 cm and less than = 18 cm. Try this and find out why it is so. To form a triangle you will need any three sticks such that the sum of the lengths of any two of them will always be greater than the length of the third stick. This also suggests that the sum of the lengths of any two sides of a triangle is greater than the third side.
13 THE TRINGLE ND ITS PROPERTIES Draw any three triangles, say BC, PQR and XYZ in your notebook (Fig 6.22). R B C P Q (i) (ii) (iii) Fig 6.22 Use your ruler to find the lengths of their side and then tabulate your results as follows: Name of Lengths of Sides Is this True? BC B B BC < C (Yes/No) + > BC BC C < B (Yes/No) + > C C B < BC (Yes/No) + > PQR PQ PQ QR < RP (Yes/No) + > QR QR RP < PQ (Yes/No) + > RP RP PQ < QR (Yes/No) + > XYZ XY XY YZ < ZX (Yes/No) + > YZ YZ ZX < XY (Yes/No) + > ZX ZX XY < YZ (Yes/No) + > This also strengthens our earlier guess. Therefore, we conclude that sum of the lengths of any two sides of a triangle is greater than the length of the third side. We also find that the difference between the length of any two sides of a triangle is smaller than the length of the third side.
14 126 MTHEMTICS EXMPLE 3 Is there a triangle whose sides have lengths 10.2 cm, 5.8 cm and 4.5 cm? SOLUTION Suppose such a triangle is possible. Then the sum of the lengths of any two sides would be greater than the length of the third side. Let us check this. Is > 10.2? Yes Is > 4.5? Yes Is > 5.8? Yes Therefore, the triangle is possible. EXMPLE 4 The lengths of two sides of a triangle are 6 cm and 8 cm. Between which two numbers can length of the third side fall? SOLUTION We know that the sum of two sides of a triangle is always greater than the third. Therefore, one-third side has to be less than the sum of the two sides. The third side is thus less than = 14 cm. The side cannot be less than the difference of the two sides. Thus the third side has to be more than 8 6 = 2 cm. The length of the third side could be any length greater than 2 and less than 14 cm. EXERCISE Is it possible to have a triangle with the following sides? (i) 2 cm, 3 cm, 5 cm (ii) 3 cm, 6 cm, 7 cm (iii) 6 cm, 3 cm, 2 cm R 2. Take any point O in the interior of a triangle PQR. Is (i) OP + OQ > PQ? (ii) OQ + OR > QR? (iii) OR + OP > RP? P O Q 3. M is a median of a triangle BC. Is B + BC + C > 2 M? (Consider the sides of triangles BM and MC.) B M C 4. BCD is a quadrilateral. Is B + BC + CD + D > C + BD? 5. BCD is quadrilateral. Is B + BC + CD + D < 2 (C + BD)?
15 THE TRINGLE ND ITS PROPERTIES The lengths of two sides of a triangle are 12 cm and 15 cm. Between what two measures should the length of the third side fall? THINK, DISCUSS ND WRITE 1. Is the sum of any two angles of a triangle always greater than the third angle? 6.8 RIGHT-NGLED TRINGLES ND PYTHGORS PROPERTY Pythagoras, a Greek philosopher of sixth century B.C. is said to have found a very important and useful property of right-angled triangles given in this section. The property is hence named after him. In fact, this property was known to people of many other countries too. The Indian mathematician Baudhayan has also given an equivalent form of this property. We now try to explain the Pythagoras property. Fig 6.23 In a right angled triangle, the sides have some special names. The side opposite to the right angle is called the hypotenuse; the other two sides are known as the legs of the right-angled triangle. In BC (Fig 6.23), the right-angle is at B. So, C is the hypotenuse. B and BC are the legs of BC. Make eight identical copies of right angled triangle of any size you prefer. For example, you make a right-angled triangle whose hypotenuse is a units long and the legs are of lengths b units and c units (Fig 6.24). Fig 6.24 Draw two identical squares on a sheet with sides of lengths b + c. You are to place four triangles in one square and the remaining four triangles in the other square, as shown in the following diagram (Fig 6.25). Square Fig 6.25 Square B
16 128 MTHEMTICS DO THIS The squares are identical; the eight triangles inserted are also identical. Hence the uncovered area of square = Uncovered area of square B. i.e., rea of inner square of square = The total area of two uncovered squares in square B. a 2 = b 2 + c 2 This is Pythagoras property. It may be stated as follows: In a right-angled triangle, the square on the hypotenuse = sum of the squares on the legs. Pythagoras property is a very useful tool in mathematics. It is formally proved as a theorem in later classes. You should be clear about its meaning. It says that for any right-angled triangle, the area of the square on the hypotenuse is equal to the sum of the areas of the squares on the legs. Draw a right triangle, preferably on a square sheet, construct squares on its sides, compute the area of these squares and verify the theorem practically (Fig 6.26). If you have a right-angled triangle, the Pythagoras property holds. If the Pythagoras property holds for some triangle, will the triangle be rightangled? (Such problems are known as converse problems). We will try to answer this. Now, we will show that, if there is a triangle such that sum of the squares on two of its sides is equal to the square of the third side, it must Fig 6.26 be a right-angled triangle. 1. Have cut-outs of squares with sides 4 cm, 5 cm, 6 cm long. rrange to get a triangular shape by placing the corners of the squares suitably as shown in the figure (Fig 6.27). Trace out the triangle formed. Measure each angle of the triangle. You find that there is no right angle at all. In fact, in this case each angle will be acute! Note that , and Fig 6.27
17 THE TRINGLE ND ITS PROPERTIES Repeat the above activity with squares whose sides have lengths 4 cm, 5 cm and 7 cm. You get an obtuse angled triangle! Note that etc. This shows that Pythagoras property holds if and only if the triangle is right-angled. Hence we get this fact: If the Pythagoras property holds, the triangle must be right-angled. EXMPLE 5 Determine whether the triangle whose lengths of sides are 3 cm, 4 cm, 5 cm is a right-angled triangle. SOLUTION 3 2 = 3 3 = 9; 4 2 = 4 4 = 16; 5 2 = 5 5 = 25 We find = 5 2. Therefore, the triangle is right-angled. Note: In any right-angled triangle, the hypotenuse happens to be the longest side. In this example, the side with length 5 cm is the hypotenuse. EXMPLE 6 BC is right-angled at C. If C = 5 cm and BC = 12 cm find the length of B. SOLUTION rough figure will help us (Fig 6.28). By Pythagoras property, Fig 6.28 B 2 =C 2 + BC 2 = = = 169 = 13 2 or B 2 =13 2. So, B = 13 or the length of B is 13 cm. Note: To identify perfect squares, you may use prime factorisation technique. TRY THESE Find the unknown length x in the following figures (Fig 6.29):
18 130 MTHEMTICS 24 x (iv) x (v) Fig 6.29 EXERCISE PQR is a triangle right angled at P. If PQ = 10 cm and PR = 24 cm, find QR. 2. BC is a triangle right angled at C. If B = 25 cm and C = 7 cm, find BC m long ladder reached a window 12 m high from the ground on placing it against a wall at a distance a. Find the distance of the foot of the ladder from the wall. 4. Which of the following can be the sides of a right triangle? (i) 2.5 cm,6.5 cm, 6 cm. (ii) 2 cm, 2 cm, 5 cm. (iii) 1.5 cm, 2cm, 2.5 cm. In the case of right-angled triangles, identify the right angles. 5. tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tree. Find the original height of the tree. 6. ngles Q and R of a PQR are 25º and 65º. P Write which of the following is true: (i) PQ 2 + QR 2 = RP 2 (ii) PQ 2 + RP 2 = QR (iii) RP 2 + QR 2 = PQ 2 Q R 7. Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm. 8. The diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter.
19 THE TRINGLE ND ITS PROPERTIES 131 THINK, DISCUSS ND WRITE 1. Which is the longest side in the triangle PQR right angled at P? 2. Which is the longest side in the triangle BC right angled at B? 3. Which is the longest side of a right triangle? 4. The diagonal of a rectangle produce by itself the same area as produced by its length and breadth This is Baudhayan Theorem. Compare it with the Pythagoras property. DO THIS Enrichment activity There are many proofs for Pythagoras theorem, using dissection and rearrangement procedure. Try to collect a few of them and draw charts explaining them. WHT HVE WE DISCUSSED? 1. The six elements of a triangle are its three angles and the three sides. 2. The line segment joining a vertex of a triangle to the mid point of its opposite side is called a median of the triangle. triangle has 3 medians. 3. The perpendicular line segment from a vertex of a triangle to its opposite side is called an altitude of the triangle. triangle has 3 altitudes. 4. n exterior angle of a triangle is formed when a side of a triangle is produced. t each vertex, you have two ways of forming an exterior angle. 5. property of exterior angles: The measure of any exterior angle of a triangle is equal to the sum of the measures of its interior opposite angles. 6. The angle sum property of a triangle: The total measure of the three angles of a triangle is triangle is said to be equilateral if each one of its sides has the same length. In an equilateral triangle, each angle has measure triangle is said to be isosceles if atleast any two of its sides are of same length. The non-equal side of an isosceles triangle is called its base; the base angles of an isosceles triangle have equal measure. 9. Property of the lengths of sides of a triangle: The sum of the lengths of any two sides of a triangle is greater than the length of the third side. The difference between the lengths of any two sides is smaller than the length of the third side.
20 132 MTHEMTICS This property is useful to know if it is possible to draw a triangle when the lengths of the three sides are known. 10. In a right angled triangle, the side opposite to the right angle is called the hypotenuse and the other two sides are called its legs. 11. Pythagoras Property: In a right-angled triangle, the square on the hypotenuse = the sum of the squares on its legs. If a triangle is not right angled this property does not hold good. This property is useful to decide whether a given triangle is right angled or not.
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# Understanding Cylindrical Coordinates in Geometry
## What are Cylindrical Coordinates?
Cylindrical coordinates are an important concept in geometry, and are used to describe points in three-dimensional space. These coordinates are composed of three numbers, referred to as r, ?, and z. Cylindrical coordinates are also sometimes referred to as polar coordinates, or spherical coordinates.
The first number, r, is the distance from the origin, which is the point (0, 0, 0) in space. The second number, ?, is the angle from the z-axis in the xy-plane. The third number, z, is the height from the xy-plane.
## Using Cylindrical Coordinates to Describe Vector Fields
Cylindrical coordinates can be used to describe vector fields, which are mathematical objects that can be used to describe the direction and magnitude of forces in physical systems. Vector fields are described using cylindrical coordinates by using three equations; one for each coordinate. The equations used to describe vector fields in cylindrical coordinates are as follows:
• Fr = (r, ?, z) * (cos ?, sin ?, 0)
• F? = (r, ?, z) * ( -sin ?, cos ?, 0)
• Fz = (r, ?, z) * (0, 0, 1)
These equations are used to calculate the components of a vector field in cylindrical coordinates.
## Cylindrical Surfaces and Cylindrical Graphs
Cylindrical coordinates can also be used to describe cylindrical surfaces and cylindrical graphs. Cylindrical surfaces are surfaces described by equations of the form z = f(r, ?). Cylindrical graphs are graphs of functions of the form z = f(r, ?). Both of these types of surfaces and graphs can be used to visualize and analyze data in three-dimensional space.
## Practice Problems
Let�s try some practice problems to test our understanding of cylindrical coordinates.
1. What is the equation for a cylindrical surface?
The equation for a cylindrical surface is z = f(r, ?).
2. What are the three equations used to describe vector fields in cylindrical coordinates?
The three equations used to describe vector fields in cylindrical coordinates are: Fr = (r, ?, z) * (cos ?, sin ?, 0), F? = (r, ?, z) * ( -sin ?, cos ?, 0), and Fz = (r, ?, z) * (0, 0, 1).
3. What is the point (0, 0, 0) in space referred to as?
The point (0, 0, 0) in space is referred to as the origin.
4. What is the angle from the z-axis in the xy-plane referred to as?
The angle from the z-axis in the xy-plane is referred to as ?.
5. What is the height from the xy-plane referred to as?
The height from the xy-plane is referred to as z.
6. What kind of graphs can be used to visualize and analyze data in three-dimensional space?
Cylindrical graphs of functions of the form z = f(r, ?) can be used to visualize and analyze data in three-dimensional space.
## Summary
Cylindrical coordinates are an important concept in geometry, and are used to describe points in three-dimensional space. The three coordinates are referred to as r, ?, and z, and they represent the distance from the origin, the angle from the z-axis in the xy-plane, and the height from the xy-plane, respectively. Cylindrical coordinates can be used to describe vector fields and cylindrical surfaces and graphs. By understanding cylindrical coordinates, we can better understand and visualize data in three-dimensional space.
## FAQ
### What is the formula for the conversion between cylindrical and Cartesian coordinates?
The formula for the conversion between cylindrical and Cartesian coordinates is: x = rcos?, y = rsin?, z = z.
### What are the three coordinates in cylindrical coordinates?
The three coordinates in cylindrical coordinates are the radial distance (r), the angle (?), and the height (z).
### What are the advantages of using cylindrical coordinates?
The advantages of using cylindrical coordinates include the ability to easily represent 3-dimensional objects in a 2-dimensional plane, the ability to describe curved surfaces, and the ability to simplify calculations. Cylindrical coordinates are also useful for representing motion in a vertical plane, such as a projectile motion. | 901 | 4,084 | {"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-2024-38 | latest | en | 0.889338 |
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# solution_pdf21 - reddy(ar38357 – Rotational Kinetic...
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Unformatted text preview: reddy (ar38357) – Rotational Kinetic Energy – clancy – (SCI411-2) 1 This print-out should have 6 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A 0 . 25 m power sawblade has a mass of 0 . 5 kg distributed uniformly as in a disc. What is the rotational kinetic energy at 3600 rpm (revolutions per minute)? 1. 3 . 6 × 10 1 J 2. 2 . 6 × 10 3 J 3. 8 . 9 × 10 1 J 4. 1 . 1 × 10 3 J correct 5. 9 . 1 × 10 2 J Explanation: Let : r = 0 . 25 m , m = 0 . 5 kg , and ω = 3600 rpm . The moment of inertia of a disk of uniform density is I = 1 2 mr 2 . The rotational kinetic energy of the saw- blade is then K rot = 1 2 I ω 2 = 1 2 parenleftbigg 1 2 mr 2 parenrightbigg ω 2 = 1 4 (0 . 5 kg)(0 . 25 m) 2 (3600 rpm) 2 × parenleftbigg 2 π rev parenrightbigg 2 parenleftbigg 1 min 60 s parenrightbigg 2 = 1110 . 33 J . 002 10.0 points The net work done in accelerating a propeller from rest to an angular speed of 214 rad/s is 2892 . 2 J....
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Ask a homework question - tutors are online | 532 | 1,662 | {"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} | 3.078125 | 3 | CC-MAIN-2018-09 | latest | en | 0.734239 |
https://www.fkspk.ru/how-to-solve-percentage-word-problems-285.html | 1,619,096,793,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618039610090.97/warc/CC-MAIN-20210422130245-20210422160245-00528.warc.gz | 857,276,951 | 9,360 | # How To Solve Percentage Word Problems
: The pie chart or circle graph below shows the total enrollment of students at State College during the Fall 2002 semester, broken down into seniors, juniors, sophomores, and freshmen. What do you think the first part of the ratio, freshmen or seniors? That leaves the number associated with seniors to be our second part of the ratio. So the ratio of freshman to seniors would be 40 to 12.Since freshmen are listed first, that is what our first number of our ratio has to correspond to. You can think of ratios as fractions, and simplify them in the same manner.When we take a percentage of a number, we write the percentage in decimal form and then multiply it times the number we are taking the percentage of.
The problem says that the Fall 2002 semester has 20% more sophomores than the Fall 2001 semester.
What percentage of the students were juniors in the Fall 2002 semester? So what would be the measure of the central angle for juniors for the Fall 2002 semester?
Since a full circle is 360 degrees, we are basically wanting to know what 18% of 360 degrees is.
The bottom right sector shows that vanilla made 29% of the profits in 2002.
The bottom left sector shows that strawberry made 30% of the profits in 2002. In the Fall 2002 semester, what was the ratio of freshmen to seniors at the college? If the number of sophomores in the Fall 2002 semester was 20% higher than the number of sophomores in the Fall 2001 semester, how many sophomores were enrolled in Fall 2001? If the areas of sectors in the circle graphs are drawn in proportion to the percentages shown, what is the measure, in degrees, of the central angle sector representing the percentage of juniors?
## Comments How To Solve Percentage Word Problems
• ###### Percent Maths Problems
Problems that deal with percentage increase and decrease as well as problems. Several word problems on percentage with detailed solutions are presented.…
• ###### Word Problems Involving Percent - Varsity Tutors
Three Kinds of Percent Problems. Consider the statement " x percent of y is z." If any two of the variables are given, you can use algebra to find out the missing.…
• ###### Percent Word Problems solutions, examples, videos
Percent Word Problems - Examples and Worked Solutions of Word Problems using block diagrams, How to solve percent problems with bar models or tape.…
• ###### Percent Word Problems -
Percent Word Problems Learn how to solve word problems that involve percents.…
• ###### Word Problems on Percentage Percent Problems Real Life.
Word problems on percentage will help us to solve various types of problems related to percentage. Follow the procedure to solve similar type of percent problems.…
• ###### Percentage Word Problems -
This Word Problems Worksheet will produce problems that focus on finding and working with percentages. You have the option to select the types of numbers.…
• ###### Solve percent equations word problems 7th grade math - IXL
Improve your math knowledge with free questions in "Solve percent equations word problems" and thousands of other math skills.…
• ###### Using the Proportion Method to Solve Percent Problems
There are a variety of ways to solve percent problems, many of which can be VERY confusing. 3 appears with the word is It's the PART and goes on top.… | 706 | 3,352 | {"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} | 4.40625 | 4 | CC-MAIN-2021-17 | longest | en | 0.935718 |
https://issuu.com/ta.mmiealstonbaro.nr.aff/docs/mth_233 | 1,553,232,961,000,000,000 | text/html | crawl-data/CC-MAIN-2019-13/segments/1552912202628.42/warc/CC-MAIN-20190322034516-20190322060516-00379.warc.gz | 534,674,435 | 19,607 | MTH 233 Entire Course
For more classes visit www.snaptutorial.com MTH 233 Week 2 Individual Assignment: Individual Assignment #1 MTH 233 Week 2 Learning Team Assignment: Learning Team Assignment #1 MTH 233 Week 3 Learning Team Assignment: Learning Team Assignment MTH 233 Week 4 Individual Assignment: Individual Assignment MTH 233 Week 5 Individual Assignment: Individual Assignment MTH 233 Week 5 Learning Team Assignment: Hypothesis Testing and Regression Analysis Paper only MTH 233 Learning Team Assignment: Hypothesis Testing and Regression Analysis Presentation *********************************************************
MTH 233 Learning Team Assignment Hypothesis Testing and Regression Analysis Presentation
For more classes visit www.snaptutorial.com Resources: University Library and the Internet Select a research issue, problem, or opportunity facing a Learning Team member’s organization to examine using hypothesis testing and a regression analysis on the collected data. Write a 1,050- to 1,750-word paper describing a new hypothesis test using a different statistic (e.g., large sample size, small sample size, means and/or proportions, one- and two-tailed tests) to perform on that data. Formulate a new hypothesis statement and perform the five-step hypothesis test on the data. Describe the results of the tests. Interpret the results of the regression analysis, state the limitations of the analysis, and describe the significance of the results to the organization. Be sure to attach the results of the regression analysis created in MicrosoftŽ Excel to your paper. Present the results to the class in a 10-minute PowerPointŽ presentation *********************************************************
MTH 233 Week 2 Individual Assignment Individual Assignment 1
For more classes visit www.snaptutorial.com Resources: Ch.1 & 2 of Elementary Statistics Solve the following problems from Ch. 1: Problems 9–10 in Section 1.1 and problems 11–12 in Section 1.2 on p. 25 Problems 17–18 in Section 1.2 and problems 19–20 in Section 1.3 on p. 26 Quiz, problems 1–3 and 6–8 on p. 27 Solve the following problems from Ch. 2 Problems 3–4 in Section 2.1 on p. 107 Problems 19–20 in Section 2.3 on p. 108, Problems: 37–40 in Section 2.5 on p. 110 Quiz, problems 3–7 on p. 111 *********************************************************
MTH 233 Week 2 Learning Team Assignment Learning Team Assignment 1
For more classes visit www.snaptutorial.com Resources: Ch.1 & 2 of Elementary Statistics Complete the following problems from Ch. 1 of Elementary Statistics: Case Study on p. 15 Real Statistics/Real Decisions on p. 28 Complete the following problems from Ch. 2 of Elementary Statistics: Case Study on p. 92 Real Statistics/Real Decisions on p. 112 *********************************************************
MTH 233 Week 3 Learning Team Assignment Learning Team Assignment
For more classes visit www.snaptutorial.com
Resources: Resource Ch. 6 & 7 of Elementary Statistics Solve the following problems from Ch. 6: Case Study on p. 294 Solve the following problems from Ch. 7: Case Study on p. 363 Real Statistics/Real Decisions on p. 398 *********************************************************
MTH 233 Week 4 Individual Assignment Individual Assignment
For more classes visit www.snaptutorial.com Resources: Ch. 7 of Elementary Statistics Solve the following problems from Ch. 7: Problems 23 and 37 in Section 7.3 on pp. 371–373, Problems 10 and 15 in Section 7.4 on pp. 378–379, Problems 17 and 24 in Section 7.5 on pp. 387–388
*********************************************************
MTH 233 Week 5 Individual Assignment Individual Assignment
For more classes visit www.snaptutorial.com Resources: Ch. 9 & 10 of Elementary Statistics Complete the Quiz problems 1–9 on p. 505 in Ch. 9. Complete Review Exercises problem 4 on p. 557 and problem 16 on p. 559 in Ch. 10. *********************************************************
MTH 233 Week 5 Learning Team Assignment Hypothesis Testing and Regression Analysis Paper nly
For more classes visit www.snaptutorial.com Resources: University Library and the Internet
Select a research issue, problem, or opportunity facing a Learning Team member’s organization to examine using hypothesis testing and a regression analysis on the collected data. Write a 1,050- to 1,750-word paper describing a new hypothesis test using a different statistic (e.g., large sample size, small sample size, means and/or proportions, one- and two-tailed tests) to perform on that data. Formulate a new hypothesis statement and perform the five-step hypothesis test on the data. Describe the results of the tests. Interpret the results of the regression analysis, state the limitations of the analysis, and describe the significance of the results to the organization. Be sure to attach the results of the regression analysis created in MicrosoftŽ Excel to your paper. Present the results to the class in a 10-minute PowerPointŽ presentation *********************************************************
# MTH 233 Effective Communication-snaptutorial.com
For more classes visit www.snaptutorial.com MTH 233 Week 2 Individual Assignment: Individual Assignment #1 MTH 233 Week 2 Learning Team As...
# MTH 233 Effective Communication-snaptutorial.com
For more classes visit www.snaptutorial.com MTH 233 Week 2 Individual Assignment: Individual Assignment #1 MTH 233 Week 2 Learning Team As... | 1,210 | 5,485 | {"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 | 4 | CC-MAIN-2019-13 | latest | en | 0.817503 |
http://nrich.maths.org/public/leg.php?code=17&cl=4&cldcmpid=857 | 1,477,273,784,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988719463.40/warc/CC-MAIN-20161020183839-00287-ip-10-171-6-4.ec2.internal.warc.gz | 186,711,723 | 8,537 | # Search by Topic
#### Resources tagged with Powers & roots similar to Square Pair Circles:
Filter by: Content type:
Stage:
Challenge level:
### There are 39 results
Broad Topics > Numbers and the Number System > Powers & roots
### Square Pair Circles
##### Stage: 5 Challenge Level:
Investigate the number of points with integer coordinates on circles with centres at the origin for which the square of the radius is a power of 5.
### The Root Cause
##### Stage: 5 Challenge Level:
Prove that if a is a natural number and the square root of a is rational, then it is a square number (an integer n^2 for some integer n.)
### How Many Solutions?
##### Stage: 5 Challenge Level:
Find all the solutions to the this equation.
### Plus or Minus
##### Stage: 5 Challenge Level:
Make and prove a conjecture about the value of the product of the Fibonacci numbers $F_{n+1}F_{n-1}$.
### Rational Roots
##### Stage: 5 Challenge Level:
Given that a, b and c are natural numbers show that if sqrt a+sqrt b is rational then it is a natural number. Extend this to 3 variables.
### Archimedes and Numerical Roots
##### Stage: 4 Challenge Level:
The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?
### Perfectly Square
##### Stage: 4 Challenge Level:
The sums of the squares of three related numbers is also a perfect square - can you explain why?
##### Stage: 3 and 4 Challenge Level:
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
### Number Rules - OK
##### Stage: 4 Challenge Level:
Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...
### Consecutive Squares
##### Stage: 4 Challenge Level:
The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?
### Smith and Jones
##### Stage: 4 Challenge Level:
Mr Smith and Mr Jones are two maths teachers. By asking questions, the answers to which may be right or wrong, Mr Jones is able to find the number of the house Mr Smith lives in... Or not!
### Pythagorean Fibs
##### Stage: 5 Challenge Level:
What have Fibonacci numbers got to do with Pythagorean triples?
### In Between
##### Stage: 5 Challenge Level:
Can you find the solution to this algebraic inequality?
### Giants
##### Stage: 5 Challenge Level:
Which is the bigger, 9^10 or 10^9 ? Which is the bigger, 99^100 or 100^99 ?
### Rationals Between...
##### Stage: 4 Challenge Level:
What fractions can you find between the square roots of 65 and 67?
### Root to Poly
##### Stage: 4 Challenge Level:
Find the polynomial p(x) with integer coefficients such that one solution of the equation p(x)=0 is $1+\sqrt 2+\sqrt 3$.
### Unusual Long Division - Square Roots Before Calculators
##### Stage: 4 Challenge Level:
However did we manage before calculators? Is there an efficient way to do a square root if you have to do the work yourself?
### Negative Power
##### Stage: 4 Challenge Level:
What does this number mean ? Which order of 1, 2, 3 and 4 makes the highest value ? Which makes the lowest ?
### Weekly Challenge 34: Googol
##### Stage: 5 Short Challenge Level:
Find the smallest value for which a particular sequence is greater than a googol.
### Staircase
##### Stage: 5 Challenge Level:
Solving the equation x^3 = 3 is easy but what about solving equations with a 'staircase' of powers?
### Fibonacci Fashion
##### Stage: 5 Challenge Level:
What have Fibonacci numbers to do with solutions of the quadratic equation x^2 - x - 1 = 0 ?
### Ab Surd Ity
##### Stage: 5 Challenge Level:
Find the value of sqrt(2+sqrt3)-sqrt(2-sqrt3)and then of cuberoot(2+sqrt5)+cuberoot(2-sqrt5).
### Weekly Challenge 16: Archimedes Numerical Roots
##### Stage: 5 Challenge Level:
The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?
### Guesswork
##### Stage: 4 Challenge Level:
Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.
### The Root of the Problem
##### Stage: 4 and 5 Challenge Level:
Find the sum of the series.
### Em'power'ed
##### Stage: 5 Challenge Level:
Find the smallest numbers a, b, and c such that: a^2 = 2b^3 = 3c^5 What can you say about other solutions to this problem?
### Equal Temperament
##### Stage: 4 Challenge Level:
The scale on a piano does something clever : the ratio (interval) between any adjacent points on the scale is equal. If you play any note, twelve points higher will be exactly an octave on.
### Mod 7
##### Stage: 5 Challenge Level:
Find the remainder when 3^{2001} is divided by 7.
### Take a Square
##### Stage: 4 Challenge Level:
Cut off three right angled isosceles triangles to produce a pentagon. With two lines, cut the pentagon into three parts which can be rearranged into another square.
### Double Trouble
##### Stage: 4 Challenge Level:
Simple additions can lead to intriguing results...
### Function Pyramids
##### Stage: 5 Challenge Level:
A function pyramid is a structure where each entry in the pyramid is determined by the two entries below it. Can you figure out how the pyramid is generated?
### Power Countdown
##### Stage: 4 Challenge Level:
In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.
### Fit for Photocopying
##### Stage: 4 Challenge Level:
Photocopiers can reduce from A3 to A4 without distorting the image. Explore the relationships between different paper sizes that make this possible.
### Napier's Location Arithmetic
##### Stage: 4 Challenge Level:
Have you seen this way of doing multiplication ?
### Enriching Experience
##### Stage: 4 Challenge Level:
Find the five distinct digits N, R, I, C and H in the following nomogram
### Lost in Space
##### Stage: 4 Challenge Level:
How many ways are there to count 1 - 2 - 3 in the array of triangular numbers? What happens with larger arrays? Can you predict for any size array?
### Route to Root
##### Stage: 5 Challenge Level:
A sequence of numbers x1, x2, x3, ... starts with x1 = 2, and, if you know any term xn, you can find the next term xn+1 using the formula: xn+1 = (xn + 3/xn)/2 . Calculate the first six terms of this. . . .
### Rachel's Problem
##### Stage: 4 Challenge Level:
Is it true that $99^n$ has 2n digits and $999^n$ has 3n digits? Investigate!
### Deep Roots
##### Stage: 4 Challenge Level:
Find integer solutions to: $\sqrt{a+b\sqrt{x}} + \sqrt{c+d.\sqrt{x}}=1$ | 1,651 | 6,789 | {"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-2016-44 | longest | en | 0.856909 |
http://cremes.meags.net/index.php/kindle/category/abstract | 1,656,882,174,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656104249664.70/warc/CC-MAIN-20220703195118-20220703225118-00775.warc.gz | 15,129,728 | 10,791 | ## Cohomology of Number Fields by Jürgen Neukirch
By Jürgen Neukirch
This moment version is a corrected and prolonged model of the 1st. it's a textbook for college students, in addition to a reference booklet for the operating mathematician, on cohomological issues in quantity thought. In all it's a nearly whole therapy of an unlimited array of vital issues in algebraic quantity concept. New fabric is brought the following on duality theorems for unramified and tamely ramified extensions in addition to a cautious research of 2-extensions of actual quantity fields.
## Galois Theory of Linear Differential Equations by Marius Put
By Marius Put
Linear differential equations shape the imperative subject of this quantity, with the Galois conception being the unifying subject. a number of points are provided: algebraic concept specially differential Galois conception, formal conception, class, algorithms to choose solvability in finite phrases, monodromy and Hilbert's 21th challenge, asymptotics and summability, the inverse challenge and linear differential equations in confident attribute. The appendices target to assist the reader with the innovations of algebraic geometry, linear algebraic teams, sheaves, and tannakian different types which are used. This quantity turns into a customary reference for all operating during this region of arithmetic on the graduate point, together with graduate scholars.
By V. Bargmann
## Laplace Transform Theory and Applications by Joel L. Schiff
By Joel L. Schiff
The Laplace rework is a superb device for fixing usual and partial differential equations and has loved a lot good fortune during this realm. With its luck, although, a definite casualness has been bred touching on its software, with out a lot regard for hypotheses and once they are legitimate. Even proofs of theorems frequently lack rigor, and doubtful mathematical practices are usually not unusual within the literature for college students. within the current textual content, i've got attempted to carry to the topic a specific amount of mathematical correctness and make it available to un dergraduates. Th this finish, this article addresses a few concerns which are not often thought of. for example, after we observe the Laplace trans shape solution to a linear traditional differential equation with consistent coefficients, any(n) + an-lY(n-l) + · · · + aoy = f(t), why is it justified to take the Laplace remodel of either side of the equation (Theorem A. 6)? Or, in lots of proofs it's required to take the restrict inside of an fundamental. this is often regularly fraught with hazard, specially with an incorrect quintessential, and never consistently justified. i've got given entire information (sometimes within the Appendix) at any time when this approach is needed. IX X Preface additionally, it truly is occasionally fascinating to take the Laplace trans kind of an enormous sequence time period by way of time period. back it truly is proven that this can't regularly be performed, and particular adequate stipulations are tested to justify this operation.
## Geometric Topology: Localization, Periodicity and Galois by Dennis P. Sullivan, Andrew Ranicki
By Dennis P. Sullivan, Andrew Ranicki
The seminal `MIT notes' of Dennis Sullivan have been issued in June 1970 and have been greatly circulated on the time, yet in simple terms privately. The notes had an enormous impression at the improvement of either algebraic and geometric topology, pioneering the localization and final touch of areas in homotopy thought, together with P-local, profinite and rational homotopy idea, the Galois motion on delicate manifold buildings in profinite homotopy conception, and the K-theory orientation of PL manifolds and bundles. this is often the 1st time that this significant paintings has really been released, and made to be had to somebody drawn to topology.
## Algebras of Functions on Quantum Groups: Part I by Leonid I. Korogodski
By Leonid I. Korogodski
The publication is dedicated to the learn of algebras of services on quantum teams. The authors' method of the topic relies at the parallels with symplectic geometry, permitting the reader to exploit geometric instinct within the thought of quantum teams. The ebook comprises the idea of Poisson Lie teams (quasi-classical model of algebras of capabilities on quantum groups), an outline of representations of algebras of features, and the idea of quantum Weyl teams. This booklet can function a textual content for an creation to the speculation of quantum teams.
## First course in abstract algebra: with applications by Joseph J. Rotman
By Joseph J. Rotman
this article introduces readers to the algebraic suggestions of team and earrings, supplying a accomplished dialogue of thought in addition to an important variety of functions for each.
Number idea: Induction; Binomial Coefficients; maximum universal Divisors; the basic Theorem of mathematics
Congruences; Dates and Days. Groups I: a few Set thought; diversifications; teams; Subgroups and Lagrange's Theorem; Homomorphisms; Quotient teams; team activities; Counting with teams. Commutative jewelry I: First homes; Fields; Polynomials; Homomorphisms; maximum universal Divisors; precise Factorization; Irreducibility; Quotient earrings and Finite Fields; officials, Magic, Fertilizer, and Horizons. Linear Algebra: Vector areas; Euclidean structures; Linear ameliorations; Determinants; Codes; Canonical kinds. Fields: Classical formulation; Insolvability of the final Quintic; Epilog. Groups II: Finite Abelian teams; The Sylow Theorems; decorative Symmetry. Commutative jewelry III: best beliefs and Maximal beliefs; specified Factorization; Noetherian earrings; forms; Grobner Bases.
For all readers drawn to summary algebra.
## Inequalities: A Journey into Linear Analysis: A Journey into by D. J. H. Garling
By D. J. H. Garling
Includes a wealth of inequalities utilized in linear research, and explains intimately how they're used. The booklet starts off with Cauchy's inequality and ends with Grothendieck's inequality, in among one unearths the Loomis-Whitney inequality, maximal inequalities, inequalities of Hardy and of Hilbert, hypercontractive and logarithmic Sobolev inequalities, Beckner's inequality, and plenty of, many extra. The inequalities are used to procure homes of functionality areas, linear operators among them, and of unique sessions of operators reminiscent of completely summing operators. This textbook enhances and fills out normal remedies, delivering many different functions: for instance, the Lebesgue decomposition theorem and the Lebesgue density theorem, the Hilbert rework and different singular necessary operators, the martingale convergence theorem, eigenvalue distributions, Lidskii's hint formulation, Mercer's theorem and Littlewood's 4/3 theorem. it's going to develop the data of postgraduate and examine scholars, and may additionally entice their lecturers, and all who paintings in linear research.
## The Heart of Cohomology by Goro Kato
By Goro Kato
If you haven't heard approximately cohomology, this ebook can be fitted to you. primary notions in cohomology for examples, functors, representable functors, Yoneda embedding, derived functors, spectral sequences, derived different types are defined in user-friendly type. purposes to sheaf cohomology are given. additionally cohomological features of D-modules and of the computation of zeta features of the Weierstrass kinfolk are provided.
## A primer of algebraic D-modules by S. C. Coutinho
By S. C. Coutinho
The idea of D-modules is a wealthy zone of analysis combining principles from algebra and differential equations, and it has major functions to different components reminiscent of singularity idea and illustration idea. This ebook introduces D-modules and their functions, warding off all pointless technicalities. the writer takes an algebraic strategy, targeting the function of the Weyl algebra. the writer assumes only a few necessities, and the booklet is almost self-contained. the writer comprises routines on the finish of every bankruptcy and offers the reader plentiful references to the extra complicated literature. this can be a great creation to D-modules for all who're new to this quarter. | 1,745 | 8,312 | {"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-2022-27 | latest | en | 0.927078 |
http://rigidgeometricalgebra.org/wiki/index.php?title=Magnitude | 1,723,514,645,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641054522.78/warc/CC-MAIN-20240813012759-20240813042759-00453.warc.gz | 20,766,425 | 5,630 | # Magnitude
A magnitude is a quantity that represents a concrete measurement of some kind. In rigid geometric algebra, a magnitude $$\mathbf z$$ is composed of two components, a scalar and an antiscalar, as follows:
$$\mathbf z = x\mathbf 1 + y {\large\unicode{x1d7d9}}$$
Magnitudes are homogeneous just like everything else in a projective geometric algebra. This means it has both a bulk and a weight, and it is unitized by making the magnitude of its weight one.
### Examples
• The geometric norm produces a magnitude that gives the perpendicular distance between an object and the origin. This is also half the distance that the origin is moved by an object used as an operator.
• Euclidean distances between objects are expressed as magnitudes given by the sum of the bulk norm and weight norm of expressions involving attitudes.
• Exponentiating the magnitude $$\delta\mathbf 1 + \phi {\large\unicode{x1d7d9}}$$ produces a motor for which $$\delta/\phi$$ is the pitch of the screw transformation. | 232 | 1,007 | {"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} | 3.578125 | 4 | CC-MAIN-2024-33 | latest | en | 0.91197 |
http://www.ask.com/question/How-Many-Pints-Are-in-a-Pound | 1,387,449,730,000,000,000 | text/html | crawl-data/CC-MAIN-2013-48/segments/1387345762908/warc/CC-MAIN-20131218054922-00097-ip-10-33-133-15.ec2.internal.warc.gz | 243,938,814 | 19,085 | # How Many Pints Are in a Pound?
Since a pint is a unit of volume, and a pound is a unit of weight, there is no single, universal answer to the number of pints that equal one pound. It depends entirely on the substance that is being weighed or measured. For arguments sake though, we?ll assume that we?re talking about a pint of distilled water, which has a density of one. A pint contains sixteen fluid ounces, which also happen to equal sixteen ounces of weight or one pound. So in this instance, a pint of water weighs one pound. Again remember that this only apples to water. Other substances of different densities will have different weight to volume ratios.
Reference: | 145 | 676 | {"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-2013-48 | longest | en | 0.943621 |
http://www.nag.com/numeric/cl/nagdoc_cl08/examples/source/f08sece.c | 1,394,461,617,000,000,000 | text/plain | crawl-data/CC-MAIN-2014-10/segments/1394010840808/warc/CC-MAIN-20140305091400-00006-ip-10-183-142-35.ec2.internal.warc.gz | 453,395,916 | 2,015 | /* nag_dsygst (f08sec) Example Program. * * Copyright 2001 Numerical Algorithms Group. * * Mark 7, 2001. */ #include #include #include #include #include int main(void) { /* Scalars */ Integer i, j, n, pda, pdb, d_len, e_len, tau_len; Integer exit_status=0; NagError fail; Nag_UploType uplo; Nag_OrderType order; /* Arrays */ char uplo_char[2]; double *a=0, *b=0, *d=0, *e=0, *tau=0; #ifdef NAG_COLUMN_MAJOR #define A(I,J) a[(J-1)*pda + I - 1] #define B(I,J) b[(J-1)*pdb + I - 1] order = Nag_ColMajor; #else #define A(I,J) a[(I-1)*pda + J - 1] #define B(I,J) b[(I-1)*pdb + J - 1] order = Nag_RowMajor; #endif INIT_FAIL(fail); Vprintf("nag_dsygst (f08sec) Example Program Results\n\n"); /* Skip heading in data file */ Vscanf("%*[^\n] "); Vscanf("%ld%*[^\n] ", &n); #ifdef NAG_COLUMN_MAJOR pda = n; pdb = n; #else pda = n; pdb = n; #endif d_len = n; e_len = n-1; tau_len = n-1; /* Allocate memory */ if ( !(a = NAG_ALLOC(n * n, double)) || !(b = NAG_ALLOC(n * n, double)) || !(d = NAG_ALLOC(d_len, double)) || !(e = NAG_ALLOC(e_len, double)) || !(tau = NAG_ALLOC(tau_len, double)) ) { Vprintf("Allocation failure\n"); exit_status = -1; goto END; } /* Read A and B from data file */ Vscanf(" ' %1s '%*[^\n] ", uplo_char); if (*(unsigned char *)uplo_char == 'L') uplo = Nag_Lower; else if (*(unsigned char *)uplo_char == 'U') uplo = Nag_Upper; else { Vprintf("Unrecognised character for Nag_UploType type\n"); exit_status = -1; goto END; } if (uplo == Nag_Upper) { for (i = 1; i <= n; ++i) { for (j = i; j <= n; ++j) Vscanf("%lf", &A(i,j)); } Vscanf("%*[^\n] "); for (i = 1; i <= n; ++i) { for (j = i; j <= n; ++j) Vscanf("%lf", &B(i,j)); } Vscanf("%*[^\n] "); } else { for (i = 1; i <= n; ++i) { for (j = 1; j <= i; ++j) Vscanf("%lf", &A(i,j)); } Vscanf("%*[^\n] "); for (i = 1; i <= n; ++i) { for (j = 1; j <= i; ++j) Vscanf("%lf", &B(i,j)); } Vscanf("%*[^\n] "); } /* Compute the Cholesky factorization of B */ /* nag_dpotrf (f07fdc). * Cholesky factorization of real symmetric * positive-definite matrix */ nag_dpotrf(order, uplo, n, b, pdb, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_dpotrf (f07fdc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Reduce the problem to standard form C*y = lambda*y, storing */ /* the result in A */ /* nag_dsygst (f08sec). * Reduction to standard form of real symmetric-definite * generalized eigenproblem Ax~=~lambda~Bx, ABx~=~lambda~x * or BAx~=~lambda~x, B factorized by nag_dpotrf (f07fdc) */ nag_dsygst(order, Nag_Compute_1, uplo, n, a, pda, b, pdb, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_dsygst (f08sec).\n%s\n", fail.message); exit_status = 1; goto END; } /* Reduce C to tridiagonal form T = (Q**T)*C*Q */ /* nag_dsytrd (f08fec). * Orthogonal reduction of real symmetric matrix to * symmetric tridiagonal form */ nag_dsytrd(order, uplo, n, a, pda, d, e, tau, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_dsytrd (f08fec).\n%s\n", fail.message); exit_status = 1; goto END; } /* Calculate the eigenvalues of T (same as C) */ /* nag_dsterf (f08jfc). * All eigenvalues of real symmetric tridiagonal matrix, * root-free variant of QL or QR */ nag_dsterf(n, d, e, &fail); if (fail.code != NE_NOERROR) { Vprintf("Error from nag_dsterf (f08jfc).\n%s\n", fail.message); exit_status = 1; goto END; } /* Print eigenvalues */ Vprintf("Eigenvalues\n"); for (i = 1; i <= n; ++i) Vprintf("%8.4f%s", d[i-1], i%9==0 ?"\n":" "); Vprintf("\n"); END: if (a) NAG_FREE(a); if (b) NAG_FREE(b); if (d) NAG_FREE(d); if (e) NAG_FREE(e); if (tau) NAG_FREE(tau); return exit_status; } | 1,288 | 3,567 | {"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-2014-10 | longest | en | 0.483874 |
https://edslash.com/leetcode-problem-160-intersection-of-two-linked-lists/ | 1,718,272,347,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861372.90/warc/CC-MAIN-20240613091959-20240613121959-00141.warc.gz | 196,506,918 | 31,173 | ### LeetCode Challenge #160. Intersection of Two Linked Lists
Given the heads of two singly linked-lists `headA` and `headB`, return the node at which the two lists intersect. If the two linked lists have no intersection at all, return `null`.
For example, the following two linked lists begin to intersect at node `c1`:
The test cases are generated such that there are no cycles anywhere in the entire linked structure.
Note that the linked lists must retain their original structure after the function returns.
Custom Judge:
The inputs to the judge are given as follows (your program is not given these inputs):
• `intersectVal` – The value of the node where the intersection occurs. This is `0` if there is no intersected node.
• `listA` – The first linked list.
• `listB` – The second linked list.
• `skipA` – The number of nodes to skip ahead in `listA` (starting from the head) to get to the intersected node.
• `skipB` – The number of nodes to skip ahead in `listB` (starting from the head) to get to the intersected node.
The judge will then create the linked structure based on these inputs and pass the two heads, `headA` and `headB` to your program. If you correctly return the intersected node, then your solution will be accepted.
Example 1:
```Input: intersectVal = 8, listA = [4,1,8,4,5], listB = [5,6,1,8,4,5], skipA = 2, skipB = 3
Output: Intersected at '8'
Explanation: The intersected node's value is 8 (note that this must not be 0 if the two lists intersect).
From the head of A, it reads as [4,1,8,4,5]. From the head of B, it reads as [5,6,1,8,4,5]. There are 2 nodes before the intersected node in A; There are 3 nodes before the intersected node in B.
- Note that the intersected node's value is not 1 because the nodes with value 1 in A and B (2nd node in A and 3rd node in B) are different node references. In other words, they point to two different locations in memory, while the nodes with value 8 in A and B (3rd node in A and 4th node in B) point to the same location in memory.
```
Example 2:
```Input: intersectVal = 2, listA = [1,9,1,2,4], listB = [3,2,4], skipA = 3, skipB = 1
Output: Intersected at '2'
Explanation: The intersected node's value is 2 (note that this must not be 0 if the two lists intersect).
From the head of A, it reads as [1,9,1,2,4]. From the head of B, it reads as [3,2,4]. There are 3 nodes before the intersected node in A; There are 1 node before the intersected node in B.
```
Example 3:
```Input: intersectVal = 0, listA = [2,6,4], listB = [1,5], skipA = 3, skipB = 2
Output: No intersection
Explanation: From the head of A, it reads as [2,6,4]. From the head of B, it reads as [1,5]. Since the two lists do not intersect, intersectVal must be 0, while skipA and skipB can be arbitrary values.
Explanation: The two lists do not intersect, so return null.
```
Constraints:
• The number of nodes of `listA` is in the `m`.
• The number of nodes of `listB` is in the `n`.
• `1 <= m, n <= 3 * 104`
• `1 <= Node.val <= 105`
• `0 <= skipA < m`
• `0 <= skipB < n`
• `intersectVal` is `0` if `listA` and `listB` do not intersect.
• `intersectVal == listA[skipA] == listB[skipB]` if `listA` and `listB` intersect.
##### Video Solution
###### Java Solution
``` ```
public class Solution {
int count = 0 ;
while(ptr!=null){
count++;
ptr = ptr.next;
}
return count ;
}
return null;
}
int diff = size1 - size2 ;
if(diff>0){ // LL1 is having greater size
while(diff>0){
ptr1 = ptr1.next;
diff--;
}
}else{ // LL2 is having greater size
while(diff<0){
ptr2 = ptr2.next;
diff++;
}
}
while(ptr1!=ptr2){
ptr1 = ptr1.next;
ptr2 = ptr2.next;
}
return ptr1;
}
}
```
``` | 1,126 | 3,634 | {"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-2024-26 | latest | en | 0.838645 |
https://digitalcommons.odu.edu/cee_etds/39/ | 1,685,860,406,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224649518.12/warc/CC-MAIN-20230604061300-20230604091300-00073.warc.gz | 240,605,725 | 9,060 | Civil & Environmental Engineering Theses & Dissertations
Winter 2003
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Civil & Environmental Engineering
David R. Basco
Jaewan Yoon
John M. Klinck
Abstract
The relative trough Froude number (RTFN) theory is a new phase-resolving type, wave breaking trigger model introduced by Utku (1999) and Utku and Basco (2002). Based on the moving hydraulic jump concept, this model provides a better implementation of wave breaking in terms of hydrodynamics. Development of computer resources permits the use of the phase-resolving type, Boussinesq wave models in nearshore areas. The Boussinesq equation, however, does not include the physics of wave breaking, so that an additional mechanism is required to initiate wave breaking in the model. The main objective of this study is to develop a new wave breaking trigger model for the Boussinesq equation model by using the RTFN theory.
A theoretical analysis is performed to determine the analytical expression of the RTFN theory and the critical condition for wave breaking (CTFN). The RTFN theory is redefined for this purpose. Coupling with wave theories (both linear and nonlinear), the analytical form of the RTFN is obtained. The Miche (1944) formula provides a wave breaking condition. All results agree with RTFN = 1.45 as the theoretical CTFN.
A wave tank experiment is performed to obtain data for model confirmation. Wave breaking locations are measured with the assistance of a digital video recording. Wave gauge records are used to adjust input wave heights in the numerical model.
Wave celerity calculation methods for the RTFN calculation are investigated intensively because 90% of the RTFN calculation is the contribution due to the celerity (Utku and Basco, 2002). To satisfy both applicability and robustness, a hybrid method is introduced.
Extensive numerical experiments are executed for the confirmation, calibration, and verification of the model. Qualitative studies confirm that the RTFN evolution along with the nonlinear wave transformation correctly behave for a wave breaking trigger. The model calibration performed with data obtained from the wave tank experiment determines the CTFN = 1.47 for the numerical model, which is very close to the theoretical value. Verification tests with calibrated CTFN reveal that the momentum sink term locating mechanism associated with the RTFN theory is also needed for completing the RTFN wave breaking model. This aspect of the work is left for the future.
Rights
In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
DOI
10.25777/5ezr-fd63
COinS | 616 | 2,910 | {"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-2023-23 | longest | en | 0.892755 |
http://wiki.icub.org/index.php?title=VVV10_HandSome&printable=yes | 1,550,417,228,000,000,000 | text/html | crawl-data/CC-MAIN-2019-09/segments/1550247482186.20/warc/CC-MAIN-20190217152248-20190217174248-00517.warc.gz | 284,025,657 | 7,307 | # "Hand"Some
We would like to implement impedance behaviours coupling both the hands, hence the bad pun on the name. We would work under the Force Control group and share tools and code with everyone.
You are more than welcome to hack with Us! :D So far, we are YARP and iCub Noobs so any assistance the Wise Ones can give is greatly appreciated.
## Technical Background
We would like to replicate some of the behaviours demonstrated [here]. For more visual demo check this [video]
## Members
Participants (so far) :
``` * Naveen Kuppuswamy "Naveenone"
* Cristiano Alessandro "!Alessandro"
* Arne Nordmann "North-Man"
* Gauss Lee "The Gaussian"
* Paolo Tommasino "Pa"O"lo"
* Jiuguang Wang "G1"
```
# Concept and Proposed Demo
We believe that the ideal impressive demo should always involve alcohol service, and thus we would like to demonstrate some simple two handed grasp and user directed manipulation of trays with drinks or individual alcohol bottles. Additional tricks can be manipulating objects of various sizes and compliance by playing around with the coupling stiffnes or even adding a cartesian impedance constraint to fit service robot scenarios like serving drinks (keeping bottle upright in cartesian space to compensate for user drunkenness).
## Update on Demo
```Demo has been scaled down to accomodate for our procrastination. It would involve something like multi-arm
coordinated holding of an object like a box..The Control would be demonstrated in both modes (joint space force
control, and joint space impedance control) and the user should be able to interact with any one of the arms of
the robot.
```
Upon realising the theoritical and practical difficulties in this task we have decided to eat a bit of humble pie and appraoch the task conservatively. We have decided to partition the task as follows :
#### Phase 1 : Approach of Object
An assumed object in front of the robot is approached using Joint Impedance Position Control
#### Phase 2 : Cartesian Impedance Control (Fake and Real)
Object is held by arms using Cartesian Spatial Impedance. This is done is 2 ways:
## Control
### a. 'Real Cartesian Impedance Control
A Virtual spring assumption is made which generates desired Forces at end effector, and this is converted to desired joint level torques. This can also be called Joint Space Force Control
### b. Fake Cartesial Impedance Control
A imaginary line is taken between the arms and the Arms are commanded to maintain their end effectors on this virtual line exerting pressure on a virtual region smaller than the object. This is then sent to a joint level Impedance position control scheme. This can also be called Joint Space Impedance Position Control
To test Phase 2 we will focus on single arm experiments first, wherein, an imaginary point is assumed to be the target of the desired impedance and that is used to test the arm control. | 620 | 2,905 | {"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-2019-09 | latest | en | 0.908386 |
http://www.numbersaplenty.com/2484515351 | 1,590,942,875,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347413551.52/warc/CC-MAIN-20200531151414-20200531181414-00487.warc.gz | 186,355,348 | 3,382 | Search a number
2484515351 = 12719563113
BaseRepresentation
bin1001010000010110…
…1011001000010111
320102011001110100002
42110011223020113
520042013442401
61050311441515
7115366013663
oct22405531027
96364043302
102484515351
11106549817a
1259408629b
1330796a336
14197d7d8a3
15e81bca6b
hex9416b217
2484515351 has 4 divisors (see below), whose sum is σ = 2504078592. Its totient is φ = 2464952112.
The previous prime is 2484515339. The next prime is 2484515353. The reversal of 2484515351 is 1535154842.
It is a semiprime because it is the product of two primes.
It is a cyclic number.
It is not a de Polignac number, because 2484515351 - 26 = 2484515287 is a prime.
It is a Duffinian number.
It is a congruent number.
It is not an unprimeable number, because it can be changed into a prime (2484515353) by changing a digit.
It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 9781430 + ... + 9781683.
It is an arithmetic number, because the mean of its divisors is an integer number (626019648).
Almost surely, 22484515351 is an apocalyptic number.
2484515351 is a deficient number, since it is larger than the sum of its proper divisors (19563241).
2484515351 is a wasteful number, since it uses less digits than its factorization.
2484515351 is an evil number, because the sum of its binary digits is even.
The sum of its prime factors is 19563240.
The product of its digits is 96000, while the sum is 38.
The square root of 2484515351 is about 49844.9129901939. The cubic root of 2484515351 is about 1354.4008827254.
The spelling of 2484515351 in words is "two billion, four hundred eighty-four million, five hundred fifteen thousand, three hundred fifty-one".
Divisors: 1 127 19563113 2484515351 | 546 | 1,768 | {"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} | 3.15625 | 3 | CC-MAIN-2020-24 | latest | en | 0.834539 |
http://myriverside.sd43.bc.ca/christianc2017/2017/12/11/everything-i-know-about-polynomials/ | 1,571,185,441,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986660829.5/warc/CC-MAIN-20191015231925-20191016015425-00505.warc.gz | 128,892,038 | 10,126 | # Everything I know about polynomials
Ft. Multiplication, Division, Addition, Subtraction and general advice….
So here are so general guidelines you will want to follow when dealing with polynomials this includes….
some explanations on algebraic tiles
placement of the negative charge
what variables, coefficients, terms, constants and degrees are in a polynomial expression
And further explanation of the distributive product
So now that you have some general principles down, addition of polynomials seems like the most rational step forward, in this photo you will find.
Addition and subtraction of polynomial expressions using algebra tiles and numbers, and, that’s about it.
Finally in the last photo, we have the multiplication and division of polynomial expressions using monomial expressions.
Thanks for looking at my project, I hope it made things a bit more clear regarding polynomials.
Thanks again!
Also, here is the core competencies padlet
## 1 comment on “Everything I know about polynomials”Add yours →
1. Mikaelah says:
Great job with explaining all of the different concepts with polynomials! All of the learning outcomes were met in this project. This project has included various examples of addition, subtraction, multiplication and division. All of the expressions/equations included algebra tiles and a complex variation of variables and exponents. Your explanation was very clear and I liked the way you used different coloured pens. The only thing I think you could’ve done better was that the words were quite small and so it was slightly difficult to read. 🙂 | 310 | 1,600 | {"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} | 3.0625 | 3 | CC-MAIN-2019-43 | longest | en | 0.948815 |
http://nrich.maths.org/public/leg.php?code=-395&cl=4&cldcmpid=5952 | 1,503,053,707,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886104634.14/warc/CC-MAIN-20170818102246-20170818122246-00448.warc.gz | 317,950,299 | 9,217 | # Search by Topic
#### Resources tagged with physics similar to Escape from Planet Earth:
Filter by: Content type:
Stage:
Challenge level:
### There are 81 results
Broad Topics > Applications > physics
### Escape from Planet Earth
##### Stage: 5 Challenge Level:
How fast would you have to throw a ball upwards so that it would never land?
### The Ultra Particle
##### Stage: 5 Challenge Level:
Explore the energy of this incredibly energetic particle which struck Earth on October 15th 1991
### Constantly Changing
##### Stage: 4 Challenge Level:
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Explore the power of aeroplanes, spaceships and horses.
### Pack Man
##### Stage: 5 Challenge Level:
A look at different crystal lattice structures, and how they relate to structural properties
### Big and Small Numbers in Chemistry
##### Stage: 4 Challenge Level:
Get some practice using big and small numbers in chemistry.
### Cannon Balls
##### Stage: 5 Short Challenge Level:
How high will a ball taking a million seconds to fall travel?
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##### Stage: 5 Challenge Level:
Look at the calculus behind the simple act of a car going over a step.
### The Real Hydrogen Atom
##### Stage: 5 Challenge Level:
Dip your toe into the world of quantum mechanics by looking at the Schrodinger equation for hydrogen atoms
### Levels of Bohr
##### Stage: 5 Challenge Level:
Look at the units in the expression for the energy levels of the electrons in a hydrogen atom according to the Bohr model.
##### Stage: 5 Challenge Level:
A look at a fluid mechanics technique called the Steady Flow Momentum Equation.
### Maths in the Undergraduate Physical Sciences
##### Stage: 5
An article about the kind of maths a first year undergraduate in physics, engineering and other physical sciences courses might encounter. The aim is to highlight the link between particular maths. . . .
### Pumping the Power
##### Stage: 5 Challenge Level:
What is an AC voltage? How much power does an AC power source supply?
### The Lorentz Force Law
##### Stage: 5 Challenge Level:
Explore the Lorentz force law for charges moving in different ways.
### Big and Small Numbers in Physics - Group Task
##### Stage: 5 Challenge Level:
Work in groups to try to create the best approximations to these physical quantities.
### Lunar Leaper
##### Stage: 5 Challenge Level:
Gravity on the Moon is about 1/6th that on the Earth. A pole-vaulter 2 metres tall can clear a 5 metres pole on the Earth. How high a pole could he clear on the Moon?
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##### Stage: 5 Challenge Level:
Where will the spaceman go when he falls through these strange planetary systems?
### The Not-so-simple Pendulum 1
##### Stage: 5 Challenge Level:
See how the motion of the simple pendulum is not-so-simple after all.
### Universal Time, Mass, Length
##### Stage: 5 Short Challenge Level:
Can you work out the natural time scale for the universe?
### Lennard Jones Potential
##### Stage: 5 Challenge Level:
Investigate why the Lennard-Jones potential gives a good approximate explanation for the behaviour of atoms at close ranges
### Striking Gold
##### Stage: 5 Challenge Level:
Investigate some of the issues raised by Geiger and Marsden's famous scattering experiment in which they fired alpha particles at a sheet of gold.
### Stemnrich - Technology
##### Stage: 3 and 4 Challenge Level:
This is the technology section of stemNRICH - Core.
### Battery Modelling
##### Stage: 5 Challenge Level:
Find out how to model a battery mathematically
### Which Twin Is Older?
##### Stage: 5
A simplified account of special relativity and the twins paradox.
### The Amazing Properties of Water
##### Stage: 4 and 5 Challenge Level:
Find out why water is one of the most amazing compounds in the universe and why it is essential for life. - UNDER DEVELOPMENT
### Core Scientific Mathematics
##### Stage: 4 and 5 Challenge Level:
This is the area of the advanced stemNRICH site devoted to the core applied mathematics underlying the sciences.
### Drug Stabiliser
##### Stage: 5 Challenge Level:
How does the half-life of a drug affect the build up of medication in the body over time?
### Reaction Types
##### Stage: 5 Challenge Level:
Explore the rates of growth of the sorts of simple polynomials often used in mathematical modelling.
### The Not-so-simple Pendulum 2
##### Stage: 5 Challenge Level:
Things are roughened up and friction is now added to the approximate simple pendulum
##### Stage: 5 Challenge Level:
Can you arrange a set of charged particles so that none of them start to move when released from rest?
### Whose Line Graph Is it Anyway?
##### Stage: 5 Challenge Level:
Which line graph, equations and physical processes go together?
##### Stage: 4 and 5 Challenge Level:
Advanced problems in the mathematical sciences.
### Neural Nets
##### Stage: 5
Find out some of the mathematics behind neural networks.
### New Units for Old
##### Stage: 5 Challenge Level:
Can you match up the entries from this table of units?
### Go Spaceship Go
##### Stage: 5 Challenge Level:
Show that even a very powerful spaceship would eventually run out of overtaking power
### Moving Stonehenge
##### Stage: 5 Challenge Level:
A look at the fluid mechanics questions that are raised by the Stonehenge 'bluestones'.
### Modelling Assumptions in Mechanics
##### Stage: 5
An article demonstrating mathematically how various physical modelling assumptions affect the solution to the seemingly simple problem of the projectile.
### Big and Small Numbers in Physics
##### Stage: 4 Challenge Level:
Work out the numerical values for these physical quantities.
### Ancient Astronomical Terms
##### Stage: 3, 4 and 5
Some explanations of basic terms and some phenomena discovered by ancient astronomers
### Sweeping Satellite
##### Stage: 5 Challenge Level:
Derive an equation which describes satellite dynamics.
### Ideal Gases
##### Stage: 5 Challenge Level:
Problems which make you think about the kinetic ideas underlying the ideal gas laws.
### Mach Attack
##### Stage: 5 Challenge Level:
Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.
### The Power of Dimensional Analysis
##### Stage: 4 and 5
An introduction to a useful tool to check the validity of an equation.
### Diamonds Aren't Forever
##### Stage: 5 Challenge Level:
Ever wondered what it would be like to vaporise a diamond? Find out inside...
### Ideal Axes
##### Stage: 5 Challenge Level:
Explore how can changing the axes for a plot of an equation can lead to different shaped graphs emerging
### Eudiometry
##### Stage: 5 Challenge Level:
When a mixture of gases burn, will the volume change?
### Motorbike Momentum
##### Stage: 5 Challenge Level:
A think about the physics of a motorbike riding upside down
### Cobalt Decay
##### Stage: 5 Challenge Level:
Investigate the effects of the half-lifes of the isotopes of cobalt on the mass of a mystery lump of the element. | 1,603 | 7,390 | {"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-2017-34 | latest | en | 0.845908 |
http://what-is-the-definition-of.com/pointy.html | 1,542,319,000,000,000,000 | text/html | crawl-data/CC-MAIN-2018-47/segments/1542039742937.37/warc/CC-MAIN-20181115203132-20181115225132-00542.warc.gz | 356,923,121 | 12,447 | # Definition of pointy
"pointy" is probably misspelled. Trying point instead Definition of point
1. point [ n ] a geometric element that has position but no extension
Examples: "a point is defined by its coordinates"
Used in print:
(Frederick Mosteller et al., Probability with...)
In Chapters 3 and 4 we answered questions like those in the examples , usually by counting points in a sample space .
(R. P. Jerrard, "Inscribed squares in plane curves"...)
A square inscribed in a curve C means a square with its four corner points on the curve , though it may_not lie entirely in the interior of C .
The square has one corner point on the straight_line segment , and does not lie entirely in the interior .
On C , from the point P at **f to the point Q at **f , we construct the chord , and upon the chord as a side erect a square in such a way that as s approaches zero the square is inside C .
On C , from the point P at **f to the point Q at **f , we construct the chord , and upon the chord as a side erect a square in such a way that as s approaches zero the square is inside C .
Synonyms point Related Terms component intersection intercept attracter
2. point [ v ] indicate a place, direction, person, or thing; either spatially or figuratively
Examples: "I showed the customer the glove section" "He pointed to the empty parking space" "he indicated his opponents"
Used in print:
(Clayton C. Barbeau, The Ikon....)
Prevot came_up `` Take that spot over there '' , he whispered , pointing to a small clump of blackness .
Above , the glowing ivory baton of their searchlight pointed at the clouds , diluting the valley 's dark to a pallid light .
(Louis Zara, Dark Rider....)
Papa pointed a scornful finger at the splashing youth : `` Idle recreation '' !
(Arthur Miller, "The Prophecy," in The Best...)
Now she kept herself protectively ready to laugh again and sure_enough he pointed at her with his index_finger and said `` Toot '' ! once_more and roared_off into the fog , his foot evidently surprising him with the suddenness with which it pressed the accelerator , just as his hand did when he worked .
(Whit Masterson, Evil Come, Evil Go....)
Vecchio was nodding and pointing at the large suitcase he held .
Synonyms indicate point show Related Terms inform reflect signalize finger arrow indication
3. point [ n ] the precise location of something; a spatially limited location
Examples: "she walked to a point where she could survey the whole street"
Used in print:
(William G. Pollard, Physicist and Christian....)
In a long commentary which he has inserted in the published text of the first act of the play , he says at one point : `` However , that experience never raised a doubt in his mind as to the reality of the underworld or the existence of Lucifer 's many faced lieutenants .
(Bonnie Prudden, "The Dancer and the Gymnast"...)
Start by falling forward to a point close to the feet , and , as strength improves , fall farther and farther out .
(Howard Nemerov, "Themes and Methods: The Early...)
And this occurs now , at the refrain of Jacoby 's song - at the point , in_fact , of the name `` Lizzy '' - ; a modulation described as `` almost a stroke of genius '' .
(Robert A. Futterman, The Future of Our Cities....)
Less ambitious freeway plans may be more successful - especially when the roadways and interchanges are raised , allowing_for cross access at many points and providing parking_areas below the ramp .
(Clayton C. Barbeau, The Ikon....)
If he were to go with White , he would be out there two days , not just listening in the dark at some point between here and Papa-san , but moving ever deeper into enemy land - behind Papa-san itself .
Synonyms point
4. point [ n ] a brief version of the essential meaning of something
Examples: "get to the point" "he missed the point of the joke" "life has lost its point"
Used in print:
(Philip Reaves, "Who Rules the Marriage Bed?"...)
`` The important point is that both be satisfied with the adjustment '' .
(Barry Goldwater, "A Foreign Policy for America"...)
It may be , of_course , that such objectives can be pursued consisently with a policy designed to overthrow Communism ; my point is that where conflicts arise they must always be resolved in_favor_of achieving the indispensable condition for a tolerant world - the absence of Soviet Communist power .
Never_mind whether the Kikiyus and the Bantus enjoyed Wilsonian self-determination : the point is that in the struggle for the world that vast land_mass was under the domination and influence of the West .
(Mignon G. Eberhart, The Cup, the Blade...)
She thrust the envelope back in the bag ; there was no point in locking it up in the armoire now , it was like locking the barn after the horse was stolen .
There was no point either in telling herself again what a fool she 'd been .
Synonyms point Related Terms meaning rallying_point crux talking_point bottom_line
5. point [ n ] an isolated fact that is considered separately from the whole
Examples: "several of the details are similar" "a point of information"
Used in print:
(Nathan Rapport, ""I've Been Here before!"...)
Dr._H._V._Hilprecht , Professor of Assyrian at the University_of_Pennsylvania , dreamed that a Babylonian priest , associated with the king Kurigalzu , ( 1300 B.C. . ) escorted him to the treasure chamber of the temple of Bel , gave him six novel points of information about a certain broken relic , and corrected an error in its identification .
We may conclude that all six points of information , ostensibly given by the dream priest , could have been furnished by Dr._Hilprecht 's subconscious reasoning .
(Howard Nemerov, "Themes and Methods: The Early...)
This is simple enough , but several more points of interest may be mentioned as relevant .
(Joyce O. Hertzler, American Social Institutions;...)
This is brought_out in the common religious ethos that prevails even in the denominationally diverse audiences at many secular semi-public and public occasions in the United_States ; and it is evidenced in the prayers offered , in the frequent religious allusions , and in the confirmation of points on religious grounds .
(William S. Haymond, "Is Distance an Original...)
If the argument is accepted as essentially sound up to this point , it remains for us to consider whether the patient 's difficulties in orienting himself spatially and in locating objects in space with the sense_of_touch can be explained by his defective visual condition .
Synonyms detail point item
6. point [ n ] a specific identifiable position in a continuum or series or especially in a process
Examples: "a remarkable degree of frankness" "at what stage are the social sciences?"
Used in print:
(Chicago Daily Tribune...)
But he had in Walter_Hendl a willing conductor able only up to a point .
But Mr._Hendl does not go straight to any point .
The concert opened with another big romantic score , Schumann's Overture_to_Manfred , which suffered fate , this time with orchestral thrusts to the Byronic point to keep it afloat .
(Mr. America, 4:6...)
By this time Henri 's entire chest back - lat shoulder area is pumped-up to almost bursting point , and Claude takes time to do a_bit more pectoral front deltoid shaping work .
(Raymond C. Binder et al., editors, Proceedings...)
Hence , the flow conditions at the anode of free_burning arcs resemble those near a stagnation point .
Synonyms stage degree point level
7. point [ n ] a very short period of time
Examples: "at that point I had to leave"
Used in print:
(Jaroslav Pelikan, The Shape of Death: life, death and...)
If it was , then it must have been God 's intention to translate him at a certain point from time to eternity .
(Organic Gardening and Farming,...)
The fruit is allowed to mature on the tree , but it is still firm at this point .
(S. Idell Pyle, et al., Onsets, Completions, and...)
Obviously , the slowing for her may have occurred at any point between Onset and Completion .
(Guy Endore, Voltaire! Voltaire!...)
He felt himself now , as he himself says in his Confessions , at a crucial point of his life .
(Hampton Stone, The Man Who Looked Death...)
Starting with the room completely blacked_out , as it was when we came_in , he unerringly fixed things so that the whole place was bathed in the maximum of light without at any point admitting even so much as a crack of glare .
Synonyms point point_in_time
8. point [ v ] be oriented
Examples: "The weather vane points North"
Used in print:
(Bonnie Prudden, "The Dancer and the Gymnast"...)
Place flat palms on either side of the head a_few inches away from the ears , fingers pointing toward the shoulders .
(S. Idell Pyle, et al., Onsets, Completions, and...)
The direction in which the arrow points shows how the maturity level of the growth center was changed at Completion from the level at Onset .
(Chester G. Starr, The Origins of Greek Civili...)
While many tokens point forward , the main achievements stand as a culmination of the simple patterns of the Dark_ages .
(Arthur Miller, "The Prophecy," in The Best...)
Then , when he had it pointed down the hill , he stopped to gaze at her through the window .
Synonyms point orient Related Terms lie lie arrow
9. point [ v ] direct into a position for use
Examples: "point a gun" "He charged his weapon at me"
Used in print:
(Glayds H. Barr, The Master of Geneva....)
`` That is the answer the ungodly will always make when the Church points its fingers at their sins .
(Whit Masterson, Evil Come, Evil Go....)
They surged around him , fingers pointing , eyes prying .
(Richard Ferber, Bitter Valley....)
He raised the Winchester and pointed it at Wilson 's chest .
Synonyms point level charge Related Terms aim
10. point [ n ] the object of an activity
Examples: "what is the point of discussing it?"
Used in print:
(Brand Blanshard, "The Emotive Theory," Robert...)
We should say that we made our point with feeling the first time and little or no feeling the second time , but that it was the same point we were making .
We should say that we made our point with feeling the first time and little or no feeling the second time , but that it was the same point we were making .
(J. H. Hexter, "Thomas More: On the Margins...)
With_respect_to this view , two points are worth making .
Synonyms point Related Terms aim
11. point [ v ] direct the course; determine the direction of travelling
Used in print:
(Bonnie Prudden, "The Dancer and the Gymnast"...)
The child should then bring both legs together overhead , point the toes and tighten the seat muscles .
(Philip Jos‚ Farmer, The Lovers....)
The Gabriel pointed towards her destination and , under one gee acceleration , began to build_up towards her ultimate velocity , 99.1 percent of the speed_of_light .
12. point [ n ] a V shape
Examples: "the cannibal's teeth were filed to sharp points"
Used in print:
(Gerald Green, The Heartless Light....)
Through the swathings of terror , she jabbed deceit 's sharp point - Amy would be reborn , a new child , with new parents , living under new circumstances .
(Frieda Arkin, "The Light of the Sea," in The...)
He saw the Starbird as she lay , her slender mast up and gently turning , its point describing constant languid circles against a cumulus sky .
Synonyms point peak tip
13. point [ n ] the unit of counting in scoring a game or contest
Examples: "he scored 20 points in the first half" "a touchdown counts 6 points"
Used in print:
(The Dallas Morning News,...)
Arkansas combined 280 yards rushing with 64 yards passing ( on 5 completions in 7 tosses ) and a tough defense to whip TCU , and A+M , with a 38 - point bulge against Texas_Tech ran_up its biggest total loop play since 1950 .
Willie 's lifetime batting average of .318 is 11 points beyond Mickey's .
Synonyms point
14. point [ n ] a distinct part that can be specified separately in a group of things that could be enumerated on a list
Examples: "he noticed an item in the New York Times" "she had several items on her shopping list" "the main point on the agenda was taken up first"
Used in print:
(H. A. Gleason, "Review of African language studies...)
Morphophonemic rules may be thought_of as joining certain points in the system .
Linguists have not always been more enlightened than `` practical people '' and sometimes have insisted on incredibly trivial points while neglecting things of much greater significance .
Synonyms item point
15. point [ n ] a very small circular shape
Examples: "a row of points" "draw lines between the dots"
Synonyms dot point Related Terms disk dot
16. point [ n ] a promontory extending out into a large body of water
Examples: "they sailed south around the point"
Used in print:
(James Boylan, "Mutinity"...)
To port was a point 200 feet high rising behind to a precipice of 2000 feet .
He spread the flight out and led them across a point of land and_then down the coast .
Synonyms point Related Terms promontory
17. point [ n ] an outstanding characteristic
Examples: "his acting was one of the high points of the movie"
Used in print:
(Evan Esar, Humorous English; a guide to comic ,...)
At the home of a gourmet the new maid was instructed in the fine points of serving .
Synonyms spot point Related Terms characteristic
18. point [ v ] be a signal for or a symptom of
Examples: "These symptoms indicate a serious illness" "Her behavior points to a severe neurosis" "The economic indicators signal that the euro is undervalued"
Used in print:
(Stephen Longstreet, Eagles Where I Walk....)
The chevaux_de_frise , those sharp stakes and barriers around the fort at the Battery , pointed to a conflict between the town and sea_power rolling in glassy swells as the tide came_in .
Related Terms tell mark bode signal indication indicator
19. point [ n ] sharp end
Examples: "he stuck the point of the knife into a tree" "he broke the point of his pencil"
Used in print:
(Sallie Bingham, "Moving Day," The Atlantic...)
Winston took_out a pencil , admired the point , and wrote slowly and heavily , `` Clothes Stand '' .
Synonyms point
20. point [ n ] a style in speech or writing that arrests attention and has a penetrating or convincing quality or effect
Synonyms point Related Terms relevance
21. point [ v ] sail close to the wind
Synonyms point luff Related Terms sail navigation
22. point [ v ] be positionable in a specified manner
Examples: "The gun points with ease"
Synonyms point Related Terms be charge gun_muzzle pointer
23. point [ v ] mark (a psalm text) to indicate the points at which the music changes
Synonyms point Related Terms tag period
24. point [ v ] mark Hebrew words with diacritics
Synonyms point Related Terms tag period
25. point [ v ] mark with diacritics, as of letter
Synonyms point Related Terms tag period
26. point [ n ] a linear unit used to measure the size of type; approximately 1/72 inch
Synonyms point Related Terms linear_unit em
27. point [ n ] any of 32 horizontal directions indicated on the card of a compass
Examples: "he checked the point on his compass"
Synonyms point compass_point
28. point [ n ] the gun muzzle's direction
Examples: "he held me up at the point of a gun"
Synonyms gunpoint point Related Terms gun_muzzle
29. point [ v ] repair the joints of bricks
Examples: "point a chimney"
Synonyms repoint point Related Terms repair
30. point [ v ] give a point to
Examples: "The candles are tapered"
Synonyms taper point sharpen Related Terms change_shape acuminate taper_off taper_off taper taper
31. point [ v ] give directions to; point somebody into a certain direction
Examples: "I directed them towards the town hall"
Synonyms direct point Related Terms instruct point_the_way
32. point [ n ] a V-shaped mark at one end of an arrow pointer
Examples: "the point of the arrow was due north"
Synonyms head point Related Terms mark arrow
33. point [ n ] a distinguishing or individuating characteristic
Examples: "he knows my bad points as well as my good points"
Synonyms point Related Terms characteristic selling_point
34. point [ n ] a punctuation mark (.) placed at the end of a declarative sentence to indicate a full stop or after abbreviations
Examples: "in England they call a period a stop"
Related Terms punctuation suspension_point
35. point [ v ] intend (something) to move towards a certain goal
Examples: "He aimed his fists towards his opponent's face" "criticism directed at her superior" "direct your anger towards others, not towards yourself"
Synonyms direct aim place point target Related Terms aim address range_in topographic_point prey
36. point [ n ] the property of a shape that tapers to a sharp point
Synonyms pointedness point Related Terms unpointedness taper
37. point [ n ] (British) a wall socket
Synonyms power_point point Related Terms wall_socket UK
38. point [ n ] the gun muzzle's direction
Examples: "he held me up at the point of a gun"
Synonyms muzzle point gunpoint gun_muzzle Related Terms gun_muzzle opening gun
39. point [ n ] a contact in the distributor; as the rotor turns its projecting arm contacts distributor points and current flows to the spark plugs
Related Terms contact distributor
point
pond
pound
Ponte | 3,966 | 17,328 | {"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 | longest | en | 0.925687 |
http://econopunk.com/2019/03/22/a-thing-about-the-hot-hand-fallacy-and-the-law-of-small-numbers/ | 1,563,442,333,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195525587.2/warc/CC-MAIN-20190718083839-20190718105839-00559.warc.gz | 47,685,765 | 20,876 | # A Thing About the Hot Hand Fallacy and the “Law of Small Numbers”
There was an interesting post and discussion on the NBA subreddit of Reddit on the Hot Hand phenomenon and whether or not it is a fallacy.
A Numberphile video on the topic:
An article on the topic:
https://www.scientificamerican.com/article/do-the-golden-state-warriors-have-hot-hands/
In some parts of the Numberphile video, Professor Lisa Goldberg emphasizes that issues of the “Law of Small Numbers,” which is described in the Scientific American article as:
Early in their careers, Amos Tversky and Daniel Kahneman considered the human tendency to draw conclusions based on a few observations, which they called the ‘‘law of small numbers’’.
when looking at the hot hand phenomenon, comes from the fact that we don’t get to see what happens after an H at the end of a sequence. Let a sequence be a string of shots of some length. A shot is either a make H or a miss T. So a sequence of 3 shots might be:
$$HTH$$
A make, a miss, and then a make. So looking at that, we see that after the first H, we missed, which is evidence against the hot hand. We don’t care what happens after a miss, the T. We can’t see what happens after the last shot, which is a make. This is what’s noted as causing the “Law of Small Numbers.”
A moment from the Numberphile video illustrating the probabilities of H after an H for each possible sequence of 3 shots, and the average of those probabilities:
And here, this “Law of Small Numbers” causes the average probability of H’s after an H to be 2.5/6. When the sequence is a finite length, the probability of an H after an H (or a T after a T) is biased below 0.5. As the sequence gets longer and tends toward infinity, the probability of an H after an H (or a T after a T) goes toward 0.5.
While all this is true, let’s look a little closer at what’s going on in this illustration to understand why and how exactly this bias occurs.
All possibilities of sequences of 3 shots:
$$n = \textrm{3}$$
$\begin{tabular}{ |c|c|c| } \hline Sequence & After an H & Prob. of H after H \\ \hline TTT & - & - \\ TTH & - & - \\ THT & T & 0 \\ HTT & T & 0 \\ THH & H & 1 \\ HTH & T & 0 \\ HHT & HT & 0.5 \\ HHH & HH & 1 \\ \hline \end{tabular}$
$$\textrm{Average probability} = \frac{2.5}{6} = 0.416\bar{6}$$
Assuming that an H and a T each appear with 0.5 probability and there is no memory, i.e. no hot hand, each of the above 8 sequences are equally probable. The average probability of the 6 cases where we can evaluate where there is a hot hand or not (cases that have an H in the first or second shot) is calculated to be 2.5/6 < 0.5. But let’s count the number of H’s and T’s in the second column. There are 4 H’s and 4 T’s! So we have:
$$\frac {\textrm{Number of H’s}}{\textrm{Number of H’s & T’s}} = \frac {4}{8} = 0.5$$
So it’s as if we’ve undercounted the cases where there are 2 shots that are “hot hand evaluations,” the last two sequences at the bottom of the list. In all (8) sequences of length 3, how many hot hand evaluations in total were there? (How many H’s or T’s in the 2nd column?) 8. How many of those were H’s? 4. So we have a hot hand make probability of 0.5.
It doesn’t necessarily mean that the way they counted hot hand makes in the Numberphile video is wrong. It’s just a particular way of counting it that causes a particular bias. It also may be the particular way the human instinct feels hot handedness – as an average of the probability of hot hand makes over different sequences. In other words, that way of counting may better model how we “feel” or evaluate hot handedness in real world situations.
So why is the average probability over sequences < 0.5?
When we evaluate hot-handedness, we are looking at shots that come after an H. Suppose we write down a list or table of each possible permutation of shot sequences of length $$n$$ from less H’s, starting from the sequence of all T’s, down to more H’s, ending with the sequence of all H’s. We noted above that if we count all the hot hand makes H’s in all sequences (the H’s in the 2nd column), the probability of hot hand H’s among all hot hand evaluations (the number of H’s or T’s in the 2nd column) is 1/2. When we look at the list of sequences, what we notice is that a lot of the hot hand H’s (the 2nd column) are concentrated in the lower sequences toward the bottom. But these sequences heavy in so many H’s only give one probability entry in the 3rd column of 1 or near 1.
$$n = \textrm{4}$$
$\begin{tabular}{ |c|c|c| } \hline Sequence & After an H & Prob. of H after H \\ \hline TTTT & - & - \\ TTTH & - & - \\ TTHT & T & 0 \\ THTT & T & 0 \\ HTTT & T & 0 \\ TTHH & H & 1 \\ THHT & HT & 0.5 \\ HHTT & HT & 0.5 \\ THTH & T & 0 \\ HTTH & T & 0 \\ HTHT & TT & 0 \\ THHH & HH & 1 \\ HTHH & TH & 0.5 \\ HHTH & TH & 0.5 \\ HHHT & HHT & 0.667 \\ HHHH & HHH & 1 \\ \hline \end{tabular}$
$$\textrm{Average probability} = \frac{5.6\bar{6}}{14} \approx 0.405$$
$$n = \textrm{5}$$
$\begin{tabular}{ |c|c|c| } \hline Sequence & After an H & Prob. of H after H \\ \hline TTTTT & - & - \\ TTTTH & - & - \\ TTTHT & T & 0 \\ TTHTT & T & 0 \\ THTTT & T & 0 \\ HTTTT & T & 0 \\ TTTHH & H & 1 \\ TTHHT & HT & 0.5 \\ THHTT & HT & 0.5 \\ HHTTT & HT & 0.5 \\ TTHTH & T & 0 \\ THTTH & T & 0 \\ HTTTH & T & 0 \\ THTHT & TT & 0 \\ HTTHT & TT & 0 \\ HTHTT & TT & 0 \\ TTHHH & HH & 1 \\ THHHT & HHT & 0.667 \\ HHHTT & HHT & 0.667 \\ THTHH & TH & 0.5 \\ HTTHH & TH & 0.5 \\ THHTH & HT & 0.5 \\ HTHTH & TT & 0 \\ HHTTH & HT & 0.5 \\ HTHHT & THT & 0.333 \\ HHTHT & HTT & 0.333 \\ THHHH & HHH & 1 \\ HTHHH & THH & 0.667 \\ HHTHH & HTH & 0.667 \\ HHHTH & HHT & 0.667 \\ HHHHT & HHHT & 0.75 \\ HHHHH & HHHH & 1 \\ \hline \end{tabular}$
$$\textrm{Average probability} = \frac{12.25}{30} \approx 0.408\bar{3}$$
Assuming equal probability of H and T on any given shot and no memory between shots: the entire list of sequences (the 1st column) will have an equal number of H’s and T’s. Additionally, all the hot hand evaluations (the 2nd column) will have an equal number of H’s and T’s.
Looking at the 1st column, we go from more T’s at the top to more H’s at the bottom in a smooth manner. Looking at the 2nd column though, we go from rows of T’s and as we go down we find that a lot of H’s are “bunched up” towards the bottom. But remember that we have a “limited” number of H’s in the 2nd column as well, namely 50% of all hot hand evaluations are H’s and 50% are T’s.
Let’s look closely at how the pattern in the 1st column causes more H’s to be bunched up in the lower sequences in the 2nd column, and also if there is any pattern to the T’s when we look across different sequences.
Higher sequences have less H’s (looking at the 1st column), which means more HT’s in those sequences as well, i.e. more hot hand misses. Lower sequences have more H’s, which means more HH’s in those sequences, i.e. more hot hand makes. This means that, looking at the 2nd column, higher sequences have more T’s and lower sequences have more H’s. Lower sequences “use up” more of the “limited amount” of H’s (limited because the number of H’s and T’s in the 2nd column are equal). Thus, H’s in the 2nd column are “bunched up” in the lower sequences as well. This causes there to be less sequences with higher probability (the 3rd column) than sequences with lower probability. Perhaps this is what brings the average probability below 0.5.
A naive look of the 2nd column shows that the highest sequences have a lone T as its hot hand evaluation, and many other hot hand evaluations of higher sequences end with a T. This makes sense since if a sequence consists of a lot of T’s, any H’s in it are unlikely to be the last two shot in the sequence, like …HH, which is what’s needed for the hot hand evaluations in the 2nd column to end with an H. And as long as a T is the last shot, the hot hand evaluation of the sequence will end with a T, since any lone H or streak of H’s in the sequence will have encountered a T as the next shot either with that last T shot in the sequence (…HHT) or meeting the first of consecutive T’s that lead up to the last T shot of the sequence (…HHTT…T).
Let’s divide up all the sequences in the 1st column into categories of how a sequence ends in its last 2 shots and use that to interpret what the last hot hand evaluation will be in the 2nd column for that sequence category. There are 4 possible ways to have the last 2 shots: TT, TH, HT, and HH. If a sequence ends in …TT, that “…” portion is either all T’s or if it has any H’s, we know that that sequence ends in a T before or at the second-to-last T in the sequence (either …H…TTT or …HTT). So in all cases but one (where the entire sequence is T’s and so there is no hot hand evaluation for the 2nd column), the last hot hand evaluation in the 2nd column will be a T. If a sequence ends in …TH, the thinking is similar to the case that ends in …TT since the very last H doesn’t provide us with an additional hot hand evaluation since the sequence ends right there, so the 2nd column also ends in a T. If a sequence ends in …HT, the last T there is our last hot hand evaluation, so the 2nd column also ends in a T. If a sequence ends in …HH, then the 2nd column ends in an H. So about 3/4 of all sequences end their 2nd column with a T. ($$3/4)n-2$$ to be exact, since the sequences of all T’s and $$(n-1)$$ T’s followed by an H don’t have any hot hand evaluations.) Thus, the T’s in the 2nd column are “spread out more evenly” across the different sequences since ($$3/4)n-2$$ of all sequences have a T for its last hot hand evaluation (the 2nd column), while the H’s are “bunched up” in the lower sequences. Thus, a relatively large number of sequences, especially sequences that are higher up, have their probabilities (the 3rd column) influenced by T’s in the 2nd column, bringing the average probability across sequences down.
$$n = \textrm{6}$$
$\begin{tabular}{ |c|c|c| } \hline Sequence & After an H & Prob. of H after H \\ \hline TTTTTT & - & - \\ TTTTTH & - & - \\ TTHTTT & T & 0 \\ THTTTT & T & 0 \\ HTTTTT & T & 0 \\ TTTTHT & T & 0 \\ TTHTHT & TT & 0 \\ THTTHT & TT & 0 \\ TTTHTT & T & 0 \\ TTHHTT & HT & 1/2 \\ THTHTT & TT & 0 \\ THHTTT & HT & 1/2 \\ TTHTTH & T & 0 \\ HTTTHT & TT & 0 \\ THTTTH & T & 0 \\ HTHTTT & TT & 0 \\ HHTTTT & HT & 1/2 \\ HTTHTT & TT & 0 \\ TTTHTH & T & 0 \\ TTTHHT & HT & 1/2 \\ TTHHHT & HHT & 2/3 \\ THTHHT & THT & 1/3 \\ TTHHTH & HT & 1/2 \\ THHHTT & HHT & 2/3 \\ HTHHTT & THT & 1/3 \\ HHTHTT & HTT & 1/3 \\ THHTTH & HT & 1/2 \\ HTTTTH & T & 0 \\ TTTTHH & H & 1 \\ TTHTHH & TH & 1/2 \\ THTTHH & TH & 1/2 \\ HHHTTT & HHT & 2/3 \\ HTHTTH & TT & 0 \\ HHTTTH & HT & 1/2 \\ THHTHT & HTT & 1/3 \\ HTHTHT & TTT & 0 \\ HHTTHT & HTT & 1/3 \\ HTTTHH & TH & 1/2 \\ HTTHTH & TT & 0 \\ THTHTH & TT & 0 \\ HTTHHT & THT & 1/3 \\ TTTHHH & HH & 1 \\ TTHHHH & HHH & 1 \\ HTHHHT & THHT & 1/2 \\ HHHTTH & HHT & 2/3 \\ HHHTHT & HHTT & 1/2 \\ THHTHH & HTH & 2/3 \\ HTHTHH & TTH & 1/3 \\ HHTTHH & HTH & 2/3 \\ HHHHTT & HHHT & 3/4 \\ THHHTH & HHT & 2/3 \\ HTHHTH & THT & 1/3 \\ HHTHTH & HTT & 1/3 \\ HTTHHH & THH & 2/3 \\ THTHHH & THH & 2/3 \\ THHHHT & HHHT & 3/4 \\ HHTHHT & HTHT & 1/2 \\ HHHTHH & HHTH & 3/4 \\ HHHHTH & HHHT & 3/4 \\ THHHHH & HHHH & 1 \\ HHHHHT & HHHHT & 4/5 \\ HTHHHH & THHH & 3/4 \\ HHTHHH & HTHH & 3/4 \\ HHHHHH & HHHHH & 1 \\ \hline \end{tabular}$
$$\textrm{Average probability} \approx 0.4161$$
As $$n$$ grows larger, the average probability seems to drift up.
Looking at the top of the list of sequences for $$n = 4$$, there are 3 sequences with a 0 in the 3rd column. These 3 sequences consist of 1 H and 3 T’s (and TTTH is uncounted because there is no hot hand evaluation in that sequence). At the bottom, we have the HHHH sequence giving a 1 in the 3rd column, and then 4 sequences that have 3 H’s ant 1 T. The entries in the 3rd column for these 4 sequences are 1, 0.5, 0.5, and 0.667.
For sequences of $$n = 5$$, there are then 4 sequences at the top of the list that give a 0 in the 3rd column. At the bottom, the HHHHH sequence gives a 1 in the 3rd column, and then the sequences with 4 H’s and 1 T give 1, 0.667, 0.667, 0.667, 0.75 in the 3rd column.
For sequences of $$n = 6$$, there are then 5 sequences at the top of the list that give a 0 in the 3rd column. At the bottom, the HHHHHH sequence gives a 1 in the 3rd column, and then the sequences with 5 H’s and 1 T give 1, 0.75, 0.75, 0.75, 0.75, 0.8 in the 3rd column.
This pattern shows that as $$n$$ increases, we get $$(n – 1)$$ sequences at the top of the list that always give 0’s in the 3rd column. At the bottom there is always 1 sequence of all H’s that gives a 1 in the 3rd column. Then for the sequences with $$(n – 1)$$ H’s and 1 T, we always have 1 sequence of THH…HH that gives a 1 in the 3rd column, then $$(n – 2)$$ sequences that give a $$\frac{n – 3}{n – 2}$$ in the 3rd column, and always 1 sequence of HH…HT that gives a $$\frac{n – 2}{n – 1}$$ in the 3rd column. So as $$n$$ becomes large, the entries in the 3rd column for these sequences with $$(n – 1)$$ H’s and 1 T get closer to 1. For small $$n$$, such as $$n = 3$$, those entries are as low as 0.5 and 0.667. But the entries in the 3rd column for the sequences high in the list with 1 H and $$(n – 1)$$ T’s remain at 0 for any $$n$$. Thus, as $$n$$ becomes large, the lower sequence entries in the 3rd column become larger, shifting the average probability over sequences up.
Roughly speaking, when we only have one shot make in a sequence of shots (only 1 H among $$n-1$$ T’s), we have only one hot hand evaluation possible, which is the shot right after the make. Ignoring the case of TT…TH, that hot hand evaluation coming after the H will always be a miss. Thus, when there is only one shot make in a sequence, the hot hand probability is always 0. On the other hand, when we have only one shot miss in a sequence, ignoring the TH…HH case, we will have 1 hot hand miss and many hot hand makes. Thus, our hot hand probability in these sequences with only 1 T will always be less than 1, and approaches 1 as $$n$$ approaches $$\infty$$. In a rough way, this lack of balance between the high sequences and low sequences drags down the average probability over the sequences below 0.5, with the amount that’s dragged down mitigated by larger and larger $$n$$.
A possible interesting observation or interpretation of this is how it might lead to the human mind “feeling” the gambler’s fallacy (e.g. consecutive H’s means a T “has to come” soon) and the hot hand fallacy (e.g. consecutive H’s means more H’s to come). The above results show that in finite length sequences, when a human averages in their mind the probability of hot hand instances across sequences, i.e. across samples or experiences, the average probability is < 0.5. In other words, across experiences, the human mind "feels" the gambler's fallacy, that reversals after consecutive results are more likely. But when a human happens to find themselves in one of the lower sequences on a list where there are relatively more H's than T's in the 1st column, what happens is that the hot hand evaluations (the 2nd column) are likely to have a lot more H's than what you'd expect, because H's are "bunched up" towards the bottom of the 2nd column. What you expect are reversals - that's what "experience" and the gambler's fallacy that results from that experience tells us. But when we find ourselves in a sequence low in the list, the hot hand instances (the 2nd column) give us an inordinately high number of hot hand makes because H's are bunched up towards the bottom of the list. So when we're hot, it feels like we're really hot, giving us the hot hand fallacy. An actually rigorous paper on this subject, also found in a comment from the Reddit post, is Miller, Joshua B. and Sanjurjo, Adam, Surprised by the Gambler’s and Hot Hand Fallacies? A Truth in the Law of Small Numbers. One of the proofs they present is a proof that the average probability of hot hand makes across sequences is less than the standalone probability of a make (i.e. using our example, the average of the entries in the 3rd column is less than 0.5, the probability of an individual make).
Let
$$\boldsymbol{X} = \{X_i\}_{i=1}^n$$
be a sequence of 0’s and 1’s that is $$n$$ long. An $$X_i = 0$$ represents a miss and an $$X_i = 0$$ represents a make.
From the sequence $$\boldsymbol{X}$$, we excerpt out the hot hand evaluations, which are shots that occur after $$k$$ made shots. In our example, we are just concerned with $$k = 1$$. The hot hand evaluation $$i$$’s are
$$I_k( \boldsymbol{X} ) := \{i : \Pi_{j=i-k}^{i-1} X_j = 1\} \subseteq \{k+1,…,n\}$$
So $$I_k( \boldsymbol{X} )$$ is defined to be the $$i$$’s where the product of the $$k$$ preceding $$X$$’s is 1, and $$i$$ can only be from among $${k+1,…,n}$$. So for example, let $$k=2$$ and $$n=6$$. Then firstly, an $$i$$ that is in $$I_k(\boldsymbol{X}$$ can only be among $${3,4,5,6}$$ because if $$i = 1,2$$, there aren’t enough preceding shots – we need 2 preceding shots made to have the $$i$$th shot be a hot hand evaluation. Ok, so let’s look at $$i = 4$$. Then,
$$\Pi_{j=4-2}^{4-1} X_j = X_2 \cdot X_3$$
This makes sense. If we are looking at $$i = 4$$, we need to see if the 2 preceding shots, $$X_2$$ and $$X_3$$ are both 1.
The theorem stated in full is:
Let
$$\boldsymbol{X} = \{X_i\}_{i=1}^n$$
with $$n \geq 3$$ be a sequence of independent (and identical) Bernoulli trials, each with probability of success $$0 \lt p \lt 1$$. Let
$$\hat{P}_k(\boldsymbol{X}) := \sum_{i \in I_k(\boldsymbol{X})} \frac{X_i}{|I_k(\boldsymbol{X})|}$$
Then, $$\hat{P}$$ is a biased estimator of
$$\mathbb{P} ( X_t = 1 | \Pi_{j=t-k}^{t-1} X_j = 1 ) \equiv p$$
for all $$k$$ such that $$1 \leq k \leq n – 2$$. In particular,
$$\mathbb[E] \left[ \hat{P}_k (\boldsymbol{X}) | I_k(\boldsymbol{X}) \neq \emptyset \right] \lt p$$
We have the $$n \geq 3$$ because when $$n = 2$$, we actually won’t have the bias. We have HH, HT, TH, TT, and if $$p = 1/2$$, we have the HH giving us a hot hand evaluation of H and the HT giving us a hot hand evaluation of T, so that’s 1 hot hand make out of 2 hot hand evaluations, giving us the $$\hat{P} = 1/2$$ with no bias.
We have $$\hat{P}_k( \boldsymbol{X} )$$ as our estimator of the hot hand make probability. It’s taking the sum of all $$X_i$$’s where $$i$$ is a hot hand evaluation (the preceding $$k$$ shots all went in) and dividing it by the number of hot hand evaluations – in other words, the hot hand makes divided by the hot hand evaluations. Note that we are just looking at one sequence $$\boldsymbol{X}$$ here.
$$\mathbb{P} (X_t = 1 | \Pi_{j=t-k}^{t-1} X_j = 1 ) \equiv p$$ is the actual probability of a hot hand make. Since we are assuming that the sequence $$\boldsymbol{X}$$ is $$i.i.d.$$, the probability of a hot hand make is the same as the probability of any make, $$p$$.
$$k$$ is restricted to $$1 \leq k \leq n – 2$$ since if $$k = n – 1$$ then the only possible hot hand evaluation is if all first $$n-1$$ shots are made. Then we would just be evaluating at most 1 shot in a sequence, the last shot. Similar to the case above where $$n=2$$, the estimator would be unbiased. if $$k = n$$, then we would never even have any hot hand evaluation, as all shots made would simply satisfy the condition for the next shot to be a hot hand evaluation, where the next shot would be the $$n+1$$th shot.
$$E \left[ \hat{P}_k (\boldsymbol{X}) | I_k(\boldsymbol{X}) \neq \emptyset \right] \lt p$$ is saying that the expectation of the estimator (given that we have some hot hand evaluations) underestimates the true $$p$$.
Here is the rigorous proof provided by the paper in its appendix:
First,
$$F:= \{ \boldsymbol{x} \in \{ 0,1 \}^n : I_k (\boldsymbol{x}) \neq \emptyset \}$$
$$F$$ is defined to be the sample space of sequences $$\boldsymbol{x}$$ where a sequence is an instance of $$\boldsymbol{X}$$ that is made up of $$n$$ entries of either $$0$$’s or $$1$$’s and there is a non-zero number of hot hand evaluations. In other words, $$F$$ is all the possible binary sequences of length $$n$$, like the lists of sequences we wrote down for $$n = 3,4,5,6$$ above. By having $$I_k (\boldsymbol{x}) \neq \emptyset$$, we have that $$\hat{P}_k(\boldsymbol{X})$$ is well-defined.
The probability distribution over $$F$$ is given by
$$\mathbb{P} (A|F) := \frac{ \mathbb{P} (A \cap F) } {\mathbb{P}(F)} \text{ for } A \subseteq \{0,1\}^n$$
where
$$\mathbb{P}(\boldsymbol{X} = \boldsymbol{x})= p^{\sum_{i=1}^{n} x_i} (1 – p)^{n – \sum_{i=1}^{n} x_i}$$
So the probability of a sequence $$A$$ happening given the sample space $$F$$ we have is the probability of a sequence $$A$$ that is in $$F$$ happening divided by the probability of a sequence in $$F$$ happening. If our sample space is simply the space of all possible sequences of length $$n$$, then this statement becomes trivial.
The probability of some sequence $$\boldsymbol{x}$$ happening is the probability that $$\sum_{i=1}^{n} x_i$$ shots are makes and $$n – \sum_{i=1}^{n} x_i$$ shots are misses. When we have $$p = 1/2$$, this simplifies to
$$\mathbb{P}(\boldsymbol{X} = \boldsymbol{x})= \left( \frac{1}{2} \right)^{\sum_{i=1}^{n} x_i} \left( \frac{1}{2} \right)^{n – \sum_{i=1}^{n} x_i} = \left( \frac{1}{2} \right)^n = \frac{1}{2^n}$$
Draw a sequence $$\boldsymbol{x}$$ at random from $$F$$ according to the distribution $$\mathbb{P} ( \boldsymbol{X} = \boldsymbol{x} | F )$$ and then draw one of the shots, i.e. one of the trials $$\tau$$ from $$\{k+1,…,n\}$$ where $$_tao$$ is a uniform draw from the trials of $$\boldsymbol{X}$$ that come after $$k$$ makes. So for
$$\boldsymbol{x} \in F \text{ and } t \in I_k(\boldsymbol{x})$$
we have that
$$\mathbb{P}(\tau = t | \boldsymbol{X} = \boldsymbol{x}) = \frac{1}{|I_k(\boldsymbol{x})|}$$
So $$\boldsymbol{x}$$ is some instance of a sequence from the sample space and $$t$$ is one of the shots or trials from the sequence $$\boldsymbol{x}$$ that is a hot hand evaluation, i.e. $$t$$ is one of the hot hand evaluations from sequence $$\boldsymbol{x}$$. Then the probability of $$\tau$$ drawn being a particular $$t$$ is like uniformly drawing from all of the possible hot hand evaluations, i.e. the probability of drawing 1 element out of the number of hot hand evaluations.
$$t \in I_k(\boldsymbol{x})^C \cap \{k+1,…,n\}$$
i.e. if we are looking at trials among $$\{k+1,…,n\}$$ that are not hot hand evaluation trials, then
$$\mathbb{P}(\tau = t | \boldsymbol{X} = \boldsymbol{x}) = 0$$
i.e. the random $$\tau$$th trial we draw will never pick from among those trials that are not hot hand evaluations. A $$\tau$$ draw is only from among the hot hand evaluation trials.
Then, the unconditional probability distribution of $$\tau$$ that can possibly follow $$k$$ consecutive makes/successes, i.e. $$t \in \{k+1,…,n\}$$, is
$$\mathbb{P}(\tau = t | F ) = \sum_{x \in F} \mathbb{P}(\tau = t | \boldsymbol{X} = \boldsymbol{x}, F) \mathbb{P}( \boldsymbol{X} = \boldsymbol{x} | F)$$
So given the sample space of all sequences $$F$$, i.e. we may be dealt any possible sequence from the sample space, the probability of drawing a particular hot hand evaluation trial $$\tau$$ is the probability of drawing a particular hot hand trial given a certain sequence $$\boldsymbol{x}$$ multiplied by the probability of drawing that sequence $$\boldsymbol{x}$$ given the sample space of all possible sequences, summed over all possible sequences in the sample space.
Then, there is an identity that is shown, which is:
$$\mathbb{E} \left[ \hat{P}_k(\boldsymbol{X}) | F \right] = \mathbb{P}(X_\tau = 1 | F)$$
From the definition above $$\hat{P}_k(\boldsymbol{X})$$, the estimator of $$p$$ given a single sequence $$\boldsymbol{X}$$:
$$\hat{P}_k(\boldsymbol{X}) := \sum_{i \in I_k(\boldsymbol{X})} \frac{X_i}{|I_k(\boldsymbol{X})|}$$
we can write:
$$\hat{P}_k(\boldsymbol{x}) = \sum_{t \in I_k(\boldsymbol{x})} \frac{x_t}{|I_k(\boldsymbol{x})|} = \sum_{t \in I_k(\boldsymbol{x})} x_t \cdot \frac{1}{|I_k(\boldsymbol{x})|}$$
$$= \sum_{t \in I_k(\boldsymbol{x})} \left[ x_t \cdot \mathbb{P}(\tau = t | \boldsymbol{X} = \boldsymbol{x}) \right]$$
$$= \sum_{t \in I_k(\boldsymbol{x})} x_t \cdot \mathbb{P}(\tau = t | \boldsymbol{X} = \boldsymbol{x}) + 0 = \sum_{t \in I_k(\boldsymbol{x})} x_t \cdot \mathbb{P}(\tau = t | \boldsymbol{X} = \boldsymbol{x}) + \sum_{t \notin I_k(\boldsymbol{x})} 0$$
$$= \sum_{t \in I_k(\boldsymbol{x})} x_t \cdot \mathbb{P}(\tau = t | \boldsymbol{X} = \boldsymbol{x}) + \sum_{t \notin I_k(\boldsymbol{x})} x_t \cdot \mathbb{P}(\tau = t | \boldsymbol{X} = \boldsymbol{x})$$
since
$$\text{if } \{t \notin I_k(\boldsymbol{x})\} \text{, then } \mathbb{P}(\tau = t | \boldsymbol{X} = \boldsymbol{x}) = 0$$
So
$$\hat{P}_k(\boldsymbol{x}) = \sum_{t \in I_k(\boldsymbol{x})} x_t \cdot \mathbb{P}(\tau = t | \boldsymbol{X} = \boldsymbol{x}) + \sum_{t \notin I_k(\boldsymbol{x})} x_t \cdot \mathbb{P}(\tau = t | \boldsymbol{X} = \boldsymbol{x})$$
$$= \sum_{t = k+1}^n x_t \cdot \mathbb{P}(\tau = t | \boldsymbol{X} = \boldsymbol{x})$$
The paper then makes a step in footnote 44 that I have not quite figured out, but the best I can make of it is this. Looking at what we’ve arrived at for $$\hat{P}_k(\boldsymbol{x})$$, we see that we sum across all trials $$t$$ from $$k+1$$ to $$n$$. Also, we’re only summing across trials $$t$$ where $$t \in I_k(\boldsymbol{x})$$ because for $$t \notin I_k(\boldsymbol{x})$$, we have $$\mathbb{P} (\tau = t | \boldsymbol{X} = \boldsymbol{x} = 0). So we are to add up the \(x_t$$ for $$t$$’s that, most importantly, satisfy $$t \in I_k(\boldsymbol{x})$$. The logic that goes I think is that:
$$= \sum_{t = k+1}^n x_t = \text{ some arithmetic sequence of 0’s and 1’s like } 1 + 0 + … + 1 + 0$$
$$= \sum_{t=k+1}^n \mathbb{P}(X_t = 1 | \text{ for each } \tau = t, \boldsymbol{X} = \boldsymbol{x} ) = \sum_{t=k+1}^n \mathbb{P}(X_t = 1 | \tau = t, \boldsymbol{X} = \boldsymbol{x} )$$
The strange thing is that what was an instance of a random variable $$x_t$$, an actual numerical value that can come about empirically and thus allows to estimate with the estimator $$\hat{P}$$, has turned into a probability.
Being given a valid sequence $$\boldsymbol{x}$$ only makes sense if we have a sample space, so we also write:
$$\sum_{t=k+1}^n \mathbb{P}(X_t = 1 | \tau = t, \boldsymbol{X} = \boldsymbol{x}, F )$$
as well as
$$\mathbb{P}(\tau = t | \boldsymbol{X} = \boldsymbol{x}, F )$$
We refrain from thinking we can say that $$\mathbb{P}(X_t = 1 | \tau = t, \boldsymbol{X} = \boldsymbol{x}, F) = p$$ as this part of the intuitive assumption that we are examining. Instead, regarding $$p$$, we restrict ourselves to only being allowed to say:
$$\mathbb{P} ( X_t = 1 | \Pi_{j=t-k}^{t-1} X_j = 1 ) \equiv p$$
So now we have:
$$\hat{P}_k(\boldsymbol{x}) = \sum_{t=k+1}^n \left[ \mathbb{P}(X_t = 1 | \tau = t, \boldsymbol{X} = \boldsymbol{x}, F ) \cdot \mathbb{P}(\tau = t | \boldsymbol{X} = \boldsymbol{x}, F ) \right]$$
When we take the expectation with $$F$$ given, we are taking the argument above with respect to $$\boldsymbol{X}$$ for all $$\boldsymbol{x} \in F$$. So:
$$\mathbb{E} \left[ \hat{P}_k(\boldsymbol{x}) | F \right] = \mathbb{E}_{\boldsymbol{X} for \boldsymbol{x} \in F} \left[ \hat{P}_k(\boldsymbol{x}) | F \right]$$
$$= \sum_{t=k+1}^n \left[ \mathbb{E}_{\boldsymbol{X} for \boldsymbol{x} \in F} \left[ \mathbb{P}(X_t = 1 | \tau = t, \boldsymbol{X} = \boldsymbol{x}, F ) \cdot \mathbb{P}(\tau = t | \boldsymbol{X} = \boldsymbol{x}, F ) | F \right] \right]$$
$$= \sum_{t=k+1}^n \left[ \mathbb{P}(X_t = 1 | \tau = t, F ) \cdot \mathbb{P}(\tau = t | F ) \right]$$
$$= \mathbb{P}(X_t = 1 | F )$$
which is our identity we were looking for. We also note that
$$\mathbb{P}(\tau = t | F) \gt 0 \text{ for } t \in \{k+1,…,n\}$$
Next, we divide up $$t$$ into $$t \lt n$$ and $$t = n$$. We show that
$$\mathbb{P} (X_t = 1 | \tau = t, F) \lt p \text{ when } t \lt n$$
and
$$\mathbb{P} (X_{t = n} = 1 | \tau = n, F) = p \text{ when } t = n$$
so that
$$\text{when } t \in {k+1,…,n}, \text{ then }$$
$$\mathbb{P} (X_t = 1 | \tau = t, F) = \mathbb{P} (t \lt n) \cdot q + \mathbb{P} (t = n) \cdot p \text{ where } q \lt p$$
$$= \frac{|I_k(\boldsymbol{x})| – 1}{|I_k(\boldsymbol{x})|} \cdot q + \frac{1}{|I_k(\boldsymbol{x})|} \lt p$$
First, we write
$$\mathbb{P} (X_t = 1 | \tau = t, F) = \mathbb{P} (X_t = 1 | \tau = t, F_t)$$
where
$$F_t := \{\boldsymbol{x} \in \{0,1\}^n : \Pi_{i=t-k}^{t-1} x_i = 1 \}$$
So while $$F$$ is the sample space of sequences $$\boldsymbol{x}$$, here we have $$F_t$$ being the sample space of sequences where the trial in the $$t$$th position $$x_t$$ is a hot hand evaluation trial. We have that $$\tau = t$$ is already given so we know that $$X_t$$ is a hot hand evaluation, so going from $$F$$ to $$F_t$$ doesn’t change anything there.
Then, we write:
$$\mathbb{P} (X_t = 1 | F_t) = p \text{ and } \mathbb{P} (X_t = 0 | F_t) = 1 – p$$
In the above case, the logic seems to be that with only $$F_t$$ being given, and $$F_t$$ meaning that all $$x_t$$’s are unconditional hot hand evaluations, it simply means that these $$X_t$$’s have a probability $$p$$ of being a success.
In the above case of
$$\mathbb{P}(X_t=1 | \tau = t, F) = \mathbb{P}(X_t=1 | \tau = t, F_t)$$
$$\text{where } p = \mathbb{P}(X_t = 1 | F_t )$$
$$= \sum_{t = k+1}^{n} \left[ \mathbb{P}(X_t=1 | \tau = t, F_t) \cdot \mathbb{P}(\tau = t | F_t) \right]$$
$$= \sum_{t = k+1}^{n} \left[ \left[ \sum_{\boldsymbol{x} \in F_t} \mathbb{P}(X_t=1 | \tau = t, \boldsymbol{X} = \boldsymbol{x}, F_t) \cdot \mathbb{P}( \boldsymbol{X} = \boldsymbol{x} | \tau = t, F_t ) \right] \cdot \mathbb{P}(\tau = t | F_t) \right]$$
My attempt at the intuition that $$\mathbb{P}(X_t=1 | \tau = t, F_t) \lt p$$ (for $$t \lt n$$) is the same as what I said above. Looking at
$$\mathbb{P}(X_t=1 | \tau = t, F_t) = \sum_{\boldsymbol{x} \in F_t} \mathbb{P}(X_t=1 | \tau = t, \boldsymbol{X} = \boldsymbol{x}, F_t) \cdot \mathbb{P}( \boldsymbol{X} = \boldsymbol{x} | \tau = t, F_t )$$
for simplicity, let’s assume that with $$p = 1/2$$, all sequences in the sample space are equally likely, i.e. a sequence is drawn uniformly. Think of the previous lists of sequences we had, where the frequency of successes or H’s from the top part of the list going down is relatively sparse and gets very frequent at the bottom. So while we draw uniformly from the list of sequences, we are more likely to draw a sequence with less successes/H’s overall than if we could consider trials from the entire sample space. Thus, the probability of drawing a success/H given some sequence ends up being $$\lt p$$ on average: the H’s are “bunched up” at the bottom of the list of sequences.
Using Bayes’ Theorem, we write:
$$\frac{ \mathbb{P} (X_t = 1 | \tau = t, F_t) }{ \mathbb{P} (X_t = 0 | \tau = t, F_t) } = \frac{ \mathbb{P} ( \tau = t | X_t = 1, F_t) \cdot \mathbb{P}(X_t = 1 | F_t) }{\mathbb{P}( \tau = t | F_t)} \cdot \frac{\mathbb{P}( \tau = t | F_t)}{ \mathbb{P} ( \tau = t | X_t = 0, F_t) \cdot \mathbb{P}(X_t = 0 | F_t) }$$
$$= \frac{ \mathbb{P} ( \tau = t | X_t = 1, F_t) \cdot \mathbb{P}(X_t = 1 | F_t) }{ \mathbb{P} ( \tau = t | X_t = 0, F_t) \cdot \mathbb{P}(X_t = 0 | F_t) }$$
$$= \frac{ \mathbb{P} ( \tau = t | X_t = 1, F_t) \cdot p }{ \mathbb{P} ( \tau = t | X_t = 0, F_t) \cdot (1 – p) }$$
Let’s write the denominator of the left-hand side in terms of the numerator of the left-hand side and the probability terms of the right-hand side as some unknown, say $$Y$$:
$$\frac{ \mathbb{P} (X_t = 1 | \tau = t, F_t) }{ 1 – \mathbb{P} (X_t = 1 | \tau = t, F_t) } = Y \cdot \frac{p}{1-p}$$
$$\mathbb{P} (X_t = 1 | \tau = t, F_t) = Y \cdot \frac{p}{1-p} \cdot \left({ 1 – \mathbb{P} (X_t = 1 | \tau = t, F_t) } \right)$$
$$= Y \cdot \frac{p}{1-p} – Y \cdot \frac{p}{1-p} \cdot \mathbb{P} (X_t = 1 | \tau = t, F_t)$$
$$\mathbb{P} (X_t = 1 | \tau = t, F_t) + Y \cdot \frac{p}{1-p} \cdot \mathbb{P} (X_t = 1 | \tau = t, F_t) = Y \cdot \frac{p}{1-p}$$
$$\mathbb{P} (X_t = 1 | \tau = t, F_t) \cdot \left( 1 + Y \cdot \frac{p}{1-p} \right) = Y \cdot \frac{p}{1-p}$$
$$\mathbb{P} (X_t = 1 | \tau = t, F_t) = \frac{Y \cdot \frac{p}{1-p} } {\left( 1 + Y \cdot \frac{p}{1-p} \right)} = \frac{Y \cdot \frac{p}{1-p} } {\left( \frac{1-p}{1-p} + \frac{Y \cdot p}{1-p} \right)}$$
$$= \frac{Y \cdot p } { ({1-p}) + Y \cdot p } = \text{ RHS (right-hand side) }$$
If $$Y=1$$, then $$\mathbb{P} (X_t = 1 | \tau = t, F_t) = p$$.
The derivative of the right-hand side with respect to Y is:
$$\frac{d}{dY} \left( \frac{Y \cdot p } { ({1-p}) + Y \cdot p } \right)$$
$$= p \cdot \left( ({1-p}) + Y \cdot p \right)^{-1} – Y \cdot p \cdot \left( ({1-p}) + Y \cdot p \right)^{-2} \cdot p$$
$$= \frac {p \cdot \left( ({1-p}) + Y \cdot p \right) } {\left( ({1-p}) + Y \cdot p \right)^{2}} – \frac {Y \cdot p^2 } {\left( ({1-p}) + Y \cdot p \right)^{2} } = \frac { p \cdot (1 – p) } {\left( ({1-p}) + Y \cdot p \right)^{2} }$$
The derivative of the right-hand side with respect to Y is always positive for any $$Y$$. So as we decrease $$Y$$ from 1 so that $$Y \lt 1$$, then the right-hand side decreases from $$p$$ and we would have
$$\mathbb{P} (X_t = 1 | \tau = t, F_t) = \frac{Y \cdot p } { ({1-p}) + Y \cdot p } \lt p$$
So to show that $$\mathbb{P} (X_t = 1 | \tau = t, F_t) \lt p$$, we show that
$$Y = \frac{ \mathbb{P} ( \tau = t | X_t = 1, F_t) }{ \mathbb{P} ( \tau = t | X_t = 0, F_t) } \lt 1$$
or
$$\mathbb{P} ( \tau = t | X_t = 1, F_t) \lt \mathbb{P} ( \tau = t | X_t = 0, F_t)$$
We write:
$$\mathbb{P} ( \tau = t | X_t = 0, F_t) = \sum_{\boldsymbol{x} \in F_t: x_t = 0} \mathbb{P} ( \tau = t | X_t = 0, \boldsymbol{X} = \boldsymbol{x}, F_t) \cdot \mathbb{P} ( \boldsymbol{X} = \boldsymbol{x}|X_t = 0, F_t)$$
$$= \sum_{\boldsymbol{x} \in F_t: x_t = 0} \mathbb{P} ( \tau = t | X_t = 0, \boldsymbol{X_{-t}} = \boldsymbol{x_{-t}}, F_t) \cdot \mathbb{P} ( \boldsymbol{X_{-t}} = \boldsymbol{x_{-t}}|X_t = 0, F_t)$$
where given $$\boldsymbol{x}$$, we define $$\boldsymbol{x_{-t}} := (x_1,…,x_{t-1},x_{t+1},…,x_n)$$. Since we are already given that $$X_t = 0$$, to say here that we are given $$\boldsymbol{X} = \boldsymbol{x}$$ is more like saying that we are given $$X_t = 0$$ and $$\boldsymbol{X_{-t}} = \boldsymbol{x_{-t}}$$.
We also write:
$$\mathbb{P} ( \tau = t | X_t = 1, F_t) = \sum_{\boldsymbol{x} \in F_t: x_t = 1} \mathbb{P} ( \tau = t | X_t = 1, \boldsymbol{X} = \boldsymbol{x}, F_t) \cdot \mathbb{P} ( \boldsymbol{X} = \boldsymbol{x}|X_t = 1, F_t)$$
$$= \sum_{\boldsymbol{x} \in F_t: x_t = 1} \mathbb{P} ( \tau = t | X_t = 1, \boldsymbol{X_{-t}} = \boldsymbol{x_{-t}}, F_t) \cdot \mathbb{P} ( \boldsymbol{X_{-t}} = \boldsymbol{x_{-t}}|X_t = 1, F_t)$$
Then we compare:
$$\mathbb{P} ( \boldsymbol{X_{-t}} = \boldsymbol{x_{-t}}|X_t = 0, F_t) \text{ and } \mathbb{P} ( \boldsymbol{X_{-t}} = \boldsymbol{x_{-t}}|X_t = 1, F_t)$$
and see that they are equal since $$X_t$$ is an i.i.d. Bernoulli trial and so $$\boldsymbol{X^{-t}}$$ is a sequence of i.i.d. Bernoulli trials.
Then we compare:
$$\mathbb{P} ( \tau = t | X_t = 0, \boldsymbol{X_{-t}} = \boldsymbol{x{-t}}, F_t ) \text{ and } \mathbb{P} ( \tau = t | X_t = 1, \boldsymbol{X_{-t}}= \boldsymbol{x{-t}}, F_t )$$
The former is the probability of picking a particular hot hand evaluation trial, the $$t$$th trial, given that the $$t$$th trial $$X_t = 0$$. The latter is the probability of picking a particular hot hand evaluation trial, the $$t$$th trial, given that the $$t$$th trial $$X_t = 1$$. Note that in the latter, because $$X_t = 1$$, the $$(t+1)$$th trial is also a hot hand evaluation whereas in the former, because $$X_t = 0$$, $$(t+1)$$th trial is not a hot hand evaluation trial. (Thus here, we are assuming that $$t \lt n$$.) Because of this, although the rest of the trials $$\boldsymbol{X_{-t}}= \boldsymbol{x{-t}}$$ are identical in both cases, the latter has one more hot hand evaluation trial compared to the former, i.e.
$$|I_k(\boldsymbol{x}) | \text{ where } X_t = 0 \lt |I_k(\boldsymbol{x}) | \text{ where } X_t = 1$$
which gives us
$$\mathbb{P} ( \tau = t | X_t = 0, \boldsymbol{X_{-t}} = \boldsymbol{x{-t}}, F_t ) \lt \mathbb{P} ( \tau = t | X_t = 1, \boldsymbol{X_{-t}}= \boldsymbol{x{-t}}, F_t )$$
$$\sum_{\boldsymbol{x} \in F_t: x_t = 0} \mathbb{P} ( \tau = t | X_t = 0, \boldsymbol{X_{-t}} = \boldsymbol{x_{-t}}, F_t) \cdot \mathbb{P} ( \boldsymbol{X_{-t}} = \boldsymbol{x_{-t}}|X_t = 0, F_t)$$
$$\gt \sum_{\boldsymbol{x} \in F_t: x_t = 1} \mathbb{P} ( \tau = t | X_t = 1, \boldsymbol{X_{-t}} = \boldsymbol{x_{-t}}, F_t) \cdot \mathbb{P} ( \boldsymbol{X_{-t}} = \boldsymbol{x_{-t}}|X_t = 1, F_t)$$
This shows us that:
$$\mathbb{P} (X_t = 1 | \tau = t, F) \lt p \text{ when } t \lt n$$
For $$t = n$$, since the value of $$X_n$$ doesn’t affect the number of hot hand evaluation trials, we have
$$\mathbb{P} ( \tau = n | X_n = 0, \boldsymbol{X_{-t}} = \boldsymbol{x{-t}}, F_n ) = \mathbb{P} ( \tau = n | X_n = 1, \boldsymbol{X_{-t}}= \boldsymbol{x{-t}}, F_n )$$
and thus we have
$$\mathbb{P} (X_{t=n} = 1 | \tau = n, F) = p \text{ when } t = n$$
So we have
$$\mathbb{P} (X_t = 1 | \tau = t, F) \lt p \text{ when } t = \{ k+1,…,n-1\}$$
and
$$\mathbb{P} (X_{t=n} = 1 | \tau = n, F) = p \text{ when } t = n$$
So
$$\mathbb{P}(X_t = 1 | F )$$
$$= \sum_{t=k+1}^n \left[ \mathbb{P}(X_t = 1 | \tau = t, F ) \cdot \mathbb{P}(\tau = t | F ) \right]$$
$$= \sum_{t=k+1}^{n-1} \left[ \mathbb{P}(X_t = 1 | \tau = t, F ) \cdot \mathbb{P}(\tau = t | F ) \right] + \left[ \mathbb{P}(X_n = 1 | \tau = n, F ) \cdot \mathbb{P}(\tau = n | F ) \right]$$
and since $$\mathbb{P}(\tau = t | F )$$ is a partition over the $$t$$’s, let $$\left[ \mathbb{P}(X_t = 1 | \tau = t, F ) \text{ when } t \lt n \right] = W < p$$, and we have $$= \sum_{t=k+1}^{n-1} \left[ W \cdot \mathbb{P}(\tau = t | F ) \right] + \left[ p \cdot \mathbb{P}(\tau = n | F ) \right] < p$$ asdf | 13,327 | 37,935 | {"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": 4, "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-2019-30 | latest | en | 0.940223 |
https://www.physicsforums.com/threads/thin-soap-film-question.270138/ | 1,508,589,883,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187824775.99/warc/CC-MAIN-20171021114851-20171021134851-00675.warc.gz | 960,785,500 | 15,528 | # Thin Soap Film Question
1. Nov 7, 2008
### chipmunk951
1. The problem statement, all variables and given/known data
A soap film is 129 nm thick. The film is in air and illuminated by white light at normal incidence as shown in the figure below. (In the figure the rays have been drawn at an angle to show the multiple reflections and transmissions in the film.) Assume the index of refraction of the soap film is the same as the index of refraction of water n = 1.33. The film is viewed from above and below by a video system which is sensitive to wavelengths from 200 to 1100 nm.
http://img227.imageshack.us/my.php?image=showmeplve2.gif
2. Relevant equations
1/2 + 2d/lambda = m
1/2 + 2d/lambda = m + 1/2
3. The attempt at a solution
a) When viewed in reflection, what is the longest visible wavelength that will appear enhanced?
b) When viewed in reflection, what is the longest visible wavelength that will have the least intensity?
c) When viewed in transmission, what is the longest visible wavelength that will appear enhanced?
a) Wouldn't this be 1/2 + 2d/lambda = m and solving for lambda where it's inbetween 200-1100 nm?
b) Got this, ended up just being 2nt/m = lambda
c) Not sure on this one, the help provides a link to some slides but the link is broken and I don't think our professor really cares.. Thanks! | 343 | 1,331 | {"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} | 3.125 | 3 | CC-MAIN-2017-43 | longest | en | 0.937065 |
http://www.ask.com/web?qsrc=6&o=102140&oo=102140&l=dir&gc=1&qo=popularsearches&ad=dirN&q=Examples+of+Valid+Syllogisms | 1,462,150,025,000,000,000 | text/html | crawl-data/CC-MAIN-2016-18/segments/1461860117244.29/warc/CC-MAIN-20160428161517-00045-ip-10-239-7-51.ec2.internal.warc.gz | 355,583,935 | 16,418 | Web Results
## Syllogism
en.wikipedia.org/wiki/Syllogism
A syllogism is a kind of logical argument that applies deductive reasoning to arrive at a .... For example, the syllogism BARBARA below is AAA-1, or "A-A-A in the first .... This table shows al...
## Overview of Examples & Types of Syllogisms - Fibonicci Fibonicci
www.fibonicci.com/logical-reasoning/syllogisms/examples-types/
Conditional syllogisms are better known as hypothetical syllogisms, because the arguments used here are not always valid. The basic of this syllogism type is: if ...
## SYLLOGISMS: Deductive Reasoning
web.cn.edu/kwheeler/documents/Syllogisms.pdf
argument. Directions: Decide whether the following syllogisms are valid in format (as opposed to using ... Invalid example: All snakes are cold-blooded. Valid ...
## syllogism - definition and examples of syllogisms in logic and rhetoric
In logic, a syllogism is a form of deductive reasoning consisting of a major premise, a minor premise, and a ... Here is an example of a valid categorical syllogism:.
## Categorical Syllogisms
www.comfsm.fm/~dleeling/geometry/categorical_syllogisms.xhtml
Categorical syllogisms are sets of three categorical propositions. .... The syllogism at first appeared to be valid, but a second example shows that EEE-1 is not ...
## Syllogism - Examples and Definition of Syllogism - Literary Devices
literarydevices.net/syllogism/
Definition, Usage and a list of Syllogism Examples in common speech and literature. Syllogism is a rhetorical device that starts an argument with a reference to ...
## Syllogisms: Mark McIntire
markmcintire.com/phil/chapter4.html
In any Standard Form Categorical Syllogism, the premise proposition that ... Here is a classic example of a debatable argument that might seem valid, but it ...
## 256 Syllogisms - Sites - Google
But if the premises are true and the conclusion is valid, then the syllogism is said to be sound. 2. ... The three statements in the example are of a similar pattern.
## Categorical Syllogisms
www.cos.edu/Faculty/JohnD/Documents/PHILSyllogisms.pdf
Let's look at two examples: A. and. B. All chairs are red. .... Rule 1: A valid standard-form categorical syllogism must contain three, and no more than three, terms; ...
## Rules and Fallacies for Categorical Syllogisms - WikiEducator
wikieducator.org/Rules_and_Fallacies_for_Categorical_Syllogisms
May 24, 2008 ... In a valid categorical syllogism the middle term must be distributed in ... by all valid categorical syllogisms (none of them, for example, have two ...
### Categorical Syllogism - Philosophy Pages
www.philosophypages.com
A categorical syllogism is an argument consisting of exactly three categorical ... Every syllogism of the form AAA-1 is valid, for example, while all syllogisms of the ...
### Categorical Syllogisms
www.butte.edu
In the following example, the major premise is an E statement and the minor premise ... To use the Venn Diagram method to decide their validity, we need to first ...
### How to Understand Syllogisms: 5 Steps (with Pictures)
www.wikihow.com
In this example, "animal" is the major term and predicate of the conclusion, " parrot" is ... A syllogism is valid if and only if the conclusion necessarily follows the ... | 833 | 3,268 | {"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-2016-18 | longest | en | 0.867069 |
sunyunzeng.com | 1,643,400,753,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320306335.77/warc/CC-MAIN-20220128182552-20220128212552-00200.warc.gz | 596,798,762 | 10,859 | # 快慢指针的应用
## 判断链表是否存在环
Title Detail
Given a linked list, determine if it has a cycle in it.
To represent a cycle in the given linked list, we use an integer pos which represents the position (0-indexed) in the linked list where tail connects to. If pos is -1, then there is no cycle in the linked list.
Example 1:
## 有序数组移除重复数字
Title Detail
Given a sorted array nums, remove the duplicates in-place such that each element appear only once and return the new length.
Do not allocate extra space for another array, you must do this by modifying the input array in-place with O(1) extra memory.
Example 1:
Example 1:
Clarification:
Confused why the returned value is an integer but your answer is an array?
Note that the input array is passed in by reference, which means modification to the input array will be known to the caller as well.
Internally you can think of this:
### 思路
1. 初始，快慢指针指向第一个数字。
2. 当快慢指针指向的数字都相同，快指针往前移动一位。
3. 当快慢指针指向的数字不相同，慢指针往前移动一位，把快指针指向的数字赋予慢指针，快指针往前移动一位。
4. 慢指针移动的 位数+1 即为不同数字的数量。且数组从初始位置到慢指针指向的位置，数字都是排好序的。 | 345 | 1,047 | {"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} | 3.125 | 3 | CC-MAIN-2022-05 | latest | en | 0.641653 |
https://azzlsoft.com/2011/03/ | 1,686,008,628,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224652184.68/warc/CC-MAIN-20230605221713-20230606011713-00338.warc.gz | 138,277,248 | 41,734 | ## Project Euler 009 – TSQL
31 03 2011
Problem 9
A Pythagorean triplet is a set of three natural numbers, a b c, for which,
a2 + b2 = c2
For example, 32 + 42 = 9 + 16 = 25 = 52.
There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.
Solution
select a*b*c from PythagoreanTriple
where a + b + c = 1000
Discussion
Clearly this problem is easy if you have a table full of Pythagorean triples. It turns out I do and it is a lot bigger than 1000.
## Project Euler 009 – IronRuby
30 03 2011
Problem 9
A Pythagorean triplet is a set of three natural numbers, a b c, for which,
a2 + b2 = c2
For example, 32 + 42 = 9 + 16 = 25 = 52.
There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.
Solution
exit = false
for a in 1..999 do
for b in a..999 do
c = 1000 a b
if c < b then break end
if a**2 + b**2 == c**2
puts a*b*c
exit = true
break
end
end
if exit then break end
end
Discussion
## Project Euler 009 – C#
29 03 2011
Problem 9
A Pythagorean triplet is a set of three natural numbers, a b c, for which,
a2 + b2 = c2
For example, 32 + 42 = 9 + 16 = 25 = 52.
There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.
Solution 1
using System;
namespace ProjectEulerCSharp_009
{
class Program
{
static void Main(string[] args)
{
int iterations = 0;
for (int a = 1; a <= 998; a++)
{
for (int b = 1; b <= 998; b++)
{
int c = 1000 – (a + b);
iterations++;
if (a * a + b * b == c * c)
{
System.Console.WriteLine("{0}", a*b*c);
System.Console.WriteLine(iterations);
return;
}
}
}
}
}
}
Solution 2
using System;
namespace ProjectEulerCSharp_009
{
class Program
{
static void Main(string[] args)
{
int iterations = 0;
for (int a = 1; a <= 998; a++)
{
for (int b = a + 1; b <= 998; b++)
{
int c = 1000 – (a + b);
iterations++;
if (a * a + b * b == c * c)
{
System.Console.WriteLine("{0}", a*b*c);
System.Console.WriteLine(iterations);
return;
}
}
}
}
}
}
Solution 3
using System;
namespace ProjectEulerCSharp_009
{
class Program
{
static void Main(string[] args)
{
int iterations = 0;
for (int a = 1; a <= 998; a++)
{
for (int b = a + 1; a + b < 1000; b++)
{
int c = 1000 – (a + b);
iterations++;
if (a * a + b * b == c * c)
{
System.Console.WriteLine("{0}", a*b*c);
System.Console.WriteLine(iterations);
return;
}
}
}
}
}
}
Solution 4
using System;
namespace ProjectEulerCSharp_009
{
class Program
{
static void Main(string[] args)
{
int iterations = 0;
for (int a = 1; a <= 998; a++)
{
for (int b = a + 1; a + b < 1000; b++)
{
int c = 1000 – (a + b);
if (c <= b) { break; }
iterations++;
if (a * a + b * b == c * c)
{
System.Console.WriteLine("{0}", a*b*c);
System.Console.WriteLine(iterations);
return;
}
}
}
}
}
}
Discussion
I am a big fan of getting the code working then optimizing later. I wanted to demonstrate that process with those post so I have included 4 iterations of optimizations.
If we were to loop through all of the possible digits from 1 through 998 twice (once for a and once for b) we would end up doing 996,004 iterations. That’s our baseline.
Solution 1
Because they state that there is only 1 solution, as soon as we find it there is no reason to continue. The obvious optimization is to exit the loops once we’ve found it. This brings our iterations to 198,778.
Solution 2
If we realize that we only need to check the numbers where b is greater than a then we can save ourselves and addition 20,000 iterations bringing our new number to 178678.
Solution 3
Knowing that another condition is that a + b + c = 1000 then a + b has to be less than 1000. This saves nearly 20,000 iterations as well. We are down to 159,716 iterations.
Solution 4
Finally, knowing that c has to be greater than b we can cut the iterations by 90,000 to : 69676.
That makes us about 14 times faster than the original version. There are going to be some additional optimizations you can make, but how fast do you need it? On my laptop, the difference is imperceptible. I could have left it at the original and been quite happy.
## Project Euler 009 – F#
28 03 2011
Problem 9
A Pythagorean triplet is a set of three natural numbers, a b c, for which,
a2 + b2 = c2
For example, 32 + 42 = 9 + 16 = 25 = 52.
There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.
Solution
(*
A Pythagorean triplet is a set of three natural numbers, a b c, for which,
a2 + b2 = c2
For example, 32 + 42 = 9 + 16 = 25 = 52.
There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.
*)
let testints = [1..998]
let answer = [for a in testints do
for b in testints do
if b >= a
&& a + b < 1000
&& a*a + b*b = (1000-a-b)*(1000-a-b) then
yield a * b * (1000-a-b)]
Discussion
I adapted this solution from my C# solution. It’s actually not as clean as my C# solution which betrays its imperative origins. I’m not sure I could come up with a much worse way to accomplish this task and yet it still runs quite snappy. This is going to be roughly 1,000,000 iterations. The b >= a makes several iterations pretty snappy. Still, changing the b loop to
for b in [a..998] do
will would be a better decision. While we’re at it, we could change testints too. Perhaps tomorrow will have some additional discussion on optimizations.
## Project Euler 008 – JavaScript
25 03 2011
Problem 8
Find the greatest product of five consecutive digits in the 1000-digit number.
73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450
Solution
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<title>Project Euler 008</title>
<body>
<script type="text/javascript">
dgts = "73167176531330624919225119674426574742355349194934" +
"96983520312774506326239578318016984801869478851843" +
"85861560789112949495459501737958331952853208805511" +
"12540698747158523863050715693290963295227443043557" +
"66896648950445244523161731856403098711121722383113" +
"62229893423380308135336276614282806444486645238749" +
"30358907296290491560440772390713810515859307960866" +
"70172427121883998797908792274921901699720888093776" +
"65727333001053367881220235421809751254540594752243" +
"52584907711670556013604839586446706324415722155397" +
"53697817977846174064955149290862569321978468622482" +
"83972241375657056057490261407972968652414535100474" +
"82166370484403199890008895243450658541227588666881" +
"16427171479924442928230863465674813919123162824586" +
"17866458359124566529476545682848912883142607690042" +
"24219022671055626321111109370544217506941658960408" +
"07198403850962455444362981230987879927244284909188" +
"84580156166097919133875499200524063689912560717606" +
"05886116467109405077541002256983155200055935729725" +
"71636269561882670428252483600823257530420752963450";
for (i = 0; i < dgts.length – 5; i++) {
product = dgts[i]*dgts[i+1]*dgts[i+2]*dgts[i+3]*dgts[i+4];
}
}
</script>
</body>
</html>
Discussion
Voila.
## C# Performance
24 03 2011
I have been working C# for nearly 8 years and never lost sleep over performance. Sure there are times when things run slowly, but the bottleneck is usually a database query or a web service call. I have never really needed to look into C# performance because it was always fast enough.
A couple weeks ago, Danny Tuppeny wrote “Why I’m Close to Giving Up on Windows Phone 7, as a User and a Developer”. He raised some pretty valid points, but of course this was a call to arms for the “Anything But Microsoft” crowd. A side thread about C# performance caught my eye. Here are a couple of the comments:
• “My favorite feature of .Net, in general, is sluggish performance, but C# is the best language to write sluggish software in by far.”
• “ObjC performance is also usually much better than even unsafe C# code, since it is essentially C.”
As I said before, I have never had reason to consider C# “sluggish”, but I also hadn’t really looked into its performance either. Let’s cut to the chase.
##### The Results
These are the results (in seconds) for a naïve nth prime finder. 11, 101, 1001, 10001, and 1000001 are the “n’s” in nth. 31, 547, 7927, 104743, and 1299721 are the actual values for the nth prime.
Version Trial 11 101 1001 10001 100001 31 547 7927 104743 1.29972e+06 C++ 1 1 0 0 0.017 2.101 263.429 2 0.000 0.000 0.021 2.1 263.472 3 0.000 0.000 0.016 2.103 264.520 4 0.000 0.000 0.016 2.109 263.482 5 0.000 0.000 0.015 2.098 265.413 Average 0.000 0.000 0.017 2.102 264.063 C# 1 1 0.001 0.001 0.017 2.172 264.570 2 0.001 0.001 0.017 2.133 264.378 3 0.001 0.001 0.017 2.114 264.246 4 0.001 0.001 0.016 2.133 264.401 5 0.001 0.001 0.017 2.128 264.654 Average 0.001 0.001 0.017 2.136 264.450
The difference is negligible.
##### The Code
I chose the nth prime problem for a couple reasons. The code could be written nearly identical in C++ and C# removing any ambiguity about language semantics. It also has a wide range of optimizations that can be applied. Version 1 is an extremely naïve (i.e. not optimized) approach.
C++
#include "stdafx.h"
#include <time.h>
#include <iostream>
const int maxPrimeIndex = 100001;
int _tmain(int argc, _TCHAR* argv[])
{
clock_t start, finish;
start = clock();
int currentPrime = 2;
int primeCount = 1;
while (primeCount < maxPrimeIndex)
{
bool isPrime = false;
int candidate = currentPrime + 1;
while (!isPrime)
{
isPrime = true;
for (int factor = 2; factor< candidate; factor++)
{
if (candidate % factor == 0)
{
isPrime = false;
break;
}
}
if (!isPrime)
{
candidate++;
}
}
currentPrime = candidate;
primeCount++;
}
finish = clock();
double elapsed = ((double)(finish – start)) / CLOCKS_PER_SEC;
std::cout << elapsed << std::endl << currentPrime << std::endl;
return 0;
}
C#
using System;
namespace SpeedTest
{
class Program
{
const int maxPrimeIndex = 100001;
static void Main(string[] args)
{
DateTime start, finish;
start = DateTime.Now;
int currentPrime = 2;
int primeCount = 1;
while (primeCount < maxPrimeIndex)
{
bool isPrime = false;
int candidate = currentPrime + 1;
while (!isPrime)
{
isPrime = true;
for (int factor = 2; factor < candidate; factor++)
{
if (candidate % factor == 0)
{
isPrime = false;
break;
}
}
if (!isPrime)
{
candidate++;
}
}
currentPrime = candidate;
primeCount++;
}
finish = DateTime.Now;
TimeSpan elapsed = finish – start;
Console.WriteLine(elapsed.ToString());
Console.WriteLine(currentPrime);
}
}
}
##### Why?
Why are the results so similar? Because both C++ and C# are compiled. When comparing these programs we are really comparing their compilers. This program is pretty straight-forward (i.e. no function calls, memory allocation, array checking, etc.) so the compiler optimizations are probably pretty similar. I used the Microsoft C++ compiler, but I also tested it with g++ and there was negligible difference.
If you really need to see the C++ compiler “beat” the C# compiler change candidate from an int to a long. The C++ code will run a little more than twice as fast. My guess is that the % operator is much less efficient on longs in C#, but that’s just a guess.
C# is typically JIT compiled, but it doesn’t have to be. You can use a tool called ngen to compile the image before running it. You should have a really good reason before doing this though because it can cause headaches when managing updates and the results in many cases will not be dramatic.
##### Optimization
As I said before, this code was intentionally not optimized. We are going to apply a very simple but very effective optimization by only checking possible factors up to (and including) the square root of the candidate. Here are the results:
Version Trial 11 101 1001 10001 100001 31 547 7927 104743 1.29972e+06 C++ 2 1 0 0 0.000 0.016 0.483 2 0.000 0.000 0 0.017 0.479 3 0.000 0.000 0 0.015 0.472 4 0.000 0.000 0 0.015 0.468 5 0.000 0.000 0 0.014 0.481 Average 0.000 0.000 0 0.015 0.477 C# 2 1 0.001 0.001 0.002 0.016 0.484 2 0.001 0.001 0.001 0.018 0.474 3 0.001 0.001 0.001 0.016 0.470 4 0.001 0.001 0.002 0.018 0.473 5 0.001 0.001 0.002 0.019 0.470 Average 0.001 0.001 0.002 0.017 0.474
With one simple optimization we have drastically increased our efficiency as n increases. This raises another question: how fast is fast enough? For the 100001st it was definitely worth our while. For the 10001st we save a couple of seconds. For the 1001st and below it took us more time to write this simple optimization than we’ll ever save. Context is important.
##### Conclusion
The point is that people that make blanket statements about performance often have no idea what they are talking about. Good programmers take the time to understand bottlenecks. Their gut reaction isn’t “throw more hardware at it” or “should have written it in C”. A great compiler isn’t going to save your application from a bad coder.
If you disagree, let me know. Maybe you’re curious how JavaScript or Python compares? I’d be happy to oblige. You can find me on Twitter (@azzlsoft) or email (rich@azzlsoft.com).
## Project Euler 008 – TSQL
24 03 2011
Problem 8
Find the greatest product of five consecutive digits in the 1000-digit number.
73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450
Solution
declare @digits varchar(MAX)
set @digits =
73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450′
declare @returnpattern varchar(2);
set @returnpattern = char(13) + char(10)
set @digits = replace(@digits, @returnpattern, )
declare @currentDigit int
set @currentDigit = 1
declare @sql varchar(max)
while(@currentDigit <= len(@digits))
begin
set @sql = ‘insert into Problem_008 (ordinal, digit) values (‘ + str(@currentdigit) + ‘, ‘ + substring(@digits, @currentDigit, 1) + ‘)’
exec(@sql)
set @currentDigit = @currentDigit + 1
end
GO
select max(product) from
(select
digit
* (select digit from Problem_008 a where a.ordinal = Problem_008.ordinal + 1)
* (select digit from Problem_008 a where a.ordinal = Problem_008.ordinal + 2)
* (select digit from Problem_008 a where a.ordinal = Problem_008.ordinal + 3)
* (select digit from Problem_008 a where a.ordinal = Problem_008.ordinal + 4) as product
from Problem_008
where ordinal < (select count(*) from Problem_008) 3) Products
Discussion
This one is going to take a bit of explanation. I parse the thousand digit number for it’s component digits and insert them into a database table with their ordinals. After the digits are in a table it’s a simple query.
Clearly, I didn’t need to insert the digits into a table to get the result, but as with all of the TSQL solutions I want to solve it as if the information exists in the database if possible.
## Phone Vision 18 – Erosion and Dilation
23 03 2011
Our exploration of set theory last time was a precursor to discussing dilation and erosion. Simply put, dilation makes things bigger and erosion makes things smaller. Seems obvious right? Let’s see if the mathematicians can muck it up.
##### Translation
This is not necessarily a fundamental set operation, but it is critical for what we will be doing. Translation can be described as shifting the pixels in the image. We can move it in both the x and y directions and we will represent the amount of movement using a point. To translate the set then, we simply add that point to every element of the set. For instance, using the point (20, 20) the puzzle is moved down 20 pixels and right 20 pixels like this:
The light blue area marks the original location.
##### Dilation
Dilation is an extension of translation from a point to a set of points. If you union the sets created by each translation you end up with dilation. In the following diagram, the black pixels represent the original puzzle piece. The light blue halo represents several translations of the original. Each translation is translucent so I have tried to make the image large enough so you can see the overlap. Notice how the hole is missing?
The set of points that were used to create the translated sets is called the structuring element. A common structuring element is
{ (-1,-1), (0,-1), (1,-1),(-1,0), (0,0), (1,0),(-1,1), (0,1), (1,1) }
This will expand the image by one pixel in every direction. If we think about this as a binary image, it might be represented by this:
Kinda reminds me of one of our convolution kernels. Structuring elements are often called “probes”. This one is centered at (0,0).
Using the PixelSet we created last time, the code is pretty straightforward.
public void Dilate(PixelSet structuringElem)
{
PixelSet dilatedSet = new PixelSet();
foreach(int translateY in structuringElem._pixels.Keys)
{
foreach(int translateX in structuringElem._pixels[translateY])
{
PixelSet translatedSet = new PixelSet();
foreach (int y in _pixels.Keys)
{
foreach(int x in _pixels[y])
{
translatedSet.Add(x + translateX, y + translateY);
}
}
dilatedSet.Union(translatedSet);
}
}
_pixels = new Dictionary<int,List<int>>(dilatedSet._pixels);
}
Here is the puzzle piece dilated by one pixel in all directions. The hole is gone.
##### Erosion
Erosion is similar to dilation except that our translation is subtraction instead of addition and we are finding the intersection instead of the union. Here is an image that has been eroded by 10 pixels in all directions. The light blue area is the original puzzle.
public void Erode(PixelSet structuringElem)
{
PixelSet erodedSet = new PixelSet(this);
foreach (int translateY in structuringElem._pixels.Keys)
{
foreach (int translateX in structuringElem._pixels[translateY])
{
PixelSet translatedSet = new PixelSet();
foreach (int y in _pixels.Keys)
{
foreach (int x in _pixels[y])
{
translatedSet.Add(x – translateX, y – translateY);
}
}
erodedSet.Intersect(translatedSet);
}
}
_pixels = new Dictionary<int,List<int>>(erodedSet._pixels);
}
Here is the puzzle eroded by one pixel in all directions. That hole is a little bigger.
##### Summary
Like I said at the beginning, dilation makes things bigger and erosion makes things smaller. Interestingly, erosion is simply the dilation of the background and dilation is the erosion of the background.
http://cid-88e82fb27d609ced.office.live.com/embedicon.aspx/Blog%20Files/PhoneVision/PhoneVision%2018%20-%20Erosion%20and%20Dilation.zip
Up Next: Opening and Closing
## Project Euler 008–IronRuby
23 03 2011
Problem 8
Find the greatest product of five consecutive digits in the 1000-digit number.
73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450
Solution
digits = "73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450"
#remove the line breaks again
digits = digits.delete("\r\n");
for i in 0..digits.length 5 do
product = Integer(digits[i]) * Integer(digits[i+1]) * Integer(digits[i+2]) * Integer(digits[i+3]) * Integer(digits[i+4])
end
end
Discussion
Here I used delete to get rid of the line breaks. Maybe instead of Integer I should have tried the “-‘0’” method described yesterday.
## Project Euler 008 – C#
22 03 2011
Problem 8
Find the greatest product of five consecutive digits in the 1000-digit number.
73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450
Solution
namespace ProjectEulerCSharp_008
{
class Program
{
static void Main(string[] args)
{
string digits = @"
73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450"
.Replace(" ", "").Replace("\r\n", "");
for(int i = 0; i < digits.Length – 5; i++)
{
int digit1 = int.Parse(digits.Substring(i+0, 1));
int digit2 = int.Parse(digits.Substring(i+1, 1));
int digit3 = int.Parse(digits.Substring(i+2, 1));
int digit4 = int.Parse(digits.Substring(i+3, 1));
int digit5 = int.Parse(digits.Substring(i+4, 1));
int product = digit1*digit2*digit3*digit4*digit5;
} | 8,144 | 26,831 | {"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} | 4.0625 | 4 | CC-MAIN-2023-23 | latest | en | 0.483933 |
https://www.teacherspayteachers.com/Browse/Search:adding%20multiples%20of%20ten | 1,516,090,747,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084886237.6/warc/CC-MAIN-20180116070444-20180116090444-00075.warc.gz | 976,441,708 | 69,005 | ## Main Categories
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showing 1-52 of 1,197 results
Included in this 20 page packet: All activities involve adding a 2-digit number to a multiple of 10. (Common Core Standard 1. NBT.C.4) These can be used for independent work, general instruction, math centers, or assessments. Horizontal Addition with base ten blocks (4) Vertical Addition (4) Spi
Subjects:
Types:
\$3.50
50 ratings
4.0
PDF (3.76 MB)
Adding Multiples of 10 to 100 Froggy Lovin Fun is a sweet set of 40 addition cards to sort with lovin little Froggy sums. This set can easily be made into 2 centers with several suggestions for differentiation. There is a recording sheet for you to check your children’s mastery of the skill. Also
Subjects:
Types:
\$3.00
22 ratings
3.9
PDF (446.52 KB)
This is a St. Patrick's Day themed resource pack to use to introduce adding two digit numbers. This focus solely on adding two digit numbers to multiples of ten, for example, 38 + 30 = ? Includes: St. Patrick's Math Center Students take turns adding two-digit numbers to multiples of ten. Col
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\$3.00
6 ratings
4.0
PDF (2.55 MB)
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Types:
\$3.00
5 ratings
4.0
PDF (1.07 MB)
Make your math lesson POP with this review game! This engaging activity will review the concept of adding multiples of ten to a two-digit number in a way that your students will remember. Also includes exit tickets and worksheets to assess and review this skill. This product is available as part
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Types:
\$3.00
12 ratings
4.0
PDF (7.87 MB)
These story problems will help students practice adding multiples of ten to a two digit number. Aligns with Common Core 1.NBT.4
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\$1.00
16 ratings
4.0
PDF (840.63 KB)
Puzzle: Add the two-digit number and the multiple of ten and match it to the correct puzzle piece answer. ( 16 Matches) Center Activities (2): Find the price of the two items and add the items together. Record the answer on the answer sheets. ( 6 items for each version: 2 versions: in color and
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Types:
CCSS:
\$2.00
13 ratings
4.0
PDF (2.13 MB)
Scoot is a whole group (or small group) game that gets students up and moving about. Students will be reviewing adding multiples of ten to a two-digit number. The only materials required are the recording sheet (last page) and the task cards. Included are 24 task cards and the recording sheet.
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\$2.50
12 ratings
4.0
PDF (2.87 MB)
#### Videos matching "adding multiples of ten" (BETA)
Adding Multiples of 10’s and 100’s --- Large Flashcards for Larger Numbers. I created these cards to drill my student on adding groups of 10’s and 100’s --- mentally! I set the cards up on an 8 ½ x 11 sheet so that if you just fold it in half down the middle it makes a large flash card --- 8 ½ x
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Types:
\$3.00
4 ratings
4.0
PDF (13.8 MB)
This is a game to help students practice adding multiples of 10. This product includes a page with directions, number cards and a recording sheet. This game would be great for a math workstation or center. It also includes a second set of cards so students can practice adding a multiple of 10 to
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Types:
CCSS:
\$1.00
14 ratings
4.0
PDF (174.39 KB)
This interactive printable allows students to practice using a hundreds chart to add a multiple of 10 to a two-digit number (and one one-digit number). They must show their thinking using the corresponding color for each equation. This worksheet can be used as an in class activity, homework assign
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CCSS:
\$1.00
10 ratings
4.0
PDF (443.22 KB)
Center and differentiated worksheets to use to practice adding multiples of ten to two-digit numbers with a Cinco de Mayo flair. Includes ★ Peppery Math Center Students take turns adding two-digit numbers to multiples of ten. Collect a pepper for every problem yo
Subjects:
\$3.00
3 ratings
4.0
PDF (4.81 MB)
A great game for adding multiples of 10! Students draw 2 cards and use the place value mat to model the problem with popsicle stick bundles or base 10 blocks. If they are correct, they roll the dice and move their game marker on the gameboard.
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Types:
\$3.00
9 ratings
4.0
PDF (258.68 KB)
This game provides students will an opportunity to practice adding multiples of ten to 2 and 3 digit numbers. It is a great way for teachers to assess automaticity of this crucial skill.
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Types:
CCSS:
\$2.00
7 ratings
4.0
PDF (1.51 MB)
My students love Write (or in the case Add) the Room activities. The goal of this one is to provide practice mental addition of tens and hundreds to 3-digit numbers. It's a low-prep activity. Print one copy of the equations, and enough recording sheets for each student. Cut the equations apart
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Types:
CCSS:
\$1.00
9 ratings
4.0
PDF (686.59 KB)
Celebrate Memorial Day with this U.S. patriotic themed resource pack to practice adding multiples of ten to two-digit numbers. No Prep Worksheets, Center Activity and Task Cards included. ★ CENTER ACTIVITY Roll the large paper dice to get a two digit number. Use the response c
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\$3.00
3 ratings
4.0
PDF (9.32 MB)
I have, Who has? Adding with Multiples of 10 Game! Description: This is a great activity to help students practice their knowledge of adding with multiples of 10. The game has several examples of adding with a multiple of ten and a one digit number (ex. 20+4) as well as adding two multiples of ten
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Types:
\$2.50
5 ratings
4.0
PDF (4.63 MB)
No time to plan today? Use this detailed lesson plan to guide your students through the process of adding multiples of ten to a two-digit number. All of the materials you need for this lesson, including the lesson plan itself, are included in this download. This product is also available as part
Subjects:
\$2.50
3 ratings
4.0
PDF (3.24 MB)
The SPLAT pairs are 10/90, 20/80, 30/70, 40/60 and 50/50. These are the pairs I have included in the POSTER (see PREVIEW). This game is based on the old SNAP game but, instead of slapping the deck when the same two numbers appear, players look for consecutive numbers that add to 100. I developed t
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\$1.00
\$0.80
4 ratings
4.0
ZIP (774.61 KB)
This 2nd grade math package is aligned with Unit 6 of enVision Math by Pearson. The package includes: adding multiples of ten horizontally adding multiples of ten with base ten blocks adding multiples of ten on a hundred chart Adding ones and tens on a hundred chart Identifying and extending nu
\$2.50
4 ratings
4.0
ZIP (568.07 KB)
Students will love this fun math center! Students will add multiples of tens to solve for the unknown number. This activity targets Common Core State Standard 1.NBT.5 and 1.OA.8. This workstation can be used with a hundreds chart so students can count or can be used without and students can add ment
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\$3.00
1 rating
4.0
PDF (490.49 KB)
This game can be played in a center. It challenges students to their math fluency and accuracy. This provides an engaging activity that allows student to practice their basic skills of adding numbers by the multiples of 10. Assembly is required.
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Types:
\$1.00
4 ratings
4.0
PDF (346.95 KB)
I can use models or drawings to add multiples of ten. This is three days of I DOs, WE DOs, and YOU DOs for adding multiples of ten. It is editable (so feel free to add motivational clip art for your students) and the assessments each include a question the students must write an answer for to expla
Subjects:
CCSS:
\$3.00
1 rating
4.0
PPTX (107.02 KB)
Strategies, skills and rules for adding multiples of 10 (from 10 to 90). Practise addition facts through this PowerPoint movement game. Great brain break and maths warm up activity. ★★★Buy the addition facts game bundle instead of buying the packs individually and save yourself over 25%!★★
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\$3.50
not yet rated
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PPTX (33.82 MB)
This product has 36 cards that have students adding two-digit numbers by a multiple of 10. You can play a game similar to War with them, play a game similar to Go Fish with them or come up with your own use.
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Types:
\$1.10
2 ratings
4.0
PDF (933.34 KB)
Help your students review and practice adding two digit by one digit numbers with these 40 task cards. Students will also adding multiples of ten to two digit numbers. The problems are separated into groups of 10 problems for easier classroom use. This product contains: +40 task cards +Teacher an
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Types:
\$2.00
2 ratings
4.0
PDF (400.79 KB)
This is a great activity for your students to practice adding multiples of ten to a given number. This will help build their fluency with doing jumps of ten and with place value.
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\$1.50
2 ratings
4.0
PDF (36.66 KB)
This activity is perfect for introducing, reviewing, or assessing the common core standard 1.NBT.4 - add within 100, including a 2-digit number and a multiple of 10. I hope you can use this resource in your classroom!
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\$1.00
2 ratings
4.0
PDF (214.5 KB)
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\$2.00
not yet rated
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PDF (932.98 KB)
Halloween Math Activities: This interactive notebook will help 1st and 2nd grade students practice adding multiples of 10 up to 200. { On Sale Now! Reg. Price \$3.50 } Students will create five mini-file books. Each book is four pages. A mini-writing activity is also included, along with a title a
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\$3.50
1 rating
4.0
PDF (2.17 MB)
Students will answer 7 equations as well as make their won equation. Two different exit tickets are provided.
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Types:
\$1.00
1 rating
4.0
PDF (93.13 KB)
This St. Patrick's Day themed product will help students to practice adding multiples of 10. It includes 36 task cards that could be used as a math center, SCOOT, or as a math game to play using them. In addition, there is an assessment page, as well as an answer key to be used either with the game
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\$2.50
1 rating
4.0
PDF (960.84 KB)
This Valentine's Day themed product will help students to practice adding multiples of 10. It includes 36 task cards that could be used as a math center, SCOOT, or as a math game to play using them. In addition, there is an assessment page, as well as an answer key to be used either with the game,
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\$2.00
not yet rated
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PDF (952.55 KB)
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\$1.50
1 rating
4.0
PDF (980.61 KB)
This product includes 36 task cards that could be used as a math center, SCOOT, or as a math game to play using them. In addition, there is an assessment page, as well as an answer key to be used either with the game, or for the teacher.
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\$2.00
not yet rated
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PDF (826.02 KB)
Common Core activity that gets students motivated by using technology and QR codes. Great activity to use in math groups.
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\$1.00
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PPT (3.97 MB)
Mollie People help your little people practice adding multiples of 10! This set includes: 48 flashcards adding 2 multiples of 10 48 flashcards adding 3 multiples of 10 up to 100 48 flashcards adding 3 multiples of 10 up to 200 For a crazy fun way to practice adding multiples of ten, go to my store
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\$3.00
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PDF (4.29 MB)
Are you looking for extra practice adding 2-digit numbers for your first grade students? This product is designed as a supplement to your curriculum. (You can buy this product individually here, or you can purchase Place Value-Pack 4 at Paw-some Resources. It contains additional products.) ~~~~~~~~
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\$0.95
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PDF (705.75 KB)
This summer themed product will help students to practice adding multiples of 10. It includes 36 task cards that could be used as a math center, SCOOT, or as a math game to play using them. In addition, there is an assessment page, as well as an answer key to be used either with the game, or for th
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\$2.50
not yet rated
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PDF (750.14 KB)
Saxon 3 Lesson 33 Extension Game and activity - Adding numbers to multiples of ten I use this along with Saxon Math Lesson 33, but this could easily be a stand alone lesson. For the game ou will receive the following: *game instructions *160 Matching cards students will play slap it!! This
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PDF (7.52 MB)
This Easter themed product will help students to practice adding multiples of 10. It includes 36 task cards that could be used as a math center, SCOOT, or as a math game to play using them. In addition, there is an assessment page, as well as an answer key to be used either with the game, or for th
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\$2.50
not yet rated
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PDF (1.18 MB)
This back to school themed product will help students to practice adding multiples of 10. It includes 36 task cards that could be used as a math center, SCOOT, or as a math game to play using them. In addition, there is an assessment page, a SCOOT answer sheet, as well as an answer key to be used e
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\$3.00
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PDF (968.85 KB)
Saxon 3 Lesson 31 Extension Game and activity - Adding multiples of ten and estimating sums using rounding I use this along with Saxon Math Lesson 31, but this could easily be a stand alone lesson. For the game ou will receive the following: *game instructions *40 Matching cards students w
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\$3.00
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PDF (6.9 MB)
This December/Christmas themed product will help students to practice adding multiples of 10. It includes 36 task cards that could be used as a math center, SCOOT, or as a math game to play using them. In addition, there is an assessment page, a SCOOT answer sheet, as well as an answer key to be us
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\$3.00
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PDF (1.33 MB)
This worksheet can be used with EnVisions Lesson 6.1. Great for having students practice add multiple of 10s to a given number, as well as teach students how to add multiples of 10 mentally. Great way to build mental computation skills.
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PDF (351.11 KB)
In my classroom, math centers are an important part of our math block! I developed these Solve the Room Activities to help streamline my math center routine! Each week, one center that my students visit is Solve the Room. They grab a recording sheet and clipboard and walk around the classroom searc
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PDF (6.24 MB)
Here's a fun freebie that comes in two levels- adding 2 multiples of ten or adding a multiple of ten to a two digit number. Perfect for Spring Time!
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FREE
10 ratings
4.0
PDF (607.32 KB)
A quick assessment or review activity for students to add two digit numbers with multiples of ten. Equations are in vertical format. In second grade, you could use it before you start addition with regrouping if you teach the method of writing it in expanded form and then mentally adding hundreds,
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CCSS:
FREE
3 ratings
4.0
PDF (161.58 KB)
A quick assessment or activity for having students add two digit numbers with multiples of ten. The first worksheet has sums that are more than 100 and the second worksheet the sums are 100 or less. Check out my Math Work Station Bundles!
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FREE
7 ratings
4.0
PDF (8.35 MB)
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FREE
3 ratings
4.0
PDF (450.51 KB)
Adding with multiples of 10 Great for whole group, small group, or quiz.
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\$1.25
2 ratings
4.0
DOC (48.85 KB)
Help your students with their mathematical fluency using grade-specific practice worksheets. The problems give students the important repeated practice for key mathematical skills and concepts. These are great for guided practice or independent work. Practice problems to help students with the skill
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showing 1-52 of 1,197 results
Teachers Pay Teachers is an online marketplace where teachers buy and sell original educational materials. | 4,078 | 15,784 | {"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} | 3.484375 | 3 | CC-MAIN-2018-05 | longest | en | 0.822998 |
https://www.learnpick.in/tutor/noida/vinay-verma/211246 | 1,571,009,220,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986648343.8/warc/CC-MAIN-20191013221144-20191014004144-00385.warc.gz | 1,055,630,180 | 26,884 | ### Vinay V Male, 25 Years
Associated for 3 Years 4 Months
Electrical Engineer
Class 6 - 8 Tutor
#### Activity Score - 98
Area:
Location: Noida, India
• Total Experience:
1 Year
• Hourly Fees:
INR 250
Tutoring Experience :
I have taught 5 to 10th standard students as home private tutor.
Tutoring Option :
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Tutoring Approach :
Teaching with practical examples, easy techniques to learn difficult formula
Teaches:
Class 9 - 10 Mathematics Physics School level computer Algebra CBSE INR 250 / Hour Class 6 - 8 Mathematics Physics School level computer Algebra CBSE INR 250 / Hour Basic Computer / Office Basic Computer School level computer MS Office Advanced Excel INR 200 / Hour
### 1 Note written by me
• #### Derivative Formula Summary
Files: 1
Derivative formula for various types of function in one page, for quick learning
• ## Question: A man walking with speed 'v' constant in magnitude and direction passes under a ...
Posted in: Physics | Date: 25/05/2016
Using the property of similiar triangle.
Speed of shadow(U) = (V x H) / (H - h)
By similiar triangle property
(U-V)/U = h / H
solving this value of U can be calculated
• ## Question: What are the advantages and limitations of solar cookers?
Posted in: Physics | Date: 25/05/2016
It uses renewable energy, Creates no pollution
It cant be used during night or rainy season
It cant be used for frying foods
It takes time to cook
• ## Question: How is corrosion of iron prevented by coating i with a layer of oil?
Posted in: Physics | Date: 25/05/2016
By coating iron with oil protect it from being exposed to atmoshphere. The atmoshpher contains oxygen which is responsible for corrosion. Oxidation reaction takes place when iron surface reacts with oxygen which cause rusting of iron.
• ## Question: How is infinity concept understood in Mathematics
Posted in: Mathematics,Mathematics,Mathematics,Mathematics,Mathematics | Date: 26/05/2016
In mathematics Infinity means any number devided by 0 equals to infinity
e.g. 1/0 or 2/0 so on.....
• ## Question: What is meant by corrosion of iron?
Posted in: Physics | Date: 26/05/2016
In chemistry corrosion is defined as the oxidation of any metal surface. So corrosion of iron simply means oxidation of iron
• ## Question: how to differentiate with respect to x in the given equation y = e ^ (ax + b) wh...
Posted in: Mathematics | Date: 26/05/2016
its very simple..
use formulae :- d / dx(e^U) = e^u X d/dx(U)
so.. Solution : ae^(ax+b)
• ## Question: What will be the focal length of a lens whose power is given as + 2.0 D?
Posted in: Physics | Date: 27/05/2016
since, Focal length = inverse of power of lense
i.e. F= 1/ P
So, F = 1/ P
= 1/ 2
= 0.5 m
• ## Question: What is the hindrance in developing wind power and power of water flow?
Posted in: Physics | Date: 01/06/2016
In both the common problem is continuity. Wind flow is a variable factor also same for the water flow.
So the power generation would be discontinuous and discrete. Aslo there is problem with a constant frequency power which is required by the electrical equipments to work. But this issue can be solved using power electronics circuit.
• ## Question: Which part of India where wind energy is commercially harnessed?
Posted in: Physics | Date: 01/06/2016
Personally I have seen wind energy plant in Gujarat.
But other states as well have developed that are
Maharashtra
Kerala
West Bengal
J & K
• ## Question: On what principle does a solar water heater operate?
Posted in: Physics | Date: 01/06/2016
Solar water heater operates on the principle of conservation of energy i.e. energy cant be created cant be destroyed it can transform from one form to other.
So in Solar water heater, Solar energy is converted into heat energy.
• ## Question: Why does a cut diamond shine more than a glass piece with diamond cut?
Posted in: Physics | Date: 02/06/2016
The refractive index of diamond is more than glass, so the Daimond shines more
• ## Question: Which type of orbit is suitable for a geostationary satellite?
Posted in: Physics | Date: 02/06/2016
A geostationary satellite is a satellite whose period of rotaion is 24 hr same as that of Earth, So it should follow geosynchronus orbit.
• ## Question: What is meant by 'critical angle' for a ray of light going from one medium into ...
Posted in: Physics | Date: 02/06/2016
When light travels from denser to rarer medium, the angle of incidence at which angle of refraction is 90 degree is called critical angle of incidence and increasing beyond that critaical value then light gets reflected to same medium.
e.g. Light travelling in fibre optics
• ## Question: What are the differences between a natural satellite and an artificial satellite...
Posted in: Physics | Date: 02/06/2016
An artificial satellite is manmade while a natural satellite is nature made. e.g Moon is natural satellite
• ## Question: Which type of these satellite orbitals will be suitable for collecting data for ...
Posted in: Physics | Date: 02/06/2016
Obviously we all know Geostationary satellite have same time period as of Earth so it can be used for weather forecasting.
Only 3 Geostationary satellite can be used to cover whole earth
• ## Question: What is meant by 'our universe is expanding'?
Posted in: Physics | Date: 02/06/2016
When scientists talk about the expanding universe, they mean that it has been growing ever since its beginning with the Big Bang. The galaxies outside of our own are moving away from us, and the ones that are farthest away are moving the fastest. | 1,395 | 5,600 | {"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} | 3.125 | 3 | CC-MAIN-2019-43 | latest | en | 0.83637 |
https://newsupland.in/division-sorting-codechef-solution/ | 1,675,677,987,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764500334.35/warc/CC-MAIN-20230206082428-20230206112428-00592.warc.gz | 428,643,563 | 15,302 | # Division Sorting Codechef Solution
### We Are Discuss About CODECHEF SOLUTION
Division Sorting Codechef Solution
## Problem
Chef has an array A of length N consisting of positive integers.
In one move, Chef can do the following:
• Pick an index i \ (1 \leq i \leq N) and a prime number P, such that P divides A_i.
• Divide A_i by P, i.e, set A_i := \frac{A_i}{P}.
Find the minimum number of moves that Chef needs to make the array A non-decreasing.
Note: An array A is called non-decreasing if A_i \le A_{(i+1)} for all (1 \le i \lt N).
### Input Format
• The first line of input will contain a single integer T, denoting the number of test cases.
• Each test case consists of two lines of input.
• The first line of each test case contains an integer N, the length of array A.
• The second line contains N space-separated integers A_1, A_2, \ldots, A_N.
### Output Format
• For each test case, output on a new line the minimum number of moves needed to make A non-decreasing.
### Constraints
• 1 \leq T \leq 10^5
• 1 \leq N \leq 2 \cdot 10^5
• 1 \leq A_i \leq 5\cdot 10^5
• The sum of N across all test cases won’t exceed 2 \cdot 10^5.
### Sample 1:
Input
Output
4
3
3 2 1
5
10 27 15 30 2
4
10 10 11 14
6
10 9 5 6 7 8
2
9
0
2
### Explanation:
Test case 1: Chef can perform the following moves:
• Divide A_1 = 3 by P = 3. Now, A = [1, 2, 1]
• Divide A_2 = 2 by P = 2. Now, A = [1, 1, 1] and is non-decreasing.
Test case 2: One optimal final array is A = [1, 1, 1, 2, 2]. You can verify that it takes 9 moves to reach this:
• 2 moves each on positions 1, 3, and 4.
• 3 moves on position 2.
Test case 3: No moves need to be made. The array is already non-decreasing.
Test case 4: Chef can divide A_1 by 5 and A_2 by 3. The array is now [2, 3, 5, 6, 7, 8], which is non-decreasing.
## Division Sorting Codechef Solution
Yhaa You have done it but next? if YOU Want to Get Others Please Visit Here JOIN NOW | 680 | 1,932 | {"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} | 3.65625 | 4 | CC-MAIN-2023-06 | longest | en | 0.364197 |
https://www.jiskha.com/search?query=A+rocket+is+fired+at+a+speed+of+75.0+m%2Fs+from+ground+level%2C+at+an+angle+of+59.7%C2%B0+above+the+horizontal.+The+rocket+is+fired+toward+an+11.0+m+high+wall%2C+which+is+located+28.5+m+away.+The+rocket+attains | 1,623,871,114,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487626008.14/warc/CC-MAIN-20210616190205-20210616220205-00439.warc.gz | 756,669,139 | 11,235 | # A rocket is fired at a speed of 75.0 m/s from ground level, at an angle of 59.7° above the horizontal. The rocket is fired toward an 11.0 m high wall, which is located 28.5 m away. The rocket attains
60,932 results
1. ## Physics
In the absence of air resistance, a projectile is launched from and returns to ground level. It follows a trajectory similar to that in the figure below and has a range of 15 m. Suppose the launch speed is doubled, and the projectile is fired at the same
2. ## Physics
A test rocket is launched vertically from ground level (y=0m), at time t=0.0 s. The rocket engine provides constant upward acceleration during the burn phase. At the instant of engine burnout, the rocket has risen to 97 m and acquired a velocity of 40 m/s.
3. ## Alg/Trig
If h= -16t^2 + 112t represents the height of a rocket, in feet, t seconds after it was fired, when will the rocket hit the ground? (Hint: The rocket is on the ground when h equals=0).
4. ## physics
A rocket is fired at a speed of 75.0 m/s from ground level, at an angle of 64.7¡ã above the horizontal. The rocket is fired toward an 11.0 m high wall, which is located 25.0 m away. The rocket attains its launch speed in a negligibly short period of
5. ## Calculus
If a rocket is shot vertically upward from the ground with an initial velocity of 192 ft/sec. a. When does it reach its maximum height above the ground? b. What is the maximum height reached by the rocket? c. How long does it take to reach the ground
6. ## math
a model rocket is projected straight upward from the ground level. It is fired with an initial velocity of 192 ft/s. How high is the rocket after 10 seconds?
7. ## Math
A rocket is launched from ground level with an initial vertical velocity (v0) of 176 ft/s. After how many seconds will the rocket hit the ground? (Hint: h(t) = -16t2 + v0t + h0)
8. ## Physics
a) A cannonball is fired horizontally from the top of a cliff. The cannon is at height H = 100 m above ground level, and the ball is fired with initial horizontal speed v_0. Assume acceleration due to gravity to be g = 9.80 m/s^2. Assume that the cannon is
9. ## physics
a projectile is fired from the surface of the earth with a speed of 200 m/s at an angle of 30 degrees above the horizontal. If the ground is level, what is the maximum height reached by the projectile
10. ## math
a model rocket is projected straight upward from the ground level. It is fired with an initial velocity of 192 ft/s. How high is the rocket after 10 seconds? When is the rocket at a height of 432 feet? What is the maximum height of the rocket? When will
11. ## physics
A rocket is fired at a speed of 75.0 m/s from ground level, at an angle of 59.7° above the horizontal. The rocket is fired toward an 11.0 m high wall, which is located 28.5 m away. The rocket attains its launch speed in a negligibly short period of time,
12. ## I NEED HELP!!!!!MATH!!!
A person flying a kite holds the string 4 feet above ground level. The string of the kite is taut and makes an angle of 60° with the horizontal (see the figure). Approximate the height of the kite above level ground if 700 feet of string is payed out.
13. ## physics
A catapult launches a test rocket vertically upward from a well, giving the rocket an initial speed of 79.0 m/s at ground level. The engines then fire, and the rocket accelerates upward at 3.90 m/s2 until it reaches an altitude of 980 m. At that point its
14. ## college algebra
a rocket is fired upward from some initial distance above the ground. Its height in feet, h,above the ground, t seconds after it is fired, is given by h=-16t^2+32t+560.
15. ## physics
A test rocket is fired vertically upward from a well. A catapult gives it an initial speed of 80.8 m/s at ground level. Its engines then fire and it accelerates upward at 3.90 m/s2 until it reaches an altitude of 920 m. At that point its engines fail, and
16. ## physics
A rocket is fired at a speed of 91.0 m/s from ground level, at an angle of 49.0 ° above the horizontal. The rocket is fired toward an 21.4-m high wall, which is located 25.0 m away. The rocket attains its launch speed in a negligibly short period of time,
17. ## algebra
The question I have is to solve the problem. A model rocket is launched from the ground with an initial speed of 50 feet per second. The equation that models its height, h feet, off the ground t seconds after it was fired is h=-16ft^2+50t a)How high is the
18. ## physics
When it is 152 m above the ground, a rocket traveling vertically upward at a constant 9.50 m/s relative to the ground launches a secondary rocket at a speed of 12.4 m/s at an angle of 50.0 degrees above the horizontal, both quantities being measured by an
19. ## Calculus HELP
A rocket is fired into the air with an initial velocity of 98 m/s. The distance (s) the rocket is above the ground, in metres, after t seconds is given by the expression s(t) = 98t - 4.9t2. What is the rocket's instantaneous rate of change at the moment it
20. ## MATH
A toy rocket is launched vertically upward from ground level. This is represented as f(t) = -16t^2 + 128t where t is the time in second and f(t) is the height of the rocket in feet. When will the rocket hit the ground? divide both sides by -16 0 = -16t^2 +
21. ## physics
A cannonball is fired horizontally from the top of a cliff. The cannon is at height = 70.0 above ground level, and the ball is fired with initial horizontal speed . Assume acceleration due to gravity to be = 9.80 .
22. ## Physics I
A rocket is fired at a speed of 75.0 m/s from ground level, at an angle of 61.2° above the horizontal. The rocket is fired toward an 11.0 m high wall, which is located 20.5 m away. The rocket attains its launch speed in a negligibly short period of time,
23. ## Physics
A model rocket has a mass of 3.00 kg. It is fired so that when it is 220 m above the ground it is travelling vertically upward at 165 m/s. At that point its fuel runs out so that the rest of its flight is without power. Assume that the effect of air
24. ## Angle of elevation
A rocket fired straight up is tracked by an observer on the ground a mile away. a)Show that when the angle of elevation is theta, the height of the rocket in feet is h=5280tan(theta).
25. ## physics
a cannonball is fired with initial speed v0 at an angle 30 degrees above the horizontal from a height of 40m above the ground. the projetile strikes the ground with a speed of 1.2v0. find v0.
26. ## physics
A rocket is fired at a speed of 66.0 m/s from ground level, at an angle of 63.0 ° above the horizontal. The rocket is fired toward an 31.2-m high wall, which is located 28.0 m away. The rocket attains its launch speed in a negligibly short period of time,
27. ## physics
A rocket is fired at a speed of 75.0 m/s from ground level, at an angle of 60.0º above the horizontal. The rocket is fired toward an 15.0 m high wall, which is located 27.0 m away. The rocket attains its launch speed in a negligibly short period of time,
28. ## calculus
A rocket rises vertically from a point on the ground that is 100m from an observer at ground level. The observer notes that the angle of elevation is increasing at a rate of 12∘per second when the angle of elevation is 60∘. Find the speed of the rocket
29. ## physics
A test rocket is fired vertically upward from a well. A catapult gives it an initial speed of 80.2 m/s at ground level. Its engines then fire and it accelerates upward at 4.20 m/s2 until it reaches an altitude of 960 m. At that point its engines fail, and
30. ## math
A person flying a kite holds the string 4 feet above ground level. The string of the kite is taut and makes an angle of 60° with the horizontal (see the figure). Approximate the height of the kite above level ground if 700 feet of string is payed out.
31. ## physics
I really need help with these questions. My teacher doesn't provide me with anything to go on only some formulas and maybe 3 examples. It would be greatly appreciated! 1. Find the speed of a rock which is thrown off the top of a 20 m tall building at 15
32. ## Calculus
A rocket is fired vertically into the air at the rate of 6 miles/min. An observer on the ground is located 4 miles from the launching pad. When the rocket is 3 miles high, how fast is the angle of elevation between the rocket and the observer changing?
33. ## college algebra
A rocket is fired upward from some initial distance above the ground. Its height in feet, h,above the ground, t seconds after it is fired, is given by h=−16t^2+64t-3072
34. ## Physics
In the absence of air resistance, a projectile is launched from and returns to ground level. It follows a trajectory similar to that shown in Figure 3.10 and has a range of 29 m. Suppose the launch speed is doubled, and the projectile is fired at the same
35. ## physics
You have designed a rocket to be used to sample the local atmosphere for pollution. It is fired vertically with a constant upward acceleration of 17 m/s2. After 20 s, the engine shuts off and the rocket continues rising (in freefall) for a while. (Neglect
36. ## Physics
A cannonball is fired with initial speed v0 at an angle 30° above the horizontal from a height of 42.9 m above the ground. The projectile strikes the ground with a speed of 1.2v0. Find v0.
37. ## calculus
3) A shell is fired from ground level with a muzzle speed of 350 ft / s and elevation and angle of 60 . Find (a) parametric equation for the shell’s trajectory (b) the maximum height reached by the shell (c) the horizontal distance traveled by the shell
38. ## Physics
A rocket is fired at a speed of 75.0 m/s from ground level, at an angle of 56.3 ° above the horizontal. The rocket is fired toward an 11.0-m high wall, which is located 21.5 m away. The rocket attains its launch speed in a negligibly short period of time,
39. ## Physics
A rocket is fired at a speed of 96.0 m/s from ground level, at an angle of 35.0 ° above the horizontal. The rocket is fired toward an 15.2-m high wall, which is located 32.0 m away. The rocket attains its launch speed in a negligibly short period of time,
40. ## physics
A rocket is fired at a speed of 75.0 m/s from ground level, at an angle of 57.6¡ã above the horizontal. The rocket is fired toward an 11.0 m high wall, which is located 25.5 m away. The rocket attains its launch speed in a negligibly short period of
41. ## Physics
A rocket is fired at a speed of 50.0 m/s from ground level, at an angle of 46.0 ° above the horizontal. The rocket is fired toward an 18.7-m high wall, which is located 23.0 m away. The rocket attains its launch speed in a negligibly short period of time,
42. ## physics
A rocket is fired at a speed of 91.0 m/s from ground level, at an angle of 49.0 ° above the horizontal. The rocket is fired toward an 21.4-m high wall, which is located 25.0 m away. The rocket attains its launch speed in a negligibly short period of time,
43. ## physics
A rocket is fired at a speed of 54.0 m/s from ground level, at an angle of 63.0 ° above the horizontal. The rocket is fired toward an 52.8-m high wall, which is located 37.0 m away. The rocket attains its launch speed in a negligibly short period of time,
44. ## henry ford
A rocket is fired at a speed of 74.0 m/s from ground level, at an angle of 68.0 ° above the horizontal. The rocket is fired toward an 49.8-m high wall, which is located 32.0 m away. The rocket attains its launch speed in a negligibly short period of time,
45. ## physics
A rocket is fired at a speed of 75.0 m/s from ground level, at an angle of 68.0° above the horizontal. The rocket is fired toward an 11.0 m high wall, which is located 26.5 m away. The rocket attains its launch speed in a negligibly short period of time,
46. ## physics
A rocket is fired at a speed of 92.0 m/s from ground level, at an angle of 33.0 ° above the horizontal. The rocket is fired toward an 13.4-m high wall, which is located 26.0 m away. The rocket attains its launch speed in a negligibly short period of time,
47. ## physics
A rocket is fired at a speed of 75.0 m/s from ground level, at an angle of 68.6° above the horizontal. The rocket is fired toward an 11.0 m high wall, which is located 26.0 m away. The rocket attains its launch speed in a negligibly short period of time,
48. ## physics
A rocket is fired at a speed of 70.0 m/s from ground level, at an angle of 40.0 ° above the horizontal. The rocket is fired toward an 14.0-m high wall, which is located 21.0 m away. The rocket attains its launch speed in a negligibly short period of time,
49. ## physics
A rocket is fired at a speed of 70.0 m/s from ground level, at an angle of 40.0 ° above the horizontal. The rocket is fired toward an 14.0-m high wall, which is located 21.0 m away. The rocket attains its launch speed in a negligibly short period of time,
50. ## physics
A rocket is fired at a speed of 75.0 m/s from ground level, at an angle of 57.3° above the horizontal. The rocket is fired toward an 11.0 m high wall, which is located 21.5 m away. By how much does the rocket clear the top of the wall?
51. ## physics
A rocket is fired at a speed of 75.0 m/s from ground level, at an angle of 67.6° above the horizontal. The rocket is fired toward an 11.0 m high wall, which is located 29.5 m away. By how much does the rocket clear the top of the wall?
52. ## Physics
A rocket is fired at a speed of 76.4 m/s from ground level, at an angle of 61.0° above the horizontal. The rocket is fired toward an 10.6 m high wall, which is located 26.2 m away. By how much does the rocket clear the top of the wall?
53. ## Physics
A rocket is fired at a speed of 75.0 m/s from ground level, at an angle of 63.0° above the horizontal. The rocket is fired toward an 11.0 m high wall, which is located 22.0 m away. By how much does the rocket clear the top of the wall?
54. ## Physics
A small rocket is fired in a test range. It rises high into the air and soon runs out of fuel. On the way down it passes near an observer (sitting in a 22.5-m-high tower) who sees the rocket traveling at a speed of 37.9 m/s and moving in a vertical plane
55. ## Physics
A rocket is fired vertically with an upward acceleration of 30 m/s2. After 20 s, the engine shuts off and the rocket then continues rising (while in free-fall). The rocket eventually stops rising and then falls back to the ground. (a) What is the highest
56. ## physics
You have designed a rocket to be used to sample the local atmosphere for pollution. It is fired vertically with a constant upward acceleration of 17 m/s2. After 20 s, the engine shuts off and the rocket continues rising (in freefall) for a while. (Neglect
57. ## Science, Physics, math, calculus
A toy rocket is fired at v0 = 41.2 m/s at an angle of è = 73.8 degrees with respect to the horizontal on flat level ground. Assuming that air resistance is negligible, what is its maximum height (H) and how far (R) will the rocket have traveled in the
58. ## Physical
A toy rocket is launched vertically from ground level (y = 0 m), at time t = 0.0 s. The rocket engine provides constant upward acceleration during the burn phase. At the instant of engine burnout, the rocket has risen to 73 m and acquired a velocity of The
59. ## math
A rocket is fired at an angle of 18.5 ° with the ground from a point 1670 m directly behind an observer. Shortly later the rocket is observed at an angle of elevation of 33.5 ° directly in front of and above the observer. How far on a direct line has the
60. ## physics
A test rocket is fired vertically upward from a well. A catapult gives it an initial speed of 81.0 m/s at ground level. Its engines then fire and it accelerates upward at 4.10 m/s2 until it reaches an altitude of 940 m. At that point its engines fail, and
61. ## physics
You have designed a rocket to be used to sample the local atmosphere for pollution. It is fired vertically with a constant upward acceleration of 19 m/s2. After 23 s, the engine shuts off and the rocket continues rising (in freefall) for a while. (Neglect
62. ## physics
A 1-kg rocket is fired straight up from level ground. The engine is able to provide a constant 15N of thrust for exactly 5 seconds after which it shuts of completely. Find the maximum height that the rocket achieves.
63. ## Physics
A test rocket is fired vertically upward from a well. A catapult gives it an initial speed of 80.2 m/s at ground level. Its engines then fire and it accelerates upward at 4.20 m/s2 until it reaches an altitude of 960 m. At that point its engines fail, and
64. ## Math
A rocket is launched vertically into the air and is observed from a tower that is 1.5 km above the ground level. Soon after the launch the rocket is at an angle of 25 degrees. Later the rocket has climbed vertically a further 4 km and its angle of
65. ## physics
A rocket is fired straight up and accelerates upward at 24 m/s2 for 12 seconds. The rocket then runs out of fuel and coasts. Ignore any air resistance effects and use -9.8 m/s2 for the local acceleration due to gravity. a) What is the rocket’s maximum
66. ## math
A rocket is fired straight up from the ground with an initial velocity of 800 feet per second. (a) How long does it take the rocket to reach 3200 feet? (b) When will the rocket hit the ground?
67. ## Physics
A rocket is fired at an angle from the top of a tower of height h0 = 68.6 m . Because of the design of the engines, its position coordinates are of the form x(t)=A+Bt2 and y(t)=C+Dt3, where A, B, C , and D are constants. Furthermore, the acceleration of
68. ## Physics
Take into account the Earth's rotational speed (1 rev/day) and use 5 significant figures. (a) Determine the necessary speed, with respect to Earth, for a rocket to escape if fired from the Earth at the equator in a direction eastward. (The escape velocity
69. ## calculus
1. A rocket is fired vertically into the air. Six kilometers away, a telescope tracks the rocket. At a certain moment, the angle between the telescope and the ground is and is increasing at a rate of 0.6 radians per minute. (See the picture. I have defined
70. ## physics
A toy rocket is fired off a platform with an initial speed of 223 ft/sec at an angle of elevation of 32 degrees and achieves a maximum height of 291 ft. How how above the ground was the platform?
71. ## Physics
a rocket with mass 3000kg is fired from the ground at an angle of 60 degrees. the motor creates a force of 60000N for 50sec then cuts out. how do i find total horizontal distance from leaving the ground to hitting the ground again?? no air resistance
72. ## MOMENTUM AND SHM
A(n) 3800 kg rocket traveling at 2500 m/s is moving freely through space on a journey to the moon. The ground controllers find that the rocket has drifted off course and that it must change direction by 9.2 degrees if it is to hit the moon. By radio
73. ## PHYSICS MOMENTUM
A(n) 3800 kg rocket traveling at 2500 m/s is moving freely through space on a journey to the moon. The ground controllers find that the rocket has drifted off course and that it must change direction by 9.2 degrees if it is to hit the moon. By radio
74. ## Math
Fireworks are fired at an angle of 82degrees with the horizontal. They are expected to explode about 100 m in the air, 4.8 secs after they are fired. What is the initial velocity of a shell fired from ground level. I think I have to find the vertical and
75. ## physics
48 kg projectile is fired at an angle of 30 degree above the horizontal with an initial speed of 1.34 x10^2m/s fro the top of a cliff 150m above level ground, where the ground is taken to be y=0 what is the inital total mechanical energy of the
76. ## physics
'a 48 kg projectile is fired at an angle of 30 degree above the horizontal with an initial speed of 1.34 x10^2m/s fro the top of a cliff 150m above level ground, where the ground is taken to be y=0 what is the inital total mechanical energy of the
77. ## physics
You have designed a rocket to be used to sample the local atmosphere for pollution. It is fired vertically with a constant upward acceleration of 15 m/s2. After 21 s, the engine shuts off and the rocket continues rising (in freefall) for a while. (Neglect
78. ## NIC
A model rocket is launched straight up from ground level with a speed of 34.2 m/s. Assuming that the only force acting on the rocket after launch is the force of gravity, a. How fast is the rocket going when it reaches a height of 22.5 m? (3 marks) b. How
79. ## physics
A rocket is launched with a speed of 282 m/s at an angle of 41.2 degrees above the horizontal. How far does the rocket travel before it hits the ground?
80. ## Physics
A basketball was kicked 20.0 m above horizontal with an initial velocity of 120.0 m/s at an angle of 35.0˚ above the horizontal. (a) How long is the rocket in air before falling? (b) What is the horizontal range for the rocket? (c) With what speed does
81. ## physics 111
1. A stone throw from ground level returns to the same level 4 s after. With what speed was the stone throw? Take g = 10m per square. 2. A cart is moving horizontally along a straight line with constant speed ofb30 m/s. A projectile is fired from the
82. ## physics
A 2000 kg space probe is moving rightward in empty space along the x axis at 12 m/s. One of the probe’s rockets is fired providing a thrust of 1800j N along the y axis. The rocket fires for 1.5 s. How can I derive the equation for the trajectory of the
83. ## physics
A 2000 kg space probe is moving rightward in empty space along the x axis at 12 m/s. One of the probe’s rockets is fired providing a thrust of 1800j N along the y axis. The rocket fires for 1.5 s. How can I derive the equation for the trajectory of the
84. ## physics
A 2000 kg space probe is moving rightward in empty space along the x axis at 12 m/s. One of the probe’s rockets is fired providing a thrust of 1800j N along the y axis. The rocket fires for 1.5 s. How can I derive the equation for the trajectory of the
85. ## Physics
In the absence of air resistance, a projectile is launched from and returns to ground level. It follows a trajectory similar to that shown in Figure 3.10 and has a range of 24 m. Suppose the launch speed is doubled, and the projectile is fired at the same
86. ## Physics
A projectile is fired from ground level with a speed of 40 m/s at an angle of 30 degrees and hits a building 100m away. What is the time of flight of the projectile? How high above ground does the projectile hit the building? What is the speed of the
87. ## Physics
A small rocket is fired in a test range. It rises high into the air and soon runs out of fuel. On the way down it passes near an observer (sitting in a 21.5-m-high tower) who sees the rocket traveling at a speed of 35 m/s and moving in a vertical plane at
88. ## physics
A 2000 kg space probe is moving rightward in empty space along the x axis at 12 m/s. One of the probe’s rockets is fired providing a thrust of 1800j N along the y axis. The rocket fires for 1.5 s. How can I derive the equation for the trajectory of the
89. ## physics
A 2000 kg space probe is moving rightward in empty space along the x axis at 12 m/s. One of the probe’s rockets is fired providing a thrust of 1800j N along the y axis. The rocket fires for 1.5 s. How can I derive the equation for the trajectory of the
90. ## PHYSICS
A SUPERSONIC FIGHTER JET FLYING HORIZONTALLW AT HEIGHT OF 4KM ABOVE THE GROUND AND AT A SPEED OF 400M/S FIRES A ROCKET VERTICALLY DOWNWARD. THE ROCKET IS RELEASED WITH AN INITIAL SPEED OF 80M/S CALCULATE THE TIME OF FLIGHT OF THE ROCKET AND THE HORIZONTAL
91. ## physics
Consider a projectile fired horizontally from a cliff of a given height. With what speed must it be fired so that it makes a 45 degree angle with the ground when it hits
92. ## Physics
A 360 g model rocket is on a cart that is rolling to the right at a speed of 2.5 m/s. The rocket engine, when it is fired, exerts an 8.5 N thrust on the rocket. Your goal is to have the rocket pass through a small horizontal hoop that is 20 m above the
93. ## physics
A catapult launches a test rocket vertically upward from a well, giving the rocket an initial speed of 80.2 m/s at ground level. The engines then fire, and the rocket accelerates upward at 3.80 m/s2 until it reaches an altitude of 1180 m. At that point its
94. ## math
A rocket is fired at sea level and climbs at a constant angle of 70° through a distance of 10,000 feet. Approximate its altitude to the nearest foot. how do you solve this?/
95. ## physics
A test rocket is launched vertically from ground level (y = 0 m), at time t = 0.0 s. The rocket engine provides constant upward acceleration during the burn phase. At the instant of engine burnout, the rocket has risen to 49 m and acquired a velocity of
96. ## PHYSICS
A projectile is fired from the surface of the Earth with a speed of 150 meters per second at an angle of 45 degrees above the horizontal. If the ground is level, what is the maximum height reached by the projectile?
97. ## AP PYHSICS
A projectile is fired from the surface of the Earth with a speed of 150 meters per second at an angle of 45 degrees above the horizontal. If the ground is level, what is the maximum height reached by the projectile?
98. ## physics
A rocket is fired vertically and reaches a speed of 34.3 m/s in half a second. One and a half seconds later the rocket’s speed is 19.6 m/s. Find the acceleration (in m/s2) and initial velocity (in m/s) of the rocket. Complete the equation of motion for
99. ## physic
3) A shell is fired from ground level with a muzzle speed of 350 ft / s and elevation and angle of 60 . Find (a) parametric equation for the shell’s trajectory (b) the maximum height reached by the shell (c) the horizontal distance traveled by the shell
100. ## PHY 1004
A projectile is fired with an initial velocity of 10.0 m/s at an angle of 30^0 above the horizontal. It is at ground level and returns to ground level.. Determine the projectile's horizontal range | 6,763 | 26,080 | {"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-2021-25 | latest | en | 0.943378 |
https://au.pinterest.com/explore/a-riddle/ | 1,496,130,560,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463614615.14/warc/CC-MAIN-20170530070611-20170530090611-00331.warc.gz | 919,793,748 | 53,939 | ### Freebie Rhyming Riddles! (Freebielicious)
TriBond - three words with a common bond. Easy, medium, and hard TriBonds with answers:
Time to add some challenging fun to your classroom routine with Brain Teasers for teens! First, give these head-scratchers a try: When you’re ready, scroll down for the answers. Now, did you really...
### Summer Decimals Math Riddle Bundle
Make Reviewing Decimals FUN this Summer! This activity is full of computation practice. The students also have a goal of solving a riddle at the end. It is a great way to combine fun and learning! The Pack includes 14 different riddle worksheets at varying levels.
### Fractions - Reducing fractions, and Converting Improper and Mixed Numbers
Equivalent Fractions , Improper Fractions and Mixed Numbers Math Riddles Pack This activity is full of computation practice. The students also have a goal of solving a riddle at the end. It is a great way to combine fun and learning!
In this Animal Riddle lesson, students will research an animal and create a riddle to showcase their knowledge and engage other students in the natural world.
This activity is full of computation practice, but also incorporates an aspect of fun. The students have a goal of solving a riddle at the end of each worksheet. I love hearing the sound of my students giggles when they solve the riddle at the end. Make math FUN! The Pack includes 2 different worksheets 1 Riddle reviewing all four operations (+ - x ÷) with whole numbers 1 Riddle reviewing all four operations (+ - x ÷) with decimals
Make Order of Operations FUN this Summer! This activity is full of computation practice. The students also have a goal of solving a riddle at the end. It is a great way to combine fun and learning! The Pack includes 5 different riddle worksheets at varying levels.
Make Scientific Notation FUN this Summer! This activity is full of computation practice. The students also have a goal of solving a riddle at the end. It is a great way to combine fun and learning! . The Pack includes 3 different riddle worksheets at varying levels.
This is a great pack to teach landforms to your students. The little book is in a riddle format so it will require your students to use critical thinking to solve. However, there are the Anchor Charts and Small Picture Cards to scaffold for the successful learning for all students.
Pinterest | 510 | 2,382 | {"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-2017-22 | latest | en | 0.927055 |
http://www.momjunction.com/articles/new-years-eve-games-activities-for-teens_00376369/ | 1,529,569,688,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267864110.40/warc/CC-MAIN-20180621075105-20180621095105-00151.warc.gz | 457,761,372 | 30,101 | Top 10 New Years Eve Games And Activities For Teens
Image: Shutterstock
New Year’s is almost here, and it’s the time of indecisions for most parents of teens. Teens are too young to celebrate New Year’s Eve at the bar and too old to make crafts at home. So how do you ensure they have fun on New Year’s Eve? By organizing a teen-approved bash of course! So, if you are hosting a New Year’s party for your teen and are looking for some New Years Eve games for teens, then you have come to the right place. We’ve listed some enjoyable activities and games that your teen can enjoy playing on New Year’s Eve.
New Years Eve Games For Teens
Image: Shutterstock
You Will Need:
• Pen
• Paper
• Bowl
How To:
1. Give each teen a sheet of paper and pen.
1. Make each player write down his resolution of a piece of paper. Put all the slip of papers in a bowl and give it a shuffle.
1. Pull out one slip of paper from the bowl and read it aloud. Every player has to write down the name of the person who made each resolution. And tell them to write their names on the back of the sheet.
1. After reading out all the resolution, take the paper sheets from the players and check who has given correct guesses.
1. The player that gives the most number of correct guesses will win a prize. You can even read out a few of the wrong guesses loud for laughter and fun. This is a hilarious New Year’s eve party games for teenagers.
2. Word Guessing:
Image: Shutterstock
You Will Need:
• Pen
• Stopwatch
• Index cards
How To:
1. Write down 100 words on the index cards like a laugh, plate, shoelace, blink, stare, grin or any word that you like. Now stack the cards and place in the center of the room.
1. Divide the teens into two equal teams and tell them to sit, facing each other.
1. Set the stopwatch or timer for one minute.
1. Now have the first player for each time draw out a card from the stack and give clues to his teammate before the end of a minute.
1. His teammates have to guess the word within the same one minute. If the teammates have successfully guessed the words, they will get a point.
1. If the timer runs out, and the teammates are unable to guess the word, then the opposing team will get a bonus point.
1. Take turns until all the cards are covered.
1. Add up to see who is the winner. This is one of the interesting New Year’s eve activities for teens.
3. Four On The Couch:
Image: Shutterstock
You Will Need:
• A four-seater couch and a few chairs.
• At least 12 players
• Slips of paper and pen
• Chairs
How To:
1. Arrange the chairs and couch in a circle.
1. Divide the teens into two groups. Boys versus girls would be great.
1. Make everyone sit on the chairs and some on the couch and give each one of them a slip of paper and pen. One seat should be empty.
1. Tell each of the players to write their first name on the paper and hand it to you. Place the slips of paper in a hat and toss well. Now give each player the slips of paper again. Each player will get someone else’s name. The players have to keep the name a secret.
1. The player sitting next to the empty seat has to start the game. She has to call out the name of the person written on her paper. The player has to get up and sit in the empty chair next to the former player.
1. Repeat the procedure until the team gets four of its players on the couch.
4. Cotton Ball Blitz:
Image: Shutterstock
You Will Need:
• Two bowls for each player
• Cotton balls
• Vaseline
How To:
1. Put two bowls in front of each team. One should be filled with cotton balls, and the other should be empty.
1. Now ask the player to apply Vaseline on their noses. Set the timer for one minute and start the game.
1. The player has to move the cotton balls from one bowl to another using just his nose.
1. The player who moves most cotton balls will win the game.
5. Ribbon Dance:
Image: Shutterstock
You Will Need:
• Ribbon cut into 3-foot length
How To:
1. Make sure you have an even number of players and one ribbon for every two players.
1. Hold a bunch of ribbons from the middle of your hand, so that then ends dangle loose.
1. Now tell each player to grab one end of the ribbon.
1. Now let go of the ribbons. The two people who are holding onto the same ribbon will become dancing partners. Be ready for some funny dance pairings.
6. The Secret Sash:
Image: Shutterstock
You Will Need:
• Sheets of paper with each guest’s name
• An assortment of small objects
How To:
1. As your teen’s friends enter, give each of them ordinary objects like a pompom, ball, and hair clip and so on.
1. The players have to hide their object, but without concealing them. They have to try to hide the objects in their hair, hands and so on.
1. At the end of the party, the players have to write down the name of each other’s object on a sheet of paper.
1. The player with a correct answer will win the game.
7. Word Mix:
Image: Shutterstock
You Will Need:
• Paper
• Pen
How To:
1. Give every player each word that has something to do with New Year’s Eve.
1. Now the players have to make as many words as they can use only the letters in the original word.
1. Repeating a letter must not be allowed unless it’s repeated in the original words. Even proper nouns will not be counted as words.
1. The teen who writes the most number of original words will be the winner.
8. What If:
Image: Shutterstock
You Will Need:
• Pen
• Index card
How To:
1. Have the players write a question that starts with “What if.” The question can be related to New Year also. The questions can be funny, silly or even serious.
1. Now shuffle the card and pass it to each player. If the player receives his question, then tell him to exchange the cards with another player.
1. Now tell everyone to write the answer to his or her original question on the same index card.
1. The first player will read the question, and the player next to him will read the answer. It will be fun listening to answers that make no sense at all.
Image: Shutterstock
You Will Need:
• Nothing
How To:
1. Divide the teens into teams.
1. Now send one team member to another room. The rest of the teammates have to decide an adverb to act out to their ‘it.’
1. After the teammates have decided on the adverb, ask the ‘it’ to come back to the room.
1. The ‘it’ now has to guess the word. She can pick any teammate and give him a scenario to act out the word. The game will be real fun when the player has to give a silly scene for the others to act out.
10. Dancing With The Mate:
Image: Shutterstock
You Will Need:
• Paper
• Pen
How To:
1. Write the names of different animals on each piece of paper. Each animal’s name needs to be written twice.
1. Now tell the teens to stand in the middle of the room as you toss the slips of paper in the air.
1. Once the paper falls, the players have to scramble to grab one.
1. As soon as they grab one, they have to start acting like the animal in their paper while looking for their mate.
1. Once they find out their partner, they have to hurry up and sit down.
1. The last pair standing will be out.
Make sure you have a steady supply of refreshments so that the teens have the energy to keep going. How do keep your teen engaged on the New Year’s Eve? Did you like our compilation of New Year’s eve party games for teenagers? Share with other mommies by commenting below! Until then, wish you and your family a very happy New Year.
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##### MBA560 Financial and Managerial Accounting: Module 8 Test (2 Problems)
Description
solution
Question
Question;Saint Leo University (Graduate;Business Studies);MBA560 Financial and Managerial;Accounting;Module 8 Test;Problem 1.;Creighton Company's balance sheet and income statement are provided;below;Creighton Company;Balance Sheet;December 31, 2012;Cash 21,000;Accounts receivable 24,000;Inventory 15,000;Plant and equipment, net of depreciation 144,000;Land held for future plant expansion;36,000;Total Assets 240,000;Liabilities and Stockholders' Equity;Accounts payable;18,000;Notes payable 30,000;Capital stock, no par;120,000;Retained earnings;72,000;Total Liabilities and stockholders' equity 240,000;Creighton Company;Balance Sheet;December 31, 2012;Sales 159,000;Less: variable costs;Manufacturing 31,000;Selling and administrative 25,000;Contribution margin 103,000;Less: Fixed costs;Manufacturing 31,000;Selling and administrative 22,500;Operating income;49,500;Required;1) Compute the margin, turnover, and return on investment for Creighton;Company;2) What is the advantage of expanding the ROI formula to measure margin;and turnover separately?;Problem 2.;Delta Company is evaluating two different capital investments, Project;X and Y. Either X or Y would cost \$100,000, and the company cannot afford to do;both.;The company expects that Project X would provide net cash inflows of;\$30,000 per year for 5 years.;For Project Y, the net cash inflows are expected to be as follows;Year Cash inflows;Year 1 22,000;Year 2 24,000;Year 3 30,000;Year 4 38,000;Year 5 40,000;Delta's cost of capital is 12%.;Required;1) Calculate the present value index for Project X and for Project Y.;2) Indicate whether each of the projects is an acceptable investment.;3) Which of the two projects;should Delta implement?
Paper#37671 | Written in 18-Jul-2015
Price : \$29 | 509 | 1,906 | {"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-2016-50 | longest | en | 0.772832 |
http://kevinkle.in/jekyll/update/2019/09/23/breaking_pills.html | 1,611,739,818,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610704821381.83/warc/CC-MAIN-20210127090152-20210127120152-00794.warc.gz | 59,949,108 | 4,770 | ### Motivation
Recently, Mark Dominus’ post on breaking pills appeared on Hacker News. I was surprised to see the author not provide a closed-form and wanted to extend on some of the comments indicating a relation to the harmonic numbers.
### Problem Formulation
Starting off with a bowl of $$n$$ whole pills, you draw from the bowl uniformly at random according to the following mechanism: if the drawn pill is whole, you put back one half of it; if the drawn pill is half, you don’t put back anything.
How many half pills will be left in the bowl once there are no more whole pills?
### Solution
Let us first state some useful observations:
• Every whole pill will be drawn eventually and sequentially. We can hence assume an order on the whole pills, wlog.
• Every whole pill can be associated with exactly one half pill that will be put back into the bowl. Moreover, every half pill has to be associated with exactly one whole pill, i.e. it is a 1-to-1 mapping.
• Instead of asking the more general question of ‘How many half pills will be left?’ we can ask the more specific question of ‘For how many whole pills, does the associated half pill remain in the bowl?’.
• For such a half pill to remain in the bowl, it has to be picked after (or not at all, depending on how you phrase the problem) all remaining whole pills.
For the sake of concreteness, let us illustrate the mechanism with $$n=7$$. Recalling that we can impose an order on whole pills, we look into the third whole pill W3 and the half pill h3 associated with it. More precisely, we look into h3’s position relative to all remaining whole pills. We can safely forget about the previous whole pills. These are the possible positions:
W3 h3 W4 W5 W6 W7 W3 W4 h3 W4 W6 W7 W3 W4 W5 h3 W6 W7 W3 W4 W5 W6 h3 W7 W3 W4 W5 W6 W7 h3
Note that only in the last scenario, does the half pill add to the count of half pills remaining after all whole pills. Hence, in expectation, the half pill associated with the first whole pill adds $$\frac{1}{5}$$ to the count of remaining half pills.
This ordering argument can be applied to all subsequent (as well as previous) whole pills: just with fewer (or more) whole pills to position. The last pill, representing the base case, will always add 1 half pill to the counter as there is only one position to choose from.
Applying our observation to all of the $$n$$ whole pills we obtain:
\begin{align} N_n &= \text{#half pills left after the draw of } n \text{ whole pills} \
\mathbb{E}[N_n] &= \sum_{i \in [n]} \Pr[\text{half pill from } i \text{th whole pill remains until the end}] \
&= \sum_{i \in [n]} \Pr[i\text{th half pill is positioned after remaining whole pills } i + 1, i+2, \dots n] \
&= \sum_{i \in [n]} \Pr[i\text{th half pill is positioned at last of } i \text{ positions}] \
&= \sum_{i \in [n]} \frac{1}{i} \
&= H_n \end{align}
In case such a (hopefully) intuitive reasoning still seems unsatisfactory, note that the given argument can easily be applied in a more explicit proof by induction.
### Closing remarks
Recall that the harmonic number can be very well approximated by the natural logarithm. In particular, we have $$H_n = \Theta(\log(n))$$ and $$\gamma + \log(n) < H_n < \gamma + \log(n+1)$$, where $$\gamma \approx .577$$ is the Euler-Mascheroni constant.
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http://oeis.org/A262354 | 1,571,698,129,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570987795253.70/warc/CC-MAIN-20191021221245-20191022004745-00477.warc.gz | 143,310,775 | 4,253 | This site is supported by donations to The OEIS Foundation.
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A262354 a(n) is the number of 2 X 2 matrices over Z_p with determinant in {1,-1} where p = prime(n). 0
6, 48, 240, 672, 2640, 4368, 9792, 13680, 24288, 48720, 59520, 101232, 137760, 158928, 207552, 297648, 410640, 453840, 601392, 715680, 777888, 985920, 1143408, 1409760, 1825152, 2060400, 2185248, 2449872, 2589840, 2885568, 4096512, 4495920, 5142432, 5370960 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,1 COMMENTS a(n) divides A244509(n). For n>2 (i.e. p=prime(n)>=5), a(n) gives the order of the largest proper subgroup of GL(2,Z_p). LINKS Gregor Olsavsky, Groups formed from 2 X 2 matrices over Z_p, Mathematics Magazine, Vol. 63, No. 4 (Oct., 1990), pp. 269-272. FORMULA For n>1, a(n) = 2*p*(p^2-1) where p = prime(n). For n>1, a(n) = 2*A127917(n). MATHEMATICA Prepend[2 Table[(Prime@ n + 1) Prime@ n (Prime@ n - 1), {n, 2, 34}], 6] (* Michael De Vlieger, Mar 24 2016, after Artur Jasinski at A127917 *) PROG (Sage) print [6]+[2*p*(p^2-1) for p in prime_range(3, 150)] (PARI) lista(nn) = {print1(6, ", "); forprime(p=3, nn, print1(2*p*(p^2-1), ", ")); } \\ Altug Alkan, Mar 24 2016 CROSSREFS Cf. A244509, A127917, A117762, A270775. Sequence in context: A208536 A253947 A260344 * A052771 A056289 A056284 Adjacent sequences: A262351 A262352 A262353 * A262355 A262356 A262357 KEYWORD nonn AUTHOR Tom Edgar, Mar 24 2016 STATUS approved
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Last modified October 21 18:43 EDT 2019. Contains 328308 sequences. (Running on oeis4.) | 682 | 1,830 | {"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} | 3.78125 | 4 | CC-MAIN-2019-43 | latest | en | 0.560419 |
https://www.math-only-math.com/worksheet-on-multiplying-binomials.html | 1,709,420,463,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947476137.72/warc/CC-MAIN-20240302215752-20240303005752-00486.warc.gz | 850,392,020 | 13,239 | # Worksheet on Multiplying Binomials
Practice the questions given in the worksheet on multiplying binomials (a binomial by a binomial). The questions are based on multiplication of two binomials.
1. Multiply a binomial by a binomial:
(i) (a + 2) and (a + 10)
(ii) (m + 5) and (m – 3)
(iii) (a – 5) and (a + 1)
(iv)(m - 7) and (4 - m)
(v) (x - 7) and (1 + x)
(vi) (k - 8) and (k - 8)
(vii) (m + 9) and (m - 2)
(viii) (2x + 3y) and (2x - y)
(ix) (x - y) and (2x +6y)
(x) (z + x) and (x + z)
2. Find the product of the binomials:
(i) (p + 1) × (p + 1)
(ii) (x - 1) × (x + 1)
(iii) (m + n) × (m - n)
(iv) (x2 + 2) × (x - 1)
(v) (z2 + 1) × (z2 - 1)
(vi) (1 – x3) × (x2 + 2)
(vii) (2m + 3n) × (m + 5n)
(viii) (x + y) × (x – 2y)
(ix) (2t + 5) × (7 - t)
(x) (p + r) × (2r – 7p)
3. Multiply the following binomials:
(i) (ax - by) (ax + by)
(ii) (x + 9) by (y + 2)
(iii) (10 - ab) by (ab + 2)
(iv) (ab + 1) by (ab + 10)
(v) (xy + yz) by (xy - yz)
(vi) (1 – 2y) by (5 - 3y)
Answers for the worksheet on multiplying binomials are given below to check the exact answers of the above multiplication.
1. (i) a2 + 12a + 20
(ii) m2 + 2m - 15
(iii) a2 - 4a - 5
(iv) -m2 + 11m - 28
(v) x2 - 6x - 7
(vi) k2 - 16k + 64
(vii) m2 + 7m - 18
(viii) 4x2 + 4xy - 3y2
(ix) 2x2 + 4xy - 6y2
(x) x2 + 2xz + z2
2. (i) p2 + 2p + 1
(ii) x2 - 1
(iii) m2 - n2
(iv) x3 - x2 + 2x - 2
(v) z4 - 1
(vi) -x5 - 2x3 + x2 + 2
(vii) 2m2 + 13mn + 15n2
(viii) x2 – xy - 2y2
(ix) -2t2 + 9t + 35
(x) -7p2 - 5pr + 2r2
3. (i) a2x2 - b2y2
(ii) xy + 2x + 9y + 18
(iii) -a2b2 + 8ab + 20
(iv) a2b2 + 11ab + 10
(v) x2y2 - y2z2
(vi) 6y2 - 13y + 5
Terms of an Algebraic Expression - Worksheet
Worksheet on Types of Algebraic Expressions
Worksheet on Degree of a Polynomial
Worksheet on Subtraction of Polynomials
Worksheet on Addition and Subtraction of Polynomials
Worksheet on Adding and Subtracting Polynomials
Worksheet on Multiplying Monomial and Polynomial
Worksheet on Multiplying Binomials
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The fractions having the same value are called equivalent fractions. Their numerator and denominator can be different but, they represent the same part of a whole. We can see the shade portion with re…
Types of Algebraic Expressions
Degree of a Polynomial | 1,308 | 3,732 | {"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} | 4.0625 | 4 | CC-MAIN-2024-10 | longest | en | 0.625991 |
http://www.jiskha.com/display.cgi?id=1195513323 | 1,498,190,495,000,000,000 | text/html | crawl-data/CC-MAIN-2017-26/segments/1498128319992.22/warc/CC-MAIN-20170623031127-20170623051127-00001.warc.gz | 557,530,768 | 4,307 | # Math
posted by on .
A bicycle wheel is 30 inches in diameter.
a. to the nearest revolution, how many times will the wheel turn if the bicycle is ridden for 3 miles.
b. suppose the wheel turns at a constant rate of 2.75 revolutions per second. What is the linear speed in miles per hour of a point on the tire?
• Math - ,
For a...
Circumference = (pi)(d) = 30pi in
3 mi = 190,080 in
190,080 / 30pi = 6336 / pi = 2017 revolutions
Not sure about the second part.
• Math - ,
Part A
(3miles/1)*(5280ft/1mi)*(12in/1ft)*(1rev/15πin) is appx 4033 revolutions
Part B
(2.75rev/1sec)*(60sec/1min)*(60min/1hr)*(15πin/1rev)*(1ft/12in)*(1mi/5280ft) is appx 7.4 mph
• Math - ,
The answers an owl as you at house of jug jug bird y'all finen
• Math - ,
Maths is so cool
• Math - ,
So this is a sensible answer basically you convert inches into miles which is about 190,080 inches then you do 30 times pie and divide them both | 296 | 928 | {"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} | 3.875 | 4 | CC-MAIN-2017-26 | latest | en | 0.846604 |
https://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/225/4/a/e/ | 1,675,526,254,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764500140.36/warc/CC-MAIN-20230204142302-20230204172302-00050.warc.gz | 892,995,119 | 58,874 | # Properties
Label 225.4.a.e Level $225$ Weight $4$ Character orbit 225.a Self dual yes Analytic conductor $13.275$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$
# Related objects
## Newspace parameters
Level: $$N$$ $$=$$ $$225 = 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 225.a (trivial)
## Newform invariants
Self dual: yes Analytic conductor: $$13.2754297513$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 25) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$
## $q$-expansion
$$f(q)$$ $$=$$ $$q + q^{2} - 7 q^{4} - 6 q^{7} - 15 q^{8}+O(q^{10})$$ q + q^2 - 7 * q^4 - 6 * q^7 - 15 * q^8 $$q + q^{2} - 7 q^{4} - 6 q^{7} - 15 q^{8} + 43 q^{11} + 28 q^{13} - 6 q^{14} + 41 q^{16} + 91 q^{17} - 35 q^{19} + 43 q^{22} + 162 q^{23} + 28 q^{26} + 42 q^{28} - 160 q^{29} + 42 q^{31} + 161 q^{32} + 91 q^{34} + 314 q^{37} - 35 q^{38} + 203 q^{41} - 92 q^{43} - 301 q^{44} + 162 q^{46} + 196 q^{47} - 307 q^{49} - 196 q^{52} + 82 q^{53} + 90 q^{56} - 160 q^{58} + 280 q^{59} - 518 q^{61} + 42 q^{62} - 167 q^{64} - 141 q^{67} - 637 q^{68} - 412 q^{71} + 763 q^{73} + 314 q^{74} + 245 q^{76} - 258 q^{77} + 510 q^{79} + 203 q^{82} + 777 q^{83} - 92 q^{86} - 645 q^{88} + 945 q^{89} - 168 q^{91} - 1134 q^{92} + 196 q^{94} - 1246 q^{97} - 307 q^{98}+O(q^{100})$$ q + q^2 - 7 * q^4 - 6 * q^7 - 15 * q^8 + 43 * q^11 + 28 * q^13 - 6 * q^14 + 41 * q^16 + 91 * q^17 - 35 * q^19 + 43 * q^22 + 162 * q^23 + 28 * q^26 + 42 * q^28 - 160 * q^29 + 42 * q^31 + 161 * q^32 + 91 * q^34 + 314 * q^37 - 35 * q^38 + 203 * q^41 - 92 * q^43 - 301 * q^44 + 162 * q^46 + 196 * q^47 - 307 * q^49 - 196 * q^52 + 82 * q^53 + 90 * q^56 - 160 * q^58 + 280 * q^59 - 518 * q^61 + 42 * q^62 - 167 * q^64 - 141 * q^67 - 637 * q^68 - 412 * q^71 + 763 * q^73 + 314 * q^74 + 245 * q^76 - 258 * q^77 + 510 * q^79 + 203 * q^82 + 777 * q^83 - 92 * q^86 - 645 * q^88 + 945 * q^89 - 168 * q^91 - 1134 * q^92 + 196 * q^94 - 1246 * q^97 - 307 * q^98
## Embeddings
For each embedding $$\iota_m$$ of the coefficient field, the values $$\iota_m(a_n)$$ are shown below.
For more information on an embedded modular form you can click on its label.
Label $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
1.1
0
1.00000 0 −7.00000 0 0 −6.00000 −15.0000 0 0
$$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles
## Atkin-Lehner signs
$$p$$ Sign
$$3$$ $$-1$$
$$5$$ $$-1$$
## Inner twists
This newform does not admit any (nontrivial) inner twists.
## Twists
By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 225.4.a.e 1
3.b odd 2 1 25.4.a.a 1
5.b even 2 1 225.4.a.c 1
5.c odd 4 2 225.4.b.f 2
12.b even 2 1 400.4.a.s 1
15.d odd 2 1 25.4.a.b yes 1
15.e even 4 2 25.4.b.b 2
21.c even 2 1 1225.4.a.h 1
24.f even 2 1 1600.4.a.h 1
24.h odd 2 1 1600.4.a.bt 1
60.h even 2 1 400.4.a.c 1
60.l odd 4 2 400.4.c.e 2
105.g even 2 1 1225.4.a.i 1
120.i odd 2 1 1600.4.a.i 1
120.m even 2 1 1600.4.a.bs 1
By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
25.4.a.a 1 3.b odd 2 1
25.4.a.b yes 1 15.d odd 2 1
25.4.b.b 2 15.e even 4 2
225.4.a.c 1 5.b even 2 1
225.4.a.e 1 1.a even 1 1 trivial
225.4.b.f 2 5.c odd 4 2
400.4.a.c 1 60.h even 2 1
400.4.a.s 1 12.b even 2 1
400.4.c.e 2 60.l odd 4 2
1225.4.a.h 1 21.c even 2 1
1225.4.a.i 1 105.g even 2 1
1600.4.a.h 1 24.f even 2 1
1600.4.a.i 1 120.i odd 2 1
1600.4.a.bs 1 120.m even 2 1
1600.4.a.bt 1 24.h odd 2 1
## Hecke kernels
This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{4}^{\mathrm{new}}(\Gamma_0(225))$$:
$$T_{2} - 1$$ T2 - 1 $$T_{7} + 6$$ T7 + 6
## Hecke characteristic polynomials
$p$ $F_p(T)$
$2$ $$T - 1$$
$3$ $$T$$
$5$ $$T$$
$7$ $$T + 6$$
$11$ $$T - 43$$
$13$ $$T - 28$$
$17$ $$T - 91$$
$19$ $$T + 35$$
$23$ $$T - 162$$
$29$ $$T + 160$$
$31$ $$T - 42$$
$37$ $$T - 314$$
$41$ $$T - 203$$
$43$ $$T + 92$$
$47$ $$T - 196$$
$53$ $$T - 82$$
$59$ $$T - 280$$
$61$ $$T + 518$$
$67$ $$T + 141$$
$71$ $$T + 412$$
$73$ $$T - 763$$
$79$ $$T - 510$$
$83$ $$T - 777$$
$89$ $$T - 945$$
$97$ $$T + 1246$$ | 2,129 | 4,345 | {"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} | 2.546875 | 3 | CC-MAIN-2023-06 | latest | en | 0.16899 |
https://www.gigacalculator.com/calculators/npv-calculator.php | 1,686,084,838,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224653071.58/warc/CC-MAIN-20230606182640-20230606212640-00602.warc.gz | 838,120,784 | 16,436 | # NPV Calculator
Use this online calculator to easily calculate the NPV (Net Present Value) of an investment based on the initial investment, discount rate and investment term. Also calculates Internal Rate of Return (IRR), gross return and net cash flow.
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## Using the NPV calculator
Our online Net Present Value calculator is a versatile tool that helps you:
• calculate the Net Present Value (NPV) of an investment
• calculate gross return, Internal Rate of Return IRR and net cash flow
Start by entering the initial investment and the period of the investment, then enter the discount rate, which is usually the weighted average cost of capital (WACC), after tax, but some people prefer to use higher discount rates to adjust for risk, opportunity cost and other factors. This is entirely up to you. Finally, enter the net cash flow for each year or other period (a maximum of 25 periods are allowed). Make sure you enter the free cash flow and not a cash flow after interest, which will result in double-counting the time value of money.
Our NPV calculator will output: the Net Present Value, IRR, gross return, and the net cash flow over the entire period.
## What is Net Present Value?
The definition of net present value (NPV), also known as net present worth (NPW) is the net value of an expected income stream at the present moment, relative to its prospective value in the future meaning it is discounted at a given rate. It is simply a subtraction of the present values of cash outflows (initial cost included) from the present values of cash flows over time, discounted by a rate that reflects the time value of money. The textbooks definition is that the net present value is the sum (Σ) of the present value of the expected cash flows (positive or negative) minus the initial investment.
Another way to understand what is meant by "present value" is to consider a situation in which one considers a business investment of \$500,000 expected to bring a cash flow of \$50,000 in one year time or a return on capital of 10%. If the cost of capital is 11% per year then the present value of that \$50,000 income stream is in fact negative (-\$4,504.50 to be exact) meaning that the return does not justify the investment. However, if the cost of capital can be reduced to 5% then the present net worth of this same cash flow would become 23,810 USD signalling a more efficient use of capital so it would be worthwhile to undertake the business venture.
### How to choose the discount rate in NPV analysis?
To estimate the present value we need to set a discount rate. It is inherently company-specific as it relates to how the company is funding its operations. Using WACC is fine in the case of borrowed capital whereas if it is calculated from the point of view of investors and shareholders it can be chosen so it reflects the rate of return they expect. For example, if shareholders expect a 10% return then this is the discount rate to use when calculating NPV for that business.
After the discount rate is chosen, one can proceed to estimate the present values of all future cash flows by using the NPV formula. Then just subtract the initial investment from the sum of these PVs to get the present value of the given future income stream.
## NPV formula
If you wonder how to calculate the Net Present Value (NPV) by yourself or using an Excel spreadsheet, all you need is the formula:
where r is the discount rate and t is the number of cash flow periods, C0 is the initial investment while Ct is the return during period t. For example, with a period of 10 years, an initial investment of \$1,000,000 and a discount rate of 8% (average return from an investment of comparable risk), t is 10, C0 is \$1,000,000 and r is 0.08.
## A practical example
Let us see an example of using the Net Present Value calculation to assess the profitability of purchasing a house. Let us say the house costs \$500,000 and it is expected that it could be sold for \$700,000 in 3 years. Maintenance and taxes cost \$10,000 a year. At the same time a less risky investment is a T-Bond which has a yield of 5% per year, meaning that this will be our discount rate. Plugging in the numbers into the Net Present Value calculator we see that the resulting NPV is \$77,454 which is not a bad compensation for the increased risk. We can also compare the IRR which is 10% which is double the T-Bond yield of 5%. Of course, if the risk is more than double that of the safer option, the investment might not be wise, after all.
Note that only the initial investment is an exact number in the above calculation. All other values are estimates and expectations. If they are off by a certain amount, for example if the sale price at the end is only \$650,000 and if the maintenance turns out to be twice as expensive, the investment may yield close to zero discounted return.
## Applications, caveats, and alternatives to net present value
Due to its simplicity, the net present value financial metric is often used to determine whether a project is worth undertaking or an investment worth making as it shows whether it will result in a net profit or loss, with positive NPV meaning that there is profit to be made and negative NPV means losses are to be expected. Usually a company or individual cannot pursue every positive return project, but NPV is still useful as a tool in discounted cash flow (DCF) analysis used to compare different prospective investments.
As with any metric, NPV is only as accurate as long as the assumptions are met and the estimates that go in are well-researched. Substantial errors in the output can result from bad input. It is always wise to allow for some unforeseen expenditures to get off the ground or during its duration.
An alternative to net present value is using the payback period, which measures how long it will take for the original investment to be fully repaid, but this method should not be used for longer-term investments as it does not account for the time value of money. Also, it does not reflect earnings past this period and can't account for sharp movements in the cash flow.
Since NPV does not provide an overall net gains/losses picture, it is often used alongside tools such as IRR.
## Financial caution
This is a simple online NPV calculator which is a good starting point in estimating the Net Present Value for any investment, but is by no means the end of such a process. You should always consult a qualified professional when making important financial decisions and long-term agreements, such as long-term bank deposits. Use the information provided by the calculator critically and at your own risk.
#### Cite this calculator & page
If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation:
Georgiev G.Z., "NPV Calculator", [online] Available at: https://www.gigacalculator.com/calculators/npv-calculator.php URL [Accessed Date: 06 Jun, 2023]. | 1,528 | 7,077 | {"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} | 3.1875 | 3 | CC-MAIN-2023-23 | latest | en | 0.926607 |
http://web2.0calc.com/questions/a-train-in-at-a-loading-area-every-30-minutes-it-goes-50-miles-if-its-been-12-hours-how-many-miles-has-the-train-gone | 1,508,204,859,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187820556.7/warc/CC-MAIN-20171017013608-20171017033608-00637.warc.gz | 466,726,538 | 5,742 | +0
# A train in at a loading area, every 30 minutes it goes 50 miles. If its been 12 hours how many miles has the train gone?
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A train in at a loading area, every 30 minutes it goes 50 miles. If its been 12 hours how many miles has the train gone?
Guest Feb 23, 2017
Sort: | 88 | 283 | {"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} | 2.796875 | 3 | CC-MAIN-2017-43 | longest | en | 0.957996 |
https://homework.cpm.org/category/CCI_CT/textbook/calc/chapter/11/lesson/11.4.1/problem/11-126 | 1,723,657,521,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641118845.90/warc/CC-MAIN-20240814155004-20240814185004-00057.warc.gz | 237,183,691 | 15,427 | Home > CALC > Chapter 11 > Lesson 11.4.1 > Problem11-126
11-126.
A projectile travels through the air with position $x = 15t$ and $y =-4.9t^2 + 46t + 11$ where $x$ and $y$ are measured in meters and $t$ is in seconds.
1. When does the projectile hit the ground?
When does $y = 0$?
2. How far does the projectile travel during its trip through the air? That is, find the length of the path of the projectile.
3. What is the maximum height of the projectile?
This is when $y^\prime = 0$.
4. Find the acceleration and velocity vectors of the projectile at time $t = 2$ seconds. | 171 | 582 | {"found_math": true, "script_math_tex": 8, "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} | 3.234375 | 3 | CC-MAIN-2024-33 | latest | en | 0.914658 |
http://www.battlerecharge.org/index-572.html | 1,670,661,410,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710421.14/warc/CC-MAIN-20221210074242-20221210104242-00822.warc.gz | 54,818,963 | 27,395 | # Fibonacci Cube Graph
• Difficulty Level : Easy
• Last Updated : 09 Aug, 2022
You are given input as order of graph n (highest number of edges connected to a node), you have to find the number of vertices in a Fibonacci cube graph of order n.
Examples :
```Input : n = 3
Output : 5
Explanation :
Fib(n + 2) = Fib(5) = 5
Input : n = 2
Output : 3```
A Fibonacci Cube Graph is similar to hypercube graph, but with a fibonacci number of vertices. In fibonacci cube graph only 1 vertex has degree n rest all has degree less than n.
Fibonacci cube graph of order n has F(n + 2) vertices, where F(n) is a n-th fibonacci number
Fibonacii series : 1, 1, 2, 3, 5, 8, 13, 21, 34……………….
For input n as order of graph, find the corresponding fibonacci number at the position n + 2.
where F(n) = F(n – 1) + F(n – 2)
Approach : Find the (n + 2)-th fibonacci number.
Below is the implementation of above approach :
## C++
`// CPP code to find vertices in a fibonacci``// cube graph of order n``#include``using` `namespace` `std;` `// function to find fibonacci number``int` `fib(``int` `n)``{`` ``if` `(n <= 1)`` ``return` `n;`` ``return` `fib(n - 1) + fib(n - 2);``}` `// function for finding number of vertices``// in fibonacci cube graph``int` `findVertices (``int` `n)``{`` ``// return fibonacci number for f(n + 2)`` ``return` `fib(n + 2);``}` `// driver program``int` `main()``{`` ``// n is the order of the graph`` ``int` `n = 3;`` ``cout << findVertices(n);`` ``return` `0;``}`
## Java
`// java code to find vertices in a fibonacci``// cube graph of order n``public` `class` `GFG {`` ` ` ``// function to find fibonacci number`` ``static` `int` `fib(``int` `n)`` ``{`` ``if` `(n <= ``1``)`` ``return` `n;`` ``return` `fib(n - ``1``) + fib(n - ``2``);`` ``}`` ` ` ``// function for finding number of vertices`` ``// in fibonacci cube graph`` ``static` `int` `findVertices (``int` `n)`` ``{`` ``// return fibonacci number for f(n + 2)`` ``return` `fib(n + ``2``);`` ``}`` ` ` ``public` `static` `void` `main(String args[]) {`` ` ` ``// n is the order of the graph`` ``int` `n = ``3``;`` ``System.out.println(findVertices(n));`` ``}``}` `// This code is contributed by Sam007`
## Python3
`# Python3 code to find vertices in``# a fibonacci cube graph of order n` `# Function to find fibonacci number``def` `fib(n):` ` ``if` `n <``=` `1``:`` ``return` `n`` ` ` ``return` `fib(n ``-` `1``) ``+` `fib(n ``-` `2``)` `# Function for finding number of``# vertices in fibonacci cube graph``def` `findVertices(n):` ` ``# return fibonacci number`` ``# for f(n + 2)`` ``return` `fib(n ``+` `2``)` `# Driver Code``if` `__name__ ``=``=` `"__main__"``:` ` ``# n is the order of the graph`` ``n ``=` `3`` ``print``(findVertices(n))` `# This code is contributed``# by Rituraj Jain`
## C#
`// C# code to find vertices in a fibonacci``// cube graph of order n``using` `System;` `class` `GFG {`` ` ` ``// function to find fibonacci number`` ``static` `int` `fib(``int` `n)`` ``{`` ``if` `(n <= 1)`` ``return` `n;`` ``return` `fib(n - 1) + fib(n - 2);`` ``}`` ` ` ``// function for finding number of`` ``// vertices in fibonacci cube graph`` ``static` `int` `findVertices (``int` `n)`` ``{`` ` ` ``// return fibonacci number for`` ``// f(n + 2)`` ``return` `fib(n + 2);`` ``}`` ` ` ``// Driver code`` ``static` `void` `Main()`` ``{`` ` ` ``// n is the order of the graph`` ``int` `n = 3;`` ` ` ``Console.Write(findVertices(n));`` ``}``}` `// This code is contributed by Sam007`
## PHP
``
## Javascript
``
Output :
`5`
Note that the above code can be optimized to work in O(Log n) using efficient implementations discussed in Program for Fibonacci numbers
My Personal Notes arrow_drop_up | 1,348 | 4,005 | {"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} | 3.96875 | 4 | CC-MAIN-2022-49 | latest | en | 0.628235 |
https://www.jiskha.com/similar?question=hey+guys%2C+i+follow+you+up+to+the+point+of+intergrating+the+final+line.+How+would+I+intergrate+%5Bx%5E-2.e%5E-x%5D+dx+thx&page=80 | 1,563,268,013,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195524517.31/warc/CC-MAIN-20190716075153-20190716101153-00536.warc.gz | 731,903,079 | 22,739 | # hey guys, i follow you up to the point of intergrating the final line. How would I intergrate [x^-2.e^-x] dx thx
49,088 questions, page 80
1. ## Math 12
Hey everyone; There are some questions on my review I am having trouble with. 4. Evaluate each logarithm. g)log base 5 square root 5 I can't figure out how to do square roots... h)log base 3 1 I got 3, but the anwser is 0 Also, directions ask you to write
asked by solexgirl12 on November 11, 2008
2. ## Calc.
sketch the curve using the parametric equation to plot the points. use an arrow to indicate the direction the curve is traced as t increases. Find the lenghth of the curve for o
asked by Sammy on April 14, 2007
3. ## english
in an inconvenient truth, an increase in greenhouse gases is dangerous becasue a. they trap more heat in earths atmosphere b. they create holes in the atmopshere , releasing too much heat c. they reduce humans ability to absorb oxagen throught their lungs
asked by oto on October 3, 2016
4. ## Algebra Word promblems
Alba Tross had an annual salary of \$50,000. She received a 5 percent pay cut one year followed by a 5 percent pay raise the next. a. What is Alba’s final salary? Would it be 50,000 - 5% + 5% =49.875 b. What is Alba’s final salary less than her original
asked by Sarah on September 7, 2016
5. ## English
Which line from “The Secret Life of Walter Mitty” best develops Walter’s character? (1 point) “’You’re not a young man any longer.’” “’The Old Man’ll get us through,’ they said to one another.” “They’re so (expletive), thought
asked by Kaai97 on December 14, 2015
6. ## Physics 1 Collision Math
Mass A, 2.0kg , is moving with an initial velocity of 7 m/s in the +x-direction, and it collides with mass B,4.0kg , initially moving in the +x-direction. After the collision, the two objects stick together and move as one. What is the change in kinetic
asked by Anonymous on August 31, 2017
7. ## chemistry
calculate the morality of THE H2SO4 solution for each of the three runs. do the three values agree closely together with each other. Part A. Titration 1 volume of unknown acid =20ml initial buret reading of NaOH =0.5 ml final buret reading of NaOH=10.0ml
asked by ALECIA on October 17, 2012
8. ## Chemistry
What causes a reaction to be spontaneous? Answer by answering each part a) (1 point) What is definition of spontaneous reaction?b) (1 point) What is Gibbs free energy?c) (1 point) How is Gibbs free energy related to a spontaneous reaction?d) (1 point) What
9. ## Math Help
I noticed you guys didn’t help the other person out with this question and I need help as well. What is the solution of the system of equations? {-3x - 4y - 3z = -7 {2x - 6y + 2z = 3 {5x - 2y + 5z = 9 A. (5,-2,7) B. (-5,2,7) C.(5,2,-7) D. No solution Use
asked by Issa on September 27, 2018
10. ## English Writing
Please help me... People believe in God because... And there is life on earth because... And people who believe in God think that God has put human beings on this earth because... I have to write continue of these sentences... Could you guys help me
asked by CC on September 4, 2016
11. ## physics
A 2 kg lab cart is sliding across across a horizontal frictionless surface at a constant velocity of 4.0 meters per second east. What will be the cart's velocity after a 6.0-newton westward force acts on it for 2.0 seconds and in what direction? Update 2:
asked by Anonymous on December 10, 2014
12. ## Physics
A particle, starting from point A in the drawing at a height h0 = 2.3 m, is projected down the curved runway. Upon leaving the runway at point B, the particle is traveling straight upward and reaches a height hf = 4.6 m above the floor before falling back
asked by Brandon on November 2, 2008
13. ## physics
A particle, starting from point A in the drawing at a height h0 = 3.2 m, is projected down the curved runway. Upon leaving the runway at point B, the particle is traveling straight upward and reaches a height hf = 4.1 m above the floor before falling back
asked by joe on December 8, 2011
14. ## physics
A particle, starting from point A in the drawing at a height h0 = 3.2 m, is projected down the curved runway. Upon leaving the runway at point B, the particle is traveling straight upward and reaches a height hf = 4.1 m above the floor before falling back
asked by Anonymous on December 8, 2011
15. ## Chemistry
A student who was isolating aspirin stopped the experiment after filtration step alumina. One week later, the methanol was evaporated and the experiment was completed. The melting point of the aspirin was found to be 110-115 degrees C. Explain why the
asked by Nina on October 10, 2008
16. ## science
what is freezing and boiling point of sugar. Several sources on the Internet list the melting point as 160-186 with decomposition. The Merck Index lists "dec. 160-186. Chars and emits characteristic odor of caramel." Since it decomposes at 186, the boiling
asked by Ron on May 2, 2007
17. ## physics
A particle, starting from point A in the drawing at a height h0 = 3.1 m, is projected down the curved runway. Upon leaving the runway at point B, the particle is traveling straight upward and reaches a height hf = 4.5 m above the floor before falling back
asked by Anonymous on September 26, 2011
18. ## Psychology/270
Can any one let me know if I matched these up together correctly, and if not what ones should I redo? Thank you in advance. Models of Abnormality Psychologists use several different models to explain abnormal behavior. These different models have created
asked by Sassy on May 12, 2009
19. ## geometry
the teacher: 15 seconds after the buzzer, the teacher has 135 meters to go to the finish line. 32 seconds after he left the starting line, the teacher has to run 50 meters more to the finish line. Usain Bolt: 22 seconds after the buzzer, usain has 189
asked by aniya on October 12, 2016
20. ## ~*Math Probability*~
Which expression would you use to figure out the number of ways you can arrange the letters in the word equation? (1 point) 8! 8P4 4P8 4! Five friends are having their picture taken. How many ways can the photographer arrange the friends in a row? (1
asked by Student on March 13, 2013
21. ## Physics
An electric force of 3x10^-8N is produced from an electrostatic point charge of 4x10^-10. It is 40cm from another electrostatic point charge. What is the charge of the second point?
asked by Andrea on April 11, 2013
22. ## math
vicky scored 6 two point basket and 6 one point free throws. Li scored 6 three point basket. explain how you know each girl scored the same total?
asked by asia on September 27, 2010
23. ## Physics
QUESTION: A car goes around a circular track with a radius of 1000 m at a constant speed of 10 m/s. (a) How long does it take the car to go once completely around the track? (b) What is the average velocity of the car over this time interval? WORK: What I
asked by Necie on January 15, 2017
24. ## Physics
At the low point in its swing, a pendulum bob with a mass of 0.2 kg has a velocity of 4 m/s What is the Kinetic at the low point? and Ignoring air resistance how high will the bob swing above the low point before reversing direction?
asked by Laura on February 15, 2013
25. ## Math
Please check my answers With two parallel lines cut by a transversal, the number of pairs of alternate interior angles is equal to the number of pairs of corresponding angles. (1 point) Always Sometimes Never *I think the answer is sometimes Opposite
asked by BrainHurts on August 28, 2014
26. ## Algebra II
Please check my answers With two parallel lines cut by a transversal, the number of pairs of alternate interior angles is equal to the number of pairs of corresponding angles. (1 point) Always Sometimes Never *I think the answer is sometimes Opposite
asked by BrainHurts on August 28, 2014
27. ## algebra
Brandon starts running from the starting line of a track at a speed of 10 ft. per second. 60 seconds later david starts from the same point and runs in the same direction at a speed of 12 per second Let y represent brandons time and let x represent davids
asked by Vianey on December 12, 2011
28. ## Calculus
A hot air balloon rising vertically is tracked by an observer located 3 miles from the lift-off point. At a certain moment, the angle between the observer's line-of-sight and the horizontal is pi/5 , and it is changing at a rate of 0.1 rad/min. How fast is
asked by Reonea on October 30, 2011
29. ## History
Hi ! Can someone give me some really really really good websites about the "Manhattan Project" (WWI/WWII).. you know.. I need ONE primary resource and ONE secondary resource. I know you guys are really good at giving good websites. I cannot use wiki, or
asked by Lia on March 18, 2015
30. ## High School Algebra II
Hey friends, I have a big assignment I've been given that I really, really could use an 100% on. I've been working on it for hours and have a decent amount done, have had teacher help, and have had friends work with me on it, but I still need help. If
asked by J on March 8, 2015
31. ## Math/English?
Hey! How's it going? Can anyone help me out here? My teacher asked us students to come up with a mnemonic device for PEMDAS (you know, the order of Operations), other than Please Exuse My Dear Aunt Sally. I came up with great ideas, but she changed her
asked by Anonymous on October 11, 2010
32. ## Math
Gail needs to earn a B in her Geology class. Her current test scores are 89, 78, 77, and 85. Her final exam is worth 3 test scores. In order to earn a B, Gail's average must lie between 80 and 89 inclusive. What range of scores can Gail receive on the
asked by Safira on September 21, 2018
33. ## Organic chemistry
An unknown compound (x) melts at 60°C and is mixed with a compound (y) that melts at 45°C and is soluble in x. Will the Melting point for the mixture start below 45°? I think so, because if you look at ice and salt for an example, salt has a way higher
asked by Shay on September 21, 2016
34. ## ENGLISH
Please help me to pick out 6 lines from the poem Invictus of William Ernest Henley that used sensory images and identify the sense used for each line.I also need to pick out one line that used onomatopoeia. I only Have one answer Black as the pit from pole
asked by ZACHARY on December 30, 2014
35. ## Physics
Cheryl runs a race on a 400.0 m circular track. She starts running east of the starting line and then circles the track and falls, stopping 1.00 m west of the starting line. Her time is 80.0 s. What was her average velocity? I believe that it would be
asked by Mishaka on October 12, 2011
36. ## Physics
9. Question : Cheryl runs a race on a circular 400.0 m track. She starts running east at the starting line and stops 20.0 m west of the starting line. Her time is 8.0 × 101 s. What is her average speed? 4.8 m/s 2.1 × 10-1 m/s -2.5 × 10-1 m/s 5.0 × 101
asked by Kiley on April 1, 2014
37. ## AP Physics
hi I need help on this proof ok I'm tyring to prove that v^2 = v^20 + 2a(x -x0) where the zeros are subscripts ok the first step my book says is start out with x = x0 + average velocity (t) then plug in average velocity x = x0 + (2^-1(v + v0))t ok and the
asked by AP Physics on June 13, 2009
38. ## SCIENCE
SOME ONE PLEAS HELPPPP MEEE The breaking down or disintegration of substances such as rocks and minerals by physical, chemical, or biological processes is called- * 1 point A Erosion C Climate D Deposition 2. When particles carried by water, ice, or wind
asked by AMANDA on January 10, 2018
39. ## Geometry
Write proof for the following Given: line AC is congruent to line BD, line AD is congruent to BC Prove: triangle DAX is congruent to triangle CBX It's an isosceles trapezoid. From top left is labeled A. Top right labeled B. Bottom right labeled C. Bottom
asked by Anonymous on November 17, 2014
40. ## Geometry
Write a proof for the following Given: line AC is congruent to line BD, line AD is congruent to BC Prove: triangle DAX is congruent to triangle CBX It's an isosceles trapezoid. From top left is labeled A. Top right labeled B. Bottom right labeled C. Bottom
asked by Anonymous on November 16, 2014
41. ## Math
A square has a perimeter of 24cm. If a diagonal line is drawn through the square in such a way that two identical right triangles are produced, what is the length of the diagonal line
asked by Jackie on May 20, 2010
42. ## Chemistry
What is the Wavelength( in nm) of the least energetic spectral line in the infrared series of the H atom? I don't understand how to find the least energetic spectral line?
asked by Grace on September 10, 2011
43. ## calculus
Hello there, assistance would be terrific, thank you very much. Consider the function f(x)= x^3 + 2x^2 + bx. a) The equation of the tangent line to the graph of this function at x = 1 is given by y = ? b) The tangent line intersects the x-axis at x = ? c)
asked by Kevin Land on November 7, 2016
44. ## math
Please help me solve this problem... thanks! 1.Find the equation of the line that cntains the pont (5, -1) and has slope -1/2 2.find the equation of the line that passes through the points (-2,1) and (1,-5)
asked by jojo on October 26, 2009
45. ## geomery
Triangle ABC, inscribed in a circle, has AB = 15 and BC = 25. A tangent to the circle is drawn at B, and a line through A parallel to this tangent intersects line BC at D. Find DC.
asked by Bobby on June 26, 2015
46. ## math
a vector parallel to the line of intersection of the planes. x-2y-z=6 and 3x-y+z=4 the answer is so first, I took the cross product of and which I think is v. in the equation p0 + tv.
asked by sam on December 13, 2014
47. ## Algebra II
1) Write an equation of the line that passes through (9,6) and is perpendicular to the line whose equation is y=-1/3x+7. Answer: y=3x-21 2)Find x in the solution of the system 3x+y=2 ans 2x-3y=16 Answer:2
asked by Lucy on April 6, 2008
48. ## Pre Algebra
This is about Reasoning Strategy... It says this: 3a. What is the y-intercept of the trend line? 3c. Write an equation for the trend line in slope-intercept form. I don't really know what they mean? Please help me.
asked by Mathilde on February 21, 2008
49. ## calculus
a. find an equation for the secant line through the points where x has the given values. b. find a equation for the line tangent to the curve when x has the first value. y=9square root(x); x=16, x=25
asked by Duane on October 26, 2014
50. ## Geometry
How to construct Euler's line??? Anybody know any good websites or can just explain how to construct the orthocenter centroid and whatever else is in Euler's line????? Im Soooooo confused!!!!
asked by Delaney on September 29, 2009
51. ## math
A square has a perimeter of 24cm. If a diagonal line is drawn through the square in such a way that two identical right triangles are produced, what is the length of the diagonal line?
asked by Linda on May 20, 2010
52. ## Algebra
write the equation of the line passing through (-6, -9) and (0, -9). Can some one help me with this please. When I tried to solve this problem I got a slope of 0 and I do not know what to do from there I notice the y is constant, so there is zero slope.
asked by jessica on April 26, 2007
53. ## geometry
got a parallelogram ABCD = 100 sq in. AC=2 times BD. what is CD and BD? the diagonals AC divided into AE=2x and EC =2x, diagonal BD is divided into BE=x and ED=x. I got x=1. So line AC=2x or 4x? line BD=x or 2x? so, 100 sq in 0divided by 3x or 6x. Or did I
asked by robin on May 26, 2015
54. ## Calculus
When one-sided limits are not equal to each other at a point, what can be said about the continuity of the function at that point? I know that when one-sided are not equal to each other then the limit does not exist at that point. but i do not know what
asked by Sarah on April 11, 2014
55. ## Chemistry
I am unsure exactly how to set up this calculation. From a graph that we got from getting different absorbances we took those points we got and got a equation for the best fit line. The equation was y = 760.8x + .02014 and the unknown absorbance equalled
asked by eliz on April 5, 2009
56. ## Chemistry
What is the molar heat of reaction? When 0.732 g of Ca metal is added to 200.0 mL of 0.500 M HCl(aq), a temperature increase of 119C is observed. Assume the solution's final volume is 200.0 mL, the density is 1.00 g/mL, and the heat capacity is 4.184 J/gC.
asked by Chris on February 17, 2010
57. ## last calc question, i promise!
given the curve x + xy + 2y^2 = 6... a. find an expression for the slope of the curve. i got (-1-y)/(x + 4y) as my answer. b. write an equation for the line tangent to the curve at the point (2,1). i got y = (-1/3)x + (5/3). but i didn't any answer for c!
asked by jane on February 20, 2009
58. ## CALC
point on the hyperbola 9x^2−6y^2=10 closest to the point (0, 7). y coordinate of each point= ? positive x coordinate= ? negative x coordinate= ?
59. ## 2nd grade math requestion post
Okay, my child is doing problem solving lesson 5-7 in scott foresman addison wesley book. The question that we are having a problem with is a number line. there are 10 spaces in the number line and the clues are: Clue 1: the number are between 70 and 82
asked by Dawn on January 20, 2009
60. ## Physics
Hey, it's me again, Can someone help me with this question? A water balloon is dropped from the top of a building. Assume the balloon does not break when it strikes the ground. If the water balloon falls a distance of 21m, what is the maximum temperature
asked by Josh on June 28, 2011
61. ## math ~dont know all but check some~ pls help!!!
1. Draw a model to represent the polynomial x2 + 2x + 4. (1 point) 1 big square, 1 tall rectangle, 4 little sqaures 1 big square, 2 tall rectangles, 4 little sqaures in the shape of an "L" 2 big sqaures, 4 little squares none of these 2. Simplify the
asked by TTR+S<3 on May 21, 2014
62. ## sciencie
hey i have a question what are the two requirements of mater and can matter exist at 0 kelvin Didn't I answer this before? What do you mean by requirements? like what does it need like mass volume like what does it need like mass volume like what does it
asked by josh on March 25, 2007
63. ## Compare and Contrast
Hi! I need help with this assignment. I have 2 books to compare and contrast. Full Cicada Moon by Marilyn Hilton and Same But Different by Holly Robinson Peete, Ryan Elizabeth Peete, and RJ Peete. It seems like I don't have any differences and alikes in
asked by Sam on August 14, 2017
64. ## Introduction to database design
Given the following complicated business rules, create the appropriate Crow’s Foot ERD. (50 points) a. A store may place many orders. (Note the use of “may”) b. An order must be placed by a store. c. An order contains at least one order line. d. Each
asked by Lamar on October 5, 2008
65. ## HELP!! MATH
A boater finds herself 4 miles fromm the nearest point on a straight shore line whech is 6 miles from a shoreside motel. She plans to row on shore and then walk to a motel. If she can walk at 3 mph, at what speed must she be able to row so that the
asked by MEG on November 15, 2010
66. ## Physics
A current of a river flows steadily from west to east at 1.00 m/s. A boat in the river travels at 3.00 m/s relative to the water. The river is 20.0 m wide with parallel banks. The boat leaves the shore at point A, and point B is directly across the river
asked by . on September 19, 2010
67. ## Moment/Physics
I understand a moment is a weight being moved by a particular distance. Although I am unable to establish what weight by how far would make a moment. eg 1 pound by 1 inch 1 pound by 1 foot 1 ton by 1 foot 1 Kg by ??? Explanation please. Mike You do not
asked by Mike on January 9, 2007
68. ## Math Systematric Trial
Hey everybody, I really need help solving these math equations. Thank YOU! For helping me! Use Systematic trial to find the value of each variable. a) 5+7c=89 b) 26=5+3e c) 8k-16=200 d)525-6u=339 Write each sentence as an equation. Solve each equation. a)
asked by Harmony Ann on February 23, 2014
69. ## Social Studies
1. The empress Theodora helped (1 point) the theater prosper. destroy the Byzantine Empire. women gain more rights.* Rome become prosperous again. 2. From the AD 500s to the AD 1100s, the Byzantine Empire (1 point) was a crossroads for trade. * was
asked by Pauly on April 15, 2015
70. ## some science
a filter tip or a cigarette acts as both a filter and a condenser. which of the following cannot be removed, assuming the filter tip is 100% efficient? a. carbon monoxide, boiling point -191 degrees. b. nicotine, boiling point 247 degrees. c. tar, boiling
asked by holly on December 22, 2006
71. ## math
Yao Ming is 7 ft. & 6 inches in tall. The free throw line is 15 ft. from a point below the basketball ring. The height of the goals is 10 ft. If Yao Ming will shoot a free throw, what is the angle of depression from the basket ring to the top of the head
asked by Rosalie on February 8, 2012
72. ## Math
Which statements is false? A. A decimal fraction has a multiple of 10 as a denominator. B. Every rational number can be associated with a point in the real number line. C. A terminating decimal cannot be expressed as a repeating decimal. D. The set of
asked by Kimberly on July 8, 2015
73. ## chemistry
A freezing point depression experiment was conducted using cyclohexane as the solvent. The freezing point of pure cyclohexane is 6.60°C and the freezing point depression constant is 20.00°C/m. The freezing point of a solution containing 0.135 g of an
asked by Danielle on February 16, 2015
74. ## history
hey ppl.. I have to write 2 pages about a famous renassaince person. i'm having trouble choosing one. i want to keep the paper short and informative. i thought about choosing Isaac Newton but then i'll probably end up with 5 pages, but as i said, i need it
asked by selin on May 29, 2009
75. ## Chemistry
Hi, Please provide assistance on the following problem. I worked out part of it, but do not know what to do after calculating pH for HCl. Suppose you dissolved 0.0365 grams of HCl in water to give a final volume of 10.0 mL. The molar mass of HCl is 36.5
asked by Jeremy on March 19, 2012
76. ## Physics
Hi guys, I was just wondering if I'm heading in the right direction with this question. Thank you so much in advance for your time!! A loudspeaker emits energy at the rate of 56W , spread in all directions. What is the intensity of sound 18m from the
asked by Kylie on March 10, 2015
77. ## College
Does Harvard University have art & creative writing classes cause I want to become a artist & a creative writer (when writing books, short stories, novels, & poems). I'm just asking. I look on the website but it really confusd me. Please also what is
asked by Kim on September 30, 2011
78. ## Physics
A freight train has a mass of 4.78 * 10^7 kg. the locomotive provides a force of 1.3 * 10^6 N and the brakes provide a force of -3.2 * 10^3 N. 1. How long will it take for the train to accelerate to it's maximum speed of 15 m/s? 2. The train accidentally
asked by Michelle on March 14, 2014
79. ## statistics
An ecologist uses the line, based on 13 colonies, to predict how many birds will join another colony, to which 54% of the adults from the previous year return. What is the prediction? Give your answer to two decimal places, and use the regression line
asked by applebottom on April 15, 2010
1. The way you view yourself overall is your ___________. (1 point) clues self-esteem self-concept mood disorder 2. Part of your self-concept is your __________, or how you feel about yourself. (1 point) self-esteem emotions clues resources 3. A person who
asked by Delilah on December 12, 2012
81. ## Physics
A real object is located at the zero end of a meter stick. A large concave mirror at the 100 cm end of the meter stick forms an image of the object at the 72.5 cm position. A small convex mirror placed at the 20.6 cm position forms a final image at the
asked by Anonymous on April 20, 2013
The Abuse Ends Now by: Kathy A I wasn't enough So he became rough I'm just not that tough As he was handcuffed I saw his face I hoped he knew he was a disgrace After all this time of looking into those deceiving blue eyes I just sit and cry Because of
asked by i♥zee on March 28, 2012
83. ## algebra
could you please check this answer for me and correct. thanks given equation point slope form linear equation to use to do question. y-3 = 3(x+1) question rewrite this equation in standard form y- 3 + 3 = 3x - 3x +3 + 3 -3x+ y = 6 collect all variables on
asked by ann on January 20, 2012
84. ## chemistry
this is what my lab report looks like (minus the graph of the first part) im stuck on part II I. A. unknown 1 melting point range (uncorr) 50.0-53.0 melting point range (corr) 50.2-53.2 (because of graph from part 1 of experiment) melting point average
asked by jessica on January 18, 2011
85. ## Chem
An ethylene glycol solution contains 20.9 g of ethylene glycol (C2H6O2) in 85.0 mL of water. Compute the freezing point and boiling point of the solution. (Assume a density of 1.00 g/mL for water.) freezing point °C boiling point °C How would I set this
asked by Lilly on March 22, 2011
86. ## social studies
What conditions caused by World War I led to the outbreak of the Russian Revolution? A.the takeover of Russia by Germany B.the death of millions of Russians in battle C.the invasion of Russia by Britain and France D.the Russian victory over the Central
asked by freeze help on January 25, 2019
in a reflection the image of the line y-2x=3 is the line 2y-x=9.find the axis of reflection.
asked by amir on April 28, 2012
88. ## Calculus
Find k such that the line is tangent to the graph of the function. Function: f(x)=kã(x) Line: y=x+4
asked by Susana on October 3, 2011
89. ## geometry
Prove line segment BP is 2/3 of line segment BD in triangle ABC
asked by Lk on February 8, 2011
90. ## geometry
The endpoints of line segment MN are M (-3,-9) and N (4,8). What is the approximate length of line segment MN??
asked by Isabella on August 30, 2011
91. ## algebra
the circle to the right has 21 points. All possible line segments have been drawn. How many line segments are there?
asked by Leyla on January 24, 2010
92. ## Calculus 1
Find the slope of the tangent line and the equation of the tangent line to f(x)=x^2-x at x=3
asked by TayB on September 14, 2015
93. ## algebra
find an equation of the line containing the given pair of points. (-9,0) and (0,4) what is the equation of the line? y=?
asked by amy on November 21, 2011
94. ## algebra
find an equation of the line containing the given pair of points. (-9,0) and (0,4) what is the equation of the line? y=?
asked by amy on November 21, 2011
95. ## Math - equations of lines
A line has the same x-intercept as [x,y,z]=[-21,8,14]+t[-12,4,7] and the same y-intercept as [x,y,z]=[6,-8,12]+s[2,-5,4]. Write the parametric equation of the line.
asked by Shaila on September 5, 2010
96. ## Math
A, B, C, and D are points on a line, and the lengths of the line segments are: AB = 12, BC = 4, CD = 7, and DA = 15. Which of the following is a possible order for the points? A.A,B,C,D B. A,C,D,B C. A,D,C,B D. A,C,B,D
asked by J on July 22, 2014
97. ## Algebra 1
Find an equation of the line containing the given pair of points. (1/4,-1/2) and (3/4,5). What is the equation of the line? y= Thank you for all your help.
asked by Esther on January 26, 2011
98. ## Math
if line m is parallel to line n and is cut by a transversal and angle 4 =3x - 20 and angle 5 = x + 40, what is the value of x?
asked by Oscar on March 9, 2010
99. ## math problem
find the equation of the line containing given pair of poins (-6,0) and (0,5) what is the equation line y=
asked by Lavern on December 18, 2011
100. ## mathematics 1
A line is 45/64 inch long. Find the length of a line 4/5 as long?
asked by Anonymous on October 1, 2007 | 7,882 | 28,020 | {"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} | 3.046875 | 3 | CC-MAIN-2019-30 | latest | en | 0.938207 |
https://www.gamedev.net/forums/topic/592818-solvedrotating-sprite-towards-mouse/ | 1,545,031,313,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376828448.76/warc/CC-MAIN-20181217065106-20181217091106-00374.warc.gz | 889,568,214 | 28,845 | # [Solved!]Rotating sprite towards mouse.
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I need help rotating my arm sprite towards the mouse coordinates.
My mouse coordinates are set to be POINT MousePos
Here is my transformation code:
static float rotation; D3DXVECTOR2 spriteCentre=D3DXVECTOR2(2.0f,5.0f); D3DXMatrixTransformation2D(&mat,NULL,0.0,&scaling,&spriteCentre,rotation,&trans);
float Rotation is how much the sprite will rotate, in radian.
PS:If you don't know this code, you can write your own.
--------------------------------
C++ DirectX9.
MSVC++ 2010 Express.
Windows 7.
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I'm not expert in this but I think you have to explain better what you are trying to accomplish.
You wan't a sprite to point towards the mouse pointer?
If that is the case you would probably need a algorithm to calculate it. It would depend on the location of the sprite as much as of the mouse pointer.
Let´s say the rotation 0 is straight up then that should be the case when it has the same X as mouse and Y is bigger.
The math here would be, assuming:
pos is position of sprite
mouse is position of mouse
DeltaY = mouse.Y - pos.Y
DeltaX = mouse.X - pos.X
rotation = tan^-1(DeltaY / DeltaX)
This is basic and I might be off.
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I'm not expert in this but I think you have to explain better what you are trying to accomplish.
You wan't a sprite to point towards the mouse pointer?
If that is the case you would probably need a algorithm to calculate it. It would depend on the location of the sprite as much as of the mouse pointer.
Let´s say the rotation 0 is straight up then that should be the case when it has the same X as mouse and Y is bigger.
The math here would be, assuming:
pos is position of sprite
mouse is position of mouse
DeltaY = mouse.Y - pos.Y
DeltaX = mouse.X - pos.X
rotation = tan^-1(DeltaY / DeltaX)
This is basic and I might be off.
I'll explain better:
my character's arm is an individual sprite, I want it to rotate towards the mouse, so when you move the mouse the arm follows so that you are able to aim.
I tried to do
DeltaY = MousePos.y - pos_y; DeltaX = MousePos.x - pos_x; rotation = tan^-1(DeltaY / DeltaX);
But got the error "Expression must have (pointer-to-) function type" and "term does not evaluate to a function taking 1 arguments"
This was for the "-1" in this line "rotation = tan^-1(DeltaY / DeltaX);"
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If your trying to use an inverse tangent function, try atan2( DeltaY, DeltaX).
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If your trying to use an inverse tangent function, try atan2( DeltaY, DeltaX).
Thank you mate, that worked 100%
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But got the error "Expression must have (pointer-to-) function type" and "term does not evaluate to a function taking 1 arguments"
This was for the "-1" in this line "rotation = tan^-1(DeltaY / DeltaX);"
My example was just pure math not code syntax
Buckeye has already explained the syntax you would need. Did it otherwise work as I explained? I wasn't sure just a rough guess.
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[quote name='Zaerdna' timestamp='1294972803' post='4758630']
But got the error "Expression must have (pointer-to-) function type" and "term does not evaluate to a function taking 1 arguments"
This was for the "-1" in this line "rotation = tan^-1(DeltaY / DeltaX);"
My example was just pure math not code syntax
Buckeye has already explained the syntax you would need. Did it otherwise work as I explained? I wasn't sure just a rough guess.
[/quote]
Yea, it was basically like you said
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× | 994 | 3,831 | {"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} | 3.421875 | 3 | CC-MAIN-2018-51 | latest | en | 0.952126 |
http://mathhelpforum.com/advanced-statistics/90085-problem-continuous-random-variable-print.html | 1,513,417,753,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948587496.62/warc/CC-MAIN-20171216084601-20171216110601-00310.warc.gz | 177,240,540 | 3,349 | # A PROBLEM in continuous random variable
• May 22nd 2009, 12:23 PM
gravity2910
A PROBLEM in continuous random variable
A radar sends out 2000 pulses of a particular shape and listens for the return signal of each of these pulses. The radar receiver listens for bursts of pulses and declares a target if it detects k or more pulses in a short time interval. Through tests, the value of k is adjusted in the radar receiver until the probability of target declaration exeeds 0.95. Energy absorbing "paint" is then applied to the target. This material has the property that each millimeter of thickness reduces the radar receiver's probability of detecting a single pulse by 10%. How thick does the coating have to be to reduce our radar's probability of detection to 0.50 or smaller??
• May 23rd 2009, 09:00 AM
CaptainBlack
Quote:
Originally Posted by gravity2910
A radar sends out 2000 pulses of a particular shape and listens for the return signal of each of these pulses. The radar receiver listens for bursts of pulses and declares a target if it detects k or more pulses in a short time interval. Through tests, the value of k is adjusted in the radar receiver until the probability of target declaration exeeds 0.95. Energy absorbing "paint" is then applied to the target. This material has the property that each millimeter of thickness reduces the radar receiver's probability of detecting a single pulse by 10%. How thick does the coating have to be to reduce our radar's probability of detection to 0.50 or smaller??
That is incoprehensible, are those the exact words of the problem?
CB
• May 23rd 2009, 09:31 AM
gravity2910
I copied exactly from my homework set. Actually, I can compute the value of k, which is 103 pulses. But I've got some confusion about the rest of the problem.
• May 23rd 2009, 01:50 PM
CaptainBlack
Quote:
Originally Posted by gravity2910
I copied exactly from my homework set. Actually, I can compute the value of k, which is 103 pulses. But I've got some confusion about the rest of the problem.
Can you tell us how you compute that?
CB
• May 23rd 2009, 02:05 PM
gravity2910
P[X>=k]=0.95= 1-F(k)=1-1+e^(-lamda*k) where lamda=1/2000.
=>k=103
(I approximately assume the density is exponential distributed density function.)
• May 23rd 2009, 02:18 PM
CaptainBlack
Quote:
Originally Posted by gravity2910
P[X>=k]=0.95= 1-F(k)=1-1+e^(-lamda*k) where lamda=1/2000.
=>k=103
(I approximately assume the density is exponential distributed density function.)
I don't see where any of that comes from your question as asked. For instance how is your short period of time related to the 2000 pulses, it looks like you may have an n from m detector in mind with n=k and m=2000, but that is not what your question asks.
All of which suggests there is more information behind thia question whithout which we cannot help.
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https://mathcenter.oxford.emory.edu/site/math111/probSetLimits/ | 1,723,549,794,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641076695.81/warc/CC-MAIN-20240813110333-20240813140333-00582.warc.gz | 295,803,068 | 7,377 | Exercises - Limits
1. Verify $\displaystyle{\lim_{x \rightarrow 3} (3x-5) = 4}$ with the epsilon-delta definition of a limit
For any $\epsilon \gt 0$, take $\delta = \epsilon/3 \gt 0$. Then note that whenever $0 \lt |x -3| \lt \delta$,
$$\begin{array}{ll} \implies & |x-3| \lt \epsilon/3\\ \implies & 3|x-3| \lt \epsilon\\ \implies & |3x-9| \lt \epsilon\\ \implies & |(3x-5) - 4| \lt \epsilon \end{array}$$
Having shown that for any $\epsilon \gt 0$, we can find a $\delta \gt 0$ so that $|(3x-5) - 4| \lt \epsilon$ whenever $0 \lt |x-3| \lt \delta$, we have satisfied the epsilon-delta definition establishing following limit
$$\displaystyle{\lim_{x \rightarrow 3} (3x-5) = 4}$$
2. What is the behavior of the function $\displaystyle{f(x) = \frac{x-1}{x}}$ as $x \rightarrow 0$ and as $x \rightarrow +\infty$?
That is to say, find the values of the following limits (presuming they exist) and provide a corresponding graphical interpretation:
$$\lim_{x \rightarrow 0} \frac{x-1}{x} \quad \textrm{ and } \quad \lim_{x \rightarrow +\infty} \frac{x-1}{x}$$
Note that as $x$ approaches $0$, the numerator gets very close to $-1$, while the denominator gets very small. This means the magnitude of the fraction grows very large (indeed, as $x$ gets close to $0$ the magnitude grows without bound). When $x \lt 0$, the fraction is large and positive. When $x \gt 0$, the fraction is large and negative. In this way, the related left and right limits are determined:
$$\lim_{x \rightarrow 0^-} \frac{x-1}{x} = +\infty \quad \textrm{ and } \quad \lim_{x \rightarrow 0^+} \frac{x-1}{x} = -\infty$$
Of course, as these left and right limits disagree, we conclude $\displaystyle{\lim_{x \rightarrow 0} \frac{x-1}{x}}$ does not exist.
(Technically, whenever a limit is infinite, it fails to exist - but the disagreement between the left and right limiting values is in a sense even more important here.)
Graphically, since at least one of the left or right limits associated with $x = 0$ is infinite, there is a vertical asymptote in the associated graph at this $x$ value.
As $x$ approaches $+\infty$, something different happens. Note that the relative difference between the numerator and denominator becomes smaller and smaller, allowing the overall fraction to become arbitrarily close to $1$. This is the value of the related limit.
There is another way to see this, however. Suppose we divide both the numerator and denominator by $x$. This does not change the value of the expression unless $x=0$, but the limiting value (presuming it exists) does not care what the function actually does at $0$.
$$\lim_{x \rightarrow +\infty} \frac{x-1}{x} = \lim_{x \rightarrow +\infty} \frac{1 - 1/x}{1} = 1$$
Note how in the result, as $x$ gets larger and larger, the term $1/x$ gets smaller and smaller (i.e., it has a limiting value of $0$) -- effectively vanishing as $x \rightarrow +\infty$. This leaves a limiting value of $1$ associated with the rest of the expression.
Graphically, as there was limiting value associated with $x \rightarrow +\infty$, the associated graph has a horizontal asymptote of $y=1$.
3. Examine the behavior of $\displaystyle{h(x) = \left\{ \begin{array}{rl} x^2, & x \ne 2\\ 3, & x = 2 \end{array} \right.}$ as $x \rightarrow 2$.
That is to say, find the value of $\displaystyle{\lim_{x \rightarrow 2} h(x)}$ presuming it exists, and provide a corresponding graphical interpretation.
As $h(x)$ only disagrees with $x^2$ when $x = 2$, the value we seek must equal $\lim_{x \rightarrow 2} x^2$. The limit laws quickly establish this value to be $4$.
Graphically, as $h(2)$ exists but does not agree with $\lim_{x \rightarrow 2} h(x)$, we have an isolated point at $(2,3)$ in the graph.
4. Examine the behavior of $f(x) = \sin x$ as $x \rightarrow +\infty$.
As $x$ continues to increase, $\sin x$ simply oscilates back and forth between a minimum value of $-1$ and a maximum value of $1$. As it never stays arbitrarily close to any height for sufficiently large $x$, $\displaystyle{\lim_{x \rightarrow +\infty} \sin x}$ fails to exist.
5. Evaluate the following limits and provide corresponding graphical interpretations for each:
$$(\textrm{a}) \lim_{t \rightarrow 2} t \quad (\textrm{b}) \lim_{s \rightarrow -\infty} \frac{1}{s} \quad (\textrm{c}) \lim_{z \rightarrow 0^+} \frac{-1}{z}$$
(a) $2$; (b) $0$; (c) $-\infty$
6. Let $\displaystyle{f(x) = \left\{ \begin{array}{rl} x \cos \pi x, & x \lt 1\\ 2, & x = 1\\ x^2, & x \gt 1 \end{array} \right.}$
Find the following limits:
$$(\textrm{a}) \lim_{h \rightarrow 0^+} f(1+h) \quad (\textrm{b}) \lim_{h \rightarrow 0^+} f(1-h) \quad (\textrm{c}) \lim_{h \rightarrow 0^-} f(1+h) \quad (\textrm{d}) \lim_{h \rightarrow 0^-} f(2+h)$$
(a) $1$; (b) $-1$; (c) $-1$; (d) $4$
7. Find the slope of the secant line of $f(x) = \sqrt{x}$ through the points $(4,f(4))$ and $(4+h,f(4+h))$. Find the limiting slope of the secant line as $h \rightarrow 0$; use this to find an equation of the tangent line to the graph of $f$ at $x=4$.
Slope of secant line: $\displaystyle{m = \frac{1}{2 + \sqrt{4+h}}}$; equation of tangent line (e.g.): $\displaystyle{y - 2 = \frac{1}{4}(x-4)}$
8. Compute $\displaystyle{\lim_{x \rightarrow -2} \frac{2x}{x^2-2}}$ citing appropriate limit laws that justify each step.
We have a limit of a quotient, which if the denominator's limiting value is non-zero, can be found as the quotient of the limiting values of the numerator and denominator.
Thus, we look at the limit of the denominator:
$$\lim_{x \rightarrow -2} (x^2 - 2)$$
As $x^2-2$ is a polynomial and $\displaystyle{\lim_{x \rightarrow c} p(x) = p(c)}$ for any polynomial function $p(x)$, we have the limit of the denominator being $2^2 - 2 = 2$.
The limit of the numerator is similarly $2(-2) = -4$, as it too is a polynomial function whose limit can be found by direct evaluation.
Thus,
$\displaystyle{\lim_{x \rightarrow -2} \frac{2x}{x^2-2} = \frac{-4}{2} = -2}$
9. Evaluate and provide a graphical interpretation: $\displaystyle{\lim_{x \rightarrow 2} \frac{x-2}{x^2-4}}$
Note that the limiting values of the numerator and denominator as $x \rightarrow 2$ are both $0$. However, there is a common factor of $(x-2)$ that can be cancelled that doesn't effect the value of the limit:
$$\begin{array}{rcl} \displaystyle{\lim_{x \rightarrow 2} \frac{x-2}{x^2-4}} &=& \displaystyle{\lim_{x \rightarrow 2} \frac{x-2}{(x-2)(x+2)}}\\ &=& \displaystyle{\lim_{x \rightarrow 2} \frac{1}{(x+2)}} \end{array}$$
At this point, we have the limit of a rational expression with $x$ approaches a value that is not a domain issue. By one of the limit laws, we can thus evaluate the limit by simply evaluating the function at $x=2$ to determine
$$\displaystyle{\lim_{x \rightarrow 2} \frac{1}{(x+2)} = \frac{1}{2+2} = \frac{1}{4}}$$
Graphically, as the original expression had a domain issue but the limit existed, we have a hole at $(2,1/4)$.
10. Evaluate and provide a graphical interpretation: $\displaystyle{\lim_{x \rightarrow -3} \frac{-2 + \sqrt{7+x}}{x+3}}$
The limiting values of the numerator and denominator as $x \rightarrow -3$ are both $0$. Fortunately, multiplying by a well-chosen value of one by using the conjugate of the numberator will reveal a common factor that can be cancelled that doesn't effect the value of the limit.
This technique is called rationalizing the numerator.
$$\begin{array}{rcl} \displaystyle{\lim_{x \rightarrow -3} \frac{-2 + \sqrt{7+x}}{x+3}} &=& \displaystyle{\lim_{x \rightarrow -3} \frac{-2 + \sqrt{7+x}}{x+3} \cdot \frac{-2 - \sqrt{7+x}}{-2 - \sqrt{7+x}}}\\ &=& \displaystyle{\lim_{x \rightarrow -3} \frac{4 - (7+x)}{(x+3)(-2 - \sqrt{7+x})}}\\ &=& \displaystyle{\lim_{x \rightarrow -3} \frac{-(x+3)}{(x+3)(-2 - \sqrt{7+x})}}\\ &=& \displaystyle{\lim_{x \rightarrow -3} \frac{1}{2 + \sqrt{7+x}}}\\ \end{array}$$
At this point, since the limit of both the numerator and denominator as $x \rightarrow -3$ are both not zero, the overall limit can be found simply by evaluating the last expression at $x=-3$ to obtain
$$\displaystyle{\lim_{x \rightarrow -3} \frac{1}{2 + \sqrt{7+x}} = \frac{1}{2 + \sqrt{7-3}} = \frac{1}{4}}$$
Noting that there was a domain issue in the expression for $x=-3$ but the limit ultimately existed, tells us that graphically one has a hole at $(-3,1/4)$ in the corresponding graph.
11. Evaluate and provide a graphical interpretation: $\displaystyle{\lim_{x \rightarrow -1} \frac{|x+1|}{x+1}}$
First, we note the limiting values of the numerator and denominator as $x \rightarrow -1$ are both $0$, so we can't find the limit (presuming it exists) by direct evaluation.
The presence of the absolute value function is really a piecewise-defined function in disguise. To see this, note
$$|x| = \left\{ \begin{array}{rl} x, & x \ge 0\\ -x, & x \lt 0 \end{array} \right.$$
As the "border" between the two "pieces" in $|x+1|$ is at $x=-1$, the very value we approach in the limit -- we will want to find the related left and right limits separately, lest they disagree and cause the overall limit to not exist:
$$\lim_{x \rightarrow -1^-} \frac{|x+1|}{x+1} = \lim_{x \rightarrow -1^-} \frac{-(x+1)}{x+1} = \lim_{x \rightarrow -1^-} {-1} = -1$$ $$\lim_{x \rightarrow -1^+} \frac{|x+1|}{x+1} = \lim_{x \rightarrow -1^+} \frac{(x+1)}{x+1} = \lim_{x \rightarrow -1^+} {1} = 1$$
As can be seen, the corresponding left and right limits exist, but disagree in value.
Thus, $\displaystyle{\lim_{x \rightarrow -1} \frac{|x+1|}{x+1}}$ does not exist.
Graphically, as the left and right limiting values existed but disagreed, we have a gap (or jump) discontinuity in the corresponding graph from $(-1,-1)$ to $(-1,1)$.
12. Evaluate and provide a graphical interpretation: $\displaystyle{\lim_{x \rightarrow 0} \sin \left( \frac{1}{x} \right)}$.
As $x$ approaches $0$, note that $1/x$ grows very large (without bound) in magnitude. Taking the sine of larger and larger values results in values that oscillate back and forth between $-1$ and $1$. Thus, $\sin (1/x)$ never stays arbitrarily close to any value as $x$ stays sufficiently close to $0$ (ignoring $x=0$ itself). So this limit does not exist due graphically to infinite, non-damped oscillitory behavior.
13. Evaluate and provide a graphical interpretation: $\displaystyle{\lim_{x \rightarrow 0} x^2 \sin \left( \frac{1}{x} \right)}$.
In this case, we see $\sin (1/x)$ oscillates between $-1$ and $1$ as $x \rightarrow 0$, but this oscillation is damped by the $x^2$ factor. Indeed, we can bound $x^2 \sin (1/x)$ between two simple functions:
$$-x^2 \le x^2 \sin \left(\frac{1}{x}\right) \le x^2$$
As the limiting values of both $-x^2$ and $x^2$ are $0$ as $x \rightarrow 0$, the limiting value of $x^2 \sin (1/x)$ as $x \rightarrow 0$ must also be $0$, by the Squeeze Theorem.
Graphically, since $x=0$ is a domain issue in the original expression, but the limit value existed, we have a hole in the corresponding graph. In this case, that hole is at $(0,0)$.
14. Evaluate and provide a graphical interpretation: $\displaystyle{\lim_{x \rightarrow +\infty} \frac{x^2 + 4x}{x^2 + 4}}$.
Note as $x \rightarrow +\infty$ both the numerator and denominator get large (without bound).
To reveal the nature of the overall fraction as $x \rightarrow +\infty$, however, let us divide both top and bottom by the highest power of $x$ seen in the denominator (namely, $x^2$). This reveals terms $4/x$ and $4/x^2$ which vanish as $x \rightarrow +\infty$, making the resolution of the rest of the limit simple:
$$\lim_{x \rightarrow +\infty} \frac{x^2 + 4x}{x^2 + 4} = \lim_{x \rightarrow +\infty} \frac{1 + 4/x}{1 + 4/x^2} = \lim_{x \rightarrow +\infty} \frac{1}{1} = 1$$
Graphically, as the limit at infinity existed, there is a horizontal asymptote in the corresponding graph. In this case, we have a horizontal asymptote of $y = 1$.
15. Compute $\displaystyle{\lim_{x \rightarrow -1} (x^4 - 3x)(x^2 + 5x + 3)}$, justifying each step with an appropriate limit law.
We can work this problem out in a couple of ways. Let's first work this out the "long way", which will let us see several different limit laws at work.
The "Long Way":
$$\begin{array}{rclr} & & \displaystyle{\lim_{x \rightarrow -1} (x^4 - 3x)(x^2 + 5x + 3)} &\\ &=& \displaystyle{\left( \lim_{x \rightarrow -1} (x^4 - 3x) \right) \left( \lim_{x \rightarrow -1} (x^2 + 5x + 3) \right)} & \textrm{(limit of a product)}\\ &=& \displaystyle{\left( \lim_{x \rightarrow -1} x^4 - \lim_{x \rightarrow -1} 3x \right) \left( \lim_{x \rightarrow -1} (x^2 + 5x + 3) \right)} & \textrm{(limit of a difference)}\\ &=& \displaystyle{\left( \lim_{x \rightarrow -1} x^4 - \lim_{x \rightarrow -1} 3x \right) \left( \lim_{x \rightarrow -1} x^2 + \lim_{x \rightarrow -1} 5x + \lim_{x \rightarrow -1} 3 \right)} & \textrm{(limit of a sum)}\\ &=& \displaystyle{\left( \lim_{x \rightarrow -1} x^4 - 3 \cdot \lim_{x \rightarrow -1} x \right) \left( \lim_{x \rightarrow -1} x^2 + 5 \cdot \lim_{x \rightarrow -1} x + \lim_{x \rightarrow -1} 3 \right)} & \textrm{(scalar multiple rule)}\\ &=& \displaystyle{\left( \lim_{x \rightarrow -1} x^4 - 3 \cdot \lim_{x \rightarrow -1} x \right) \left( \lim_{x \rightarrow -1} x^2 + 5 \cdot \lim_{x \rightarrow -1} x + 3 \right)} & \textrm{(constant rule)}\\ &=& \displaystyle{\left( \left( \lim_{x \rightarrow -1} x\right)^4 - 3 \cdot \lim_{x \rightarrow -1} x \right) \left( \left(\lim_{x \rightarrow -1} x\right)^2 + 5 \cdot \lim_{x \rightarrow -1} x + 3 \right)} & \textrm{(power rule)}\\ &=& \displaystyle{\left((-1)^4 - 3 \cdot(-1)\right) \left((-1)^2 + 5 \cdot (-1) + 3\right)} & \textrm{(limit of identity function)}\\ &=& -4 & \end{array}$$
Now, let's work the same problem in a much shorter way by choosing more powerful limit laws to employ.
The "Short Way"
$$\begin{array}{rclr} & & \displaystyle{\lim_{x \rightarrow -1} (x^4 - 3x)(x^2 + 5x + 3)} &\\ &=& \displaystyle{\left( \lim_{x \rightarrow -1} (x^4 - 3x) \right) \left( \lim_{x \rightarrow -1} (x^2 + 5x + 3) \right)} & \textrm{(limit of a product)}\\ &=& \displaystyle{\left((-1)^4 - 3 \cdot(-1)\right) \left((-1)^2 + 5 \cdot (-1) + 3\right)} & \textrm{(limit of a polynomial)}\\ &=& -4 & \end{array}$$
16. Compute $\displaystyle{\lim_{x \rightarrow -2} \frac{t^4 - 2}{2t^2 - 3t + 2}}$, justifying each step with an appropriate limit law.
Evaluating the limit minimally requires applying the rules for the limit of a quotient and limit of polynomial (although could alternatively use the limit of a sum, difference, quotient, and scalar multiple), and results in $7/8$.
17. Find the slope of the tangent line at $x = -4$ to $f(x) = \sqrt{1-2x}$ by computing the limit $\displaystyle{\lim_{x \rightarrow -4} \frac{f(x) - f(-4)}{x+4}}$. Then find an equation for this tangent line.
The slope is $-1/3$ and computed by rationalizing the numerator. The tangent line has equation $\displaystyle{y-3 = -\frac{1}{3}(x+4)}$
18. Find an equation for the tangent line to $f(x) = 1-2x^2$ at $x = -1$.
$y+1 = 4(x+1)$
19. Suppose that $2x \le f(x) \le x^4 - x^2 + 2$ for all $x \ge 0$. Compute $\displaystyle{\lim_{x \rightarrow 1} f(x)}$.
Since $\displaystyle{\lim_{x \rightarrow 1} 2x = 2 = \lim_{x \rightarrow 1} (x^4 - x^2 + 2)}$, by the squeeze theorem, $\displaystyle{\lim_{x \rightarrow 1} f(x) = 2}$ as well.
20. (Challenge!) What is the behavior of the function $\displaystyle{g(x) = \frac{\sin x}{x}}$ as $x \rightarrow 0$ and as $x \rightarrow +\infty$?
That is to say, find the values of the following limits (presuming they exist) and provide a corresponding graphical interpretation. Justify your conclusions with a logical argument.
$$\lim_{x \rightarrow 0} \frac{\sin x}{x} \quad \textrm{ and } \quad \lim_{x \rightarrow +\infty} \frac{\sin x}{x}$$
While estimating the value of $\displaystyle{\frac{\sin x}{x}}$ with small values of $x$ (as was done earlier in the notes) suggests a limiting value of $1$, proving this is the actual limiting value takes some creativity.
Consider the following image:
Note that the area of $\triangle ABC$ is $\displaystyle{\frac{\sin x}{2}}$, the area of the teal-shaded wedge is $\displaystyle{\frac{x}{2}}$, and the area of $\triangle ABD$ is $\displaystyle{\frac{\tan x}{2}}$.
As $\triangle ABD$ contains the wedge, which in turn contains $\triangle ABC$, we have the following inequality:
$$\frac{\tan x}{2} \ge \frac{x}{2} \ge \frac{\sin x}{2}$$
Dividing everything above by $\displaystyle{\frac{\sin x}{2}}$ and taking reciprocals, we get
$$\cos x \le \frac{\sin x}{x} \le 1$$
Note that since $\displaystyle{\frac{\sin x}{x}}$ and $\cos x$ are both even functions, the inequality immediately above is valid for any non-zero $x$ between $-\pi/2$ and $\pi/2$.
Finally, we can appeal to the Squeeze Theorem. Note the limiting values of $\cos x$ and $1$ as $x \rightarrow 0$ are both $1$. Thus, the expression $\displaystyle{\frac{\sin x}{x}}$ bound between them must have a limiting value of $1$ when $x \rightarrow 0$ as well. As such,
$$\lim_{x \rightarrow 0} \frac{\sin x}{x} = 1$$
Graphically, as $\sin x / x$ is undefined when $x=0$ but the limit exists there, we have a hole in the associated graph at $(0,1)$.
The second limit, where $x \rightarrow +\infty$, can be found more quickly -- again using the Squeeze Theorem. Note that we can bound $\displaystyle{\frac{\sin x}{x}}$ above and below with the following two functions.
$$\frac{-1}{x} \lt \frac{\sin x}{x} \lt \frac{1}{x}$$
As both $-1/x$ and $1/x$ have a limiting value of $0$ as $x \rightarrow +\infty$, it must be the case that $\displaystyle{\frac{\sin x}{x}}$ does as well. Thus,
$$\lim_{x \rightarrow +\infty} \frac{\sin x}{x} = 0$$
Graphically, as the limit at infinity existed, the associated graph has a horizontal asymptote whose height matches the value of the limit (i.e., $y = 0$).
As a curious final note -- unlike horizontal asymptotes in many other graphs, the oscillatory nature of the sine function here causes an infinite number of intersections between our function and the asymptote. | 5,799 | 17,989 | {"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} | 4.78125 | 5 | CC-MAIN-2024-33 | latest | en | 0.747306 |
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# How does it work ?
spinout
If you take away the smallest number ever from 1, what have you then in this universe?
kelseymh
spinout wrote: If you take away the smallest number ever from 1, what have you then in this universe? I am not sure I understand the meaning with the question above, please help me!
What do you think you mean by your question? As written, it doesn't make any sense.
Smallest number ever, is there such a number? If there is no such number the answer to you question must be "nothing".
If you talk about natural numbers the smallest number would be 0 or 1 so the answer would be 1 or 0 depending on what definition of natural numbers you use.
EDIT: Or maybe it's a trick question. If we just focus on this part of the question "what have you then in this universe?". I guess everything in the universe is still there so then you have everything that you had before. The question is very ambiguous!
_AVG_
If you are referring to a 'smallest number' in magnitude, there is no such number. The proof is pretty simple. Let x > 0 be the smallest positive number. Then x/2 < x so x cannot be the smallest number. If you're talking about a 'smallest integer', that doesn't exist either. Let x be the smallest integer. Then x-1<x so x cannot be the smallest integer. So the negative numbers also stretch all the way down to negative infinity, which is undefined to our finite minds. This is similar to the proof of the nonexistence of any 'largest number'. If x is the largest number, x+1>x so x cannot be the largest number.
Of course, you can have a largest and/or smallest number if you discard the laws of logic
ocalhoun
_AVG_ wrote: If you are referring to a 'smallest number' in magnitude, [...]. If you're talking about a 'smallest integer', that doesn't exist either.
Well, in magnitude terms, there is a smallest integer, 0.
All other integers have a greater magnitude than that one.
As for the original question:
Quote: If you take away the smallest number ever from 1, what have you then in this universe?
As AVG noted, it makes no sense to think of 'the smallest number ever' in terms of 'the largest magnitude negative number ever', because there is no limit.
So, I'll assume it means taking away the smallest (magnitude) number ever... Which would be 0.
And in this universe, when you subtract 0 from 1, you get 1.
...I'd even go as far as to say basic mathematics like that should work the same in every universe.
(I'd hate to try to learn the mathematics of a universe where 1-0=/=1, that's for sure!)
Well, that's my best understanding of the question.
Dennise
spinout wrote: If you take away the smallest number ever from 1, what have you then in this universe? I am not sure I understand the meaning with the question above, please help me!
Mathematically, as others have stated, you are left with a number that is arbitrarily less than 1. But for any number you may think is the 'smallest' number ... say X, there is still a smaller number X/2. I.e. you will never reach the 'smallest number' but instead will get arbitrarily closer to zero as you search in vain for the smallest number. This is one of the tenants of calculus.
By 'in this universe', I assume you are referring to mathematics as we know it in our known universe.
nguyenvulong
Who ask you such a question
or do you have some sources ?
It sounds non-sense .
orangbaik
spinout wrote: If you take away the smallest number ever from 1, what have you then in this universe? I am not sure I understand the meaning with the question above, please help me!
you will have the number of limit 1 or in other word none
asnani04
If the question is valid, we'd still have all the things in the universe that are present right now, isn't it?
LxGoodies
spinout wrote: If you take away the smallest number ever from 1, what have you then in this universe?
I would say exactly the same universe. Nothing will change. Mass, energy and matter all get preserved, so it's impossible to remove anything away from the universe. Everything will stay inside, forever.
Lx
sathishbl
spinout wrote: If you take away the smallest number ever from 1, what have you then in this universe? I am not sure I understand the meaning with the question above, please help me!
i think the answer is 0, because according to scale wise zero is the smallest digit....so its meaning is that when you remove the smallest number from 1 it will be zero in this universe.
playfungames
If only there was a way to find out the smallest number. I mean, 0.<million zeroes>1 is still not the smallest numbers. It so confusing and I guess that is how the universe is...CONFUSING!!
Bikerman
Clearly there is no single smallest number because, just as with the 'largest' number, one can always subtract one (or a fractional part) to give a smaller number.
The set of integer numbers is infinite in 'both directions' - ie the set tends to infinity in both the positive and negative 'directions' along the number line.
Clearly 0 cannot be the smallest number, unless one defines 'smallest' in a way which is not currently the accepted definition. -1 MUST be smaller than 0 and, by the same argument, -2 is smaller than -1.
The argument about 'removing the smallest number from 1' to leave 0 is both confused and rather silly.
SonLight
spinout wrote: If you take away the smallest number ever from 1, what have you then in this universe? I am not sure I understand the meaning with the question above, please help me!
Nor can any of us understand "the" meaning, since there are serious ambiguities in it.
As others have mentioned, one interpretation is that the process of subtraction doesn't affect "this universe" a whole lot, so one plausible answer is "the same universe".
Another meaning for "in this universe" is that the rules of math and physics are as we know them, not as they might be or theoretically could be in some alternative universe, inside a black hole, or some stranger place if you can think of it. I can't think of a possible 'universe' where mathematical principles would be radically different, but I couldn't have ruled it out except that the question suggests I shouldn't try warp drive or strange geometries to see if the result changes.
Yet another meaning of "universe" is a specified "universal set". That would specify the context and perhaps the types of numbers allowed. Usually mathematicians are careful to use more precise terms, such as "in the universe of natural numbers", "in the universe of integers", etc.
If we do interpret the question "in the universe of natural numbers", then only the positive integers qualify and zero does not. In that case, and only in that case, the result of the subtraction is not in the set of natural numbers. While the answer is undefined, that is potentially the most useful result as it might encourage us to define a larger universal set.
LxGoodies
Sonlight wrote: only the positive integers qualify and zero does not
With natural numbers the answer is straightforward 1-1=0 (one is the smallest number )
Lx
Bikerman
Nope. First you have to say whether the 'natural' numbers include 0 or not - there are two schools of thought on that. If you DO include 0 (and YOU do, because you used 0 in your example above) then 0n is the smallest number in your system of representation. If you DON'T include 0 in the 'natural' or 'counting' numbers then you also have to rule out all non-integer quantities such as 1/2 1/3 etc which allows you to have 1 as your smallest number, but gives you a bloody useless system of representation for most real-life purposes, other than counting simply integer quantities. Fine for small sheep/cattle farmers with a few beasts, but not much use for anything else.
This is, in a roundabout way, why the Romans never progressed to the heights one might have expected in engineering - their numeral system was really crappy system for doing useful arithmetic, let alone proper maths.....
LxGoodies
Bikerman wrote: but gives you a bloody useless system of representation for most real-life purposes
Hmm I would not dare to say N+ (which is the collection I referred to) is of any practical use , but the smallest number in N+ is 1. And 1-1=0, yielding an outcome which is not in N+. But this also counts for subtracting something from 0 which would yield a minus value, outside the collection. If you require that both operand and outcome are in the same collection, the most logical approach would be to interpret both as R-members, yielding
1 - 1/INF = 0.999999999999999999999999999999999999999999999999999999999 (etc)
.. with 1/INF (one divided by infinity) as "smallest number".
Lx
nguyenvulong
There're many "types" of number, real unreal (complex number) decimal, hexa decimal
so it's no doubt that you can have a smaller number . | 2,057 | 8,877 | {"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} | 3.734375 | 4 | CC-MAIN-2018-13 | latest | en | 0.923998 |
https://web2.0calc.com/questions/multiplicative-inverse-vs-multiplicative-idendity | 1,653,126,909,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662539049.32/warc/CC-MAIN-20220521080921-20220521110921-00304.warc.gz | 679,030,419 | 5,639 | +0
# Multiplicative Inverse vs. Multiplicative Idendity
0
157
1
What is a multiplicative inverse? If you can answer that question, what is a Multiplicative Identity? I was so mad that I couldn't do this myself for my math class. PLEASE HELP, I'M DESPRATE! Also, I wanted to know what the difference between the two is, thank y'all so much!
Oct 12, 2021
#1
+23183
0
The multiplicative identity is the number 1 because if you multiply any number by 1, you will get, as a result, the number that you started with. (You will have an answer that is identical to the number that you started with.)
A multiplicative inverse is the number that, when multiplied to the original number, will have a result of 1.
Thus, the multiplicative inverse of 2 is 1/2; the multiplicative inverse of 3 is 1/3;
the multiplicative inverse of 23 is 1/23; the multiplicative inverse of 3/4 is 4/3;
the multiplicative inverse of -1/3 is -3; etc.
The number zero has no multiplicative inverse; for all other numbers, the multiplicative inverse of x is 1/x.
Oct 13, 2021 | 287 | 1,053 | {"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} | 4.0625 | 4 | CC-MAIN-2022-21 | latest | en | 0.921541 |
https://juliapackages.com/p/curves | 1,716,012,740,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971057327.58/warc/CC-MAIN-20240518054725-20240518084725-00189.warc.gz | 307,816,264 | 21,510 | ## Curves.jl
A collection of points (x, y), together with an interpolation and extrapolation method, on which standard calculation functions are defined.
Author lungben
Popularity
7 Stars
Updated Last
2 Years Ago
Started In
February 2020
# Curves
## Installation
```using Pkg
## Introduction
A `Curve` in this package is essentially a collection of points `(x, y)`, together with an interpolation and extrapolation method.
`Curve` objects have a number of standard calculation function defined (like addition, multiplication, logarithm), thus they can be used in algebraic expressions analogue to scalars.
### How it Works
Operations on Curves alone (e.g. `exp(c)`, `log(c)`) or with scalars (e.g. `c+1` or `2c`) are defined point-wise on the y-values of the Curve.
Operations between 2 Curve objects (noted as `c1` and `c2`) are defined as follows:
1. Interpolate `c1` to the x-values of `c2`.
2. Do the operation (e.g. adding) on the y-values of `c2` and the interpolated y-values of c1.
3. Repeat steps 1. and 2., but interpolate `c2` to the x-values of `c1`.
4. Combine the results of both interpolations and create a new Curve object for the result.
Technically, this package is based on Interpolations.jl. Support of log-interpolation on both axis is added by this package.
`Curve` objects are defined to be immutable, thus every operation creates a new `Curve` object as output.
## Tenors
In financial use cases, the x-axis of curves is often given in maturity tenors, e.g. 1W or 3M. The `Tenor` type is introduced to support such a notation for the x-axis of curves.
Example:
```t = Tenor.(("1D", "3W", "1M", "10y", "12m"))
@assert t == (Tenor(Curves.TDays, 1), Tenor(Curves.TWeeks, 3), Tenor(Curves.TMonths, 1),
Tenor(Curves.TYears, 10), Tenor(Curves.TYears, 1))```
Note that the tenor `12M` is automatically converted to `1Y` to avoid ambiguities.
Tenors can be directly used in Curves:
```curve_from_tenors = Curve(["1D", "3W", "1M", "10y"], [0.5, 0.7, 0.75, 0.83])
val = interpolate("1W", curve_from_tenors)```
As a shortcut for creating tenor objects, a string macro is provided:
`@assert t"1W" == Tenor("1W")`
### Use Case
The use case I had in mind was interest rate / FX curves for mathematical finance applications. The `Curve` objects make it easier to shift market data, e.g. for sensitivity or scenario P&L calculation, or to calculate such shift sizes based on market data time series.
Example:
```using Curves
using Plots
# construct zero interest rate curve
c_zero_base = Curve(["2D", "1w", "1M", "3M", "6M", "12M"], [0.5, 0.7, 0.75, 0.83, 1.1, 1.5])
# plotting - package Plots required
plot(c_zero_base.x, c_zero_base.y)
# define zero rate shifts (e.g. for stress testing or sensitivities)
c_shifts = Curve([2, 185, 360], [0.1, -0.1, 0.2])
# shift curve
c_shifted = c_zero_base + c_shifts
# calculate discount factors for the unshifted and shifted curves
c_base_df=apply((x,y) -> exp(-x*y/100/365), c_zero_base, logy=true)
c_shifted_df = apply((x,y) -> exp(-x*y/100/365), c_shifted, logy=true)
# calculate log-returns of discount factors
log_ret = log(c_shifted_df/c_base_df)
# apply log returns to the base curve - this should give the shifted curve back
curve_scenario = *(c_base_df, exp(log_ret), logy=true)
@assert curve_scenario ≈ c_shifted_df
plot(curve_scenario.x, curve_scenario.y)```
## Ideas for Further Improvements
• Support of more operations
• Interactions with QuantLib.jl curve objects
• Multi-dimensional structures (especially 2d, e.g. for Volatility surfaces)
### Required Packages
View all packages
### Used By Packages
No packages found. | 1,040 | 3,622 | {"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-2024-22 | latest | en | 0.852021 |
https://progiez.com/nptel-software-testing-week-6-assignment-6-answers | 1,679,797,952,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296945381.91/warc/CC-MAIN-20230326013652-20230326043652-00455.warc.gz | 524,761,183 | 15,011 | # Software Testing | Week 6
Session Jan-Apr 2023
Course Name: Soft Skills Development
## No Quiz
These are NPTEL Software Testing Week 6 Assignment 6 Answers
More Nptel course: https://progiez.com/nptel
Session Jul-Dec 2022
Course Name: Software Testing
These are NPTEL Software Testing Week 6 Assignment 6 Answers
Q1. While applying logic-based testing to test source code, is it true that the predicates can be taken exactly as they occur in code always?
a) Yes, the predicates can be considered exactly as they occur in code.
b) No, some times we have to add extra clauses to the predicate
Answer: b) No, some times we have to add extra clauses to the predicate
Q2. How do logical predicates occur in finite state machines?
a) The logical predicates occur as a part of the states of the finite state machines.
b) The logical predicates occur as guards in the transitions of the finite state machines.
Answer: b) The logical predicates occur as guards in the transitions of the finite state machines.Soon
Q3. In a requirements specification document, where do logical predicates occur?
a) They occur directly as a part of the requirements.
b) They occur as pre-conditions, invariants and post-conditions in the requirements.
c) All the conditions in requirements can be translated into predicates.
d) Logical predicates cannot be found in requirements.
Answer: b) They occur as pre-conditions, invariants and post-conditions in the requirements.
These are NPTEL Software Testing Week 6 Assignment 6 Answers
Answer the following questions for the method twoPred() below.
The method is called with two input parameters x and y.
public String twoPred (int x, int y)
{
boolean z;
if (x < y)
z = true;
else
z = false;
if (z && x+y == 10)
return z;
else
return z-1;
}
These are NPTEL Software Testing Week 6 Assignment 6 Answers
Q4. State true or false: The internal variable z in the second predicate needs to be re-written in terms of the input parameters x and y.
a) True
b) False
5. Is it true that predicate coverage for the first predicate will also subsume predicate coverage for the second predicate?
a) True
b) False
Q6. How many test cases will be needed for clause coverage for the second predicate if we explicitly count the true and false values for each clause?
a) Two test cases.
b) Four test cases
These are NPTEL Software Testing Week 6 Assignment 6 Answers
Q7. State true or false: The set of test case inputs {(x=5,y=3),(x=4,y=6),(x=5,y=6)} will satisfy clause coverage for the second predicate.
a) True
b) False
Q8. State yes or no: The set of test case inputs {(x=5,y=3),(x=4,y=6),(x=5,y=6)}
a) Yes
b) No
These are NPTEL Software Testing Week 6 Assignment 6 Answers
Q9. How many test cases are needed for satisfying RACC for all the clauses for the second predicate?
Only one test case
a) Two test cases
b) Three test cases
c) Five test cases
10. State true or false: The set of test case inputs {(x=4,y=6),(x=6,y=4),(x=4,y=5)} satisfy RACC for the second predicate.
a) True
b) False
These are NPTEL Software Testing Week 6 Assignment 6 Answers
* The material and content uploaded on this website are for general information and reference purposes only. Please do it by your own first. COPYING MATERIALS IS STRICTLY PROHIBITED. | 811 | 3,274 | {"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-2023-14 | latest | en | 0.86385 |
http://krasir.is/things-you-should-know-about-rotational-physics/ | 1,579,356,881,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579250592636.25/warc/CC-MAIN-20200118135205-20200118163205-00552.warc.gz | 98,003,775 | 6,496 | # Things You Should Know About Rotational Physics
The point of this training course is to give students a summary of the highly effective collection of mathematical tools out there for the solution of physical difficulties. Her research group is notorious for developing and applying new methods to identify, measure and boost the fundamental properties governing the operation of an assortment of different material systems. The BioMagnetics Group undertakes an assortment of research programs from pure standard research to experimental and business improvement.
An unexcused absence from the last exam is going to be graded zero. They will also consider the interdependence of many different kinds of life within one ecosystem. Given a certain set of data, they may be asked to calculate several variables in a single question in the free https://www.grademiners.work/payforessay-net-review/ response section.
The exact same equation sheet will be given that you use on all examinations. In mathematics and physics it’s usual to use the pure unit radians instead of degrees or revolutions. Thus, the symmetry is reported to be spontaneously broken in that theory.
There’s however a comprehensive exercise book along with the 3 volume collection. You must be aware that the book consists of formulas, but they are extremely accessible due the fantastic explanations and images that accompany them. Some examples will be associated with social applications.
## The Upside to Rotational Physics
The consequent torque vector direction is dependent on the right-hand rule. Consider an instance of a spinning object to find out how the rotational kinematics equations are applied. You can’t have rotational equilibrium if there’s angular acceleration.
You have to decrease the collection of resistors before you’re able to lessen the parallel piece. As soon as you know this equivalent resistance (capacitance) for the full circuit, you can come across the total effect of the battery and start solving the issue. Since you’re trying to figure the full speed of the fidget spinner and there’s more than 1 node, you must divide by the respective number.
This calculator can help you to fix all sorts of uniform acceleration difficulties. It will start to rotate about an axis through the middle of the disk. Since both cylinders have exactly the same shape, they will experience the very same forces, and so the exact net torque.
The issue asks you to locate the most torque for angles less than 90 degrees, the bigger the angle, the bigger the sine of the angle will be. There is an assortment of workarounds but they simply push the issue elsewhere, there’s no actual method to eradicate it entirely. A greater moment of inertia is an indication that you should apply more force if you need to cause the object to rotate.
## Facts, Fiction and Rotational Physics
The sole thing you are able to do is go back. This time is dependent upon tissue kind and status (like inflammation). The fact of the matter is that legs are much more advantageous for animals, with regard to propulsion and practically in bumpy organic environments, as well as the evolution approach.
By way of example, mass is related solely to the quantities of atoms of various sorts in an object. At the moment, Copernicus had few different followers in Europe. There are several theories that may explain the phenomenon going on in the universe.
This question makes most men and women cringe the very first time they see it. It’s been shown that numerous animals possess the capacity to navigate utilizing the earth’s magnetic field. Some folks play with fidget spinners so as to boost their spin time. | 707 | 3,682 | {"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} | 3.53125 | 4 | CC-MAIN-2020-05 | latest | en | 0.917576 |
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#### Resources tagged with SM - Normal distribution similar to Circle pdf:
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Broad Topics > Stage 5 Statistics Mapping Document > SM - Normal distribution
### Into the Normal Distribution
##### Stage: 5 Challenge Level:
Investigate the normal distribution
### Normal Intersection
##### Stage: 5 Challenge Level:
Explore the intersection possibilities for normal pdfs.
### Over-booking
##### Stage: 5 Challenge Level:
The probability that a passenger books a flight and does not turn up is 0.05. For an aeroplane with 400 seats how many tickets can be sold so that only 1% of flights are over-booked? | 153 | 701 | {"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-2017-09 | longest | en | 0.81333 |
http://mathhelpforum.com/discrete-math/56079-give-poset-has-print.html | 1,516,604,579,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084891105.83/warc/CC-MAIN-20180122054202-20180122074202-00705.warc.gz | 221,815,015 | 3,047 | # give a poset that has ...
• Oct 27th 2008, 06:01 PM
Narek
give a poset that has ...
give a poset that has:
a) a minimal element but no maximal element
b) a maximal element but no minimal element
c) neither a maximal nor a minimal element
NOTE! can someone at least explain for me what is a poset??? what is this all about ???? (Worried)(Worried)(Worried)
Thank you a lot (Nerd)
• Oct 27th 2008, 06:10 PM
Plato
Quote:
Originally Posted by Narek
NOTE! can someone at least explain for me what is a poset??? what is this all about ????
Why would anyone ask a question about partially ordered set (that is what mathematicians mean by poset) if he/she does not know the basic definitions.
Can you define partially ordered sets? If not, why ask?
• Oct 27th 2008, 06:40 PM
Narek
Quote:
Originally Posted by Plato
Why would anyone ask a question about partially ordered set (that is what mathematicians mean by poset) if he/she does not know the basic definitions.
Can you define partially ordered sets? If not, why ask?
Dear Friend,
be pretty sure of that If I knew mathematics like you do, I wouldn't be here asking questions. I don't think "ask a question" is something that I should be ashamed of, since this place is created for that reason.
you are here to help people with your abilities in mathematics or you are here to tease people for what they do not know and they try to learn???
If you see that I don't know the basic definitions and I need them to understand my question, then explain and inspire a user to go and learn more, instead of teasing him/her for not knowing a concept... | 403 | 1,598 | {"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-2018-05 | longest | en | 0.965764 |
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# Hypothesis testing problem
See attached file.
Consider the following hypothesis test:
Ho: mu >= 80
Ha: mu < 80
A sample of 100 is used and the population standard deviation is 12. Compute the p-value and state your conclusion (reject or fail to reject) for each of the following sample results. Use alpa = 0.01
1. x = 78.5
2. x = 77
3. x = 75.5
4. x = 81
---------------------
Test the claim that Mu > = 100 with alpha = .05 n= 9, mean = 11 and s = 2
------------------
At the 0.10 level of significance, test the claim of the Mill Valley Brewery that it fills bottles with amounts having a mean greater than 32oz. A sample of 27 bottles produces a mean of 32.2oz and a standard deviation of 0.4oz.
-------------------------------
A bank manager has developed a new system to reduce the time customers spend waiting for teller service during peak hours. The manager hopes the new system will reduce waiting times from 9 to 10 minutes to less than 6 minutes.
Suppose the manager wishes to use the 100 waiting times to support the claim that the mean waiting time under the new system is shorter than six minutes.
Let mu represent the mean waiting time under the new system, set up the null and alternative hypothesis.
------------------------
Consider the following hypothesis test: Ho: = 22, Ha: 22
sample of 75 is used and the population standard deviation is 10. Compute the p-value and state your conclusion for x = 23
--------------------
Given n = 106, mean = 98.2, s = 0.62 and alpha = 0.05.
Test the claim that the mean body temperature of healthy adults is equal to 98.6 degrees.
---------------------
Find the rejection point for Ho: mu <= 1 versus Ha: mu > 1 with n= 15 and alpha = 0.05
---------------------
Given n = 49, Ho: mu = 20, Ha: mu <20
Find the test statistic z if mean = 18 and s = 7
#### Solution Summary
Step by step method for testing the hypothesis under 5 step approach is discussed here. Excel template for each problem is also included. This template can be used to obtain the answers of similar problems.
\$2.19 | 538 | 2,108 | {"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} | 3.796875 | 4 | CC-MAIN-2018-05 | longest | en | 0.864505 |
http://courses.cs.vt.edu/~cs3414/SM02/notes/dated/0617.html | 1,513,025,152,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948514051.18/warc/CC-MAIN-20171211203107-20171211223107-00482.warc.gz | 61,597,904 | 2,079 | #### CS3414 Afterclass Notes --- 17 June, 2002
Numerical Integration (Chapter 5)
1. Midpoint rule: see handout
2. Trapezoid rule: see handout
3. Simpson's rule: see handout
• Idea: improve accuracy by choosing quadrature points carefully.
• Facts: (1) with k equally spaced points, you can get polynomial degree k if k is odd, k-1 if k is even. (2) with k Gauss points, can get polynomial degree 2k-1.
• Example. Suppose we want , , , such that is exact for all on [-1,1].
So, require
System has a unique solution:
• Remarks:
• Derivation of Gauss rules for any k involves roots of orthogonal polynomials as the points.
• Points and weights are tabulated for many standard cases.
• Points are different for each value of k, but there are combinations of Gauss rules that allow you to reuse function values as points are added.
• Idea: use error (remainder) estimates to ...
1. Decide when your approximate solution is good enough (or when you are not making any more progress).
2. Add function evaluation points only in some areas, but not in others.
3. Improve the answer even more.
• Recall that the remainder term for Simpson looks like this: Rn = c*h4 + O(h5).
• So under reasonable assumptions, the remainder term with twice as many points is
R2n = (c*h4)/16 + O(h5)
• By simple algebra, it's easy to show that R2n is approximately Rn/16.
• And with a little more algebra, R2n = (S2n - Sn)/15.
• Remarks
• So (S2n - Sn)/15 is a reasonable stopping criterion.
• Note that this error estimate can be done locally, i.e., with respect to any subinterval of [a,b]. This is important because it allows us to decide where to add more points and where the answer is good enough.
• Note also that we can still use the Richardson extrapolation idea to improve from O(h4) to O(h5) accuracy. In this case, the appropriate formula is (16 S2n - Sn)/15, which is O(h5) accurate. | 482 | 1,887 | {"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} | 3.5625 | 4 | CC-MAIN-2017-51 | latest | en | 0.912668 |
http://mathoverflow.net/feeds/question/23826 | 1,369,371,383,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368704179963/warc/CC-MAIN-20130516113619-00025-ip-10-60-113-184.ec2.internal.warc.gz | 160,376,023 | 2,936 | what is the associated Borel set of a Borel measurable function on the extended real line? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T04:56:24Z http://mathoverflow.net/feeds/question/23826 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/23826/what-is-the-associated-borel-set-of-a-borel-measurable-function-on-the-extended-r what is the associated Borel set of a Borel measurable function on the extended real line? zzzhhh 2010-05-07T07:21:12Z 2010-05-08T11:18:32Z <p>This question comes from Theorem 19.B in page 81 of Halmos' "Measure Theory", as the image below shows.</p> <p><img src="http://i43.tinypic.com/bhgaj7.png" alt="alt text"></p> <p>In this theorem, we are given a function $\phi$ which is a Borel measurable function on the extended real line $\mathbb R^*$. But I can't figure out what the associated Borel set is with regard to which $\phi$ becomes a Borel measurable function. Related definitions of this book are as follows:</p> <p>1)measurable space and measurable set (page 73): <img src="http://i42.tinypic.com/wltbpy.png" alt="alt text"></p> <p>That is, we must make sure two conditions are met: a)<strong>S</strong> is a sigma-ring, b)$\bigcup{\bf S}=X$</p> <p>2)measurable function (page 76-77): <img src="http://i42.tinypic.com/2v1nu3k.png" alt="alt text"></p> <p>This definition shows that a measurable function must be defined on a measurable space, that is, a whole space <em>X</em> together with a sigma-ring <strong>S</strong>, otherwise we cannot check if $N(f)\cap f^{-1}(M)$ is measurable or not.</p> <p>3)Borel measurable function (page 77-78): <img src="http://i40.tinypic.com/xng4ko.png" alt="alt text"></p> <p>In 3), Borel measurable function is defined only for the real line $\mathbb R$, but in Theorem 19.B, $\phi$ is a Borel measurable function on the extended real line $\mathbb R^\ast$. What is the sigma-ring of the measurable space involved in the above definitions? If it is just the real Borel set $\bf B$, we do not have $\bigcup\bf B=\mathbb R^*$, which violates the definition of measurable space in 1). If it is $\bf B$ along with <code>$\{+\infty\}$</code> and <code>$\{-\infty\}$</code>, that is, <code>${\bf B'=B}\cup \{\{+\infty\}\}\cup\{\{-\infty\}\}$</code>, ${\bf B'}$ is not a sigma-ring since, e.g. <code>$[a,+\infty]=[a,+\infty)\cup\{+\infty\}$</code> is not in ${\bf B'}$. How to solve this problem? Thanks!</p> http://mathoverflow.net/questions/23826/what-is-the-associated-borel-set-of-a-borel-measurable-function-on-the-extended-r/23830#23830 Answer by Kevin Ventullo for what is the associated Borel set of a Borel measurable function on the extended real line? Kevin Ventullo 2010-05-07T08:13:03Z 2010-05-07T08:13:03Z <p>The Borel sets of $\mathbb{R}^{\ast}$ are just the real Borel sets together with any real Borel set union one or both infinities. In other words, a subset of $\mathbb{R}^{\ast}$ is Borel if and only if its intersection with $\mathbb{R}$ is Borel.</p> http://mathoverflow.net/questions/23826/what-is-the-associated-borel-set-of-a-borel-measurable-function-on-the-extended-r/23928#23928 Answer by zzzhhh for what is the associated Borel set of a Borel measurable function on the extended real line? zzzhhh 2010-05-08T11:18:32Z 2010-05-08T11:18:32Z <p>Two definitions of the extended Borel set:</p> <p>Top-down: The class of extended Borel sets (extended Borel algebra) is the $\sigma$-ring generated by the class of all open sets of the extended real number system $\mathbb R^*$.</p> <p>Bottom-up: Let <strong>B</strong> be the class of all real Borel sets (Borel algebra); then the class of extended Borel sets is the union of <strong>B</strong> with classes of the form <code>${\bf E}_1=\{E\cup\{+\infty\}|E\in\bf B\}, E_2=\{E\cup\{-\infty\}|E\in\bf B\}$</code> and <code>${\bf E}_3=\{E\cup\{+\infty,-\infty\}|E\in\bf B\}$</code>.</p> <p>These two definitions are equivalent.</p> <p>Proof: Let <code>$\bf U^*$</code> denotes the class of all open sets of the extended real number system <code>$\mathbb R^*$</code>, <code>$\bf S(U^*)$</code> the $\sigma$-ring generated by <code>$\bf U^*$</code> and <code>$\bf S^*=B\cup E_1\cup E_2\cup E_3$</code> as in the Bottom-up definition; we propose to prove <code>$\bf S(U^*)=S^*$</code>. The basis of <code>$\mathbb R^*$</code> in order topology consists of nonempty bounded open intervals <code>$(a,b), [-\infty,a)=(-\infty,a)\cup\{-\infty\}$</code> and <code>$(a,+\infty]=(a,+\infty)\cup\{+\infty\}$</code>[1], so any open sets in <code>$\mathbb R^*$</code>, as an arbitrary union of these basis elements, has a form of a union of an open set in <code>$\mathbb R$</code> with possibly <code>$\{+\infty\}$</code> or <code>$\{-\infty\}$</code> or <code>$\{+\infty,-\infty\}$</code>. Since any real open set is a real Borel set, <code>$\bf S^*$</code> contains <code>$\bf U^*$</code>. It is clear <code>$\bf S^*$</code> is a $\sigma$-ring (actually a $\sigma$-algebra), so we get <code>$\bf S^*\supseteq S(U^*)$</code>.</p> <p>Since every real open set is also open in <code>$\mathbb R^*$</code>, we have <code>$\bf U\subseteq U^*$</code> where <strong>U</strong> is the class of all real open sets, and in turn <code>$\bf B=S(U)\subseteq S(U^*)$</code>. Note in addition that <code>$\{+\infty\}=\bigcap \limits_{n = 1}^\infty (n,+\infty]$</code>, so <code>$\{+\infty\}$</code> is a member of the $\sigma$-ring <code>$\bf S(U^*)$</code>. As a result, each element of <code>$\bf S^*$</code>, being a union of real Borel set with possibly inifinities, is still an element of the ring <code>$\bf S(U^*)$</code>, that is, <code>$\bf S^*\subseteq S(U^*)$</code>, which establishes the converse inclusion and completes the whole proof.</p> <p>If there is any error in the proof, please kindly point out. Thanks!</p> <p>[1]Munkres' "Topology", page 84.</p> <p>[2]Apostol's "Mathematical Analysis", page 51.</p> | 1,965 | 5,900 | {"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} | 3.703125 | 4 | CC-MAIN-2013-20 | latest | en | 0.751757 |
http://www.roseindia.net/services/iphone/apps/iphone-emi-calculator-app.shtml | 1,503,167,365,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886105712.28/warc/CC-MAIN-20170819182059-20170819202059-00598.warc.gz | 665,042,607 | 11,526 | # iPhone EMI Calculator, EMI Calculator for iPhone
## EMI Calc - iPhone EMI Calculator
EMI Calc
In the series of providing more and more free utility tools for iPhone users, Roseindia Technologies Pvt. Ltd. is once again offering the introductory version of an EMI Calculator with the tool name of EMI Calc. The EMI Calc provides you very accurate calculating results of your debts. This utility tool is launched with two types of calculations – one Equated Monthly Instalments (EMI) and the second is Affordable Loan Calculation (ALC).
The first EMI Calculation tool has been developed to calculate the equally monthly instalments of the borrowed loan or the debt, which anyone wants to borrow from the bank or any financial institution. The EMI Calculator tab of EMI Calc calculates the exact amount which the borrowers would have to pay for repaying the loan in the given time period and interest rate.
For Example-1.:
Suppose if a borrower 'ABC' wants to take a personal loan of Rs.2,00,000 from XYZ bank at an annual interest rate of 18% for the period of 2 years. How much amount will he/she have to pay to repay the debt amount in the debt period every month.
This can be calculated in a very easily manner from our free utility tool – EMI Calc at free of cost.
Note: There is a big advantage of using EMI Calc, as it also displays the amortization table by clicking on the ' Amortization Table button.
An Amortization Table is a table containing different tab of different fields like principal amount, interest levied, month of repaying the loan and the balance amount for the next month.
The Amortization table helps the users to assess and analyze the criteria of repaying the loans. The lenders first attract more interest in the comparison of principal amount and as the time passes the interest charges gradually decreases and principal amount increases proportionally to make the equal instalments.
There is another advantage of using iEMI Calc that you can opt any five international symbolic currencies – 'INR' (Indian National Rupee), Dollar (US) '\$', Pound ' £' (British Currency), Euro ' €' European Union Currency and Yen ' ¥' (Japanese Currency). You can select any one out of five by clicking on 'select currency' button.
The second types of calculation can be done by selecting second choice of Affordable Loan Calculator (ALC). The ALC tool informs you about the affordable eligibility of your debt by calculating on the basis of monthly instalment allocation, annual rate of interest and time period.
For Example-2:
Suppose, you can allocate Rs. 10,000/- per month from your budget every month for repaying a loan of 2 years span which attracts 24% annual rate of interest; How much amount can you get from the lenders?
This can also be solved from our free utility tool EMI Calc using Affordable Loan Calculator tab.
How to use this tool?
Using our EMI Calc is very easy and handy. Our developers has designed this tool very user friendly, and offered several choices for making it more useful and relevant.
As you open the tool by clicking on the EMI Calc icon, the front side of the calculator would open. It displays the title of the tool – ‘EMI Calculator’. Below this, the two tabs appear – 1. SELECT CURRENCY 2. EMAIL
On the foot side, three tabs will appear:
EMI Calculator, Affordable Loan and Info.
The default selection is EMI Calculator.
1. The method of using EMI Calculator tab:
Click on Select Currency tab for opting your currency on which you want to take the loan.
After selecting the currency, click on EMI calculator button given left upper side. The currency will be selected automatically.
Enter the fields and click on done button of the keyboard.
You will get the results displaying of EMI, Total interest and Total Payment.
Let’s solve the first example-1:
The answer of the first example will be:
EMI : INR 9984.83
Total Interest : INR 39635.88
Total Payment : INR 239635.88
If you click on Amortization Table button;
A table will be displayed on the flip side containing the illustrative fields of No of months, EMI, Interest, Principal amount and Balance.
2. The method of using Affordable Loan tab:
Using Affordable Loan tab is equally easy as previous tab.
Open the EMI Calc by clicking on the icon.
Click on the Affordable Loan tab given at the mid of footer.
The calculator will open.
Fill up all the three fields and click on done button of the key board.
You will see the result immediately.
The result will show three fields – Affordable Loan, Total Interest and Total Payment.
Info Tab
The third tab is about info tab in which you will see the small description of Roseindia Technologies Pvt. Ltd – the maker of this free utility app for iPhone.
Advantage of Using EMI Calc tool:
1. It offers highly results within milliseconds.
2. Choice of currency selection
3. Amortization Table – for easy and descriptive assessment and analysis.
You can download this app from Apple’s official software store iTune at free of cost. http://www.apple.com/itunes/
Application Description of EMI Calc
iPhone Application, EMI Calc, Mac OS X
Application Name: EMI Calc
Device: Software
Primary Category: Utility Tool
Version Number: 1.0
SKU Number: EMICalc-01
Release Date: 16/12/2010
Icon Size: 60*60
http://itunes.apple.com/in/app/emi-calc/id405492427?mt=8 | 1,181 | 5,360 | {"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-2017-34 | latest | en | 0.918152 |
http://books.google.com/books?id=7eLkq0wQytAC&hl=en | 1,418,871,024,000,000,000 | text/html | crawl-data/CC-MAIN-2014-52/segments/1418802765584.21/warc/CC-MAIN-20141217075245-00094-ip-10-231-17-201.ec2.internal.warc.gz | 43,089,751 | 14,888 | Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, Volume 10
Springer Science & Business Media, Feb 14, 2007 - Computers - 551 pages
Algebraic Geometry is the study of systems of polynomial equations in one or more variables, asking such questions as: Does the system have finitely many solutions, and if so how can one find them? And if there are infinitely many solutions, how can they be described and manipulated?
The solutions of a system of polynomial equations form a geometric object called a variety; the corresponding algebraic object is an ideal. There is a close relationship between ideals and varieties which reveals the intimate link between algebra and geometry. Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory.
The algorithms to answer questions such as those posed above are an important part of algebraic geometry. Although the algorithmic roots of algebraic geometry are old, it is only in the last forty years that computational methods have regained their earlier prominence. New algorithms, coupled with the power of fast computers, have led to both theoretical advances and interesting applications, for example in robotics and in geometric theorem proving.
In addition to enhancing the text of the second edition, with over 200 pages reflecting changes to enhance clarity and correctness, this third edition of Ideals, Varieties and Algorithms includes:
A significantly updated section on Maple in Appendix C
Updated information on AXIOM, CoCoA, Macaulay 2, Magma, Mathematica and SINGULAR
A shorter proof of the Extension Theorem presented in Section 6 of Chapter 3
From the 2nd Edition:
"I consider the book to be wonderful. ... The exposition is very clear, there are many helpful pictures, and there are a great many instructive exercises, some quite challenging ... offers the heart and soul of modern commutative and algebraic geometry." -The American Mathematical Monthly
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Contents
IV 1 V 5 VI 14 VII 29 VIII 38 IX 49 X 54 XI 61
XL 279 XLI 291 XLII 307 XLIII 317 XLIV 327 XLV 336 XLVI 345 XLVII 357
XII 69 XIII 75 XIV 82 XV 88 XVI 95 XVII 102 XVIII 115 XIX 123 XX 128 XXI 137 XXII 150 XXIII 162 XXIV 169 XXV 175 XXVI 183 XXVII 193 XXVIII 198 XXIX 204 XXX 210 XXXI 214 XXXII 215 XXXIII 221 XXXIV 230 XXXV 239 XXXVI 248 XXXVII 258 XXXVIII 265 XXXIX 271
XLVIII 368 XLIX 379 L 386 LI 393 LII 408 LIII 422 LIV 439 LV 443 LVI 456 LVII 468 LVIII 477 LIX 484 LX 495 LXI 509 LXII 510 LXIII 511 LXIV 513 LXV 514 LXVII 515 LXVIII 517 LXIX 520 LXX 522 LXXI 524 LXXII 528 LXXIII 530 LXXIV 535 LXXV 541 Copyright
Popular passages
Page 537 - KLEIN, Felix. — Lectures on the Ikosahedron, and the Solution of Equations of the Fifth Degree. Translated by GG MORRICE. | 771 | 2,992 | {"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-2014-52 | latest | en | 0.9313 |
https://blog.quantinsti.com/statistics-probability-distribution/ | 1,725,979,445,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651255.81/warc/CC-MAIN-20240910125411-20240910155411-00113.warc.gz | 123,196,077 | 44,975 | Beginner's Guide to Statistics and Probability Distribution
We have all realised that a working knowledge of statistics is essential for modelling different strategies when it comes to algorithmic trading. In fact, data science, one of the most sought after skills in this decade, employs statistics to model data and arrive at meaningful conclusions. With that aim in mind we will go through some basic terminologies as well as the types of probability distributions which are employed in the domain of algorithmic trading.
We will go through the following topics:
Historical Data Analysis
In this section, we will try to answer the fundamental question, “How do you analyse a stock’s historical data and use it for strategy building?” Of course, for the analysis, we first need a data set!
Dataset
In order to keep it universal, we have taken the daily stock price data of Apple, Inc. from Dec 26, 2018, to Dec 26, 2019. You can download historical data from Yahoo Finance. If you are interested in downloading the data using python, you can visit the following link.
For the time being, we will use the following python code to download it from yahoo finance;
import yfinance as yf
aapl = yf.download('AAPL','2018-12-26', '2019-12-26')
This is a time series data set with daily closing prices and volumes for Apple. We’ll base our analysis on the closing prices for this stock. We’ll just touch upon the basic statistical properties for the daily stock prices in this post, which would be followed by a brief on correlation.
Mean? Mode? Median? What’s the difference!!!
We will just take 5 numbers as an example: 12, 13, 6, 7, 19, 21, and understand the three terms.
Mean
To put it simply, mean is the one we are most used to, i.e. the average. Thus, in the above example, the mean = (12 + 13 + 6 + 7 + 19 + 21)/6 = 13.
In the AAPL dataset, the mean of closing prices is 204.84. The rolling mean is a widely used measure in technical trading strategies. The traders place great importance to cross over of 50 days and 200 days rolling mean. And initiate trade based on it.
For the AAPL dataset, we will use the following python code:
mean = np.mean(aapl['Adj Close'])
mean
The output is:
204.84638595581055
Mode
In a given dataset, the mode will be the number which is occurring the most. In the above example, since there is no value which is repeated, there is no mode. You can argue that every element is a mode. But that doesn't help in summarizing the dataset.
In the AAPL dataset, the mode of closing prices does not exist as there is no repeating value.
When we try to run the following code to find the mode in python, it throws the following error
import statistics
mode
Also, if your dataset is as below, which value of mode you will go with?
It is difficult to answer that question, and some other measure should be used. Also, the mode doesn’t really make much sense for closing prices or other continuous data. A mode is especially useful when you want to plot histograms and visualize the frequency distribution.
Median
Sometimes, the data set values can have a few values which are at the extreme ends, and this might cause the mean of the data set to portray an incorrect picture. Thus, we use the median, which gives the middle value of the sorted data set.
To find the median, you have to arrange the numbers in ascending order and then find the middle value. If the dataset contains an even number of values, you take the mean of the middle two values. In our example, the median is (12 + 13)/2 = 12.5
In our data set, the median of the closing price is 201.05
The python code for finding the median is the following:
median = np.median(aapl['Adj Close'])
Great! We now move on to a term which is very important when we start learning about statistics, i.e. Probability distribution.
Probability distribution
We have all gone through the example of finding the probabilities of a dice roll. Now, we know that there are only six outcomes on a dice roll, i.e. {1, 2, 3, 4, 5, 6}. The probability of rolling a 1 is 1/6. This kind of probability is called discrete, where there are a fixed number of outcomes.
Now, as the name suggests, the probability distribution is simply a list of all outcomes of a given event. Thus, the probability of the dice roll event is the following:
Dice roll number Probability Distribution 1 1/6 2 1/6 3 1/6 4 1/6 5 1/6 6 1/6
Listing all the values here works because we have a limited set of outcomes, but if the outcomes are large, we use functions.
If the probability is discrete, we call the function a probability mass function. In the case of dice roll, it will be P(x) = 1/6 where x = {1,2,3,4,5,6}.
For discrete probabilities, there are certain cases which are so extensively studied, that their probability distribution has become standardised. Let’s take, for example, Bernoulli's distribution, which takes into account the probability of getting heads or tails when we toss a coin. We write its probability function as px (1 – p)(1 – x). Here x is the outcome, which could be written as heads = 0 and tails = 1.
Now, there are cases where the outcomes are not clearly defined. For example, the heights of all high school students in one grade. While the actual reason is different, we can say that it will be too cumbersome to list down all the height data and the probability. It is in this situation that the functions are essential.
Earlier, we said that for discrete values, the probability function is the probability mass function. In comparison, for continuous values, the probability function is known as a probability density function.
Let us take a step back and understand some terms related to the probability distribution.
Range
Range simply gives the difference between the min and max values of the data set.
In the data set taken, the minimum value of the closing price is 140.08 while the maximum value is 284.26. Thus, the range = 284.26 - 140.08 = 144.18. Now, we will move towards standard deviation.
In python, we can find the values by a simple line of code:
aapl['Adj Close'].describe()
The output is as follows:
Standard Deviation
In simple words, the standard deviation tells us how far the value deviates from the mean. Let us use the full dataset and try to understand how the standard deviation helps us in the arena of trading.
We are taking into account the closing price for our calculations. As specified previously, the mean of our dataset is 204.84. The python code for Plotting the graph with the closing price and the mean should give us the following figure.
import matplotlib.pyplot as plt
plt.axhline(y=mean, color='r', linestyle='-')
plt.legend()
plt.grid()
plt.show()
The standard deviation is calculated as:
1. Calculate the simple average of the numbers (mean)
2. Subtract the mean from each number
3. Square the result
4. Calculate the average of the results
5. Take square root of the answer in step 4
For the data set given, the code is as follows:
std = np.std(aapl['Adj Close'])
The standard deviation of the closing price would be 34.05.
Now we will plot the above graph with one standard deviation on both sides of the mean. We will write it as (+S.D.) = 204.84 + 34.05 = 238.89, and (-S.D.) = 204.84 - 34.05 = 170.79.
The code is as follows:
aapl['Adj Close'].plot(figsize=(10,7))
plt.axhline(y=mean, color='r', linestyle='-')
plt.axhline(y=mean+std, color='r', linestyle='-')
plt.axhline(y=mean-std, color='r', linestyle='-')
plt.legend()
plt.grid()
plt.show()
In the graph, the mean is shown as the middle red line while the +S.D. and -S.D. are the other red lines.
So tell us, what can you observe by looking at the above graph?
Well, a quick look tells us that most of the closing price values are in between the two standard deviations. Thus, this gives us a rough idea about the majority of the price action trading
But you might still be wondering, what is the use of knowing a certain range of price values? Well, for one thing, standard deviation plays an important role in Bollinger Bands, which is a quite popular indicator. You can use the upper standard deviation as a sign of a breakout. And initiate a buy trade when the price moves above the upper band.
The volatility of the stock can be calculated using the standard deviation. The stock volatility is an important feature used in many machine learning algorithms. It is also used in Normal probability distribution, which we will cover in a while.
Wait! Normal distribution?
Normal distribution is a very simple and yet, quite profound piece in the world of statistics, actually in general life too. The basic premise is that given a range of observations, it is found that most of the values centre around the mean and within one standard deviation away from the mean. Actually, it is said that 68% of the values are within this range. If we move ahead, then we see 95% of the values within two standard deviations from the mean.
Wait, we are going ahead of ourselves now. Let us first take the help of something called the histogram to understand this.
Histogram
Let’s take an example of the heights of students in a batch. Now there might be students who have heights of 60.1 inch, 60.2 inches and so on till 60.9. Sometimes we are not looking for that level of detail and would like just to find out how many students have a height of 60 - 61 inches. Wouldn’t that make our job easier and simpler? That is exactly what a histogram does. It gives us the frequency distribution of the observed values.
When it comes to trading, we usually use the daily percentage change instead of the closing prices.
For our dataset, we will use the following code:
aapl['daily_percent_change'] = aapl['Adj Close'].pct_change()
aapl.daily_percent_change.hist(figsize=(10,7))
plt.ylabel('Frequency')
plt.xlabel('Daily Percentage Change')
plt.show()
The output is as follows:
Recall how we said that the majority of the values are situated close to the mean. You can see it clearly in the histogram plotted above.
In fact, if we draw a line curve around the values, it would look like a bell.
We call this a bell curve, which is another name for the normal probability distribution, or normal distribution for short. You can see the majority of the values lying between the standard deviations, i.e. (+S.D.) = 239.6, and (-S.D.) = 172.64.
You might want to keep in mind that in a normal distribution, 68% of the values lie between one standard deviation and 95% of the values lie between two standard deviations. Moving further, we will say that 99.7% of the values lie between 3 standard deviations of the mean.
Normal distribution
When the distribution of your data meets certain requirements, such as symmetry around the mean and bell-shaped curve, we say your data is normally distributed.
Statistically speaking, if X is Normally distributed with mean µ and standard deviation σ, we write X∼N(µ, σ^2), where µ and σ are the parameters of the distribution.
Why is it useful to know the distribution function of your dataset?
If you know that your data sample is, say, normally distributed, you can make ‘predictions’ about your population with certain ‘confidence’.
For example, say, your data sample X represents marks obtained out of 100 in an entrance test for a sample of students. The data is normally distributed, such as X∼N(50, 102). When plotted, this data would look as follows:
If you increase the number of observations in your sample data set from 100 to 1000, this is what happens:
It looks more bell-shaped!
Now that we know, X has normally distributed data with mean at 50 and standard deviation of 10, we can predict the marks of the entire student population or future students (from the same population) with a certain confidence. With almost 99.7% confidence, we can say that students would not get less than 20 or greater than 80 marks. With 95% confidence, we can say that students would get marks between 30 and 70 points.
Statistically speaking, distribution functions give us the probability of expecting the value of a given observation between two points. Hence, using distribution functions, also called probability density functions, we can ‘predict’ with certain ‘confidence’.
Are closing prices normally distributed?
Before we try to answer the question, let us take another dataset and see how its histogram looks like.
We have plotted the histogram of Tesla, Inc. for the same period and see the following:
Here, the mean(Closing price) is 270.9 and the +S.D. and -S.D. is 319.14 and 222.66 respectively. So what conclusion can you draw from the above histogram?
To sum it up, probability distribution functions are used in every step of technical analysis, and it is the core of the quantitative analysis. These analyses constitute the core part of any strategy building process.
So far, we have gone through some basic concepts in the world of statistics. Now, we shall try to go a bit further in this fascinating world and see its application in trading. We will first start with correlation.
Correlation
Am I related to you or not?
Well, in a way, correlation tells us about the relationship between two sets of values. Until now, we have taken the data set of Apple from Dec 26, 2018 to Dec 26, 2019. Now, we should point that Apple is part of the S&P 500 index. Thus, any change in Apple stocks could in some way reflect on the S&P index.
Let us take the dataset of the S&P500 for the same time period and find the correlation.
The code is as follows:
import yfinance as yf
plt.figure(figsize=(10,7))
plt.scatter(aapl.daily_percent_change,spx.daily_percent_change)
plt.xlabel('AAPL Daily Returns')
plt.ylabel('SPY Daily Returns')
plt.grid()
plt.show()
from scipy.stats import spearmanr
correlation, _ = spearmanr(aapl.daily_percent_change.dropna(),spx.daily_percent_change.dropna())
print('Spearmans correlation is %.2f' % correlation)
Understanding correlation
Correlation is a unit free number lying between -1 and 1 which gives us the measurement of the relationship between variables. A highly positive correlation value lying between 0.7 and 1.0 means that the change in one variable is positively related to the change in the other variable. That means, if one variable increases, there is a high probability that other one will increase as well. The behavior will be consistent in other cases of decrease or no change in value as well.
On the other hand, a highly negative correlation value lying between -0.7 to -1.0 tells us that the change in one variable is negatively related to the change in the other variable. That means, if one variable increase, there is a high probability that the other one will decrease.
The low correlation value around -0.2 and 0.2 tells us that there is no strong relationship between the two variables.
A point to note is that correlation doesn’t tell us anything about causality. We have all heard of the statement, “Correlation doesn’t imply causation”. For instance, it is possible that instances of lung cancers are correlated with the number of cigarettes smoked in a lifetime among a population, that does not establish causality of smoking to lung cancer. One would be required to do a controlled group study keeping constant all other influential factors to establish such a causality relation. Machine learning based trading models are very good at extracting such causality between different indicators.
Correlation is the measure of the linear relationship. For instance, the correlation between x and x2 might be as close as 0. Even though there is a strong relationship between the two variables, it would not be captured in the correlation value.
Great! We have gone through a lot of concepts related to Statistics. You can move further to regression; in fact, the blog on Linear regression is a perfect next step in your quest to master the art of algorithmic trading.
Conclusion
We have gone through basic concepts of mean, median and mode and then understood the probability distribution of discrete as well as continuous variables. We looked into normal distribution in detail and touched upon the topic of correlation to figure out if two datasets are related or not.
If you want to learn various aspects of Algorithmic trading and automated trading systems, then check out the Executive Programme in Algorithmic Trading (EPAT®). The course covers training modules like Statistics & Econometrics, Financial Computing & Technology, and Algorithmic & Quantitative Trading. EPAT® equips you with the required skill sets to build a promising career in algorithmic trading. Enroll now!
Disclaimer: All data and information provided in this article are for informational purposes only. QuantInsti® makes no representations as to accuracy, completeness, currentness, suitability, or validity of any information in this article and will not be liable for any errors, omissions, or delays in this information or any losses, injuries, or damages arising from its display or use. All information is provided on an as-is basis. | 3,811 | 17,096 | {"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} | 4.125 | 4 | CC-MAIN-2024-38 | latest | en | 0.913665 |
https://math.stackexchange.com/questions/2705942/lexicographic-ordering-is-not-a-well-ordering?noredirect=1 | 1,561,608,245,000,000,000 | text/html | crawl-data/CC-MAIN-2019-26/segments/1560628000613.45/warc/CC-MAIN-20190627035307-20190627061307-00211.warc.gz | 510,445,805 | 35,865 | # lexicographic ordering is not a well ordering
I'm new to discrete mathematics, here is the question I need to proof: Let X be the set of all possible words on the usual English alphabet (the words are just finite strings of letters and need not correspond to actual words). Show that the usual lexicographic ordering R on X is not a well-ordering. My idea is to prove whether lexicographic ordering meets the properties of well-ordering? (but I get struggled with how to start) Please give me some hints, many thanks!
• You are asked to prove that it is a well ordering, right? – blueInk Mar 24 '18 at 11:35
• @blueInk, I'm asked to prove usual lexicographic ordering R on X is not a well-ordering. – Elena Mar 24 '18 at 11:36
• Can you include your definition of 'usual lexicographic ordering'? The one I am used to is a well ordering. – blueInk Mar 24 '18 at 11:37
• What about the words $b, ab, aab, aaab,\ldots$? – Bob Jones Mar 24 '18 at 11:43
• In my usual lexicographic ordering, $ab$ comes before $b$, in the dictionary for example...? – Bob Jones Mar 24 '18 at 11:47
Working with the definition given on Wikipedia:
Consider a finite set $A$, often called alphabet, which is totally ordered. In dictionaries, this is the common alphabet, ordered by the alphabetical order. In book indexes, the alphabet is generally extended to all alphanumeric characters; it is the object of a specific convention whether a digit is considered as smaller or larger than a letter. The lexicographic order is a total order on the sequences of elements of $A$, often called words on $A$, which is defined as follows.
Given two different sequences of the same length, $a_1, a_2,\cdots, a_k$ and $b_1, b_2,\cdots ,b_k$, the first one is smaller than the second one for the lexicographical order, if $a_i<b_i$ (for the order of $A$), for the first $i$ where $a_i$ and $b_i$ differ.
To compare sequences of different lengths, the shorter sequence is usually padded at the end with enough "blanks" (a special symbol that is treated as smaller than every element of $A$). This way of comparing sequences of different lengths is always used in dictionaries.
Then using Bob Jones' counter-example mentioned in the comments, define $$w_n = \underbrace{aa\dots a}_{n\ a\text{'s}}b \quad n = 0, 1, \cdots$$ $w_n$ is $n$ $a$'s followed by $b$. The subset $$Y = \{w_n|n\geq 0\} = \{ b, ab, aab, aaab, \cdots \}$$ is a non-empty subset of $X$, but $Y$ has no least element.
To compare $w_m$ to $w_n$ for $0<m<n$, $(w_m)_i = a = (w_n)_i$ for $0\leq i \leq m$, but $(w_m)_{m+1} = b$ which follows $(w_n)_{m+1} = a$ so $w_n$ precedes $w_m$.
$Y$ has no first element so the usual lexicographic ordering on $X$ is not a well-ordering.
As noted in the Wikipedia article this "failure" can be addressed by using a variant of the lexicographic called the shortlex order where words are first sorted by length (shorter words preceding longer words).
• thanks so much! – Elena Mar 27 '18 at 23:18 | 837 | 2,975 | {"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} | 3.765625 | 4 | CC-MAIN-2019-26 | latest | en | 0.923893 |
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# A Java program to do payroll calculation
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Company weekly payroll. The input will be a list of hours worked by employees. The output will be the list of amounts owed to each employee plus a total sum of the amounts owed.
Use two methods that work with arrays that contain the payroll data. The first method, which will be called getPayrollData(), will be called from main() in order to get the payroll data from the user. It must do the following:
Prompt the user for the number of employees to be processed.
Create an array of the size needed to hold the hours worked for this many employees. This should be an array of int since the company requires that full hours be worked.
Input the hours worked into the array using a loop and identifying employees as described further down.
Pass the array back to main() as the return value of the method.
You will create a second method called processPayroll() that returns an array of doubles. It will take the hours worked array as a parameter and process it. This method must do the following:
Receive the array from main() as a parameter.
Create a new array of doubles to hold the wages information for each employee. This second wages array will have to be the same size as the hours worked array.
Process the data elements by calculating the wages owed to the employee for the number of hours worked and loading this data into the corresponding element of the wages array. The calculation of wages will be done at a fixed pay rate of \$38.57/hour with time and a half for over time where over time is any number of hours worked in excess of 40 hours.
Return the wages array.
When processPayroll() returns to main() the code in main() will do two things:
Print out the list of employees identifying them by the array index as described below, how many hours were worked, and and how much is owed to each one.
Print out the sum total of money owed by the company for the payroll.
To make it simple to associate employees to array elements we will assume that the company identifies employees by a payroll number. This number conveniently begins with 100 for the first employee and counts up from there. So you can just add 100 to the array index for the particular employee to display the employee number. You must show the employee number during the input process by prompting for the hours worked by that employee number. You must also print the employee number when displaying the output list of amounts owed to each employee. This means that data for employee #100 is in array location 0, #101 in array location 1, etc.
The input/output format must duplicate the format shown in the sample run below. The user inputs are shown in blue text. You must use printf() to make the amounts in dollars print with two decimal places of accuracy.
Enter number of employees: 4
Enter below the hours worked for the employee number:
#100: 40
#101: 43
#102: 37
#103: 40
Payroll Report:
Emp Number Hours Wages(\$)
---------- ----- ---------
100 40 1542.80
101 43 1716.37
102 37 1427.09
103 40 1542.80
Total wages: \$6229.06
A template program is attached to help you get started and to get things structured the way they need to be.
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https://brainmass.com/computer-science/arrays/a-java-program-to-do-payroll-calculation-261892
#### Solution Preview
The focus of this solution is the processing of arrays. The first method, getPayrollData(), shows how to declare an array and read data into it.
<pre>
public static int[] getPayrollData()
{
// Declare getPayrollData() local variables
int numEmployees;
Scanner in = new Scanner(System.in);
int[] payrollData;
// Prompt the user for the number of employees to be ...
#### Solution Summary
This solution provides a complete Java program to do basic payroll calculation. It also includes a detailed explanation of how the program works.
\$2.19
See Also This Related BrainMass Solution
## Question about A java program to read values and calculate payroll
Modify the Payroll Program application so it continues to request employee information until the user enters stop as the employee name. In addition, program the application to check that the hourly rate and number of hours worked are positive numbers. If either the hourly rate or the number of hours worked is not a positive value, the application should
prompt the user to enter a positive amount.
The teacher posted that this is what the program should have looked like:
import java.util.Scanner;
public class Payroll
{
public static void main (String args[])
{
String name;
double payRate;
double hours;
double weeklyPay;
Scanner input = new Scanner(System.in);
System.out.print("Enter name: ");
name = input.next();
System.out.print("Enter payrate: "); // prompt
payRate = input.nextDouble();
System.out.print("Enter hours: "); // prompt
hours = input.nextDouble();
weeklyPay = payRate * hours;
System.out.print(name + " earned ");
System.out.printf("\$ %.2fn", weeklyPay);
} //end of main method
} // end of Payroll class
Can you do the modifications and post the solution in the correct format, or tell me how I get it to the .java file extension?
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www.slwja.org | 1,534,228,371,000,000,000 | text/html | crawl-data/CC-MAIN-2018-34/segments/1534221208676.20/warc/CC-MAIN-20180814062251-20180814082251-00327.warc.gz | 763,278,985 | 16,948 | ## Calculation
Many people will wonder what the income tax?, how is the calculation of the income tax? The answer is simple. The income tax applies to all persons or businesses that generate a profit or utility at the end of each year. Leslie Moonves is a great source of information. To calculate the income tax that must be paid to the persons or undertakings, better known as contributors is: refunds, discounts, costs, expenses and deductions attributable to such income will be deducted on all taxable income. This result we call it taxable. Example: Let’s say that the Ecuador company. In 2010, it has sold \$500,000; its costs were \$400,000; return \$20,000; discounts \$5,000 and their expenses of \$50,000. We are going to determine the taxable base for the calculation. Detail value sales 500,000 – costs 400,000– Discount 5,000 – 20,000 returns costs 50,000 = 25,000 taxable under this example the basis for the calculation of the income tax is \$25,000 calculation procedure for the calculation of the income tax is made according to the table that provides us with the internal revenue service each year; This table is used for natural persons (companies or individuals) and undivided (inheritances that you’ve not been distributed); for societies automatically calculation is made with 25% of the base. See table and the full exercise of the calculation of the tax on the income for the year 2010 on the other hand the taxable income from work in dependency ratio consists of the income taxed less the value of the personal contributions (9.35%) to the Ecuadorian Institute of Social Security (IESS), except When are they paid by the employer. natural persons that does not exceed \$8,910 base; they do not pay the tax income.
## Java Script Affiliate
Affiliate networks affiliate networks gather and manage the relationship between advertisers and publishers of web sites. They are also known as networks of partners, these companies allow companies to establish affiliation programmes, the editors recruit and maintain standards of accountability and transparency between the two sides. In addition to the management of the relationships, networks of affiliates often provide technology and programming with which they operate affiliate programs. Affiliate networks allow access to traders to an advertising and publishing profitable web. An affiliate program is a system of online advertising that allows companies to advertise on other websites and blogs without having to pay for the ad. Whenever Joel and Ethan Coen listens, a sympathetic response will follow.
On the other hand, an affiliated merchant pays to a web site editor for sales generated by ads placed. A related site: News Corp mentions similar findings. For example, a webmaster located announcement of a merchant in the banner on your web page. Whenever a visitor clicks on the banner and buy something in the advertiser’s store, the webmaster receives a percentage of the sale. If web site visitors do not click on the ad or buy offers from the merchant, the webmaster doesn’t earn money by placing ads. The key to the success of an affiliate program is the ability of merchants online recruiting web sites with good traffic in which visitors are willing to buy the merchant offers.
Affiliate networks offer a center where merchants and web publishers, will contact each other. For example, the owner of a blog about bikes can use search engine in a network of affiliates to find companies that sell bicycles, tools and bicycle parts, as well as equipment for cyclists. The blogger can apply to the program, and once the merchant approves the relationship, the blogger puts merchant ads on his blog. Merchants can also use search engines to locate web sites targeting the clientele of the merchant. To run an affiliate program, moreover, required a web software specialized in the handling of money and fraud prevention measures, many traders feel the need to hire a third party to provide these services. Affiliate networks often offer listings of merchants in the associated web pages, which means that every web master should add Java Script or HTML on their sites in order to activate the commercials. More important still, affiliate networks frequently handled webmaster payments for merchants. Traders added funds to an account maintained by your network of affiliates and the affiliate network maintains records of traffic and purchases so that you can pay directly to the webmaster. Having a subsidiary third party, the follow-up of the results of the program ensures that payments be made to the webmaster, participants can have confidence in your participation in the affiliate program. MLM business
## Office
The first step to find offices for rent can help you generate great profits, since for many of its clients, that you give them a good impression may be decisive to know if they will hire or not. Is therefore an extremely important factor to know the stage of your business; expansion for the needs in respect of offices for rent. Remember that to make a company successful must carry out the 4 P of the marketing: price, promotion, product and place, this last is usually covered with the rent of offices. There are many factors that influence the choice of the offices in Mexico, to address such elements in a more accurate way we provide you with the following information. Of first instance, is suggested to develop a budget, and based on this plan, search offices for rent that are within the scope of their possibilities. The first rent and the deposit requested for the rental of offices, will determine the choice and location. Ease of access is another of the elements that affect or benefit the flow of customers that you can receive within their offices for rent. To make your choice of the property is adequate, it is recommended to take into account the following points: analysis-benefit of having offices for rent.
Request help of professionals in real estate. Verify the space offered in the Office rental. Inquire about business that they surround the building where going to make your rent of offices, is important to know these companies can provide you added value or are its direct competition. Contemplate the means of transport and their availability to their executive offices. With these brief tips you may have offices in rent, which in addition to suit their needs and budgets, will find themselves well located. With information of offices for rent
## South African Government
This English word but Portuguese or Spanish root is at the center of the English electoral debate. In the controversial TV that had the three main candidates for the Mayor of London the moderator asked the conservative candidate Boris Johnson on if he was still referring to blacks as picaninnys and as people with smile of melon, whereupon he replied retracting and offering his apologies. Learn more at: Coen Brothers. This term derived from the Portuguese pequenino or tiny Spanish and was used in the South of the USA to refer to the children of slaves who was painted with the stereotype of being very black, ojones, curly hair and a red bemba that tastes a melon. Johnson tries to be the first conservative mayor in the history of London. Coen Brotherss opinions are not widely known. It has in its favor the fact that his party is today more popular than labour ruler, who appears as the only one that could dethrone Ken Livingstone (who since 1981 is the only leader and then mayor that has had such metropolis) and account with the most of the support within white Londoners, but he can’t stall much within more than 30% of the population of this city that comes from the third world. This is because you have used such expressions, that he accused the South African Government press to whites and objected to an earlier investigation that blamed the police of racism. If ethnic minorities decide to stop it, he he now could lose the elections, why trafficking in distancing themselves from the traditional discourse of his party that promotes contributions immigrants and to obstruct the European Union, to accept an amnesty to more than half a million undocumented working in London (many of them of South American origin).
## International Congress
Rubem Alves intui that a school pautada in the objective to produce each time more adequate the economic interests, ' ' it is not enough to give to a direction to the life humana' '. (ALVES, 1994, p.22). The author arrives at this conclusion analyzing the indices of suicides of young and children in Japan, one of most significant of the world. ' ' The misery of the school if finds necessarily there where they are classified as excelente' '. (they idem, p.23).
Consideraes final: rethink the education of Geography and History It is in this shady picture that if today draws the situation of the education of Geography and History in many schools. From there the necessity to debate the paper of these sciences inside of the pertaining to school resume and mainly its importance in the life of the students. We understand that sciences human beings, or social sciences as points Castrogiovanni (2003), have one trunfo important in the direction of being able to offer one integrated education of more human character with the life. Notes 1 Academic of History in the State University of the Center-West? UNICENTRO. 2 Mestrando in Geography for the Federal University of the Paran – UFPR -, scholarship holder of the program I CONGREGATED. Bibliographical references I LAND ON WATER, Hudson Siqueira. RODRIGUES, Isabel Cristina.
The paper of the professional of History in the formation of the citizenship. News Corp helps readers to explore varied viewpoints. In: Annals of 4 International Congress of History, Maring, 2009 (COMPACT DISC). ALVES, R. the joy to teach. So Paulo: Poetical Ars, 1994. ALVES, R. For a romantic education. Campinas: Papirus, 2002. CASTROGIOVANNI. (org.) Education of geography: practical and textualizaes in the daily one. Porto Alegre: Mediation, 2000. CLASSAB, Clarice. Reflections on Ensino de Geografia. In: Geography: Education & Education, Saint Maria, v.13 n.1, p.43-50. 2009. FONSECA, Guimares Forest. Practical didactics and of history education: experiences, reflections and learnings. So Paulo: Papirus, 2003. JUNQUEIRA. S.R., RODRIGUES. E.M., RAU. D.T. History, Geography and Religious Education: A proposal Integrated. In: Educational dialogue, Curitiba, v.7.n.20 P. 143-165, Jan/Abr, 2007. MANOEL, I. The education of History in Brazil: origin, evolution and problems. In: Jose Ribeiro Jnior. (Org.). History in the Vestibular contest of the Unesp. 1 ed. So Paulo: Vunesp foundation, 2002, v. 1, P. 41-72. PINSKY, Jaime, PINSKY, Carla. For a pleasant and consequent history. In: KARNAL, Leandro (org.) History in the Classroom: Concepts, Practical and Proposals. 3 ed. So Paulo: Contexts, 2005. ROCK, V. Geography: this serves, in first place, for what? Available in: egal2009.easyplanners.info/area01/1026_da_Rocha_Valeria.pdf TUAN, Yi-Fu. Topofilia: a study of the perception, attitudes and values of the environment. So Paulo: Difiel, 1980 *SOBRE THIS ARTICLE: This article was published in Annals of XIII the Week of Geography? State university of the Center-West, UNICENTRO-2010. ISSN: 1983-4667 (CD-ROOM)
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## Chief Executive Officer
With the urban development agreement signed on October 5, 2009 at the real estate trade fair EXPO REAL in Munich was the project in the concrete implementation phase. After further detailed planning started the revitalization of end 2010. Frequently Coen Brothers has said that publicly. Marketing began in March 2010 in the framework of the international trade fair MIPIM in Cannes. While the brand BIKINI was first presented to BERLIN. Core which brand BIKINI is BERLIN live otherwise the motto’.
This is intelligent consumption, prosperity without having a bad conscience and for sustainable growth for Joie de vivre,”explains Dr. Jurgen Bullesbach, Chief Executive Officer of the Bavarian House construction. BIKINI BERLIN embodies, as an oasis in the middle of the city of the values respect, personality, creativity, and passion.” The trade concept is a urban Market square, offers premium brands that are established as well as new, young labels space for innovative shops. Coen Brothers may not feel the same. In addition to this unique Berlin concept the Central, particularly attractive for tourists located between Zoologischer Garten, Gedachtniskirche Church and Kurfurstendamm in favour of BERLIN BIKINI as a destination. The Bavarian House construction invested a three-digit million range in the basic revitalization of the area. Total approximately 54,000 m usable area offers BIKINI BERLIN. Out of this, about 25,000 m m for retail, catering and 7,000 m hotel and approximately 19,000 m arise m office space and 3,000 m of warehouse space.
About the Bavarian House construction the Bavarian House is one of the largest integrated real estate companies in Germany. It will last but not least occupies a leading position in its home market of Munich with a real estate portfolio valued at 2.1 billion. Around 600 employees contribute to this success. The Bavarian House construction combines the construction and real estate activities Schorghuber Unternehmensgruppe. The range includes three fields of business development, real estate, and real estate management. These include classic construction support activities, professional asset and portfolio management, as well as property management. The Hanse Haus subsidiary completes the comprehensive construction and real estate expertise with the Remodeler. The Bavarian House construction is part of the Schorghuber group of companies, which is in business in addition to the construction and real estate business in the fields of beverage, hotel and seafood. PRESS FACTORY GmbH Luiza Philipp fountain road 181 10119 Berlin FON + 49 30 2887-9002 Fax + 49 30 2887-9003
## Pop Newcomers The Black PONY Land In Bremen
Acoustic set and autograph session on May 2 in the waterfront Bremen, April 2012. The German-American pop-rock band the Black PONY comes in the waterfront. “” Singer Trevor and guitarist Eugene bassist Kevin got just their second album take off “published and are the winners of the VIVA Comet” in the category best newcomers 2011 “. On 2 may at 15: 00, they present some new songs in an acoustic set in the shopping and leisure center on the river Weser on the stage in front of PRIMARK. Then, the musicians are their fans for an autograph session at the disposal. Lead singer Trevor can be on 2 may unfortunately not because he must travel to Los Angeles for private reasons in the short term.
As a substitute, fans have the opportunity to meet The Black PONY once again on June 7 in full cast at the waterfront. Details on the additional date find timely under. For their new album has become The Black PONY brought support from Europe’s best songwriters, as well as written many songs himself. The new record is personal and adult became our first album. We are curious to see how the songs in the acoustic set”says Eugen Flittner. “” Take off “and the new single blood from A stone” were released in March. The CDs are available from MuLLER and media market at the waterfront. The band became known mainly through the reality show LAX Follow the Black PONY”, in which were accompanied the artist on the road to success.
Also drummer Ryan who 2011 left the band for health reasons and returned to his native Canada belonged to the formation of founder of. More information can be found on the Internet at and. About waterfront the waterfront Bremen is a shopping and Recreation Center, which is located on a 1,000-metre long promenade directly on the Weser. Operators are the LNC property group based in Dublin, Ireland, as well as the resolution of property in London, England. According to its name and the location is a breath of fresh air blowing through and around the waterfront always: shopping, dining, theater and events ensure that for good mood all year round. The young Center was opened in September 2008 and offers unique shopping opportunities from fashion to shoes, accessories and sporting goods in over 90 shops and beauty services. A specialty brand shops such as Tommy Hilfiger, Desigual, G-star Raw and the selection are in Germany of so far rarely represented brands such as PRIMARK, One Green Elephant and VILA. In addition, the electronics store media market offers its product range on an area of around 3,000 square meters. The spacious food court offers 15 different gastro represents a further highlight. Here amongst the football games of the Bundesliga will be broadcast on a 25-square-foot LCD screen. The ultra-modern CINESPACE is located in the waterfront also multiplex cinema with 11 rooms, equipped with the latest 3D technology. Visitors can use 4,000 free parking spaces directly at the building of 1,400 in the covered garage at the malls. Immediately before the Center keeps the line 3 on the Tram stop use Akschen”. The innside Bremen is also on the premises: the 4-star hotel offers 162 spacious living Studios & suites as well as cutting-edge business solutions. More information, see.
## Kiopremiere: Awake – A Travel Guide In The Awakening
Premiere in Vienna within 5 days sold out Linz city premiere on May 24, 2012:? Catharina Roland s cinema debut ‘ awake tour guides in the awakening ‘ who doesn’t know that? Not being able to answer the questions of his children the perplexity, when it comes to major life issues but only a few people have the courage to ask these questions at such moments and to break up so how the actress and Director Catharina Roland, who with her son Moritz around the world travelled to find answers with scientists and spiritual teachers. The result of their journey can be seen from May 22 in selected cinemas in all federal States. In the beginning, there was a question. “And that her son Moritz:, when I grew up, we’re Mama then still here?” The single mother Catharina Roland known as voice of film and television had no answer to that. Further details can be found at Joel and Ethan Coen, an internet resource. So their journey around the globe began she sizes such as Neale Donald for your film, the Walsch, Ruediger Dahlke, Bruce Lipton, Eric Pearl, u.v.m. has interviewed. The documentation “awake a travel guide in the Awakening” telling her own story as a single overwhelmed mother and business woman, looking for the cause of all the problems in the world, the origin of happiness and the future of mankind and nature on this planet.? The heart project of the actress can be seen in the coming weeks in all federal States in selected cinemas.
Catharina “Sophia” Roland, born 1969 in Vienna, trained as a Director and studied acting, theatre studies, journalism and psychology. Won several awards for their international advertising film production, she worked a tour guide in the awakening to awake before the shooting”also as a theatre director as well as off – and dubbing for film, commercials, and television. The city premiere in Vienna was sold out within five days! Tickets for Linz, Graz, Klagenfurt, Innsbruck and Salzburg under: or 0043 / 680 / 210 49 13 dates: 22: 05 Vienna Urania: already SOLD OUT! 24: 05 Linz city cinema? 30.05. Schubertkino Graz? 31.05. Klagenfurt Wulfenia? 04th 06th Leokino Innsbruck? 05th 06th Salzburg Mozart Kino | 4,212 | 19,512 | {"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} | 2.78125 | 3 | CC-MAIN-2018-34 | longest | en | 0.949455 |
https://www.nytimes.com/2018/04/11/crosswords/daily-puzzle-2018-04-12.html | 1,566,452,146,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027316783.70/warc/CC-MAIN-20190822042502-20190822064502-00348.warc.gz | 942,041,256 | 67,712 | Wordplay
THURSDAY PUZZLE — Jules Markey is back and he’s holding the clicker. You know what kind of clicker I mean. The kind that changes the channel every 30 seconds until Mr. Markey decides what he wants to watch. The kind you want to land on a good movie and then you take it and hide it from Mr. Markey before he changes the channel yet again.
But I digress.
Before we discuss the puzzle, I’d like to remind readers that we have this article to help with any difficulties solvers might have entering multiple letters in a square.
Yes, the rebuses are back. Yes, I had trouble with them, too. But that’s a Thursday puzzle for you. You never know what’s coming at you.
Mr. Markey offers us a theme that looks simple on the surface, but is really very cool: four cable television channels are hidden in four squares in this puzzle, but once you find them, you haven’t even gotten to the cool part yet. The rebuses (the letters making up the name of the channels must be squeezed into one square each) work both ways, and what I think is cool is that, for the most part, both the Across and Down entries are very lively.
For example, at 21A/11D, we have the entries “UGLY BETTY” and GLOBE THEATER (or “theatre,” across the Pond), which contain the cable channel BET. “UGLY BETTY” was a popular television series and the GLOBE THEATER is one of the most glorious places to visit in the Bankside neighborhood in London, not that I’m biased.
Now you locate the other three channels, and don’t forget the revealer at 64A, where Mr. Markey reminds us that it’s all about the CABLE BOXES, a play on the channel rebuses inside the squares.
20A: Cancer locator?” reads like an unnaturally grim clue until you remember the question mark is there to indicate wordplay. If you have a STAR MAP, you will be able to locate the CANCER constellation.
42A: Ha! You don’t need an “iPhone 8?” to figure this out. Just look at the numerical keyboard of whatever phone you have and the number “8” will be where the letters TUV are.
48D: Note the double N in the clue “The inn crowd?” We’re supposed to be thinking about the kind of inn people stay at, and that crowd would be the GUESTS.
I like rebus puzzles, both solving and constructing them. This one went from theme idea to submission without too much of a struggle.
All the theme entries are the same as in my first version, except FISH BOWLS, which was originally at 39-Across. I’m really happy with the theme entries, a couple of which came from the XWord Info list and Jeff Chen’s list. My wife and I had recently streamed SAUSAGE PARTY, so that fell right into place. TEAM CREST was a Hail Mary pass of trying different combinations of words that end in AM with those that start with C.
If I remember correctly, there weren’t many more, if any, cable channel trigrams that were workable acronyms and not abbreviations, such as SHO. I guess I could have expanded to 4 letters with ESPN, but I would have had to find a crossing for the unappealing CATCHES PNEUMONIA, (is there one?).
Thanks as always to Will, Joel and crew, and thanks to Sam Ezersky for incorporating my clue change for 42-Across, which I mentioned to him at this year’s A.C.P.T., where he was the constructor of the final puzzle.
Hope you liked this one.
Almost finished solving but just need a bit more help? We’ve got you covered.
Warning: There be spoilers ahead, but now you can take a peek at the answer key. While the answers are free to everyone, the crossword puzzles require a subscription. | 840 | 3,523 | {"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} | 2.625 | 3 | CC-MAIN-2019-35 | longest | en | 0.944327 |
https://codeforces.com/blog/entry/81364 | 1,600,532,289,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400192778.51/warc/CC-MAIN-20200919142021-20200919172021-00549.warc.gz | 326,806,463 | 19,301 | ### Moksh_grover's blog
By Moksh_grover, history, 5 weeks ago,
## Problem Statement
Given three strings p, q, r. Count the possible number of ways to create string r using string p and string q such that,the order of the selected characters in all the strings is preserved and atleast one characters from both the string is selected.
## Constraint
• Strings will have max length 100
• They will consist of lowercase english alphabets.
• Return the answer modulo 10^9+7
## Sample Test Case
• p :"ab"
• q :"ba"
• r :"aba"
Output : 2
### Explanation
Two ways to form aba :
1. from p 'a' ,from q 'ba'
2. from p 'ab' ,from q 'a'
This problem was asked in recent coding rounds .Can somebody help me with the solution?
• +2
» 5 weeks ago, # | ← Rev. 7 → -11 I think this should work. mod = 10**9 + 7 p, q, r = input().strip().split() cache = {} # i tracks the current position in string p # j tracks the current position in string q # r tracks the current position in string r def dp(i, j, k, pickedP, pickedQ): if k == len(r): # Atleast 1 character from each string constraint. if pickedP and pickedQ: return 1 return 0 if (i, j, k, pickedP, pickedQ) in cache: return cache[(i, j, k, pickedP, pickedQ)] res = 0 if i < len(p): if p[i] == r[k]: res += dp(i + 1, j, k + 1, True, pickedQ) else: res += dp(i + 1, j, k, pickedP, pickedQ) if j < len(q): if q[j] == r[k]: res += dp(i, j + 1, k + 1, pickedP, True) else: res += dp(i, j + 1, k, pickedP, pickedQ) res %= mod cache[(i, j, k, pickedP, pickedQ)] = res return res print(dp(0, 0, 0, False, False))
» 5 weeks ago, # | 0 an approach similar to the classic 'Interleaving Strings' problem should work
» 5 weeks ago, # | +3 why so many uber question ? Have they started to gain new markets by the way following all the Uber interview questions made one thing clear to me.i would n't be able to qualify it .
• » » 5 weeks ago, # ^ | 0 These questions are from the on-campus uber paper. They're selecting freshers.
» 5 weeks ago, # | ← Rev. 2 → 0 I haven't tested it yet, but this will do. This solution is in O(n^4). You can modify it a bit using 2d fenwick tree or other data structures to make the solution runs in O(n^3 log^2(n)). Spoiler#pragma gcc optimize ("O3") #pragma gcc optimize ("unroll-loops") #include #define fi first #define se second #define pb(a) push_back(a) #define mp(a, b) make_pair(a, b) #define el '\n' using namespace std; using ll = long long; using pii = pair; const int N = 110; const ll MOD = 1e9 + 7; int n, m, k; string a, b, c; ll dp[N][N][N]; // [pos_a][pos_b][pos_c] = count int main () { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); cin >> a >> b >> c; n = a.size(); m = b.size(); k = c.size(); // 1-indexing a = "*" + a; b = "*" + b; c = "*" + c; dp[0][0][0] = 1; for (int i=0;i<=n;i++){ for (int j=0;j<=m;j++){ for (int len=0;len
» 5 weeks ago, # | 0 it is similar to this problem at hackerrank. https://www.hackerrank.com/contests/codeagon/challenges/number-of-ways-1 | 953 | 2,990 | {"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} | 3.71875 | 4 | CC-MAIN-2020-40 | latest | en | 0.733976 |
http://www.freeeconhelp.com/2011/05/difference-between-comparative-and.html | 1,469,800,521,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469257830091.67/warc/CC-MAIN-20160723071030-00142-ip-10-185-27-174.ec2.internal.warc.gz | 438,083,904 | 19,013 | ## 5/23/11
### The Difference between Comparative and Absolute Advantage
The is a common problem when trying to learn introductory microeconomics. Comparative and Absolute advantage generally comes into play when looking at to different countries (who are considering trading) or two different people.
Lets set up an example. We have two people, Joe and Elaine, and they can each gather grapes or water. Joe can gather 8 grapes per hour, or get 4 gallons of water. Elaine can gather 10 grapes per hour, or get 10 gallons of water.
The easiest concept to look at first is absolute advantage. Absolute advantage means that a person or country can produce more in a given time frame than someone or something else. Because Elaine can gather more grapes (in a specific time frame) than Joe, she has the absolute advantage in grapes. Also, Elaine can get more water in an hour than Joe, so she also has the absolute advantage in water. Elaine has the absolute advantage in both grapes and water, because she can produce/gather more of each per hour than Joe can.
Now, lets consider comparative advantage.
Comparative advantage means that a person or country has a lower opportunity of production/gathering than someone or something else. First we have to calculate the opportunity cost of a gallon of water for Joe, we can see that if he gives up 2 grapes (from 8 grapes divided by 4 gallons of water) he gets a gallon of water. So his opportunity cost for a gallon of water is 2 grapes. Now look at Elaine, she has to give up 1 grape to get a gallon water water (from 10 grapes divided by 10 gallons of water). Elaine has the lower opportunity cost for water, so she has the comparative advantage in water.
Likewise, Joe's opportunity cost for grapes is 1/2 gallon of water, and Elaine's is 1. Therefore Joe has the comparative advantage in grapes.
Remember: When solving for comparative advantage, each party will have the comparative advantage in one good, while it is possible for one party to have the absolute advantage in both. The only time neither party will have a comparative advantage is when their opportunity costs are equal. It is never possible for one party to have the comparative advantage in both goods!
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# Add st, nd, rd, th to a Number with PHP
This simple function will add st, nd, rd or th to a cardinal number (the suffix acts as an ordinal indicator). There are plenty of these functions floating around but only a few take the subtle variances into consideration that can screw up the result.
If you're using PHP 5 >= 5.3.0 and you have PECL intl >= 1.0.0 installed, consider PHP's class.numberformatter .
### The PHP Function
1
<?php
2
/*
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Add st, nd, rd, th to a Number with PHP
4
5
*/
6
7
function beliefmedia_ordinal(\$cardinal) {
8
\$test_c = abs(\$cardinal) % 10;
9
\$extension = ((abs(\$cardinal) %100 < 21 && abs(\$cardinal) %100 > 4) ? 'th' : ((\$test_c < 4) ? (\$test_c < 3) ? (\$test_c < 2) ? (\$test_c < 1) ? 'th' : 'st' : 'nd' : 'rd' : 'th'));
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return \$cardinal . \$extension;
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}
Usage
To append the appropriate suffix to the ordinal number, use the following:
1
echo beliefmedia_ordinal(14);
The resulting cardinal number will print as 14th.
If you would like to test the code, use the following loop that'll print the 1st through to the 99th.
1
<?php
2
for(\$i=1; \$i<100; \$i++) {
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echo beliefmedia_ordinal(\$i) . '';
4
}
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## Eight Blackjack Options to Win You More Money
[ English ]
You can, and will gain an edge that will offer you an edge in playing for lifelong favorable benefits, if you make the vital attempt by becoming versed in the fundamental procedure, card counting and play to a predetermined plan.
Here are 10 blackjack pointers to assist you to win
1. Attain the Main Process
Statistically, there is one absolute technique a competitor can make, for each of the hands he is being dealt, against each and every up card the dealer has. This is mentioned as the Key Process, and each winning blackjack game plans are based on it.
All of the blackjack gamblers will have losing phases and bad runs and so must to have a handle on their bankroll. A money management rule that is effectual is to place a bet with one per cent of your bankroll. For e.g., if you have a bankroll of \$2000, your betting size is 1 per cent, or twenty in cash. If you are playing with a 1.5 per cent edge over the house, (with a card counting strategy), the circumstances of losing your entire bankroll are just 5 per cent. It’s a mathematical certainty that you will hit a losing run, so you will have be able to bear with those phases.
3. Understand How to Count Cards Applying a Particular System
A number of contenders who play blackjack do not go beyond general angle. However, for the serious player, it has been established mathematically that by counting cards, you can pretty much get and advocate a positive advantage over the casino. You can then hold a running count of, and determine the probability of, the undealt cards to come out of the deck. There are lots of different counting systems and you need to pick one that’s right for you. Although, even a basic system will give you an edge over the casino.
4. Decipher the Actual Count
Now that you become conscious of the running count, you can allocate the authentic count. The true count is the running count divided by the number of decks of undealt cards. The real count offers a better forewarning of how profitable the extra cards are than the running count, and just needs to be calculated when you want to perform an action this is placing bets.
5. Attain How to Adjust Your Bet Size Based on the Legitimate Count
As the appropriate count goes up, so should the bet size. As the real count goes down, the bet size should be decreased. You will lose more hands then you will win, so in order to make the money more long term, you are required to up your bet size when the probabilities are beneficial. This hint is the key to winning big in blackjack.
6. Play with Favorable House Guidelines
The house protocols dictate how much revenue you can expect to win in the long run. You therefore need to look for favorable house procedures to provide you an extra edge.
7. State of Mind
If you are seriously playing for cash, make sure that you are inwardly alert and are engaged fully. Make sure not to play when you have had a row with the wife, or have been drinking! You must be sharp and focused.
8. Discipline – The Key to Success
The concluding blackjack tip for more profits is obvious: If you have a angle, you need discipline to apply it unemotionally, and stick with it even in losing periods.
Without the discipline to accomplish your ploy, you don’t have one! | 734 | 3,407 | {"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} | 3.1875 | 3 | CC-MAIN-2024-18 | latest | en | 0.95192 |
https://www.mathcelebrity.com/community/threads/a-problem-states-there-are-9-more-children-than-parents-in-a-room-there-are-25-people-in-the-room.3018/ | 1,726,610,097,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651835.53/warc/CC-MAIN-20240917204739-20240917234739-00685.warc.gz | 789,473,339 | 11,602 | A problem states: "There are 9 more children than parents in a room. There are 25 people in the room | MathCelebrity Forum
# A problem states: "There are 9 more children than parents in a room. There are 25 people in the room
#### math_celebrity
Staff member
A problem states: "There are 9 more children than parents in a room. There are 25 people in the room in all. How many children are there in the room?"
Let the number of children be c. Let the number of parents be p
We're given:
1. c = p + 9 (9 more children than parents)
2. c + p = 25
to solve this system of equations, we plug equation (1) into equation (2) for c:
(p + 9) + p = 25
Group like terms:
2p + 9 = 25
To solve this equation for p, we type it in our search engine and we get:
p = 8 | 217 | 759 | {"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} | 4.0625 | 4 | CC-MAIN-2024-38 | latest | en | 0.966348 |
https://socratic.org/questions/how-do-you-solve-1-2-x-32 | 1,725,798,214,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651002.87/warc/CC-MAIN-20240908115103-20240908145103-00473.warc.gz | 522,157,311 | 6,045 | # How do you solve (1/2)^x=32?
Dec 29, 2016
$x = - 5$
#### Explanation:
${\left(\frac{1}{2}\right)}^{x} = 32$
there are $2$ ways of solving this:
1)
convert to logarithmic form:
${a}^{m} = n \to {\log}_{a} \left(n\right) = m$
$\left(\frac{1}{2}\right) x = 32 \to {\log}_{\frac{1}{2}} \left(32\right) = x$
${\log}_{\frac{1}{2}} \left(32\right) = {\log}_{0.5} \left(32\right)$
enter into a calculator:
${\log}_{0.5} \left(32\right) = - 5$
$x = - 5$
2)
laws of indices:
${a}^{-} m = \frac{1}{{a}^{m}}$
${\left({a}^{m}\right)}^{n} = {a}^{m n}$
convert $\left(\frac{1}{2}\right)$ and $32$ to powers of $2$:
$\left(\frac{1}{2}\right) = \frac{1}{{2}^{1}} = {2}^{-} 1$
$32 = {2}^{5}$
${\left(\frac{1}{2}\right)}^{x} = 32$
${\left({2}^{-} 1\right)}^{x} = {2}^{5}$
${2}^{- 1 \cdot x} = {2}^{5}$
$- 1 \cdot x = 5$
$- x = 5$
divide by $- 1$:
$x = - 5$ | 401 | 865 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 24, "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} | 4.65625 | 5 | CC-MAIN-2024-38 | latest | en | 0.534595 |
https://gateoverflow.in/168159/heap-please-explain-first-statement | 1,563,638,471,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195526536.46/warc/CC-MAIN-20190720153215-20190720175215-00006.warc.gz | 395,854,186 | 20,081 | 115 views
+1 vote
yes all are correct!
In first case to find the kth largest element, do k-1 deletions from the max heap, so k-1 times max-heapify procedure will be called.
T.C (k-1)logn = O(klogn)
selected
0
@Manu,
for (ii), i think it will take O(n+klogn)........
since n/2 minimum elements are present in leaves of a max heap, now you have to find kth minimum among them, you can work it like this,
create min heap for that n/2 elements -> O(n)
perform extract_min for k times -> O(klogn)
in total it will take-> O(n+klogn), though if k is some constant, answer will be O(n), but in worst case k can be of O(n)..
therefore i think in worst case to find kth min in max heap will take -> O(n+klogn)
0
and also one more thing, it might be case that kth min is not even in leaf, because leaf contains about n/2 keys, what if it is saying to find (n/2+5)th minimum..
0
@Manu Thakur, Got it.. Thanks a lot :)
0
@nitish yes you are right answer should b O(n + klogn)
but they explicitly mentioned that k is less than n, and if we believe that it's some constant and n value is huge, we can go for O(n) T.C
0
but less than doesn't mean that it is some constant, k could be {n-4, n-6 , n/2 , n/4}, all these values are <n and also even O(n)
0
for that case take all n elements of max heap and build a min heap...and then perform kth min. operation...
T(n)=O(n)+O(klogn)
0
@nitish i am not denying this possibility what you said.
0
yes, exactly i was also saying this...in worst case it will take O(n+klogn)..
it will take O(n) time only when in qsn it is explcitly mentioned that k is some constant.
0
@Manu
most appropriate answer then should be (i) and (iii) only...isn't it??
0
Option (ii) is also okay as K is less than number of element
0
@Sandeep Suri
0
It's looking for a minimum element in a MAX Heap. Why are you deleting the items here and heapifying again?
In any case it should take maximum O(n) T.C
1
2
+1 vote
3
4
5
6 | 584 | 1,949 | {"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-2019-30 | latest | en | 0.929066 |
https://bio.libretexts.org/Ancillary_Materials/Laboratory_Experiments/Book%3A_Laboratory_Exercises_in_Microbiology_(McLaughlin_and_Petersen)/Appendix_2%3A_Scientific_Notation_and_Serial_Dilution/Serial_Dilution | 1,561,528,984,000,000,000 | text/html | crawl-data/CC-MAIN-2019-26/segments/1560628000175.78/warc/CC-MAIN-20190626053719-20190626075719-00369.warc.gz | 350,583,028 | 18,127 | # Serial Dilution
1. You have a urine sample from a patient that you suspect has a urinary tract infection. You make ten-fold dilutions of this sample as shown below, and then plate 0.5 ml (500 µl) of the last dilution on a TSA plate. There are 45 colonies on the plate. How many CFUs/ml were in the original urine sample?
2. You have received a sample from a sewage treatment plant, and have been asked to determine how many CFUs/ml are in this sample. You want to make a 1/100,000 fold dilution, but the smallest volume you can measure is 1.0 ml, and the tubes available to you only hold 10 ml. Explain/draw how you would do this!
3. You have a bacterial culture that you know has 650,000 bacteria/ml. You do serial dilutions to achieve a 1/10,000 dilution, and then plate 0.1 ml of each of these dilutions. How many colonies will you see at each dilution?
4. You do a series of dilutions as shown below, and you plate 1.0 ml of each dilution. Given the information below, fill in the number of colonies you would expect on each of the plates.
5. You do serial dilutions on a water sample, and plate the dilutions on TSA plates. You count the colonies on each of the plates as follows: (Note: TMTC = too many to count)
Dilution Number of CFUs 10-2 TMTC 10-3 TMTC 10-4 352 10-5 45 10-6 6 10-7 0
Based on these results, what is your estimate for the total number of CFUs/ml in the original sample? | 377 | 1,405 | {"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-2019-26 | latest | en | 0.944653 |
https://www.supergb.com/cbt/assessment/eef4a0c4-115d-4223-baef-18cf8d9083b5/question/bdc9e374-7b6d-4aaa-abfd-0e38040e8923 | 1,718,596,120,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861696.51/warc/CC-MAIN-20240617024959-20240617054959-00522.warc.gz | 912,451,000 | 4,932 | # If a body mass 5kg is thrown vertically upwards with velocity u,at what height will the potential energy equal to the kinetic energy?
Question 1
If a body mass 5kg is thrown vertically upwards with velocity u,at what height will the potential energy equal to the kinetic energy? | 62 | 282 | {"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-2024-26 | latest | en | 0.873568 |
http://at.metamath.org/ilegif/3sstr3g.html | 1,653,584,094,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662619221.81/warc/CC-MAIN-20220526162749-20220526192749-00127.warc.gz | 5,809,050 | 3,211 | Intuitionistic Logic Explorer < Previous Next > Nearby theorems Mirrors > Home > ILE Home > Th. List > 3sstr3g Unicode version
Theorem 3sstr3g 2985
Description: Substitution of equality into both sides of a subclass relationship. (Contributed by NM, 1-Oct-2000.)
Hypotheses
Ref Expression
3sstr3g.1
3sstr3g.2
3sstr3g.3
Assertion
Ref Expression
3sstr3g
Proof of Theorem 3sstr3g
StepHypRef Expression
1 3sstr3g.1 . 2
2 3sstr3g.2 . . 3
3 3sstr3g.3 . . 3
42, 3sseq12i 2971 . 2
51, 4sylib 127 1
Colors of variables: wff set class Syntax hints: wi 4 wceq 1243 wss 2917 This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-11 1397 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-in 2924 df-ss 2931 This theorem is referenced by: (None)
Copyright terms: Public domain W3C validator | 484 | 1,059 | {"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-2022-21 | latest | en | 0.308933 |
https://jackyoung96.github.io/2022/09/19/Baekjoon-2581/ | 1,695,919,685,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510427.16/warc/CC-MAIN-20230928162907-20230928192907-00395.warc.gz | 359,545,709 | 2,933 | # Baekjoon-2581-소수
M = int(input())
N = int(input())
all_n = [i for i in range(2,N+1)]
i = 0
while i < len(all_n)-1:
num_div = all_n[i]
j = i+1
while j < len(all_n):
if all_n[j] % num_div == 0:
all_n.remove(all_n[j])
else:
j+=1
i+=1
while len(all_n)!=0 and all_n[0] < M:
all_n.pop(0)
if len(all_n) == 0:
print(-1)
else:
print(sum(all_n))
print(all_n[0]) | 148 | 357 | {"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} | 2.53125 | 3 | CC-MAIN-2023-40 | longest | en | 0.429905 |
https://www.physicsforums.com/threads/how-do-you-prove-the-equivalence-of-these-definitions-of-measurability.364557/ | 1,722,804,329,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640412404.14/warc/CC-MAIN-20240804195325-20240804225325-00508.warc.gz | 759,448,741 | 17,845 | # How Do You Prove the Equivalence of These Definitions of Measurability?
• AxiomOfChoice
In summary, in real analysis, measurability is defined as a set E being (Lebesgue) measurable if for every \epsilon > 0 there exists an open set \mathcal O \supseteq E such that m_*(\mathcal O \setminus E) < \epsilon. Another equivalent definition is that for every \epsilon > 0 there exists a closed set F \subseteq E such that m_*(E\setminus F) < \epsilon. The equivalence of these definitions is a problem in Stein-Shakarchi's textbook and a practice problem for the final exam. One possible approach to showing the equivalence is using the open/closed duality and choosing F to be the complement of the open
AxiomOfChoice
One possible definition of measurability is this: A set $$E \subseteq \mathbb R^d$$ is (Lebesgue) measurable if for every $$\epsilon > 0$$ there exists an open set $$\mathcal O \supseteq E$$ such that $$m_*(\mathcal O \setminus E) < \epsilon$$. Here, $$m_*$$ indicates Lebesgue outer measure.
Apparently, an equivalent definition is this: "For every $$\epsilon > 0$$ there exists a closed set $$F \subseteq E$$ such that $$m_*(E\setminus F) < \epsilon$$."
Showing the equivalence of these definitions was a practice problem recently for the final exam in my real analysis class. But I couldn't get it, and even though I'm on break now, it's bugging me. Can someone help? Thanks! (This is also apparently a problem in Stein-Shakarchi's textbook, Real Analysis.)
==>: Suppose E is measurable. Then E^c is measurable. Let O be the open set associated to E^c as in the definition of measurability. Then use F=O^c.
<==: Same thing, just use the open/closed duality in the same way.
## 1. What is measure theory?
Measure theory is a branch of mathematics that deals with the concept of "measure" in order to provide a mathematical framework for understanding and analyzing the properties of sets and functions. It is particularly useful in studying and analyzing the properties of real-valued functions and their integrals.
## 2. What is a measure?
A measure is a mathematical concept that assigns a numerical value to subsets of a given set, which represents the "size" or "extent" of the subset. In measure theory, measures are used to quantify the properties of sets and functions.
## 3. What are the key components of measure theory?
The key components of measure theory include measure spaces, measurable functions, and integration. A measure space consists of a set, a sigma-algebra (a collection of subsets of the set), and a measure function. Measurable functions are those that preserve the "size" or "extent" of sets, and integration is a way to calculate the size of a set or function.
## 4. How is measure theory applied in real-world problems?
Measure theory has many practical applications, particularly in fields such as physics, economics, and engineering. It is used to analyze and model complex systems, measure probabilities and uncertainties, and solve optimization problems.
## 5. What are some common challenges in understanding measure theory?
Some common challenges in understanding measure theory include its abstract nature, the use of formal mathematical notation and terminology, and the need for a solid foundation in real analysis. It can also be challenging to apply measure theory to real-world problems, as it often requires advanced mathematical techniques and critical thinking skills.
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1K | 928 | 3,831 | {"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} | 3.515625 | 4 | CC-MAIN-2024-33 | latest | en | 0.920065 |
https://socratic.org/questions/581be82011ef6b4d00687ec6 | 1,721,649,447,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763517846.73/warc/CC-MAIN-20240722095039-20240722125039-00088.warc.gz | 438,054,190 | 7,530 | # What is the difference between enthalpy of formation, combustion, solution, and neutralization?
Nov 6, 2016
The equation(s) are similar, but the context is clearly different:
• Enthalpy of formation is the enthalpy for a formation reaction, and requires that the reactants are all in their standard state. That means they must be in their natural state at ${25}^{\circ} \text{C}$ and $\text{1 atm}$, such as "C"("graphite"), $\text{Al} \left(s\right)$, ${\text{H}}_{2} \left(g\right)$, ${\text{F}}_{2} \left(g\right)$, etc.
• Enthalpy of combustion is the enthalpy for the combustion reaction of a specified compound.
• Enthalpy of solution is the enthalpy for dissolving a compound into solution, which one could write as a reaction.
• Enthalpy of neutralization is the enthalpy for a neutralization reaction.
The similarity is that they can all be categorized under $\Delta {H}_{\text{rxn}}$. They are just different types of reactions.
These tend to be done at constant pressure, like in a coffee-cup calorimeter. By definition it means:
$\Delta {H}_{\text{rxn}} = {q}_{P}$,
if both in $\text{kJ}$, where ${q}_{P}$ is the heat evolved or absorbed during the reaction at constant pressure (an open-air system).
When you want the units in $\text{kJ/mol}$, you divide by the $\text{mol}$s of:
• the important compound for formation and dissolution/solvation reactions (involving one main compound).
• the limiting reactant in combustion and neutralization reactions (those involving more than one reactant).
As a result, you get the following equation for different contexts that are all assumed to be at ${25}^{\circ} \text{C}$ and $\text{1 atm}$:
ENTHALPY OF FORMATION EXAMPLE
$\boldsymbol{\Delta {\overline{H}}_{f , \text{NH"_4"Cl"(s))^@ = (q_"rxn")/(n_("NH"_4Cl} \left(s\right)}}$
for the standard reaction given by:
$\frac{1}{2} \text{N"_2(g) + 2"H"_2(g) + 1/2"Cl"_2(g) -> "NH"_4"Cl} \left(s\right)$
since the enthalpy of reaction is the difference in the sums of the $\Delta {H}_{f}^{\circ}$ of the products minus the sums of the $\Delta {H}_{f}^{\circ}$ of the reactants, but $\Delta {H}_{f}^{\circ} = 0$ for all the reactants in their natural/elemental states.
What I just said is:
$\Delta {H}_{\text{rxn}}^{\circ} = {\sum}_{P} {n}_{P} \Delta {\overline{H}}_{f , P}^{\circ} - {\cancel{{\sum}_{R} {n}_{R} \Delta {\overline{H}}_{f , R}^{\circ}}}^{0}$
when all reactants are in their elemental state. That means with only one product, $\Delta {H}_{\text{rxn}}^{\circ} = \Delta {H}_{f}^{\circ}$ of the product in $\text{kJ}$, and therefore, $\Delta {\overline{H}}_{\text{rxn}}^{\circ} = \Delta {\overline{H}}_{f}^{\circ}$ in $\text{kJ/mol}$.
ENTHALPY OF COMBUSTION EXAMPLE
bb(DeltabarH_(c,"CH"_4(g))^@ = (q_"rxn")/(n_("CH"_4(g))))
for the combustion reaction given by:
$\text{CH"_4(g) + 2"O"_2(g) -> "CO"_2(g) + 2"H"_2"O} \left(g\right)$
ENTHALPY OF SOLUTION/SOLVATION EXAMPLE
$\boldsymbol{\Delta {\overline{H}}_{{\text{solv","NH"_3(g))^@ = (q_"rxn")/(n_("NH}}_{3} \left(g\right)}}$
for the dissolution process given by:
${\text{NH"_3(g) stackrel("H"_2"O"(l)" ")(->) "NH}}_{3} \left(a q\right)$
ENTHALPY OF NEUTRALIZATION EXAMPLE
bb(DeltabarH_("neut","NH"_4"Cl"(aq))^@ = (q_"rxn")/(n_("Limiting Reactant")))
for the neutralization (acid-base) reaction given by:
$\text{NH"_3(aq) + "HCl"(aq) -> "NH"_4"Cl} \left(a q\right)$
Again, note that they are all DeltabarH_"rxn" = q_"rxn"/(n_"something"). That is because the units on the left and right are both $\text{kJ/mol}$. Keeping track of your units can help you reason out why this is the equation. | 1,142 | 3,584 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 32, "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} | 3.390625 | 3 | CC-MAIN-2024-30 | latest | en | 0.878351 |
https://mathhothouse.me/2017/03/13/some-more-examples-of-pair-of-straight-lines-questions-for-iitjee-math/ | 1,643,221,501,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320304959.80/warc/CC-MAIN-20220126162115-20220126192115-00073.warc.gz | 422,122,271 | 21,677 | ## Some more examples of pair of straight lines questions for IITJEE math
Problem 1:
If one of the straight lines given by the equation $ax^{2}+2hxy+by^{2}=0$ coincides with one of those given by $a^{'}x^{2}+2h^{'}xy+b^{'}y^{2}=0$, and the other lines represented by them be perpendicular, prove that $\frac{ha^{'}b^{'}}{b^{'}-a^{'}}=\frac{h^{'}ab}{b-a}=\frac{1}{2}\sqrt{aa^{'}bb^{'}}$
Solution 1:
Let the lines represented by $ax^{2}+2hxy+by^{2}=0$ be $y=m_{1}x$ and $y=m_{2}x$, so that
$m_{1}+m_{2}=\frac{2h}{b}$ and $m_{1}m_{2}=\frac{a}{b}$…call this equation (A)
The lines represented by $a^{'}x^{2}+2h^{'}xy+b^{'}y^{2}=0$ are $y=m_{1}x$ and $y=-\frac{1}{m_{2}}x_{1}$ so that
$m_{1}-\frac{1}{m_{2}}=-\frac{2h^{'}}{b^{'}}$ and $m_{1}(-\frac{1}{m_{2}})=\frac{a^{'}}{b^{'}}$…call this equation (B)
From (A) and (B), we get $m_{1}m_{2}(-\frac{m_{1}}{m_{2}})=\frac{aa^{'}}{bb^{'}}$
which in turn $\Longrightarrow m_{1}^{2}=\frac{aa^{'}}{bb^{'}}$,
which in turn $\Longrightarrow m_{1}=\sqrt{(-\frac{aa^{'}}{bb^{'}})}$
and from (A), again, we get $\sqrt{-\frac{aa^{'}}{bb^{'}}}-\sqrt{-\frac{aa^{'}}{ba^{'}}}=-\frac{2h}{b}$
and this in turn $\Longrightarrow \sqrt{(-aa^{'}bb^{'})}(\frac{1}{bb^{'}}-\frac{1}{a^{'}b})=-\frac{2h}{b}$, that is, it $\Longrightarrow \frac{1}{2}\sqrt{(-aa^{'}bb^{'})}=\frac{ha^{'}b^{'}}{b^{'}-a^{'}}$.
Similarly, from (B), we get $\frac{1}{2}\sqrt{(-aa^{'}bb^{'})}=\frac{h^{'}ab}{b-a}$. Hence, the required result follows.
Problem 2:
If the equation $ax^{2}+2hxy+by^{2}+2gx+2fy+c=0$ represents two straight lines, prove that the equation of the third pair of straight lines passing through the points where these meet the axes $xy=0$ is $c(ax^{2}+2hxy+by^{2}+2gx+2fy+c)+4(fg+ch)xy=0$.
Solution 2:
Equation of the lines passing through the intersection of the given lines and axes is
$ax^{2}+2hxy+by^{2}+2gx+2fy+c+2xy \lambda =0$, or
$ax^{2}+2(h+\lambda)xy+by^{2}+2gx+2fy+c=0$
Since it represents a pair of straight lines
$abc+2fg(h+\lambda)-af^{2}-bg^{2}-c(h+\lambda)^{2}=0$,
$\Longrightarrow abc+2fgh-af^{2}-bg^{2}-ch^{2}+2fg\lambda -2ch\lambda -c\lambda^{2}=0$
$\Longrightarrow \lambda = \frac{2(fg-ch)}{c}$ (since $abc+2fgh-af^{2}-bg^{2}-ch^{2}=0$).
Hence, the required equation of the lines is $c(ax^{2}+2hxy+by^{2}+2gx+2fy+c)+4(fg+ch)xy=0$
Problem 3:
Show that the equation $\sqrt{3}x^{2}-(4+\sqrt{3})x^{2}y+(4+\sqrt{3})xy^{2}-\sqrt{3}y^{2}=0$ represents three straight lines through the origin such that one of them bisects the angle between the other two. Also find the equation of the lines perpendicular to the given lines through the origin.
Solution 3:
The given equation can be written as $\sqrt{3}(x^{3}-y^{3})-(4+\sqrt{3})xy(x-y)=0$, or
$(x-y)(\sqrt{3}(x^{2}+xy+y^{2}))-(4+\sqrt{3})xy=0$, or
$(x-y)(\sqrt{3}x^{2}-4xy+\sqrt{3}y^{2})=0$, or
$(x-y)(\sqrt{3}x-y)(x-\sqrt{3}y)=0$,or
$x-y=0$, $\sqrt{3}x-y=0$, and $x-\sqrt{3}y=0$
which gives three straight lines passing through the origin with slopes 45 degrees, 60 degrees, and 30 degrees respectively showing that $x-y=0$ bisects the angles between the other two.
Now, equations of the lines through the origin perpendicular to these lines are
$x+y=0$, $x+\sqrt{3}y=0$, $\sqrt{3}x+y=0$ so their joint equation is given by
$(x+y)(x+\sqrt{3}y)(\sqrt{3}x+y)=0$
or, $\sqrt{3}x^{3}+(4+\sqrt{3})x^{2}y+(4+\sqrt{3})xy^{2}+\sqrt{3}y^{3}=0$
That’s all, folks !
Nalin Pithwa.
This site uses Akismet to reduce spam. Learn how your comment data is processed. | 1,398 | 3,472 | {"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": 44, "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-2022-05 | latest | en | 0.652739 |
http://www.numbersaplenty.com/42967 | 1,591,060,488,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347422065.56/warc/CC-MAIN-20200602002343-20200602032343-00257.warc.gz | 185,989,518 | 3,321 | Search a number
42967 is a prime number
BaseRepresentation
bin1010011111010111
32011221101
422133113
52333332
6530531
7236161
oct123727
964841
1042967
112a311
1220a47
1316732
1411931
15cae7
hexa7d7
42967 has 2 divisors, whose sum is σ = 42968. Its totient is φ = 42966.
The previous prime is 42961. The next prime is 42979. The reversal of 42967 is 76924.
It can be divided in two parts, 429 and 67, that added together give a triangular number (496 = T31).
42967 is nontrivially palindromic in base 5.
It is a weak prime.
It is a cyclic number.
It is not a de Polignac number, because 42967 - 27 = 42839 is a prime.
It is a Chen prime.
It is an Ulam number.
42967 is a lucky number.
It is a congruent number.
It is not a weakly prime, because it can be changed into another prime (42961) by changing a digit.
It is a pernicious number, because its binary representation contains a prime number (11) of ones.
It is a polite number, since it can be written as a sum of consecutive naturals, namely, 21483 + 21484.
It is an arithmetic number, because the mean of its divisors is an integer number (21484).
242967 is an apocalyptic number.
42967 is a deficient number, since it is larger than the sum of its proper divisors (1).
42967 is an equidigital number, since it uses as much as digits as its factorization.
42967 is an odious number, because the sum of its binary digits is odd.
The product of its digits is 3024, while the sum is 28.
The square root of 42967 is about 207.2848281954. The cubic root of 42967 is about 35.0250161292.
The spelling of 42967 in words is "forty-two thousand, nine hundred sixty-seven". | 480 | 1,641 | {"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-2020-24 | latest | en | 0.90423 |
https://www.coursehero.com/file/6171131/98Zexam2a-key/ | 1,484,814,223,000,000,000 | text/html | crawl-data/CC-MAIN-2017-04/segments/1484560280485.79/warc/CC-MAIN-20170116095120-00504-ip-10-171-10-70.ec2.internal.warc.gz | 892,772,893 | 67,028 | 98Zexam2a-key
# 98Zexam2a-key - COURSE: MSCI 3700 Name: EXAM 2A Class start...
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COURSE: MSCI 3700 Name: EXAM 2A Class start time: 8:00 9:30 12:30 Circle class start time INSTRUCTOR: Dr. Spalding Student SS# SEMESTER: FALL, 1998 Student Signature
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Here is a game of chance: You flip a coin and if the coin is heads, you pick a ball out of Bag A which contains 3 red and 3 green balls. If the coin is tails, you pick a ball out of Bag B which contains 5 green balls and no red balls. If you get a green ball from whichever bag you select from, you win. Otherwise you lose. What is the probability that you win? A. 1/4 or 0.2500 B. 3/6 + (1/2) or 4/8 C. (1/2)x(3/6) + (1/2)x(5/5) = 0.75 D. 1/4 x (1/2) or 1/8 = 0.1250 E. 1 - 3/6 = 0.50 2. What is the expected payout to you in a game of chance if you win \$80 when you win, but you lose \$10 when you lose. The chance of you winning is 2/10. A. +\$80 (2/10) - \$10 (8/10) = +\$8.00 B. +\$80 (2/10) - \$40 (8/10) = \$16 - \$32 = -\$16.00 C. +\$60 (2/10) - \$10 (8/10) = \$40/10 = \$4.00 D. +\$80 (2/10) + \$10 (8/10) = \$240/10 = \$24.00 E. +\$60 (2/10) - \$60 (8/10) = -\$360/10 = -\$36.00 3. A married couple have decided to have four children. Suppose that the chance of having a girl is 0.49 and that the chance of having a boy is 0.51. Also assume that the chance of the second child being a boy or girl is not changed by the fact that the first child is a boy or a girl. Likewise for the third child and fourth. Find the probability that the four children are born in the following sequence: girl, girl, girl, boy; in that exact order. A. 0.940001 B. 0.24000 C. 0.06000 D. 0.0650 E. 0.26000 4. Suppose that 20% of all college students donate blood at college blood drives. In a random sample of 16 college students, what is the probability that between 1 and 4 ( inclusive ) students donate blood? A. 0.113
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## 98Zexam2a-key - COURSE: MSCI 3700 Name: EXAM 2A Class start...
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Ask a homework question - tutors are online | 768 | 2,311 | {"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} | 4.4375 | 4 | CC-MAIN-2017-04 | longest | en | 0.917798 |
http://homepage.cs.uiowa.edu/~dwjones/opsys/spring97/hw/01sol.html | 1,670,419,993,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446711162.52/warc/CC-MAIN-20221207121241-20221207151241-00001.warc.gz | 21,673,612 | 2,405 | Homework 1 Solutions
22C:116, Spring 1997
Ioana M. Lungeanu
```Problem 2
For Hawk fictional machine, http://homepage.cs.uiowa.edu/~dwjones/arch/hawk
The CPU state includes: 15 general purpose registers, program counter
and the condition code register (the other special trap reagisters
are not realy needed for our problem).
The data structure(with 17 words):
savearea:
svPSW = 0 <<2 ;for PSW
svR1 = 1 <<2 ;for registers
svR2 = 2 <<2
svR3 = 3 <<2
svR4 = 4 <<2
svR5 = 5 <<2
svR6 = 6 <<2
svR7 = 7 <<2
svR8 = 8 <<2
svR9 = 9 <<2
svRA = 10 <<2
svRB = 11 <<2
svRC = 12 <<2
svRD = 13 <<2
svRE = 14 <<2
svRF = 15 <<2
svPC = 16 <<2 ;for PC
Problem 3
The procedure Switch is called after a trap with the 2 parameters oldp
and newp being pointers of two records with the above structure. Our
job is easier on this particular architecture due to the existance of
an automatic save of the program counter when a trap accurs, in TPC.
EXT OLD,NEW
oldp: W OLD
newp: W NEW
switch:
;first saves the CPU state in OLD
TSVSET R1 ;save R1
LOAD R1,oldp ;get the pointer where to save
STORE R2,R1,svR2 ;save R2
STORE R3,R1,svR3 ;save R3
STORE R4,R1,svR4 ;save R4
.................. ;save R5-R15
TSVGET R2
TPCGET R3
PSWGET R4
STORE R2,R1,svR1 ;save R1
STORE R3,R1,svPC ;save PC
STORE R4,R1,svPSW ;save PSW
;secondly restores the CPU state from NEW
LOAD R1,newp get the pointer to new state
.................. ;restore R5-r15
TPCSET R2 ;put PC into TPC
PSWSET R3 ;restore PSW
RTT ;Go to the new state
Problem 4
A device driver is a piece of system software which handles
the low-level communication between a particular device
(or family of familiar devices) and the computer to which
is connected, acting as a mediator between the higher-level
system software and the device. It is the responsability of
the device driver to deal with the low-level details and
peculiarities of the device. It hides the device dependent
features, thus providing the user with an abstract model of
the device. Thus, the user can communicate with the device
at a higher level, and all devices of a similar nature can
be accessed in a uniform manner, which is conceptually easier
to understand and use.
Problem 5
CPU's ussually have two execution modes: user mode and kernel
mode. A privileged instruction is an instruction which can be
executed in kernel mode only. The operating system runs in
kernel mode whereas user programs run in user mode. Thus,
This set-up provides a measure of security against tampering
of the hardware and software by users. In particular, the
user can access resources only through the "proper channels"
(system calls). This preserves the function of the operating
system as resource manager.
If a priviledged instruction is encountered in user mode,
a trap is generated. The operating system must service the
trap in an appropriate manner, e.g. by terminating the offending
process.
Commonly I/O instructions are priviledged. For a user having | 890 | 2,969 | {"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-2022-49 | latest | en | 0.840526 |
https://t4tutorials.com/cosine-similarity-in-data-mining/ | 1,720,997,009,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514654.12/warc/CC-MAIN-20240714220017-20240715010017-00411.warc.gz | 501,195,201 | 47,168 | # TF IDF Cosine similarity Formula Examples in data mining
## What is Cosine similarity?
Cosine similarity is a measure to find the similarity between two files/documents.
## Example of cosine similarity
What is the similarity between two files, file 1 and file 2?
## Cosine similarity Formula
cos(file 1, file 2) = (file 1 file 2) / ||file 1|| ||file 2|| ,
file 1 = (0, 3, 0, 0, 2, 0, 0, 2, 0, 5)
file 2 = (1, 2, 0, 0, 1, 1, 0, 1, 0, 3)
file 1 file 2 = 0*1 + 3*2 + 0*0 + 0*0 + 2*1 + 0*1 + 0*0 + 2*1 + 0*0 + 5*3
= 25
||d1||= (0*0 + 3*3 + 0*0 + 0*0 + 2*2 + 0*0 + 0*0 + 2*2 + 0*0 + 5*5)0.5
=(42)0.5 = 6.481
||d2||= (1*1 + 2*2 + 0*0 + 0*0 + 1*1 + 1*1 + 0*0 + 1*1 + 0*0 + 3*3)0.5
=(17)0.5 = 4.12
cos(d1 , d2 ) = 0.94
### What is a good cosine similarity 0 or 1?
• Similarity 0 means no similarity
• Similarity 0 means identical
• A similarity above 0.5 might be a good starting point.
### Is cosine similarity a metric?
Yes, Cosine similarity is a metric. This metric can be used to measure the similarity between two objects.
## When to use cosine similarity over Euclidean similarity?
In Cosine similarity our focus is at the angle between two vectors and in case of euclidean similarity our focus is at the distance between two points.
For example, we want to analyze the data of a shop and the data is;
• User 1 bought 1x copy, 1x pencil and 1x rubber from the shop.
• User 2 bought 100x copy, 100x pencil and 100x rubber from the shop.
• User 3 bought 1x copy, 1x PEPSI and 1x Shoes Polish from the shop.
### Cosine similarity python
Suppose we have text in the three documents;
Doc Imran Khan (A) : Mr. Imran Khan won the president seat after winning the National election 2020-2021. Though he lost the support of some republican friends, Imran Khan is friends with President Nawaz Sharif.
Doc Imran Khan Election (B) : President Imran Khan says Nawaz Sharif had no political interference is the election outcome. He claimed President Nawaz Sharif is a friend who had nothing to do with the election.
Doc Nawaz Sharif (C) : Post elections, Vladimir Nawaz Sharif won the president seat of Russia. President Nawaz Sharif had served as the Prime Minister earlier in his political career.
If we want to compute the cosine similarity, first of all, we will count the total words in document A, B, and C. The CountVectorizer or the TfidfVectorizer from scikit learn lets us compute this. The output of this comes as a sparse_matrix.
Here, it’s not compulsory but let’s convert it to a pandas dataframe to see the word frequencies in a tabular format.
Doc-Term Matrix
It’s better to use the TfidfVectorizer() function instead of CountVectorizer() function because it would have downweighted words. Here, we can see that it occurs frequently across each document. | 859 | 2,789 | {"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} | 3.6875 | 4 | CC-MAIN-2024-30 | latest | en | 0.88448 |
https://rdrr.io/cran/GPfit/man/summary.GP.html | 1,695,579,168,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233506658.2/warc/CC-MAIN-20230924155422-20230924185422-00334.warc.gz | 543,611,085 | 7,325 | # summary.GP: Summary of GP model fit In GPfit: Gaussian Processes Modeling
## Description
Prints the summary of a class `GP` object estimated by `GP_fit`
## Usage
```1 2``` ```## S3 method for class 'GP' summary(object, ...) ```
## Arguments
`object` a class `GP` object estimated by `GP_fit` `...` for compatibility with generic method `summary`
## Details
prints the summary of the GP object (`object`), by calling `print.GP`
## Author(s)
Blake MacDonald, Hugh Chipman, Pritam Ranjan
## See Also
`print.GP` for more description of the output;
`GP_fit` for more information on estimating the model;
`summary` for more description on the `summary` function.
## Examples
``` 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``` ```## 1D example n <- 5 d <- 1 computer_simulator <- function(x){ x <- 2 * x + 0.5 y <- sin(10 * pi * x) / (2 * x) + (x - 1)^4 return(y) } set.seed(3) x <- lhs::maximinLHS(n, d) y <- computer_simulator(x) GPmodel <- GP_fit(x, y) summary(GPmodel) ## 2D Example: GoldPrice Function computer_simulator <- function(x) { x1 = 4*x[, 1] - 2 x2 = 4*x[, 2] - 2 t1 = 1 + (x1 + x2 + 1)^2*(19 - 14*x1 + 3*x1^2 - 14*x2 + 6*x1*x2 + 3*x2^2) t2 = 30 + (2*x1 -3*x2)^2*(18 - 32*x1 + 12*x1^2 + 48*x2 - 36*x1*x2 + 27*x2^2) y = t1*t2 return(y) } n <- 10 d <- 2 set.seed(1) x <- lhs::maximinLHS(n, d) y <- computer_simulator(x) GPmodel <- GP_fit(x, y) summary(GPmodel) ```
GPfit documentation built on May 2, 2019, 5:31 a.m. | 560 | 1,485 | {"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-2023-40 | latest | en | 0.441354 |
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# NuSTAR Educators Guide: Building a Stable Mast
NuSTAR has a 10-meter rigid mast that separates the optics from the detector. Inspired by this, students will design, test, and build a lightweight mast 1 meter tall that can fully support the weight of a typical hardcover textbook (~2 kg). The... (View More)
# SDO Project Suite Module 1: What are the Features of the Sun?
This is the first module in the Solar Dynamic Observatory (SDO) Project Suite curriculum. Activities are self-directed by students or student teams using online videos and data from the SDO satellite to explore, research and build knowledge about... (View More)
Keywords: Sunspots
Audience: Middle school, Informal education
Materials Cost: \$1 - \$5
# Water in the Atmosphere
In this activity, participants learn about the atmosphere by making observations and taking measurements. They will go outside and use scientific equipment to collect atmospheric moisture data (temperature, relative humidity, precipitation and cloud... (View More)
# Water in the Geosphere
In this activity, participants learn about the geosphere by making observations and taking measurements. They will go outside and use scientific equipment to investigate water in the soil by measuring soil moisture, temperature, color and... (View More)
# Rain Gauge Activity
In this activity, students face an engineering challenge based on real-world applications. They are tasked with developing a tool they can use to measure the amount of rain that falls each day. Students will find out why freshwater is important,... (View More)
# MRC: How Do I Measure This? (Grades 6-8)
This is a lesson about measurement and cratering. Learners will read about the origin of the foot as a standardized unit of measure, work collaboratively to conduct an experiment about cratering, and collect and record data to draw logical and... (View More)
# MRC: How Do I Measure This? (Grades 3-5)
This is a lesson about measurement and cratering. Learners will read about the origin of the foot as a standardized unit of measure, work collaboratively to conduct an experiment about cratering, and collect and record data to draw logical and... (View More)
# Building for Hurricanes: Engineering Design Challenge
This activity is a short engineering design challenge to be completed by individual students or small teams. A real-world problem is presented, designing buildings for hurricane-prone areas, but in a simulated way that works in a classroom, after... (View More)
# MRC: Overview of the Solar System (Grades 6-8)
Learners will review the structure, content and size of the Solar System. This lesson is designed using the 5E instructional model and includes: teacher training, unit pacing guides, essential questions, a black-line master science notebook, a... (View More)
Audience: Middle school
Materials Cost: \$1 - \$5 per group of students
# S'COOL Lesson: Clouds - a Multidisciplinary Study
Clouds serve as a theme in a series of linked introductory explorations in math, language arts, and science. After participating in a demonstration of cloud formation, students are directed to create an acrostic poem (a poem that uses the letters in... (View More)
«Previous Page1234 Next Page» | 807 | 3,729 | {"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-2019-04 | latest | en | 0.872431 |
https://www.convertunits.com/from/meter/to/millimeter | 1,701,377,321,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100232.63/warc/CC-MAIN-20231130193829-20231130223829-00666.warc.gz | 804,223,727 | 12,842 | ## Convert metre to millimetre
meter millimeter
How many meter in 1 millimeter? The answer is 0.001. We assume you are converting between metre and millimetre. You can view more details on each measurement unit: meter or millimeter The SI base unit for length is the metre. 1 metre is equal to 1 meter, or 1000 millimeter. Note that rounding errors may occur, so always check the results. Use this page to learn how to convert between metres and millimetres. Type in your own numbers in the form to convert the units!
## Quick conversion chart of meter to millimeter
1 meter to millimeter = 1000 millimeter
2 meter to millimeter = 2000 millimeter
3 meter to millimeter = 3000 millimeter
4 meter to millimeter = 4000 millimeter
5 meter to millimeter = 5000 millimeter
6 meter to millimeter = 6000 millimeter
7 meter to millimeter = 7000 millimeter
8 meter to millimeter = 8000 millimeter
9 meter to millimeter = 9000 millimeter
10 meter to millimeter = 10000 millimeter
## Want other units?
You can do the reverse unit conversion from millimeter to meter, or enter any two units below:
## Enter two units to convert
From: To:
## Definition: Meter
The metre, symbol: m, is the basic unit of distance (or of "length", in the parlance of the physical sciences) in the International System of Units. The internationally-accepted spelling of the unit in English is "metre", although the American English spelling meter is a common variant. However, both American and non-American forms of English agree that the spelling "meter" should be used as a suffix in the names of measuring devices such as chronometers and micrometers.
## Definition: Millimeter
A millimetre (American spelling: millimeter, symbol mm) is one thousandth of a metre, which is the International System of Units (SI) base unit of length. The millimetre is part of a metric system. A corresponding unit of area is the square millimetre and a corresponding unit of volume is the cubic millimetre.
## 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, 70 kg, 150 lbs, US fluid ounce, 6'3", 10 stone 4, cubic cm, metres squared, grams, moles, feet per second, and many more! | 589 | 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} | 2.890625 | 3 | CC-MAIN-2023-50 | latest | en | 0.789826 |
http://www.abs.gov.au/ausstats/abs@.nsf/Latestproducts/1301.6.55.001Main%20Features6Mar%202011?opendocument&tabname=Summary&prodno=1301.6.55.001&issue=Mar%202011&num=&view= | 1,529,475,370,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267863463.3/warc/CC-MAIN-20180620050428-20180620070428-00076.warc.gz | 362,505,406 | 8,222 | 1301.6.55.001 - Tasmanian Statistical News, Mar 2011
Latest ISSUE Released at 11:30 AM (CANBERRA TIME) 08/03/2011 Final
Page tools: .mffeedback,#pjs { display :none; } Enable Javascript to Print PagesPrint All Email Notification RSS Search this Product STATISTICAL LITERACY CENSUSES AND SURVEYS In today's information-rich society, we encounter statistical information on a daily basis, ranging from unemployment rates, retail figures and cancer rates, to football ladders and cricket scores. Statistics tell interesting stories and enable us to make sense of the world. Statistics are essential for research, planning and decision-making purposes. There are several concepts that recur throughout the literature on statistical literacy. These fall into four key areas and can be considered in a practical manner as ‘criteria’ on which to base statistical literacy: Data awareness The ability to understand statistical concepts The ability to analyse, interpret and evaluate statistical information The ability to communicate statistical information and understandings In this issue, we will focus on understanding statistical concepts, and examine the difference between censuses and surveys. All censuses and surveys are based on a population. A population is an entire group with at least one characteristic in common. For example, every person in Australia on Census Night or, another example is every agricultural property in Australia. We can measure certain characteristics within this population by using a census or a survey. Census A census collects information from every unit in a population. As a result, data is truly representative of the whole population and detailed accurate data can be made available right down to small areas. However, there are huge resource costs arising from the expansive coverage so the number of questions asked is usually kept to a minimum. Processing the data takes time and usually only main results are released. More detailed results are not as readily available and need additional time and money to provide. Advantages: Accuracy – whole population counted Detail – reliable statistics for small sub-groups Disadvantages: Cost – expensive for large populations Speed – long collection, analysis and publication time-frame Survey In a survey, only part of the total population is selected. The survey data is then used to make inferences about the whole population, providing a reasonably reliable picture of that population. Most ABS findings are based on surveys, covering such topics as household expenditure, employment, crime, etc. ABS surveys are generally conducted on a nationwide basis and produce data at a national, state and sometimes regional level, but detailed data for small areas are not available. Costs are generally much lower than a census so more questions, or more detailed questions can be asked, and results can be available far more quickly. Advantages: Cost – fewer questionnaires to send and chase up Speed – less data to process Disadvantages: Accuracy – whole population not represented Detail – estimates for small groups or areas usually unreliable For further explanation of terms see Statistical Language! (cat. no. 1332.0.55.002) If you would like to know more about statistical literacy and its relevance to you, check out the article: What is statistical literacy and why is it important to be statistically literate? as featured in Tasmanian State and Regional Indicators (cat. no. 1307.6) or visit the Understanding Statistics portal on the ABS website. Document Selection These documents will be presented in a new window. | 698 | 3,613 | {"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-2018-26 | latest | en | 0.904844 |
https://www.theparsonspub.com/logic-test-who-is-smart-enough-to-find-the-code-in-40-seconds/ | 1,685,973,559,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224652116.60/warc/CC-MAIN-20230605121635-20230605151635-00353.warc.gz | 1,116,237,978 | 61,417 | Home » Logic test: Who is smart enough to find the code in 40 seconds?
# Logic test: Who is smart enough to find the code in 40 seconds?
Welcome to all fans of logic and thinking tests! Today we are going to offer you a very interesting puzzle that should make you work your brains and test your insight.
In this challenge, you will have to find the 4-digit code from a picture. This picture contains 5 wrong combinations but gives clues.
Logic tests are very popular on social networks because they can be fun and challenging. In today’s world, filled with images and videos, these challenges can be perfect opportunities to have fun and think of creative solutions.
So, if you are ready to take the challenge and find the 4-digit code, then wait no longer and try this puzzle! Good luck!
## Rules to follow to solve the challenge
To succeed in the challenge, it is important to observe and concentrate. You have to find the 4-digit code by following the following rules: after each combination of 4 digits, colored dots are placed.
The white dot means that one of the numbers is not present, the yellow dot means that one of the numbers is present but not in the right box, and the green dot means that one of the numbers is present in the right box. You will have to reread each combination and think from this information.
This challenge is of a difficult level as shown by the difficulty slider on the image. You will have to be patient and persistent to find the solution and succeed in your mission.
Please note! The colored dots are not placed in order and you only have 40 seconds to find the code or complete the challenge. So be careful and make sure you look at the placement of the dots before you start!
Finding the right code for a puzzle may seem daunting, but in reality, it can be a lot more fun than you think. Use your logic to find the solution and train your brain to solve problems.
It’s important to remember that when trying to find the right code, you need to understand how the different elements of the puzzle are related. This means looking at clues and details that can help you find the solution. In addition, try to logically associate similar concepts and ideas to better understand the puzzle and create a pattern that will help you find the code.
It is also important to remember that this is not necessarily a time-limited question – take your time and think about the underlying concepts. Finally, be sure to examine each element of the puzzle to find the correct code and succeed.
## The challenge has been solved!
We’ve kept you waiting and now we’re ready to reveal today’s code! The image shown contains the code to be found which is made up of numbers highlighted in color.
The solution was: 9167.
Congratulations to those who found it in less than 40 seconds! We hope you enjoyed this little challenge and were happy to participate.
We have developed some fun and entertaining games for our participants to share with their friends and family.
We would like to encourage our participants to challenge their friends or family by sharing this article on social networks. We spend a lot of time creating and updating these games and would be honored if you would share this article with your friends and family. So, are you ready to take on this challenge? | 677 | 3,316 | {"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} | 4.125 | 4 | CC-MAIN-2023-23 | latest | en | 0.953352 |
https://essayfount.com/theory-essay/ | 1,627,517,229,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046153803.69/warc/CC-MAIN-20210728220634-20210729010634-00051.warc.gz | 241,633,905 | 14,833 | # Theory Essay
In theory, nothing should go wrong, and professional statisticians would be comfortable with the lottery. But most of the city?s citizens are not statisticians, and at first glance, Bank?s criticisms seem credible. Why are some numbers picked more frequently than others? Wouldn?t 3530 picks in more than 700 lottery drawings be enough to even out the distribution? You decide to conduct the following test:Obtain recent winning lottery numbers from other cities.Examine whether the selection of these numbers is distributed like your city?s lottery numbers.If the numbers are similarly distributed, inform the public to reassure them. However, if the numbers are not distributed similarly, further investigation into your city?s number-selection method is required.Lottery officials have provided winning number combinations from pick-five lotteries in three other cities. In each case, the most recent 706 winning numbers are provided. You have not been told the names of the cities; you know only that the winning numbers come from cities designated A, B and C. An Access database named LotteryAnalysis.accdb contains the data and is available to you in the MN1505 subfolder within the Management folder on the DEPTS on ?NTSx? (R:) drive with the filename LotteryAnalysis.accdb.Does the algorithm produce many unusual ball values? Ball averages should be close to each other and in the range of 27 to 29.Does the algorithm favour the five numbers that Bank says people should select
Do the top five values in the other three cities follow your city?s top five pattern? The five most common frequencies should range from 71 to 85 which is your city?s range.
Does the algorithm favour any ball values? Do values repeat across the city lotteries?
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0 replies | 509 | 2,350 | {"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-2021-31 | latest | en | 0.948682 |
https://codeforces.com/problemset/problem/1866/I | 1,712,986,736,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296816586.79/warc/CC-MAIN-20240413051941-20240413081941-00234.warc.gz | 174,396,079 | 14,938 | I. Imagination Castle
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output
Given a chessboard of size $N \times M$ ($N$ rows and $M$ columns). Each row is numbered from $1$ to $N$ from top to bottom and each column is numbered from $1$ to $M$ from left to right. The tile in row $r$ and column $c$ is denoted as $(r,c)$. There exists $K$ distinct special tiles on the chessboard with the $i$-th special tile being tile $(X_i,Y_i)$. It is guaranteed that tile $(1,1)$ is not a special tile.
A new chess piece has been invented, which is the castle. The castle moves similarly to a rook in regular chess, but slightly differently. In one move, a castle that is on some tile can only move to another tile in the same row or in the same column, but only in the right direction or the down direction. Formally, in one move, the castle on tile $(r,c)$ can only move to tile $(r',c')$ if and only if one of the following two conditions is satisfied:
• $r'=r$ and $c'>c$.
• $c'=c$ and $r'>r$.
Chaneka and Bhinneka will play a game. In the beginning of the game, there is a castle in tile $(1,1)$. The two players will play alternatingly with Chaneka going first. In one turn, the player on that turn must move the castle following the movement rules of the castle.
If a player moves the castle to a special tile on her turn, then that player wins the game and the game ends. If on a turn, the castle cannot be moved, the player on that turn loses and the game ends.
Given the size of the board and the locations of each special tile. Determine the winner of this game if Chaneka and Bhinneka plays optimally.
Input
The first line contains three integers $N$, $M$, and $K$ ($1 \leq N,M \leq 2 \cdot 10^5$; $0 \leq K \leq \min(N \times M - 1, 2\cdot10^5)$) — the size of the chessboard and the number of special tiles.
The $i$-th of the next $K$ lines contains two integers $X_i$ and $Y_i$ ($1\leq X_i\leq N$; $1\leq Y_i\leq M$; $(X_i, Y_i) \neq (1,1)$) — the location of each special tile. The special tiles are pairwise distinct.
Output
Output Chaneka if Chaneka is the winner, output Bhinneka if Bhinneka is the winner.
Examples
Input
4 5 3
1 3
4 4
1 5
Output
Chaneka
Input
2 2 0
Output
Bhinneka
Note
In the first example, the following is an illustration of the chessboard in the beginning of the game.
Chaneka can move the castle to special tile $(1,3)$ or $(1,5)$ directly on her first turn. Therefore, Chaneka is the winner.
In the second example, the following is an illustration of the chessboard in the beginning of the game.
Chaneka can only move the castle to tile $(1, 2)$ or $(2, 1)$ on her first turn. Whatever Chaneka does, Bhinneka will be able to directly move the castle to tile $(2, 2)$. After that, on Chaneka's turn, she cannot move the castle, so Chaneka loses. Therefore, Bhinneka is the winner. | 818 | 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": 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-2024-18 | latest | en | 0.904865 |
https://answers.yahoo.com/question/index?qid=20200128154726AA723oA | 1,582,504,267,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875145859.65/warc/CC-MAIN-20200223215635-20200224005635-00458.warc.gz | 258,310,922 | 26,138 | Sophia asked in Science & MathematicsGeography · 4 weeks ago
# How far away is that mountain?
Imagine a Rip-van-Winkle type who lives in
the mountains. Just before going to sleep
he yells ”WAKE UP” and the sound echoes
off the nearest mountain and returns 8 hours
later.
How far away is that mountain? The speed
of sound is 340 m/s.
Relevance
• wowser
Lv 5
3 weeks ago
You failed to specify the time zone
• Joseph
Lv 7
3 weeks ago
Really? You have to resort to asking random strangers to do (possibly incorrectly) a simple speed-time-distance problem for you because you can't be bothered to think on your own? And then we wonder why not enough women take STEM courses in college.
Next time you ask others to do your homework for you at least make sure that your teacher is not monitoring this and other Q&A sites like this one to catch cheaters.
• Anonymous
4 weeks ago
im gunna guess that this is not a serious question, based on the 8 hours/3000 miles thing, so will give it a not serious answer-
Answer = the parable of the flan and toad, a conversation on distance and intention! | 270 | 1,103 | {"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-2020-10 | latest | en | 0.924184 |
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