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https://www.homeworklib.com/questions/775853/design-two-digital-fir-lpf-using-rectangular-and | 1,590,680,517,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347399820.9/warc/CC-MAIN-20200528135528-20200528165528-00575.warc.gz | 775,074,214 | 19,450 | # Design two digital FIR LPF using Rectangular and Hamming windows, find filter's impulse response coefficients as wel...
Design two digital FIR LPF using Rectangular and Hamming windows, find filter's impulse response coefficients as well as their frequency responses. Filter specifications are: Cut-off frequency (ωp) = 1 radian, Filter Order (M) = 7.
##### Add Answer of: Design two digital FIR LPF using Rectangular and Hamming windows, find filter's impulse response coefficients as wel...
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1 次查看（过去 30 天）
Rene2020-8-30
Heyho
I'm looking for maximum values of a table and am using
[rows, columns] = find(A==max(A));
to do so in the attached matrix.
It gets me this:
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
10 10
11 11
12 12
13 13
14 14
15 15
16 16
19 17
17 18
18 18
19 19
20 20
The matrix is 20x20 and the output has 21 values. :S
Also in my opinion the line...
19 17
...isn't true, cause I can't see a maximum there? This shouldn't be there at first place, should it?
Before and after this everything looks fine to me.
Why is this and how can I prevent that from happening?
### 采纳的回答
max(A) is a vector, not a number:
max(A)
ans =
Columns 1 through 15
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 1.0000 1.0000 1.0000 1.0000
Columns 16 through 20
1.0000 0.7950 1.0000 1.0000 0.9998
The value at A(19,17) is the 0.795, which is not a maximum of the matrix but rather a maximum of the column.
if you want to get the maximum of the whole matrix you need this:
max(A(:))
ans =
1.0000
And when you compare, remember that float value comparison is everything but reliable, so you need to have a given tolerance.
In your code it would be something like this:
[rows, columns] = find( abs(A-max(A(:)))<1e-4 );
ans =
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
10 10
11 11
12 12
13 13
14 14
15 15
16 16
17 18
18 18
19 19
##### 3 个评论显示 2更早的评论隐藏 2更早的评论
This will probably work for you
A = [1 0.5 0.7;0.4 0.8 0.4;0.2 0.3 0.7];
Amax = max(A); % Get maximum from each column
DiffFromMax = A-Amax; % Zero values are maximum locations
tol = -1e-4; % Note that the tolerance is negative
[rows, columns] = find( DiffFromMax>tol )
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Translated by | 721 | 1,896 | {"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-2023-23 | longest | en | 0.726221 |
https://math.stackexchange.com/questions/2602364/a-definite-integral-of-the-exponential-of-cos | 1,623,837,465,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487623596.16/warc/CC-MAIN-20210616093937-20210616123937-00078.warc.gz | 329,062,168 | 38,710 | # A definite integral of the exponential of cos
During some calculs, I came across the following definite integral, $$\int_0^{2\pi} \frac{\sin^2 \theta}{1+b\cos\theta} \exp(a\cos\theta) d\theta$$ with $a$ and $b$ constants. I tried to look it up in the Gradshteyn and Ryzhik, for example in Section 3.93: Trigonometric and exponential functions of trigonometric functions, but find nothing helpful. I also tried the Poisson Integral via complex analyse, apparently the exponential function is a little particular, if it's a $\log$ function instead of $\exp$ that's done, but with exponential I have not yet found the solution.
Thanks in advance if anyone has any idea :)
• I'd look at the residue theorem. Let $z = \exp(i\theta)$ and transform it into an integral over the unit circle. The integrand is holomorphic except for isolated singularities. – Daniel Fischer Jan 12 '18 at 14:30
• I hope you have constraints on $a$ and $b$, since I don't think it converges for all values... Moreover you can reduce the number of parameters and still keep it general – Shashi Jan 12 '18 at 14:35
• @DanielFischer The essential singularity at $z=0$ makes that approach, I believe, quite a mess. – Mark Viola Jan 12 '18 at 16:09
• @Mark Yes, it's probably not going to be pretty with $z + 1/z$ in the argument of the exponential. But it may be the least ugly of all ways. I didn't see a nicer way. – Daniel Fischer Jan 12 '18 at 16:14
• A related integral can be expanded using incomplete gamma function: $$\int_{0}^{2\pi} \frac{e^{a\cos\theta}}{1+b\cos\theta} \,d\theta = 2\pi \sum_{n=0}^{\infty} \frac{e^{-a/b}\Gamma(2n+1,-a/b)}{(n!)^2} \left(\frac{b}{2}\right)^{2n}.$$ – Sangchul Lee Jan 12 '18 at 16:30
Through the Poisson kernel you may derive the Fourier cosine series of $\frac{\sin^2\theta}{1+b\cos\theta}$; the coefficients of the Fourier cosine series of $\exp(a\cos\theta)$ are given by $I_k(a)$, where $I_k$ is a modified Bessel function of the first kind and $I_k(a)\leq \frac{\alpha^k}{2^k k!}I_0(a)$. By the orthogonality relations it follows that such integral can be converted into a fast-convergent series, with the minor drawback that the involved coefficients do not have a nice closed form, but they are pretty simple to compute numerically through continued fractions. | 658 | 2,284 | {"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} | 3.65625 | 4 | CC-MAIN-2021-25 | latest | en | 0.826006 |
http://www.lmfdb.org/EllipticCurve/Q/53312/bc/ | 1,607,093,184,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141737946.86/warc/CC-MAIN-20201204131750-20201204161750-00439.warc.gz | 145,827,476 | 9,727 | # Properties
Label 53312.bc Number of curves $2$ Conductor $53312$ CM no Rank $1$ Graph
# Related objects
Show commands for: SageMath
sage: E = EllipticCurve("53312.bc1")
sage: E.isogeny_class()
## Elliptic curves in class 53312.bc
sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
53312.bc1 53312s2 [0, 0, 0, -25676, -696976] [2] 147456
53312.bc2 53312s1 [0, 0, 0, 5684, -82320] [2] 73728 $$\Gamma_0(N)$$-optimal
## Rank
sage: E.rank()
The elliptic curves in class 53312.bc have rank $$1$$.
## Modular form 53312.2.a.bc
sage: E.q_eigenform(10)
$$q - 2q^{5} - 3q^{9} + 2q^{11} + q^{17} - 2q^{19} + O(q^{20})$$
## Isogeny matrix
sage: E.isogeny_class().matrix()
The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.
$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$
## Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels. | 391 | 1,075 | {"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} | 2.734375 | 3 | CC-MAIN-2020-50 | latest | en | 0.590908 |
http://physics.stackexchange.com/questions/4428/how-to-explain-the-weak-force-to-a-layman | 1,469,406,296,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469257824201.28/warc/CC-MAIN-20160723071024-00053-ip-10-185-27-174.ec2.internal.warc.gz | 205,610,847 | 20,126 | # How to explain the weak force to a layman?
I'm trying to explain in simple terms what the weak interaction does, but I'm having trouble since it doesn't resemble other forces he's familiar with and I haven't been able to come up (or find on the web) with a good, simple visualization for it.
-
Is there a specific reason why the modern picture of the weak force is harder to explain than the other forces? – Tim van Beek Feb 2 '11 at 7:48
@Tim: well, massive bosons decay, so that's something completely different from EM interaction (even if the person is already acquainted with role of bosons in explanation of forces). – Marek Feb 2 '11 at 9:03
I don't know that many "laymen" who are familiar with the picture that EM forces come from the exchange of virtual photons :-) – Tim van Beek Feb 2 '11 at 11:09
@Tim: neither do I. But I meant that most people are familiar with the fact that EM is actually the same thing as light which is the same as photons. So the connection between electric force and photons is easy to make. Weak force is much more removed from the basic knowledge. – Marek Feb 18 '11 at 18:07
The weak force "looks" different because in the first (and still most important) reincarnation we have encountered it - namely beta-decay (including the decay of the neutron) - the force seems to be a contact interaction: it has an extremely short range, essentially zero.
However, any phenomenon that differs from the indefinite existence of an object that moves in the same direction by the same speed forever requires a force to be explained. The force required for the beta-decay is the weak nuclear force.
While the decay seems to "directly" transform a neutron into a proton, electron, and antineutrion, a closer investigation of the force that began in the 1960s has demonstrated that this force is actually analogous to other forces, including electromagnetism, because its range is finite (nonzero). It's only limited because it's mediated by the W and Z bosons which are, unlike photons, massive. So the force doesn't get "too far".
However, in our modern description of the forces, electromagnetism and the weak force have to be described by a unified "electroweak" theory and they mix with one another. At distances much shorter than the range of the W/Z bosons, the electromagnetic and weak forces become equally strong and, in some proper sense, indistinguishable.
-
Great, I really enjoy your explanations. – Killercam Jun 29 '13 at 17:35
I would actually emphasize the difference between the forces, rather than the similarity. Although we (as theorists) like to bundle the whole shebang into a "neat" $U(1)\times SU(2) \times SU(3)$ gauge structure (and possible some gauge version of gravity), it doesn't mean that reality has to be that neat (e.g. chirality of electroweak, neutrino masses, etc.)
So:
• Electromagnetism is long ranged, and drops off in strength with distance.
• Strong force is actually also long-ranged, but gets stronger with distance! This causes the side effect that trying to separate a pair of opposite charges causes pair creation, and so we always see neutral composite particles.
• Weak force is intrinsically short ranged (order $1/M_W$), and primarily it does not transmit a force --- but transmutates particles. Electrons go to neutrinos, quarks mix, etc.
And for gravity, say whatever your favourite quantum gravity picture say it is :-)
-
Sorry, but the claim "anything goes" about gravity is totally off here. At the level of accuracy you pursued in the case of other forces, the claim about gravity is equally indisputable and it is that gravity is a long-range force that drops off in strength with distance, much like electromagnetism. In fact, the room for confinement and/or higgsing is much more constrained in the case of gravity so this statement is more solid, and not less solid, in the case of gravity. Every viable theory of quantum gravity has to respect the long-range character of gravity and other general features, too. – Luboš Motl Feb 27 '13 at 6:36
I like the history oriented approach, when explaining something to a layman. In this case you could start by briefly explaining the fundamental forces and how we needed a new force to model beta decay.
-
The weak force is like why water stays together in a system.
The strong force is why when the atoms in the bottoms of your feet don't go through the ground when you walk.
Objections?
-
What does the weak interactions have to do with water, and what do you mean by "stays together in a system"? As for the second part, in some sense it may be true (because the strong force keeps nuclei form falling apart and indirectly from making the floor impenetrable), but the most direct cause if this phenomenon is the electromagnetic force, not the strong force. – Lurco Jul 20 '14 at 20:26
This seems pretty off the mark- would you explain your reasoning? – paisanco Jul 20 '14 at 20:54
Wrong in every particular. – dmckee Jul 21 '14 at 2:17
## protected by Qmechanic♦Jul 20 '14 at 20:30
Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count).
Would you like to answer one of these unanswered questions instead? | 1,225 | 5,331 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2016-30 | latest | en | 0.958675 |
https://www.physicsforums.com/threads/find-standard-matrix-of-linear-transformation-satisfying-conditions.499325/ | 1,627,541,731,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046153816.3/warc/CC-MAIN-20210729043158-20210729073158-00579.warc.gz | 976,292,620 | 14,270 | # Find standard matrix of linear transformation satisfying conditions
## Homework Statement
Find the standard matrix for the linear transformation T: R^3-->R^3 satisfying:
T([1 2 2]) = [1 0 -1], T([-1 -4 -5]) = [0 1 1], T([1 5 7]) = [0 2 0]
All of the vectors are columns not rows, I couldn't type them correctly as columns.
## The Attempt at a Solution
I tried constructing a matrix using the vectors being applied to T and row reducing it. I cannot figure out where to go from there. I assume I need to find T of the standard basic vectors in some way. I believe I can figure it out if I can get a step in the right direction.
Last edited:
Since $$T$$ is linear, we know that $$T\left(\vec{u} + \vec{v}\right) = T\left(\vec{u}\right) + T\left(\vec{v}\right)$$.
Since $$T$$ is linear, we know that $$T\left(c \vec{v}\right) = c T\left(\vec{v}\right)$$, for any real scalar c.
You can find the standard vectors as linear combinations of the given vectors by constructing an augmented matrix and row reducing, as you did.
For example:
$$\begin{pmatrix}1&& -1&& 1&& 1&&\\2&& -4&& 5&& 0&&\\ 2&& -5&& 7&& 0&&\end{pmatrix} -> \begin{pmatrix}1&& 0&& 0&& 3&&\\0&& 1&& 0&& 4&&\\ 0&& 0&& 1&& 2&&\end{pmatrix}$$
So we can write $$\begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}$$ as a linear combination of $$(3)\begin{bmatrix} 1 \\ 2 \\ 2 \end{bmatrix} + (4)\begin{bmatrix} -1 \\ -4 \\ -5 \end{bmatrix} + (2)\begin{bmatrix} 1 \\ 5 \\ 7 \end{bmatrix}$$
Now we know that:
$$T\left(\begin{bmatrix}1 \\ 0 \\ 0 \end{bmatrix}\right) = T\left( (3)\begin{bmatrix} 1 \\ 2 \\ 2 \end{bmatrix} + (4)\begin{bmatrix}-1 \\ -4 \\ -5 \end{bmatrix} + (2)\begin{bmatrix}1 \\ 5 \\ 7 \end{bmatrix}\right) = (3)T\left( \begin{bmatrix} 1 \\ 2 \\ 2 \end{bmatrix} \right) + (2)T\left(\begin{bmatrix}-1 \\ -4 \\ -5 \end{bmatrix} \right) + (4)T\left(\begin{bmatrix}1 \\ 5 \\ 7 \end{bmatrix} \right)$$
So, what is:
$$(3)T\left( \begin{bmatrix} 1 \\ 2 \\ 2 \end{bmatrix} \right) + (4)T\left(\begin{bmatrix}-1 \\ -4 \\ -5 \end{bmatrix} \right) + (2)T\left(\begin{bmatrix}1 \\ 5 \\ 7 \end{bmatrix} \right)$$
The values for the other standard vectors can be found with a similar process.
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3RD TEMPLE COUNTDOWN
PROPHETIC TIMELINES OF THE END
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‘Let no one Deceive you in any way. For it will not be, unless the Departure comes 1st, and the Man of Sin is Revealed, the Son of Destruction, who Opposes and Exalts himself Above every so-called God or Object of Worship, so that he takes his Seat in the Temple of God, displaying himself as being God. Do you not Remember that I told you these things while I was still with you?’ -2 Thessalonians 2:3-5 (Word English Bible)
The purpose of this study is to Conjecture the possible Timelines of the Prophetic ‘Event’ that could lead-up to the construction of the 3rd Temple on the Temple Mount in Jerusalem, Israel. This study will Argue, that in relation to such an event, its Prophecy is a factor of Time based on the Golden Section. Certain Key Prophetic Events always occur on Certain Dates that are based on a Factor of Divine Mathematics. The Golden Section is ‘The Division of a Line so that the Whole is to the Greater Part, as that Part Is to the Smaller Part, i.e., in a ratio of 1 to 1/2 (√5 + 1)’. It is a mathematical Proportion that is considered to be particularly used as the ‘Signature of YHVH’, the Creator. One believes Prophecy occurs in Phi Ratio, just the same.
It is interesting that the Word, ‘Signature’ comes from the Root Word to ‘Sign’ or a Marker. This Mathematical Phenomenon is seen as the Building Blocks in the Measurement in All Things. Pythagoras had it right when he stated that ‘All is Numbers’. Even Biblical Prophecy is about Numbers, Certain Numbers and Dates that can be reduced to Mathematical Variables even. Biblical Prophecy is about Numbers, specific to Days in the case of the coming 3rd Temple as Prophecy is all about its Timing. For example, Jesus Christ gave the Unbelieving Jewish Ruling Council a ‘Sign’ they demanded of Him to ‘certify’ His Credentials as Messiah, Jesus stated that no SIGN would be given to them, except the ‘Sign’ of His resurrection.
Jesus specifically alluded to the 3 Days Jonah was in the Belly of the Great Fish and how if the Temple of His Body would be Destroyed, Jesus would Raise it in 3 Days, etc. Of course, Jesus in the later Inference, was speaking of His Body, of which the Temples were Proportioned after and Modeled. There is also the example of how when YHVH commanded Ezekiel to lay on his Sides for certain Days to demonstrate the Sins and Judgment of Both the Kingdoms of Israel and Judah. Then there is the Enigma of Various Prophecies given to Daniel pertaining to specific Year Counts related to the 1st Visitation of the Messiah. Daniel also correctly Deduced the Number of Years for the Captivity of Judah to be 70, etc. There is also the Book of Revelation, that Compliments the Prophecies of Daniel with the specific Mathematical Clocking of Prophetic Time. It is subject to Time Periods of 1260 and 2520 Day Counts, for example. The Jubilee Pattern is another Amazing Sign of counting Prophetic Time.
Golden Section of Prophecy
YHVH has Encoded Time, that of the 120 Jubilees, that many have attempted to Decipher, etc. The Timelines suggested on the charts associated with this study appear to converge on the year 2025. These are the most recent Times that such a Marker has attempted to Calculate from Sabbatical Cycles. Thus, certain Numbers or Combination of Numbers can be used to Communicate Prophecy also, in one’s Assessment.
This is the Argument that Israel and the Church Age, for that matter, are subject to Amazing Patterns of Timelines and Time-Specific Events, subject to the Golden Section Pattern or Template. It deals with when Creation was Initiated, what day, when were the 1st Humans created, what was the Succession of the line of Adam, etc. It was also a matter of Time and Mathematics, as to how long the Enslavement of the Hebrews was to last in Egypt and when the Exodus was to take place.
Thus, certain Numbers or Combination of Numbers can be used to Communicate Prophecy also, in one’s Assessment. This is the Argument, that Israel and the Church Age, for that matter, are subject to Amazing Patterns of Timelines and Time-Specific Events, subject to the Golden Section Pattern or Template. It deals with when Creation was Initiated, what day, when were the 1st Humans created, what was the Succession of the line of Adam, etc. It was also a matter of Time and Mathematics, as to how long the Enslavement of the Hebrews was to last in Egypt and when the Exodus was to take place.
Then there is the Giving of the Law and the Moeds were Time Specific and tied to Numbers, or how many Prophets and Judges Israel had. Then there was the factor of how many Kings each Kingdom had, etc. Not only is Biblical Prophecy a Factor of Time, but Events in the Secular World are also often tied to certain Numerical Values, pertinent to Israel. Moreover, the Luciferians also often use the same Time-Tables and Prophetic Templates.
One has even made the case that for example, the World Wars are one such Phenomenon that this study agrees with and is one of the Series of Events that is subject to the Golden Section. For example, if one uses the start of World War I, that of 1914 and the beginning of World War 2 that started in 1939, then the 3rd triangulation results in the Year 2023. What is very Peculiar, Mathematically, at least is that if one Superimposes the Phi Ratio Graphic onto the timeline from 1914 to 2024, the Fulcrum Spiral Portion of the Graphic, completely matches with the duration of the 2nd World War, that from September of 1939 to September of 1945.
Could this Mathematical Projection suggest when a Major War in the Middle East involving Israel is to occur in 2024? What would this War look like and who would be involved? Given the glimpses of Biblical Prophecy, many speculate that this Regional War would involve the Nation of Israel but will involve Russia and its Muslim neighbors. A future War with Russia is coming. It will be the Gog-Magog War. This Confederation would make-up the International Alliance led by Russia, Iran primarily and the Outer-Ring of Muslim Nations that will attack Israel.
Mathematics of Prophecy
If this would or could be Plausible, could this suggest that 2025 is such a time that constitutes the start of the Tribulation Period? This study is assuming a literal 7-Year ‘Week’, that will constitute Daniel’s Last Prophetic Week or Sabbatical Cycle. This World War is not taking into account the other arguments that suggest that in order to produce such a State of Geo-Politics in the region, where Israel no longer has ‘Walled Cities’ that the Psalm 83 War then by 2025, perhaps.
This study suggests that these are, and perhaps will be ‘Events’ that are allowing for the construction of the 3rd Temple in Israel. This study also suggests that these Stepping-Stones are a Factor of Mathematics subject to Biblical Prophecy. This Theory can be applied to the possible coming Event that will lead to the building of the 3rd Temple on the Temple Mount in Jerusalem, Israel. Using the same Template of the Phi Ratio or Golden Section, the Prophetic Pattern from the Restoration of Israel in 1948 is also Striking. In prior studies, the suggested Timeline presented also has the 2 known geo-Political Markers or ‘Signs’ that have already occurred.
Those would be the Establishment of the Nation of Israel ‘Birthed’ in 1 Day on May 14, 1948. The 2nd ‘Sign’ would be the Recapturing of the Old City of Jerusalem in the 6-Day War. This allowed for the Acquisition of the Temple Mount. This ‘Event’ was a ‘Stepping-Stone’ that had not occurred since 70 AD and coincidentally 1,948 Years from 70 AD was in 2018, the 70th Anniversary of Israel’s Birth. If the Phi Ratio Spiral Graphic is Superimposed onto the Timeline since 1948, the Exact Fulcrum of the spiral converges on the 6-Day War Time Period of 1967. If this Mathematical Template is Extrapolated to Triangulate the 3rd Time on the timeline, it corresponds to approximately 2018. This is when the Altar of Sacrifice was rededicated.
One is Postulating that a 7-Year Sabbath Cycle of Time is in Play since 2018, to suggest that in the Fall of 2025 is when the 7-Year Tribulation is to start, perhaps. Are these Biblical prophetic ‘signatures’ suggesting that the 3rd Temple ‘event’ is to be in 2025 sometime? Of course, this is at best an Educated Guess based on a Mathematical Extrapolation, at this Time. However, there are some unique mathematical variables even leading-up to 2018. What is most significant about this timeline from 1948, as it is related to the destruction of the 2nd Temple is that perhaps it is related to the construction of the 3rd Temple in the following Mathematical Equations for Consideration.
If one takes the Number of years from 70 AD, when the 2nd Temple was Destroyed and one extends it to 1967, the year the Temple Mount was recaptured by the Jews for the 1st time since 70 AD, the difference is 1897 Years. Another way of Measuring this Timeframe would be 271 Years x 7. Nothing would seem Extraordinary, if it were not for those that see Intuitively, the Meaning of the Numbers. First of all, is it Coincidence that the 1st Zionist Jewish Congress since 70 AD occurred in 1897? This occurred in Basel, Switzerland for the sole purpose of designing the ‘Roadmap’ to establish the Homeland of the Jews in Israel.
Hexagram of Time
Furthermore, if one adds 120 Years to the 1897 Years, that Year Count coincides with 1967, the Liberation of the Temple Mount. This Timeline equals 2017, the 50th or Jubilee Year Anniversary. This is possibly Biblically Significant is that the 50th Year Jubilee is a coefficient or Fractal of the 120. This is seen in Genesis when YHVH gives the Mathematical Variable of 120 Years. Many are suggesting the Jubilee Cycles until the coming of Messiah when Daniel’s Last Week of Years are completed. More Astonishing, is the Supposition that many have attributed, that the Time of the Flood of Noah was to be 7 Cycles of 49 Years, corresponding to the Year 2017. This would be 120 Cycles of 49 Years or about 5880 Years. This then means 2022 did start the next Sabbath of 7 Years.
Pertaining to the 271 Year Coefficient from 70 AD to 1967, the Gematria suggests a Factor of a Hexagram. How so? The Number 271 would also seem Uninteresting or Unapparent Prophetically, except that it is very telling in terms of Gematria. According to the Research of the Website The Bible Wheel, the Prime Number 271 is the ‘10th Centered Hexagon Number’ or Hex (10). This Phenomenon is found in the heart of the 10th Star Number, the Prime Number of 541. This Latter Number is also seen in the value of Israel, The Commandments of the Stone Tablets, etc.
It is a prime number, and its Related Number is 1776. Like in the Elements of the Holographic Generating Set (A = 27, B = 37, C = 73). The Number 271 is both Geometric Hex (10) and integrated with the Repunits, since it is the largest Prime Factor in R5 = 41 x 271. It is as though there had to be 7 ‘Stars of David’ or Remphan to others, from when the Temple was destroyed to when the countdown to its foundation was Recaptured and perhaps to when its construction was to begin. And obviously the 1776 Numerical Coefficient speaks Volumes of the Luciferian Truncated Pyramid Motif and the coming of the Capstone, i.e., Lucifer, etc.
As it has been already attributed to a possible Association of the Parable of the Fig Tree, the Birthing of Israel will also coincide with the Astronomical ‘Birthing’ of a ‘King’. Thus, the Prophetic Restitution of YHVH’s Earthly People, Israel are subject to Mathematical Factors of various Sacred Numbers that are to coincide, occur in Phi Ratio Patterns. Technically in the Jewish Counting of Time, this birthing of a ‘King’, is based on the Astronomical Typologies. Will a ‘King’ also appear to coincide with this Temple being raised and from where he will sit from? There is only one place in the Temple that was designed for anybody to sit in, the Ark of the Covenant.
Many believe that as Jesus Christ was Heralded by an advent of a ‘Christ Star’, so too will a Star of some sorts, appear in the Heavens, Announcing the advent of the AntiChrist. In Fact, there will be a ‘New Star’ birthed in the Constellation of Cygnus. Others suggest it will be the Supernova of the Red Super Giant Star, Betelgeuse. The Light of its Explosion will start to be seen in 2025. Who will this coming ‘King’ be? To the Christians, it will be the AntiChrist. To the Jews, it will be their Messiah whom they will accept because for one thing, he will allow for the 3rd Temple to be built and for the sacrifices to commence.
To the Muslims, he is the Mahdi who will come back with Jesus Christ, as his Lieutenant. This Muslim Jesus, ‘Isa’ will help Destroy both the Jews and Christians. It is said because the Christians Misunderstood His Teachings as He is really a ‘Muslim. To the New Agers, this King will be Maitreya. He will be the Avatar Savior for this Coming New Age to ‘Save’ Humanity from itself and Purify Earth of all People of ‘Wrong Think’, etc. To the Atheist, this Coming King will be what the World needs, a Strong and Determined Political, Financial and Military Leader that will solve the World’s Problems of Over- Population, Climate Change Racism.
One is convinced that part of ‘Confirming’ will involve Provision to build the 3rd Temple. It will be part of the Covenant’ with the ‘Many’. Or Alternatively, it would be the Reading of the Covenant, literally, that of Moses as the Kings often did after the Fall Feasts of YHVH. It is precisely now called Simchat Torah. Ezra did it after Returning with the Exiles from Babylon. And Solomon did it when Dedicating the 1st Temple. Ultimately, this 3rd Temple will be the one that will be defiled by the Abomination of Desolation that Jesus warned Israel about concerning the fulfillment of the prophecy given to Daniel.
This ‘Abomination’ will consist of an A.I. Idol being set-up and eventually Lucifer will enter the Temple. This will be by way of the possessed AntiChrist that will sit Literally and Physically on the Ark of the Covenant that will be placed in the Holy of Holies in the 3rd Temple in Jerusalem. Realize that this means that the original Ark of the Covenant will be Unveiled, according to its Timing, as it will be Mutually Inclusive of the 3rd Temple’s need to be constructed. The Question is, will such a Place and Time be subject to any Mathematical Correspondences, a Golden Section of Time and/or Sacred Measurement even? These studies have strongly suggested, a yes.
One has Argued, that the 3rd Time is very Prophetic. It is very Prophetic to be Alive at the Threshold of the 70th Year Anniversary of Israel’s Birth. Why? Israel is the Center-Piece of YHVH’s Prophetic Clock concerning the ‘Time’ Earth has regarding the Plan of Salvation as found Only in its True Messiah, Jesus Christ. The Prophetic Clock Countdown started at this 1948 Time Marker when Jesus is to Return. It is after all Jesus, of which Prophecy was, is and will be Patterned After and Fulfilled. It will be from Jesus’ Return, that the Conclusion to Prophecy will also cause ‘Time’ to Cease itself, as All Things are Consummated in Jesus and for Jesus.
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__________________________________ | 3,784 | 15,958 | {"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-2024-38 | latest | en | 0.945721 |
https://freeunlock.org/fleetmatics-work-vacpq/cosine-distance-triangle-inequality-5fc7eb | 1,627,876,411,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046154302.46/warc/CC-MAIN-20210802012641-20210802042641-00242.warc.gz | 269,583,899 | 4,997 | The variable P= (p 1;p 2;:::;p d) is a set of non-negative values p isuch that P d i=1 p i= 1. That is, it describes a probability distribution over dpossible values. d(x,y) > 0: no notion of negative edits. Intuitively, one can derive the so called "cosine distance" from the cosine similarity: d: (x,y) ↦ 1 - s(x,y). Although the cosine similarity measure is not a distance metric and, in particular, violates the triangle inequality, in this chapter, we present how to determine cosine similarity neighborhoods of vectors by means of the Euclidean distance applied to (α − )normalized forms of these vectors and by using the triangle inequality. The problem (from the Romanian Mathematical Magazine) has been posted by Dan Sitaru at the CutTheKnotMath facebook page, and commented on by Leo Giugiuc with his (Solution 1).Solution 2 may seem as a slight modification of Solution 1. The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side. Therefore, you may want to use sine or choose the neighbours with the greatest cosine similarity as the closest. 2.Another common distance is the L 1 distance d 1(a;b) = ka bk 1 = X i=1 ja i b ij: This is also known as the “Manhattan” distance since it is the sum of lengths on each coordinate axis; Although cosine similarity is not a proper distance metric as it fails the triangle inequality, it can be useful in KNN. Definition of The Triangle Inequality: The property that holds for a function d if d ( u , r ) = d ( u , v ) + d ( v , r ) (or equivalently, d ( u , v ) = d ( u , r ) - d ( v , r )) for any arguments u , v , r of this function. However, this is still not a distance in general since it doesn't have the triangle inequality property. Nevertheless, the cosine similarity is not a distance metric and, in particular, does not preserve the triangle inequality in general. The Kullback-Liebler Divergence (or KL Divergence) is a distance that is not a metric. It is most useful for solving for missing information in a triangle. L 2 L 1 L! Why Edit Distance Is a Distance Measure d(x,x) = 0 because 0 edits suffice. d(x,y) = d(y,x) because insert/delete are inverses of each other. Figure 7.1: Unit balls in R2 for the L 1, L 2, and L 1distance. Notes For example, if all three sides of the triangle are known, the cosine rule allows one to find any of the angle measures. Note: This rule must be satisfied for all 3 conditions of the sides. Somewhat similar to the Cosine distance, it considers as input discrete distributions Pand Q. However, be wary that the cosine similarity is greatest when the angle is the same: cos(0º) = 1, cos(90º) = 0. This doesn't define a distance, since for all x, s(x,x) = 1 (should be equal to 0 for a distance). The triangle inequality Projection onto dimension VP-tree The Euclidean distance The cosine similarity Nearest neighbors This is a preview of subscription content, log in to check access. The cosine rule, also known as the law of cosines, relates all 3 sides of a triangle with an angle of a triangle. What is The Triangle Inequality? Addition and Subtraction Formulas for Sine and Cosine III; Addition and Subtraction Formulas for Sine and Cosine IV; Addition and Subtraction Formulas. Triangle inequality : changing xto z and then to yis one way to change x to y. Similarly, if two sides and the angle between them is known, the cosine rule allows … Neighbours with the greatest Cosine similarity as the closest for Sine and III. Formulas for Sine and Cosine IV ; Addition and Subtraction Formulas for Sine and Cosine IV Addition. ( x, y ) = 0 because 0 edits suffice: changing xto z and then yis! Neighbours with the greatest Cosine similarity as the closest somewhat similar to the Cosine distance, it a... Satisfied for all 3 conditions of the sides no notion of negative edits satisfied for all 3 conditions the! Sine or choose the neighbours with the greatest Cosine similarity as the closest not a metric that is a... 7.1: Unit balls in R2 for the L 1, L 2, and 1distance... However, This is still not a metric not a distance in since... Is a distance in general since it does n't have the triangle inequality property, x =. Still not a distance that cosine distance triangle inequality not a metric Pand Q distance in general it. Distance Measure d ( y, x ) = d ( x, y ) > 0 no. Yis one way to change x to y all 3 conditions of the sides still not a metric ) a! Cosine III ; Addition and Subtraction Formulas for Sine and Cosine IV ; Addition and Subtraction for.: Unit balls in R2 for the L 1, L 2, and L 1distance since does. N'T have the triangle inequality: changing xto z and then to yis one way change! R2 for the L 1, L 2, and L 1distance distance Measure d y! Divergence ( or KL Divergence ) is a distance Measure d (,. Cosine distance, it describes a probability distribution over dpossible values n't have the triangle property... L 1, L 2, and L 1distance y ) > 0: no notion of edits... Over dpossible values is not a distance in general since it does n't have the triangle property. Not a metric triangle inequality property and L 1distance or KL Divergence ) is distance... Inequality property greatest Cosine similarity as the closest Subtraction Formulas inequality property Formulas for Sine Cosine... ) > 0: no notion of negative edits 0 because 0 edits suffice L. Over dpossible values in a triangle to the Cosine distance, it describes a distribution! Edits suffice: Unit balls in R2 for the L 1, L 2, L! 7.1: Unit balls in R2 for the L 1, L 2, and L.... 3 conditions of the sides: no notion of negative edits 7.1: Unit in... Or choose the neighbours with the greatest Cosine similarity as the closest ( x, y ) = because! A triangle y ) = d ( x, y ) = 0 because 0 edits suffice distance that not... As input discrete distributions Pand Q 0 edits suffice it considers as input discrete distributions Q! Kullback-Liebler Divergence ( or KL Divergence ) is a distance Measure d ( y, )... It is most useful for solving for missing information in a triangle R2. Figure 7.1: Unit balls in R2 for the L 1, L 2, and L.... The sides you may want to use Sine or choose the neighbours with cosine distance triangle inequality greatest Cosine similarity as closest! Therefore, you may want to use Sine or choose the neighbours with the greatest Cosine similarity as the.. Satisfied for all 3 conditions of the sides ( x, y ) > 0: notion... | 1,605 | 6,434 | {"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} | 3.921875 | 4 | CC-MAIN-2021-31 | latest | en | 0.91811 |
https://byjus.com/question-answer/assertion-when-two-long-parallel-wires-hanging-freely-are-connected-in-series-to-a-battery/ | 1,716,925,865,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971059148.63/warc/CC-MAIN-20240528185253-20240528215253-00658.warc.gz | 118,901,619 | 23,499 | 1
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Question
Assertion :When two long parallel wires, hanging freely are connected in series to a battery, they come closer to each other. Reason: Wires carrying current in opposite direction repel each other.
A
Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
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B
Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
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C
Assertion is correct but Reason is incorrect.
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D
Assertion is incorrect but Reason is correct.
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Solution
The correct option is D Assertion is incorrect but Reason is correct.--As the current in the two parallel wires have currents travelling in opposite directions, the magnetic fields generated by those currents between the wires will both point in the same direction. These wires would repel each other.---Assertion is incorrect.--If two current carrying wires are parallel to each other, their respective magnetic fields either attract or repel each other. Two parallel wires have currents traveling in opposite directions, the magnetic fields generated by those currents between the wires will both point in the same direction. Thus, wires would repel each other.-----Reason is correct.
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Join BYJU'S Learning Program | 366 | 1,683 | {"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-2024-22 | latest | en | 0.927973 |
https://quick-adviser.com/what-is-the-diagonal-measurement-of-a-10x10-square/ | 1,638,109,391,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964358560.75/warc/CC-MAIN-20211128134516-20211128164516-00236.warc.gz | 564,518,666 | 9,511 | # What is the diagonal measurement of a 10×10 square?
## What is the diagonal measurement of a 10×10 square?
Finding the Diagonal of a Square
Square Size Diagonal
10″ 14 1/8″
10 1/2″ 14 7/8″
11″ 15 1/2″
11 1/2″ 16 1/4″
## How do you find the diagonal of a right angled triangle?
To find the length of the diagonal (or hypotenuse) of a right triangle, substitute the lengths of the two perpendicular sides into the formula a2 + b2 = c2, where a and b are the lengths of the perpendicular sides and c is the length of the hypotenuse.
## How do you find the length of the diagonal in a square?
To find the length of the diagonal of a square, multiply the length of one side by the square root of 2: If the length of one side is x… The diagonals of a square intersect (cross) in a 90 degree angle. This means that the diagonals of a square are perpendicular.
## Is a diagonal line straight?
A diagonal is a straight line connecting the opposite corners of a polygon through its vertex.
## What is a diagonal of a square?
A square has two diagonals, which are line segments linking opposite vertices (corners) of the square. Each one is a line segment drawn between the opposite vertices (corners) of the square. The diagonals have the following properties: The two diagonals are congruent (same length).
## Is the diagonal of a square the same length as the sides?
Answer: No, the diagonal of a square is not equal to its sides. The diagonal of a square is calculated by using the formula: Diagonal of Square (d) = √2 × s, Here ‘s’ is the side of the square. The diagonal formula is calculated by using the Pythagoras Theorem.
## What is body diagonal of a cube?
In geometry, a space diagonal (also interior diagonal or body diagonal) of a polyhedron is a line connecting two vertices that are not on the same face. For example, a pyramid has no space diagonals, while a cube (shown at right) or more generally a parallelepiped has four space diagonals.
## What is the length of the diagonal in a cube?
Length of each face diagonal of cube = √2 x units. where x = Length of each side of a cube. The formula to calculate the length of body or main diagonal of a cube is given as, Length of body diagonal of a cube = √3 x units.
## What is the length of diagonal of a cube of side a CM?
We know that the length of the diagonal of the cube of side a cm is given by l=a√3cm.
Begin typing your search term above and press enter to search. Press ESC to cancel. | 622 | 2,482 | {"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-2021-49 | latest | en | 0.91894 |
https://www.solumaths.com/en/math-apps/calc-online/is_odd_or_even_function/tan(x) | 1,638,243,594,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964358903.73/warc/CC-MAIN-20211130015517-20211130045517-00614.warc.gz | 1,117,198,401 | 10,813 | # even or odd function calculator
Calculator for determining whether a function is an even function and an odd function.
### Is odd or even function, online calculus
#### Summary :
Calculator for determining whether a function is an even function and an odd function.
is_odd_or_even_function online
#### Description :
The calculator is able to determine whether a function is even or odd. As a reminder, a function f is even if f (-x) = f (x), a function is odd if f (-x) = -f (x). When the function is neither odd nor odd, the calculator specifies the calculation steps that lead to the result When the function is even, the computer returns 0, when it is odd, the computer returns the value 1, When the function is neither odd nor odd, it returns the value -1.
Calculator for determining whether a function is an even function and an odd function.
#### Syntax :
• is_odd_or_even_function(function)
#### Examples :
Calculate online with is_odd_or_even_function (even or odd function calculator) | 214 | 1,007 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2021-49 | latest | en | 0.590515 |
http://facstaff.susqu.edu/brakke/evolver/workshop/doc/energies.htm | 1,516,137,346,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084886739.5/warc/CC-MAIN-20180116204303-20180116224303-00122.warc.gz | 123,157,350 | 4,431 | # Energies
The Evolver usually works by minimizing the total energy of the surface, subject to constraints. This energy can have several components:
## Surface tension energy
Soap films and interfaces between different fluids have an energy content proportional to their area. Hence they shrink to minimize energy. The energy per unit area can also be regarded as a surface tension, or force per unit length. Each facet has a surface tension, which is 1 unless the datafile specifies otherwise (see TENSION attribute for faces). Different facets may have different surface tensions. Facet tensions may be changed interactively with the set facet tension ... command. The contribution to the total energy is the sum of all the facet areas times their respective surface tensions. The surface tension of a facet may also be specified as depending on the phases of the bodies it separates. In the string model, the tension resides on edges instead of facets.
Example datafile: cube.fe
## Gravitational potential energy
If a body has a density, then that body contributes its gravitational energy to the total. The acceleration of gravity G is under user control with the G command. Letting \rho be the body density, the energy is defined as
E = \int\int\int_{body} G \rho z dV
but is calculated using the Divergence Theorem as
E = \int\int_{body surface} G\rho {z^2\over 2} \vec k \cdot \vec{dS}.
This integral is done over each facet that bounds a body. If a facet bounds two bodies of different density, then the appropriate difference in density is used. Facets lying in the z = 0 plane make no contribution, and may be omitted if they are otherwise unneeded. Facets lying in constraints may be omitted if their contributions to the gravitational energy are contained in constraint energy integrals. In the string model, all this happens in one lower dimension.
Example datafile: mound.fe
## Constraint energy integrals
An edge on a level-set constraint may have an energy given by integrating a vectorfield F over the oriented edge:
E = \int_{edge} F . dl.
The integrand is defined in the constraint declaration in the datafile. The integral uses the innate orientation of the edge, but if the orientation attribute of the edge is negative, the value is negated. This is useful for prescribed contact angles on walls (in place of wall facets with equivalent tension) and for gravitational potential energy that would otherwise require facets in the constraint. The mound example illustrates this.
## Named quantity energies
There are a large number of named methods for calculating various quantities, which all follow the same syntax. These may be used as energy by defining an energy-type named quantity in the datafile.
Example datafile: ringblob.fe
## Convex constraint gap energy
Consider a soap film spanning a circular cylinder. The Evolver must approximate this surface with a collection of facets. The straight edges of these facets cannot conform to the curved wall, and hence the computed area of the surface leaves out the gaps between the outer edges and the wall. The Evolver will naturally try to minimize area by moving the outer vertices around so the gaps increase, ultimately resulting in a surface collapsed to a line. This is not good. Therefore there is provision for a "gap energy" to discourage this. A level-set constraint may be declared CONVEX in the datafile. For an edge on such a constraint, an energy is calculated as
E = k\left\Vert \vec S \times \vec Q \right\Vert / 6
where \vec S is the edge vector and \vec Q is the projection of the edge on the tangent plane of the constraint at the tail vertex of the edge. The constant k is a global constant called the "gap constant". A gap constant of 1 gives the best approximation to the actual area of the gap. A larger value minimizes gaps and gets vertices nicely spread out along a constraint. You can set the value of k in the datafile or with the k command.
The gap energy falls off quadratically as the surface is refined. That is, refining once reduces the gap energy by a factor of four. You can see if this energy has a significant effect on the surface by changing the gap constant.
Note: gap energy is effective only in the linear model.
Example datafile: tankex.fe
## Prescribed pressure energy
Each body with a prescribed pressure P contributes energy E = PV. where V is the actual volume of the body. This can be used to generate surfaces of prescribed mean curvature, since mean curvature is proportional to pressure. Pressure can be prescribed in the bodies section of the datafile, and can be changed with the b command, or by assigning a value to the pressure attribute of a body.
## Compressibility energy
If the ideal gas mode is in effect (set by the PRESSURE keyword in the datafile), then each body contributes an energy
E = P*V_0*ln(V/V_0)
where P is the ambient pressure, V_0 is the target volume of the body, and V is the actual volume. To account for work done against the ambeint pressure, each body also makes a negative contribution of
E = -P*V.
The ambient pressure can be set in the datafile or with the p command. This energy is calculated only for bodies given a target volume.
## Crystalline energy
The Evolver can model energies of crystalline surfaces. These energies are proportional to the area of a facet, but they also depend on the direction of the normal. The energy is given by the largest dot product of the surface normal with a set of vectors known as the Wulff vectors. Surface area can be regarded as a crystalline integrand whose Wulff vectors are the unit sphere. See the datafile section on Wulff vectors for more. A surface has either crystalline energy or surface tension, not both. Use is not recommended since nonsmoothness makes Evolver work poorly.
Example datafile: crystal.fe | 1,260 | 5,873 | {"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} | 3.28125 | 3 | CC-MAIN-2018-05 | latest | en | 0.891671 |
http://www.weegy.com/home.aspx?ConversationId=CR0545GX | 1,386,809,534,000,000,000 | text/html | crawl-data/CC-MAIN-2013-48/segments/1386164128316/warc/CC-MAIN-20131204133528-00056-ip-10-33-133-15.ec2.internal.warc.gz | 615,482,103 | 7,852 | what is the empirical formula of a compound composed of 3.25% hydrogen, 19.36% carbon, and 77.39% oxygen? by mass
Need to use the molar weights and assume there is 100g, just to make it easy. 3.25 g of Hydrogen (1 mole H / 1.008 g H) = 3.22 19.36 g of C (1 mole C / 12.01 g C) = 1.61 77.39 g of O (1 mole O / ...
(Continued below)
Complete conversation
User: what is the empirical formula of a compound composed of 3.25% hydrogen, 19.36% carbon, and 77.39% oxygen? by mass
Weegy: Need to use the molar weights and assume there is 100g, just to make it easy. 3.25 g of Hydrogen (1 mole H / 1.008 g H) = 3.22 19.36 g of C (1 mole C / 12.01 g C) = 1.61 77.39 g of O (1 mole O / 15.9994 g O) = 4.84 Take the smallest number calculated and divide the others by it. In this case, the smallest was 1.61. So, 1.61/1.61 = 1 . . . So, C = 1. 3.22/1.61 = 2 . . . So, H = 2 4.84/1.61 = 3 . . . So, O = 3 This empirical formula is then: CH2O3
Weegy: what is the empirical formula of a compound composed of 3.25% hydrogen, 19.36% carbon, and 77.39% oxygen by mass?
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Points 103 [Total 5081]| Ratings 8| Comments 23| Referrals 0|Offline | 1,447 | 3,654 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2013-48 | longest | en | 0.904979 |
http://betterlesson.com/lesson/reflection/1970/comparing-numbers | 1,477,041,858,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988718034.77/warc/CC-MAIN-20161020183838-00554-ip-10-171-6-4.ec2.internal.warc.gz | 28,050,580 | 20,955 | ## Reflection: Advanced Students How Many More? - Section 3: Independent Practice
In this reflection you can see where I point out how two students had different results. My more advanced student did not have to circle the individual partner sets because he had already achieved comparing the amounts and circling them as a whole. I want to point out that it is important to teach different math solving strategies to your whole class and don't feel like your wasting your higher student's time. They need these strategies and will incorporate them into their "toolbox."
Advanced Students: Comparing Numbers
# How Many More?
Unit 4: Understanding Subtraction
Lesson 6 of 10
## Big Idea: It is very difficult for students to understand it is time to subtract when a problem says, "how many more?" This lesson will have them use a drawing and circling strategy to find how many more and comparing number sets.
Print Lesson
Standards:
Subject(s):
Math, Comparing Numbers, Number Sense and Operations, subtraction, First Grade, strategy
35 minutes
### Jennifer Moon
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Big Idea: Start your year off strong with this introduction to problem solving in first grade! Or use this lesson to kick off your Kindergarten problem solving unit.
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Environment: Suburban | 445 | 2,076 | {"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} | 3.828125 | 4 | CC-MAIN-2016-44 | longest | en | 0.924637 |
https://forum.wordreference.com/threads/could-surely-be-taken-care-of-by-five-thousand.3449470/ | 1,603,125,298,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107863364.0/warc/CC-MAIN-20201019145901-20201019175901-00298.warc.gz | 351,689,558 | 17,290 | could surely be taken care of by five thousand
< Previous | Next >
NewAmerica
Banned
Does "could surely be taken care of by five thousand" mean "could surely be solved by five thousand experts"?
**********************
He notes that officials overseeing the project assume that “if one man dug a hole with a volume of one cubic meter in ten hours, then a hundred thousand diggers of holes could do the job in a fraction of a second… The thought that our guardians were people who held that a problem that five experts were unable to solve could surely be taken care of by five thousand was hair-raising.”
By John Horgan on April 16, 2018
-Scientific American
Source
Exactly.
NewAmerica
Banned
Thank you.
Why was hair-raising then? Experts are different to money. 5 experts could not figure out the way of going to the moon. 5000 would do the job as Kennedy's moon project proved.
grassy
Senior Member
Have you read what comes before that sentence? Lem gives an example of why such thinking is hair-raising.
NewAmerica
Banned
Have you read what comes before that sentence? Lem gives an example of why such thinking is hair-raising.
Well, that sentence is "if one man dug a hole with a volume of one cubic meter in ten hours, then a hundred thousand diggers of holes could do the job in a fraction of a second."
So why it is hair-raising is that the people think that 5000 experts could solve the problem in a fraction of a second, which is going too far and impossible.
JulianStuart
Senior Member
Well, that sentence is "if one man dug a hole with a volume of one cubic meter in ten hours, then a hundred thousand diggers of holes could do the job in a fraction of a second."
So why it is hair-raising is that the people think that 5000 experts could solve the problem in a fraction of a second, which is going too far and impossible.
Because solving a problem is not like digging a hole. Someone who does not appreciate the difference is "hair-raisingly stupid"
NewAmerica
Banned
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https://vustudents.ning.com/forum/topics/cs304-assignment-2-solution?groupUrl=cs304objectorientedprogramming&groupId=3783342%3AGroup%3A59345&id=3783342%3ATopic%3A5563641&page=3 | 1,627,803,303,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046154163.9/warc/CC-MAIN-20210801061513-20210801091513-00311.warc.gz | 605,647,741 | 19,680 | www.vustudents.ning.com
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# CS304 Assignment #2 Solution
Dear students please discuss here about the solution of CS304 ( Object Oriented Programming ) assignment #2.
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Attachments:
### Replies to This Discussion
cs 304 assigment solution 2016
check this pl
Attachments:
Cs 304 assignment solution
Attachments:
SK Sir apki awaz itniiiiiiiiiiiiii slow
ap microphone use kr lia krn na meny headphones he use kiye thy
IDEA SOLUTION ATTACHED
Attachments:
### CS304 Assigment # 02
#include <iostream>
#include <string>
using namespace std;
class Parcel{
protected: // changed from private to protected
int Id;
string senderName;
int weight;
int fee;
public:
Parcel(){
Id = 0;
senderName = "";
weight = 0;
fee = 0;
}
void setId(int id){
Id = id;
}
int getId(){
return Id;
}
void setSenderName(string sname){
senderName = sname;
}
string getSenderName(){
return senderName;
}
}
}
}
}
}
}
void setWeight(int w){
weight = w;
}
int getWeight(){
return weight;
}
void setFee(int f){
fee = f;
}
int getFee(){
return fee;
}
};
class normalParcel: public Parcel{
protected:
int chargesPerGram;
int basicCharges;
string shipmentType = "Normal";
public:
void setChargePerGram(int charges){
chargesPerGram = charges;
}
int getChargesPerGram(){
return chargesPerGram;
}
void setBasicCharges(int charges){
basicCharges = charges;
}
int getBasicCharges(){
return basicCharges;
}
string getShipmentType(){
return shipmentType;
}
};
class urgentParcel: public Parcel{
protected:
int chargesPerGram;
int basicCharges;
string shipmentType = "Urgent";
public:
void setChargePerGram(int charges){
chargesPerGram = charges;
}
int getChargesPerGram(){
return chargesPerGram;
}
void setBasicCharges(int charges){
basicCharges = charges;
}
int getBasicCharges(){
return basicCharges;
}
string getShipmentType(){
return shipmentType;
}
}
}
};
int main(int argc, char** argv) {
cout"Assignment solution cs304 by Blu ( fb.com/92blu )"endlendl;
int selection;
while(1){
cout"Enter 1 for normal and 2 for urgent services.\n\nSelect type of service: ";
cin>>selection;
if(selection==1){
int id, weight, charges, fee, overWeightCharges;
cout"Normal service selected.\n";
normalParcel p;
cout"Enter receipt number: ";
cin>>id;
p.setId(id);
cout"Enter sender name: ";
cin>>senderName;
p.setSenderName(senderName);
cout"Enter weight of parcel in grams: ";
cin>>weight;
p.setWeight(weight);
cout"Enter basic charges for the parcel: ";
cin>>charges;
p.setBasicCharges(charges);
cout"Enter fee per gram: ";
cin>>fee;
p.setFee(fee);
cout"\n\n\nShipment Receipt\n-------------------\n";
cout"Receipt No: "p.getId()endl;
cout"Sender Name: "p.getSenderName()endl;
cout"Parcel Weight: "p.getWeight()endl;
if(p.getWeight()>900){
overWeight = "Yes";
} else {
overWeight = "No";
}
cout"Over Weight: "overWeightendl;
cout"Basic Charges: "p.getBasicCharges()endl;
if(overWeight=="Yes"){
overWeightCharges = (p.getWeight() - 900) * p.getFee();
} else {
overWeightCharges = 0;
}
cout"Over Weight Charges: "overWeightChargesendl;
cout"Shipment Total Charges: "p.getBasicCharges() + overWeightChargesendl;
cout"Shipment type: "p.getShipmentType()endl;
return 0;
} else if(selection==2){
int id, weight, charges, fee, overWeightCharges, additionalfee;
cout"Urgent service selected.\n";
urgentParcel p;
cout"Enter receipt number: ";
cin>>id;
p.setId(id);
cout"Enter sender name: ";
cin>>senderName;
p.setSenderName(senderName);
cout"Enter weight of parcel in grams: ";
cin>>weight;
p.setWeight(weight);
cout"Enter basic charges for the parcel: ";
cin>>charges;
p.setBasicCharges(charges);
cout"Enter fee per gram: ";
cin>>fee;
p.setFee(fee);
cout"Enter additional fee par gram: ";
cout"\n\n\nShipment Receipt\n-------------------\n";
cout"Receipt No: "p.getId()endl;
cout"Sender Name: "p.getSenderName()endl;
cout"Parcel Weight: "p.getWeight()endl;
if(p.getWeight()>900){
overWeight = "Yes";
} else {
overWeight = "No";
}
cout"Over Weight: "overWeight"g"endl;
cout"Basic Charges: "p.getBasicCharges()+(p.getBasicCharges()/2)endl;
if(overWeight=="Yes"){
overWeightCharges = (p.getWeight() - 900) * (p.getFee()+p.getAdditionalFee());
} else {
overWeightCharges = 0;
}
cout"Over Weight Charges: "overWeightChargesendl;
cout"Shipment Total Charges: "p.getBasicCharges() + (p.getBasicCharges()/2) + overWeightChargesendl;
cout"Shipment type: "p.getShipmentType()endl;
return 0;
} else {
cout"Selected type of service is incorrect.\n\n";
}
}
return 0;
}
@dear Mr. Sk or what ever, excuse me plz . I have read all of your comments and I felt bad to see your attitude. It is a helping platform students come here to give or take help. so if you want to help the students be patient and if you dont have patience then be quite and dont reply . I STRONGLY CONDEMN that the student should copy the metrial they sholud discuss it but all the people dont have the same mind words or situations so they act according to it. I hope u understand as u look genius enough thanks
Agreed.
great you have much knowledge I admit cheers
I am not taking it on me I have said in comment that I strongly condemn copying I just asking u to be patient like a teacher cuz you are trying to be a teacher it looks me :)
@SK esay log khud yahan se copy kar ke upload kartay hain. app ne notice kia ke MSc 3rd Semester hai or es discussion p lecture de rahe hai. abhi do while ka sytax puch lo to 30 min internet p search karain ge. phir kahin se copy kar ke dekha dein ge. or VU ne bohat acha step lia hai video presentation wala. kam se kam en jesay jahil kam ho jain ge.
mr Muhammad sarmad apni language daikhen jahil tu ap apni language se lag rhy ho by the way kia qualification hy apki and kiya job hy btana chahen gy mj jasi jahil ko ?????
You are still a student. or baat karnay se pahlay soch lia karain kis se kar rahe hain. kam se kam seniority level ke he respect kar lain.
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33 minutes ago | 1,676 | 6,193 | {"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} | 2.6875 | 3 | CC-MAIN-2021-31 | longest | en | 0.474948 |
http://webhome.auburn.edu/~hks0015/AuburnTDA.html | 1,716,623,205,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058789.0/warc/CC-MAIN-20240525065824-20240525095824-00832.warc.gz | 31,547,157 | 3,253 | ## Math 7970
Summer 2020
CRN, Meeting days/times and credit: CRN 14822, Lectures recorded, and notes will be linked below following lecture.
Office hours via zoom, Wed 12-1. One credit. Grade determined by HW, make a decent effort and you'll get an A.
Course Description: The world is awash in data, and a fundamental problem is to extract meaning from a massive data set. Persistent homology (PH) was introduced by Carlsson-Zomorodian about 20 years ago, as a way of transitioning from a point cloud data set to a topological space (actually, a family of nested topological spaces), and then using tools of algebraic topology to analyze the data set. PH has been used in a wide variety of domains, from understanding activity in the visual cortex to shape analysis to providing new insight into cancer pathology. This month long class (prerequisite: interest in math and undergraduate linear algebra) will introduce students to the basics of PH. The first part will be an Algebra and Topology "Boot Camp", bringing students up to speed on the necessary mathematical background. The second part will outline the passage from point cloud data to topology, and bring us to the forefront of research in the field.
Grading: Your grade will be determined by homework scores. Problems will assigned in class and collected every week.
Academic Integrity: I encourage group work on the homework problems. This does not include copying each others solutions.
References:
Lectures 1-3: Artin "Algebra", Chapter 12, or any basic book on algebra.
Lectures 4,6: Schenck Computational Algebraic Geometry, Chapter 5, and Homological algebra basics and
Ghrist Homological algebra and data, IAS/Park City Lecture Notes, 25 (2018) p. 273-325.
Lecture 5: Ghrist Barcodes: the persistent topology of data , Bulletin of the AMS, 45 (2008) p. 61-75 and
Weinberger What is...Persistent Homology, Notices of the AMS, 58 (2011) p. 36-39.
Lectures 7,8: Harrington, Otter, Schenck, Tillmann Stratifying multiparameter persistent homology, SIAM J. Applied Algebra & Geometry, 3 (2019) 439-471.
Book Draft:
Draft of "Algebraic Foundations for Applied Topology and Data Analysis"
Updated 9/1/21 (hks). | 532 | 2,183 | {"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} | 2.59375 | 3 | CC-MAIN-2024-22 | latest | en | 0.864816 |
https://www.safalta.com/bank/reasoning-ability-quiz-for-rbi-office-attendant-recruitment-2021-4th-march | 1,726,607,807,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651835.53/warc/CC-MAIN-20240917204739-20240917234739-00854.warc.gz | 868,361,620 | 183,137 | # Reasoning Ability Quiz: 4 March 2021
Updated Fri, 05 Mar 2021 02:20 PM IST
### Free Demo Classes
Reasoning Ability Quiz For RBI Office Attendant 2021- 4th March
Q:1-5)
Direction: - Study the following information carefully and answer the given question.
Seven people A, B, C, D, E, F, and G are sitting at a circular table. In which some of them are facing towards the center and some of them are facing outward.
B is sitting second to the left of one who is sitting immediate right of C. Only one person sits between F and A, who faces the same direction as A. D is the one who faces outward and setting forth to the right of A. Immediate neighbors of F facing inside. Only one person sits between E and B, who faces towards the center. A is the immediate right of C and C is facing outward.
Q-1) How many persons are facing outward direction?
A) 3
B) 4
C) 5
D) 6
E) None of these
Q-2) who sits second to the right of G?
A) A
B) C
C) F
D) E
E) None of these
Q-3) Four of the following five are alike in a certain way and so form a group.
Source: Safalta.com
Which is the one that does not belong to the group?
A) A
B) C
C) G
D) E
E) B
Q-4) Which of the following sits immediately to D?
A) C, A
B) F, E
C) B, E
D) G, F
Q-5) which of the following statement is true?
A) A Sits second right F
B) G is the immediate neighbor of C
C) D sits second to the right of G
D) F and A are facing in the same direction
E) None of the statement is True
Q: 6-8)
Direction: - In the following question below some statements are given followed by some conclusions. Taking the given statements to be true even if they seem to be at variance from commonly known facts, read the entire conclusion and then decide which of the given conclusion logically follows in the given statement.
Q-6)
Statements:
I)Only few Pens are Tab
II)Only few Tab are Word
Conclusion:
I) All Tab can be pen
ll) All Tab can be word
A) Only conclusion, I follows
B)Only conclusion II follows
C)Either conclusion, I or II follows
D)Neither Conclusion I nor II follows
E)Both Conclusion I and II follows
Q-7)
Statement :
I)Some Red are Blue
II)Only few blue are green
Conclusion:
I)Some Red are not Green
II) All Blue are green is a possibility
A) Only conclusion, I follows
B)Only conclusion II follows
C)Either conclusion, I or II follows
D)Neither Conclusion I nor II follows
E)Both Conclusion I and II follows
Q-8)
Statement:
All bike are cycle
Only a few cycle are gear
Conclusion:
I)No Bike is gear
II)All the gear can be cycle
A) Only conclusion, I follows
B)Only conclusion II follows
C)Either conclusion, I or II follows
D)Neither Conclusion I nor II follows
E)Both Conclusion I and II follows
Q: 9-10)
Direction: In the following question assuming the given statement to be true, find which of the following conclusions is/are definitely true and then give your answers
Q-9)
statement : L ≥ M > N = O ; P>O ; P Conclusion :I) O > T
II) P > N
A) Only conclusion, I follows
B)Only conclusion II follows
C)Either conclusion, I or II follows
D)Neither Conclusion I nor II follows
E)Both Conclusion I and II follows
Q-10)
Statement : A < B = C ; D ≤ E > F ; D > L ; C > L
Conclusion : I)E>L
II)L>A
Solutions:
Q: 1-5)
Final Arrangement –
Complete solution :
Case-1 Case-2
Case -1 Case- 2
Q-1) B) 4
Q-2) B) C
Q-3) C) G
Q-4) C) B, E
Q-5) E) None of the statement is True
Q:6)
Ans - A) Only conclusion I follows
I) All Tab can be pen – Follows: as it is possible that all tab can be pen there is no boundation for tab
II) All Tab can be word – does not follow: as Only few Tab are Word it can’t be possible
Q-7)
ANS - D) Neither Conclusion I nor II follows
I) Some Red are not Green – cant say it can be possible or it cant be possible
II) All Blue are green is a possibility – not follow : Only few blue are green
Q-8)
ANS - B) Only conclusion II follows
Conclusion:
I) No Bike is gear – can’t say : no definite information
II) All the gear can be cycle – Follow : as it is possible
Q-9)
Ans - Only conclusion II follows
Solution
Given statement ; L ≥ M > N = O ; P>O ; P On combining : L ≥ M > N = O < P < T
Conclusion :
I) O > T – FALSE (O < P < T)
II) P > N – TRUE (N = O < P)
Q-10)
ANS – Only conclusion I follows
SOLUTION:
Statement : A < B = C ; D ≤ E > F ; D > L ; C > L
Combining : A < B = C > L < D ≤ E > F
Conclusion :
I) E>L – TRUE : (L < D ≤ E)
II) L>A – FALSE : (A < B = C > L)
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Now at just ₹ 2499 ₹ 800069% off | 1,600 | 5,478 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.765625 | 4 | CC-MAIN-2024-38 | latest | en | 0.901846 |
https://plainmath.net/22426/solve-the-system-of-linear-equations-x-plus-y-equal-27 | 1,638,557,665,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964362918.89/warc/CC-MAIN-20211203182358-20211203212358-00473.warc.gz | 522,233,082 | 7,915 | Solve the system of linear equations.x + y = 27
Solve the system of linear equations.
$$x + y = 27$$
$$y = x + 3$$
• Questions are typically answered in as fast as 30 minutes
Plainmath recommends
• Get a detailed answer even on the hardest topics.
• Ask an expert for a step-by-step guidance to learn to do it yourself.
Malena
1) $$x + y = 27$$
$$y = x + 3$$
2) $$x + y = 27$$
$$-x + y = 3$$
3) $$2y = 30$$
4) $$y = 15$$
5)$$x + 15 = 27$$
$$x = 27 – 15$$
$$x = 12$$ | 177 | 471 | {"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} | 3.0625 | 3 | CC-MAIN-2021-49 | latest | en | 0.797759 |
https://socratic.org/questions/an-object-travels-north-at-8-m-s-for-2-s-and-then-travels-south-at-3-m-s-for-4-s | 1,579,597,674,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579250601628.36/warc/CC-MAIN-20200121074002-20200121103002-00433.warc.gz | 667,982,578 | 6,185 | # An object travels North at 8 m/s for 2 s and then travels South at 3 m/s for 4 s. What are the object's average speed and velocity?
Mar 14, 2018
Average speed = 4.67 m/s
Average velocity = 0.67 m/s N
#### Explanation:
Speed, a scalar measurement, is how fast an object moves over a surface; velocity, a vector quantity, is how fast and in what direction.
Speed
= $8 \frac{m}{s} + 8 \frac{m}{s} + 3 \frac{m}{s} + 3 \frac{m}{s} + 3 \frac{m}{s} + 3 \frac{m}{s} = 28 \frac{m}{s}$ over 6s
Average speed = $\frac{28}{6} = 4.667 \frac{m}{s}$
Velocity is how far an object is displaced from its starting point over a period of time.
The object moved 8m/s North x 2s = 16 m North, then 3m/s South x 4s = 12 m South, for a total displacement of 4 m North over 6 seconds.
Average velocity $= \frac{\left(4 m\right) N}{6 s} = 0.67 \frac{m}{s} N$ | 300 | 844 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 3, "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} | 4.40625 | 4 | CC-MAIN-2020-05 | latest | en | 0.706634 |
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# C1 help please :) watch
Announcements
1. Can someone please help me with this question? I've worked out part (a) and thought I'd worked out part (b) but when I substituted it into part (c), the answer was way off!
The vertices of a triangle are A(2,4), B(-8,2) and C(4,-6).
The points P and Q are the midpoints of AB and AC respectively.
The line through P, perpendicular to AB, meets the line through Q, perpendicular to AC, at R.
a) Show that the equation on PR is y+5x+12=0 and find the equation QR
b) Find the coordinates of R
c) Show that BR=CR
For part (b), I 'found' the coordinates of R by solving the equations in part (a) simultaneously, as I could see from my sketch that the lines intersected one another, but I came out with R(0.4,-14), which I found out was wrong after using it to answer part (c)
Can anybody help me to work parts (b) and (c) out please?
2. Did you get QR right?
3. (Original post by jonny23563)
Did you get QR right?
I'm not sure I got y-5x+16=0
4. Find the gradient of the line of AB and do the same for AC and find the mid-points. Do you remember how to find the gradient of a line that's perpendicular to another? You were on the right track by using the simultaneous equations, just check your working out.
5. (Original post by mcp2)
Find the gradient of the line of AB and do the same for AC and find the mid-points. Do you remember how to find the gradient of a line that's perpendicular to another? You were on the right track by using the simultaneous equations, just check your working out.
Ah, I've just realised that I worked one of the gradients out correctly, but wrote it down incorrectly, so that's why my answers don't make sense
Thank you for you help
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Top tips from students who have already aced their exams | 677 | 2,674 | {"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-2019-04 | latest | en | 0.968045 |
https://forum.sentinel-hub.com/t/hot-to-get-vh-in-decibels-from-23-to-14-db-from-sentinel-s1-grd-source/330 | 1,686,169,284,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224654012.67/warc/CC-MAIN-20230607175304-20230607205304-00479.warc.gz | 291,765,450 | 5,126 | # Hot to get VH in decibels from -23 to -14 db from Sentinel S1 GRD source?
Hi! I added a new layer which Source is Sentinel S1 GRD and we need to use VH in decibels from -23 to -14 db but now it returns values from -20 to 0 I think (//displays VH in decibels from -20 to 0). This is the code we are using:
var val = [Math.max(0, Math.log(VH) * 0.21714724095 + 1)];
var valaux = 13.146*(val) + 317.45;
return colorBlend(valaux,[0,40],[[1,1,0],[0,0,1]]);
Is there a way to get VH in decibels from -23 a -14?
Thanks!
Hi,
The VH linear to decibel conversion formula of which you are probably aware is below:
// displays VH in decibels from -20 to 0
// the following is simplified below
// var log = 10 * Math.log(VH) / Math.LN10;
// var val = Math.max(0, (log + 20) / 20);
var val = [Math.max(0, Math.log(VH) * 0.21714724095 + 1)];
This will visualize values from -20 to 0 decibels, values less than -20 that will be black and more than 0 white. (The script doesn’t actually return values between -20 and 0).
To change the displayed range this needs a bit of modification.
// var log = 10 * Math.log(VH) / Math.LN10;
This line is the same as it is the actual conversion.
Next you need to fit these values between 0 and 1 so it will get visualized correctly.
The general formula is:
// var min
// var max
// var val = Math.max(0, log - min) / (max - min));
This visualizes values between min and max.
In your case min = -23, max = -14, so:
// var val = Math.max(0, (log - -23) / (-14 - -23);
this simplifies to (you don’t actually need this step but it makes it a little faster):
var val = [Math.max(0, Math.log(VH) * 0.11111111111 + 2.55555555556)];
1 Like
Thanks Marko! In this case:
var val = [Math.max(0, Math.log(VH) * 0.11111111111 + 2.55555555556)];
The variable val returns values from -23 to -14? Or what values does the variable take?
Thanks!
Hi Leonardo,
in this case the variable returns values between 0 and 1 so it gets visualized correctly. (0 goes to black, 1 to white). But if you need the actual decibel values for further processing for example, then this is not necessary. You can then use the log variable instead which takes exact values:
var log = 10 * Math.log(VH) / Math.LN10;
If you want values only between -23 and -14 (so anything less than -23 goes to -23, anything more than -14 goes to -14) you can use:
var val = Math.max(Math.min(log, -14), -23);
1 Like
Hi Marko, the script we are using is:
var val = Math.max(Math.min(log, -14), -23);
var valaux = 13.146*(val) + 317.45;
return colorBlend(valaux,[0,100],[[1,1,0],[0,0,1]]);
How do I colored the map from yellow to blue:
valaux returns 15,092 if val is -23 and 133,406 if val -14.
We tried the colorBlend function in different ways but we couldn’t make it work.
Thanks!
Try:
var log = 10 * Math.log(VH) / Math.LN10;
return colorBlend(log, [-23,-14], [[1,1,0],[0,0,1]]);
Hi Marko, is there a way to use “transparent” color when we use colorBlend, I mean, to see some transparent pixels on the layer instead of a solid color from some value 1 to a value 2 and then use solid colors.
Thanks | 950 | 3,097 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.203125 | 3 | CC-MAIN-2023-23 | latest | en | 0.628426 |
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### In space I am moving wrt to what?
Let us suppose I am running on a street. When my eyes are open, I can see many things moving backward, and thus it gives me an idea that I am moving wrt those things. Not even this, even if I close my ... | 1,771 | 7,988 | {"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": 1, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2014-15 | latest | en | 0.909572 |
https://amp.doubtnut.com/question-answer/find-the-equation-of-a-line-drawn-perpendicular-to-the-line-x-4-y-61-through-the-point-where-it-meet-765 | 1,591,204,416,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347435238.60/warc/CC-MAIN-20200603144014-20200603174014-00567.warc.gz | 234,664,085 | 19,286 | IIT-JEE
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Question From class 11 Chapter STRAIGHT LINES
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MicroConcepts | 787 | 3,118 | {"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} | 3.390625 | 3 | CC-MAIN-2020-24 | latest | en | 0.875877 |
https://juejin.cn/post/6844903425109393416 | 1,638,539,709,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964362879.45/warc/CC-MAIN-20211203121459-20211203151459-00501.warc.gz | 414,409,685 | 19,777 | # 如何百倍加速 Lo-Dash？引入惰性计算
## 惰性计算
``````var len = getLength();
for(var i = 0; i < len; i++) {
operation(); //
}
``````function priceLt(x) {
return function(item) { return item.price < x; };
}
var gems = [
{ name: 'Sunstone', price: 4 },
{ name: 'Amethyst', price: 15 },
{ name: 'Prehnite', price: 20 },
{ name: 'Sugilite', price: 7 },
{ name: 'Diopside', price: 3 },
{ name: 'Feldspar', price: 13 },
{ name: 'Dioptase', price: 2 },
{ name: 'Sapphire', price: 20 }
];
var chosen = _(gems).filter(priceLt(10)).take(3).value();
``````// 99,999 张照片
var phoneNumbers = [5554445555, 1424445656, 5554443333, … ×99,999];
// 返回包含 "55" 的照片
function contains55(str) {
return str.contains("55");
};
// 取 100 张包含 "55" 的照片
var r = _(phoneNumbers).map(String).filter(contains55).take(100);
## Pipelining
``````var result = _(source).map(func1).map(func2).map(func3).value();
``````var result = [], temp1 = [], temp2 = [], temp3 = [];
for(var i = 0; i < source.length; i++) {
temp1[i] = func1(source[i]);
}
for(i = 0; i < source.length; i++) {
temp2[i] = func2(temp1[i]);
}
for(i = 0; i < source.length; i++) {
temp3[i] = func3(temp2[i]);
}
result = temp3;
``````var result = [];
for(var i = 0; i < source.length; i++) {
result[i] = func3(func2(func1(source[i])));
}
## 延迟执行
``````var wallet = _(assets).filter(ownedBy('me'))
.pluck('value')
.reduce(sum);
\$json.get("/new/assets").success(function(data) {
assets.push.apply(assets, data); // 更新我的资金
wallet.value(); // 返回我钱包的最新的总额
}); | 533 | 1,487 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.65625 | 3 | CC-MAIN-2021-49 | latest | en | 0.112986 |
https://socratic.org/questions/how-do-you-find-the-value-of-a-given-the-points-2-5-a-7-with-a-distance-of-13 | 1,579,754,732,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579250608295.52/warc/CC-MAIN-20200123041345-20200123070345-00294.warc.gz | 673,481,301 | 6,694 | # How do you find the value of a given the points (-2,-5), (a,7) with a distance of 13?
Mar 30, 2017
a can be either -7 or 3
#### Explanation:
Distance between two points
1. $\left({x}_{1} , {y}_{1}\right)$ &
2. $\left({x}_{2} , {y}_{2}\right)$
is given by $\sqrt{{\left({x}_{1} - {x}_{2}\right)}^{2} + {\left({y}_{1} - {y}_{2}\right)}^{2}}$.
In this case,
distance = 13;
$\left({x}_{1} , {y}_{1}\right) = \left(- 2 , - 5\right)$;
$\left({x}_{2} , {y}_{2}\right) = \left(a , 7\right)$;
$\therefore$ $13 = \sqrt{{\left(- 2 - a\right)}^{2} + {\left(- 5 - 7\right)}^{2}}$
squaring both sides,
$\implies$ ${13}^{2} = \left({a}^{2} + 4 \cdot a + 4\right) + 144$
$\implies$ $169 = {a}^{2} + 4 \cdot a + 148$
$\implies$ ${a}^{2} + 4 \cdot a + 148 = 169$
$\implies$ ${a}^{2} + 4 \cdot a - 21 = 0$ which is a quadratic equation
$\because$ solution of a quadratic equation of the form $p \cdot {x}^{2} + q \cdot x + r = 0$ ;
where $p , q , r$ are constants is given by:-
$x = \frac{- q \pm \sqrt{{q}^{2} - 4 \cdot p \cdot r}}{2 \cdot}$
in our case $x$ becomes $a$ and constants $p , q , r$ become $1 , 4 , - 21$ respectively
$\therefore$ $a = \frac{- 4 \pm \sqrt{{4}^{2} - 4 \cdot \left(- 21\right) \cdot 1}}{2 \cdot 1}$
$\implies$ $a = \frac{- 4 \pm \sqrt{100}}{2}$
$\implies$ $a = \frac{- 4 \pm 10}{2}$
$\implies$ $a = - \frac{14}{2} , \frac{6}{2}$
$\implies$ $a = - 7 \mathmr{and} 3$
$\therefore$ a can be either -7 or 3. | 615 | 1,426 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 34, "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} | 4.75 | 5 | CC-MAIN-2020-05 | longest | en | 0.517163 |
https://www.airmilescalculator.com/distance/hkg-to-tvs/ | 1,603,513,121,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107881640.29/warc/CC-MAIN-20201024022853-20201024052853-00684.warc.gz | 618,491,412 | 41,938 | # Distance between Hong Kong (HKG) and Tangshan (TVS)
Flight distance from Hong Kong to Tangshan (Hong Kong International Airport – Tangshan Sannühe Airport) is 1223 miles / 1969 kilometers / 1063 nautical miles. Estimated flight time is 2 hours 48 minutes.
Driving distance from Hong Kong (HKG) to Tangshan (TVS) is 1423 miles / 2290 kilometers and travel time by car is about 24 hours 22 minutes.
## Map of flight path and driving directions from Hong Kong to Tangshan.
Shortest flight path between Hong Kong International Airport (HKG) and Tangshan Sannühe Airport (TVS).
## How far is Tangshan from Hong Kong?
There are several ways to calculate distances between Hong Kong and Tangshan. Here are two common methods:
Vincenty's formula (applied above)
• 1223.252 miles
• 1968.634 kilometers
• 1062.977 nautical miles
Vincenty's formula calculates the distance between latitude/longitude points on the earth’s surface, using an ellipsoidal model of the earth.
Haversine formula
• 1226.566 miles
• 1973.967 kilometers
• 1065.857 nautical miles
The haversine formula calculates the distance between latitude/longitude points assuming a spherical earth (great-circle distance – the shortest distance between two points).
## Airport information
A Hong Kong International Airport
City: Hong Kong
Country: Hong Kong
IATA Code: HKG
ICAO Code: VHHH
Coordinates: 22°18′32″N, 113°54′54″E
B Tangshan Sannühe Airport
City: Tangshan
Country: China
IATA Code: TVS
ICAO Code: ZBTS
Coordinates: 39°43′4″N, 118°0′9″E
## Time difference and current local times
There is no time difference between Hong Kong and Tangshan.
HKT
CST
## Carbon dioxide emissions
Estimated CO2 emissions per passenger is 162 kg (358 pounds).
## Frequent Flyer Miles Calculator
Hong Kong (HKG) → Tangshan (TVS).
Distance:
1223
Elite level bonus:
0
Booking class bonus:
0
### In total
Total frequent flyer miles:
1223
Round trip? | 505 | 1,914 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2020-45 | latest | en | 0.774779 |
https://socratic.org/questions/prove-the-following-identity-8#555208 | 1,643,384,350,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320306301.52/warc/CC-MAIN-20220128152530-20220128182530-00547.warc.gz | 585,688,217 | 6,258 | # Prove the following identity. ?
Feb 21, 2018
You must know the definition of $\sinh$ and $\cosh$ to show this.
By definition:
$\sinh x = \frac{{e}^{x} - {e}^{-} x}{2}$ and
$\cosh x = \frac{{e}^{x} + {e}^{-} x}{2}$
So we rewrite the left-hand-side of the equation as follows:
$\sinh \left(a\right) + \sinh \left(b\right) = \frac{{e}^{a} - {e}^{-} a}{2} + \frac{{e}^{b} - {e}^{-} b}{2}$
This becomes:
$= \frac{{e}^{a} - {e}^{-} a + {e}^{b} - {e}^{-} b}{2}$
and rearranging gives:
$= \frac{{e}^{a} - {e}^{-} a + {e}^{b} - {e}^{-} b}{2}$ (Eq.A)
Now for the right-hand-side of the equation, we have:
$2 \sinh \left(\frac{a + b}{2}\right) \cosh \left(\frac{a - b}{2}\right) = 2 \left[\frac{{e}^{\frac{a + b}{2}} - {e}^{- \frac{a + b}{2}}}{2}\right] \left[\frac{{e}^{\frac{a - b}{2}} + {e}^{- \frac{a - b}{2}}}{2}\right]$
We can simplify this by cancelling out the $2$ and $\frac{1}{2}$ and keep only one $\frac{1}{2}$:
$= \frac{1}{2} \left[{e}^{\frac{a + b}{2}} - {e}^{- \frac{a + b}{2}}\right] \left[{e}^{\frac{a - b}{2}} + {e}^{- \frac{a - b}{2}}\right]$
we can also factor out ${e}^{\frac{1}{2}}$ as it appears everywhere:
$= {e}^{\frac{1}{2}} / 2 \left[{e}^{a + b} - {e}^{- a - b}\right] \left[{e}^{a - b} + {e}^{- a + b}\right]$
which becomes:
$= {e}^{\frac{1}{2}} / 2 \left[{e}^{a + b + a - b} + {e}^{a + b - a + b} - {e}^{- a - b + a - b} - {e}^{- a - b - a + b}\right]$
which simplifies to:
$= {e}^{\frac{1}{2}} / 2 \left[{e}^{2 a} + {e}^{2 b} - {e}^{- 2 b} - {e}^{- 2 a}\right]$
multiply back by ${e}^{\frac{1}{2}}$ and rearrange:
$= \frac{1}{2} \left[{e}^{a} - {e}^{- a} + {e}^{b} - {e}^{- b}\right]$
and you readily see that this is the same as our (Eq.A):
$= \frac{{e}^{a} - {e}^{- a}}{2} + \frac{{e}^{b} - {e}^{- b}}{2} = \sinh \left(a\right) + \sinh \left(b\right)$
So the left and right parts of the equation are the same and the identity is correct.
Q.E.D. | 840 | 1,874 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 19, "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} | 4.625 | 5 | CC-MAIN-2022-05 | latest | en | 0.47573 |
https://edurev.in/t/119502/Force-and-Laws-of-Motion-Class-9-Notes-Science-Chapter-8 | 1,716,212,069,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058278.91/warc/CC-MAIN-20240520111411-20240520141411-00302.warc.gz | 189,385,095 | 67,792 | Short Notes - Force and Laws of Motion
Force and Laws of Motion Class 9 Notes Science Chapter 8
• Force: It is a push or pull on an object that produces acceleration in the body on which it acts. S.I. unit of force is Newton.
• A force can do three things on a body.
(a)It can change the speed of a body.
(b)It can change the direction of motion of a body.
(c)It can change the shape and size of a body.
• Balanced forces: Forces are said to be balanced forces if they nullify one another and their resultant force is zero.
• Unbalanced forces: When two opposite forces acting on a body, move a body in the direction of the greater force or forces which brings motion in a body are called as unbalanced forces.
• First law of motion: An object remains in a state of rest or of uniform motion in a straight line unless acted upon by an external unbalanced force.
Question for Short Notes - Force and Laws of Motion
Try yourself:
Which of the following is NOT a possible effect of a force acting on an object?
• Inertia: The natural tendency of an object to resist a change in its state of rest or of uniform motion is called inertia.
The mass of an object is a measure of its inertia.
Its S.I. unit is kg.
A body with greater mass has greater inertia.
• Frictional force: The force that always opposes the motion of objects is called force of friction.
• Second law of motion: The rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of the force.
Mathematically,
• Momentum: The momentum of an object is the product of its mass and velocity and has the same direction as that of the velocity. Its S.I. unit is kg m/s.
(p = mv )
1 Newton: A force of one Newton produces an acceleration of 1 m/s2 on an object of mass 1kg.
1N = 1 kg m/s2
(F = ma)
• Third law of motion: To every action, there is an equal and opposite reaction and they act on two different bodies.
The document Force and Laws of Motion Class 9 Notes Science Chapter 8 is a part of the Class 9 Course Science Class 9.
All you need of Class 9 at this link: Class 9
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FAQs on Force and Laws of Motion Class 9 Notes Science Chapter 8
1. What are the three laws of motion proposed by Sir Isaac Newton?
Ans. Sir Isaac Newton proposed the three laws of motion: 1) Law of Inertia, 2) Law of Acceleration, and 3) Law of Action-Reaction.
2. How does Newton's first law of motion relate to the concept of inertia?
Ans. Newton's first law of motion states that an object at rest will stay at rest, and an object in motion will stay in motion unless acted upon by an external force. This concept is related to inertia, which is the tendency of an object to resist changes in its motion.
3. Can you explain the concept of momentum in the context of Newton's second law of motion?
Ans. Momentum is the product of an object's mass and velocity. According to Newton's second law of motion, the acceleration of an object is directly proportional to the force acting on it and inversely proportional to its mass. Therefore, the concept of momentum helps us understand how an object's motion changes when a force is applied to it.
4. How does Newton's third law of motion explain the interaction between two objects?
Ans. Newton's third law of motion states that for every action, there is an equal and opposite reaction. This means that when one object exerts a force on another object, the second object exerts an equal and opposite force back on the first object. This law helps explain how forces are exchanged between interacting objects.
5. Can you provide an example of each of Newton's three laws of motion in everyday life?
Ans. An example of Newton's first law of motion is a ball rolling on a flat surface slowing down due to friction. An example of the second law is a moving car accelerating when the gas pedal is pressed. An example of the third law is a person jumping off a boat causing the boat to move in the opposite direction.
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; | 1,059 | 4,493 | {"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} | 4.65625 | 5 | CC-MAIN-2024-22 | latest | en | 0.93746 |
https://oldatlanticlighthouse.wordpress.com/category/republican-presidential-debates/ | 1,521,373,635,000,000,000 | text/html | crawl-data/CC-MAIN-2018-13/segments/1521257645613.9/warc/CC-MAIN-20180318110736-20180318130736-00075.warc.gz | 694,883,887 | 55,588 | ## Archive for the 'Republican Presidential Debates' Category
### Tom Tancredo: The Pause in Immigration that Assimilates us
June 5, 2007
In contrast to Senate Amnesty and Guest Worker and continued legal immigration, Tom Tancredo proposed a pause in legal immigration in the Republican presidential debate.
Against a pause:
Huckabee against pause.
Rudi Giuliani against pause. Compared Tom Tancredo to Know Nothing party. Backward looking logic. Giuliani advocated perpetual immigration. (This was proven mathematically to cause genetic extinction of those who come here and those who are here at any point in time. See Immigration Vanishing Survival Theorem
)
McCain No barriers and fences.
==
Repost in part on Unpleasant Immigration Arithmetic:
Assume US population at 300 million was the maximum. If people live 75 years, then 4 million die per year. If 2 million enter then births = 4million deaths – 2 million entrants = 2 million.
The ratio of births to deaths is 2/4 or 1/2. The time from birth to parent is roughly 25 years. So in 50 years, one has 1/4, and in 75 years 1/8 of the starting genes.
Even if population went to 450 million, deaths per year are 6 million. With even one million entrants that gives a survival ratio of 5/6. So the number left after 25*n years is (5/6)^n which goes to zero as n goes to infinity.
It goes to zero rapidly in fact.
The above implies that any law with immigration above zero on a sustained basis is unconstitutional and a crime against humanity. Causing the extinction of a group is a violation of treaties the US has passed.
The current US law is thus void. So is the proposed law.
The drop in fertility from 1800 to 1990 in one graph shows this substitution effect pressure from immigration.
Look at the graph of fertility from 1800 to 1990 below:
http://www.elderweb.com/home/node/2919
Fertility falls except during the period of immigration restriction from the 1920’s to 1965. During part of that period fertility rose, which is called the baby boom. This was a departure from the uniform fall in fertility.
Fertility is now below replacement for many groups in accordance with the theorem. Sustained immigration is omnia cleansing.
The same applies in Europe where fertility is below replacement.
We must stop immigration, we must stop legal immigration and we must stop illegal immigration. We can not have any amnesty or legalization. We have to get the rate of illegal immigration to zero, not just slow it down. We must get the rate of legal immigration to zero. The theorem requires this until the world changes so much that two way equal migration is viable. But that won’t be viable for centuries. | 607 | 2,687 | {"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-2018-13 | latest | en | 0.944408 |
https://socratic.org/questions/how-do-you-simplify-the-product-x-7-x-5-and-write-it-in-standard-form | 1,576,014,918,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575540529006.88/warc/CC-MAIN-20191210205200-20191210233200-00164.warc.gz | 557,071,110 | 6,030 | # How do you simplify the product (x + 7)(x + 5) and write it in standard form?
Jun 22, 2016
#### Answer:
${x}^{2} + 12 x + 35$
#### Explanation:
Multiply each term in the first bracket by each term in the second bracket.
Commonly called the FOIL rule..Multiply the " Firsts, Outers Inners LAsts",
${x}^{2} + 5 x + 7 x + 35$
The two middle terms can be added.
${x}^{2} + 12 x + 35$ | 130 | 390 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 3, "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} | 4.1875 | 4 | CC-MAIN-2019-51 | longest | en | 0.851593 |
http://www.wyzant.com/resources/lessons/math/algebra/Slope | 1,397,748,805,000,000,000 | text/html | crawl-data/CC-MAIN-2014-15/segments/1397609530136.5/warc/CC-MAIN-20140416005210-00176-ip-10-147-4-33.ec2.internal.warc.gz | 773,367,242 | 17,305 | Search 72,331 tutors
The concept of slope is used in various sections of mathematics and worked with quite often when solving and graphing linear equations. The slope or degree of slant of a line is defined as the degree of steepness or incline of the line.
In more mathematical terms, given a plane containing both the x-axis and y-axis, slope can be defined as change in the y-coordinate divided by change in the x-coordinate. Slope is usually denoted by m
where the Δ symbol means change in. The change in y is the distance between both y values, which is also called the rise. The change in x is the distance between both x values, which is also called the run. The slope is also known as the rise over run.
Given two points (X1,Y1) and (X2,Y2)
which is the same as
Although it doesn't matter which point you start with, consistency is a must. Below is an example of a WRONG way to calculate the slope
whatever point you choose as the starting point in the numerator MUST be the same point you pick in the denominator
Slope can be positive or negative or zero:
• Positive slope means that the line is increasing, in other words moving from left to right.
• Negative slope means that the line is decreasing or moving from right to left.
• Zero slope on the other hand means that the line is horizontal i.e. parallel to the x-axis.
In some cases, the slope may be infinite or undefined and this means that the line is vertical i.e. parallel to the y-axis. This occurs when there is no change in the x-axis i.e. (X1 - X2 = 0)
The magnitude of the slope shows the steepness of the line; the greater the magnitude of the line the steeper it is.
## Slope Intercept Form
Given a straight line with the slope-intercept form of a line, y = mx + b, where m represents the slope and b is a constant which is also called the y-intercept. The y-intercept is defined as the point on the y-axis at which the line (whose equation is given) cuts the y-axis.
Keeping in mind that at any point on the y-axis the x-coordinate is zero (x = 0), an easy way to get the y-intercept from the equation of a line y = mx + b would be to simply set x = 0 such that y = b.
For a given straight line, the slope is consistent along the line so it wouldn't matter what points on the line you pick to calculate the slope.
In geometry, given a line that makes an angle θ with the x-axis, the slope m is defined as
In geometry, the gradients of a lines can be used to determine their relationship i.e. whether the lines are parallel to each other or perpendicular. For example: Given two lines with slopes m1 and m2
• The two lines are parallel if and only if their slopes are equal (i.e. m1 = m2) and they are not coincident (i.e. don't lie on top of each other) or if they both are vertical and therefore have undefined slopes (i.e. m1 = ∞ and m2 = ∞
• The two lines are perpendicular if the product of their slopes is -1 (i.e. m1 x m2 = -1) or one has a slope of 0 (a horizontal line) and the other has an undefined slope (a vertical line) i.e m1 = 0 and m2 = ∞ or m1 = ∞ and m2 = 0.
From the above, notice that given two perpendicular lines and the slope of one line, you can always find the other slope from the relationship
i.e.
## Slope in Calculus
Calculus mostly deals with curves whose slopes/gradients may be harder to compute using the algebraic method. When dealing with curves, the gradient changes from point to point so we can only define it at a single point. The gradient at that point is defined as the gradient of the tangent line to that point. The tangent line is defined as a line to a curve that only touches one point on the curve.
Given a simple curve y = x^2
The gradient at a given point say (1,1) is found by taking the derivative of the equation and then substituting for the point i.e.
## Examples of Slope / Gradient
(1) Find the slope of the line between the points (1,2) and (3,6).
(2) Find the slope of the line 3y = 2x + 1
This equation is not in slope intercept form, so we divide by three to find our m value.
(3) Find the slope of the line 30 - 2y = -0.5x
Isolate y to put the equation in slope intercept form.
(4) Find the gradient of the given line y = mx + 3 at the point (2,5)
substitute for x and y
such that
Sign up for free to access more algebra 1 resources like . WyzAnt Resources features blogs, videos, lessons, and more about algebra 1 and over 250 other subjects. Stop struggling and start learning today with thousands of free resources! | 1,101 | 4,495 | {"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} | 4.6875 | 5 | CC-MAIN-2014-15 | longest | en | 0.962873 |
http://fsconline.info/phy-chap-8-xi/ | 1,513,477,240,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948592846.98/warc/CC-MAIN-20171217015850-20171217041850-00199.warc.gz | 118,887,129 | 25,329 | Latest
Chapter 8 Notes | Physics 1st Year
“Waves”
Index:
1. Waves
2. Matter Waves
3. Progressive Waves
4. Transverse Waves
5. Longitudinal Waves
6. Periodic Waves
7. Transverse Periodic Waves
8. Equation of Wave Speed
9. Speed of Sound in Air
10. Laplace’s Correction
11. Effect of Pressure on Velocity of Sound
12. Effect of Density
13. Effect of temperature
14. Principle of Superposition
15. Interference
16. Beats
17. Reflection of Waves
18. Stationary Waves
19. Stationary Waves in a Stretched String
20. Doppler’s Effect
21. Applications of Doppler’s Effect
Key Points:
1. Waves carry energy and this energy is carried out by a disturbance, which spreads out from the source.
2. If the particles of the medium vibrate perpendicular to the direction of propagation of the wave, then such wave is called transverse wave , e.g light waves.
3. If the particle of medium vibrate parallel to the direction of propagation of the wave, then such wave is called longitudinal wave, e.g sound wave
4. If a particle of the medium is simultaneously acted upon by two waves, then the resultant displacement of the particle is the algebraic sum of their individual displacements. this is called principle of superposition.
5. When two waves meet each other in a medium then at some points they reinforce the effect of each other and at some other points they cancel each ohter’s effect This phenomenon is called interference,
6. The periodic variations of sound between maximum and minimum loudness are called beats.
7. Stationary waves are produced in a medium, when two identical waves travelling in opposite directions interfere in that medium.
8. The apparent change in the pitch of sound caused by the relative motion of either the source of sound or the listener is called Doppler effect.
Categories: Fsc Part 1,Notes,Physics
× | 419 | 1,832 | {"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-2017-51 | latest | en | 0.861246 |
http://animatedportraits.net/excel_dashboards/cross-correlations-1.htm | 1,571,601,355,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986718918.77/warc/CC-MAIN-20191020183709-20191020211209-00049.warc.gz | 14,107,769 | 7,581 | # Use Automated Cross Correlations in Excel to Find Leading Indicators—Part 1
by Charley Kyd, MBAMicrosoft Excel MVP, 2005-2014 The Father of Spreadsheet Dashboard Reports
It all seems so simple...
To improve your forecasts of sales or other measures, you simply need to find leading indicators...measures that are highly correlated with your key measures, but with a time lag. And then you use those leading indicators as the basis of your forecast.
But when you try to make it all work, that simple idea can become a huge challenge.
Suppose, for example, that the blue Data1 line in this chart shows what you spend in advertising. And suppose that the red Data2 line shows the amount of your sales.
At first glance, it looks like you REALLY need to change your ad strategy, because...
If you want to be more precise in your analysis, you could use Excel's CORREL function to learn that Data1 and Data2 have a correlation coefficient of -.50. That is, as the chart illustrates, your advertising and sales values are negatively correlated to a significant degree.
However, that's not the end of the story.
It could be that what you spend on advertising is a leading indicator of what your sales will be several months later. This figure shows the analysis from that perspective...
Here, the table shows the correlations associated with eleven different time shifts. The version with the highest correlation has a shift of +2 months. That is, the correlation has been calculated with sales (Data2) shifted two months ahead of ad spending (Data1).
That is, ad spending could be a good leading indicator of sales performance two months later.
However, that interpretation isn't the only one you could make, as this figure illustrates:
Here, we see that sales performance could be a leading indicator of ad spending three months later. This might be because when sales rise or fall, the Marketing Department decides to spend more or less on advertising.
Both interpretations are supported by high correlations. But the reality is that you must properly interpret what analyses like this tell you.
Even so, the analysis definitely can give you additional facts on which to base your decisions. So, with that warning, let's set up the analysis.
### Cross Correlation Workbook
My workbook contains two relevant worksheets: Data and Report.
This figure shows the Data worksheet.
The Date, Data1, and Data2 columns contain the values shown.
The DateText column contains formulas that return text to be displayed in the chart. Here's the first formula, for the cell shown:
E5: =TEXT(B5,"mmm")&CHAR(13)&"'"&TEXT(B5,"yy")
The CHAR(13) section of this formula returns the carriage-return character. Excel doesn't show this character in column E. But when the text is displayed in the chart, this character causes the year text to wrap to a second line below the month text.
The NumRows cell returns the number of rows in the table. It does so because it uses the COUNT function, which counts only numbers. We'll reference this value in several dynamic range names in this workbook.
Here's the formula for that cell:
C1: =COUNT(B:B)
To name this cell, select the range B1:C1 then press Ctrl+Shift+F3 or choose Formulas, Defined Names, Create From Selection to launch the Create Names dialog. Make sure that only Left Column is checked; then choose OK.
Also, in the Report worksheet, set up the two cells shown here, then use the Create Names dialog to assign the name Shift to cell B1. (When I set up a cell with a setting, as with the Shift cell, I often give it a yellow fill.)
Set Up the Dynamic Range Names
The key to automating the cross-correlation calculations is to set up dynamic range names that expand when more data is entered, or that shift the data in response to the Shift value.
The NumRows cell makes it easy to set up dynamic range names that expand to include additional rows of data that might be added below row 25 in the data figure above.
To define the first name below, first copy the formula for the Date name to your clipboard. Then choose Formulas, Defined Names, Define Name (or press Ctrl+Alt+F3) to launch the New Name dialog. In the New Name dialog, enter Date as the name; paste the copied formula into the Refers to edit box; and then choose OK.
Repeat this process for each of the remaining names.
Date Data1 Data2 DateText =OFFSET(Data!\$B\$4,1,0,NumRows,1) =OFFSET(Data!\$C\$4,1,0,NumRows,1) =OFFSET(Data!\$D\$4,1,0,NumRows,1) =OFFSET(Data!\$E\$4,1,0,NumRows,1)
You now need to set up dynamic range names that shift the data they reference, in ways that vary depending on the sign of the Shift value. Use the New Name dialog to define each of these names.
s.Data1N s.Data1P s.Data2N s.Data2P s.DateText1N s.DateText1P s.DateText2N s.DateText2P =OFFSET(Data1,-Shift,0,NumRows+Shift,1) =OFFSET(Data1,0,0,NumRows-Shift,1) =OFFSET(Data2,0,0,NumRows+Shift,1) =OFFSET(Data2,Shift,0,NumRows-Shift,1) =OFFSET(DateText,-Shift,0,NumRows+Shift,1) =OFFSET(DateText,0,0,NumRows-Shift,1) =OFFSET(DateText,0,0,NumRows+Shift,1) =OFFSET(DateText,Shift,0,NumRows-Shift,1)
In these range names, the "s." indicates that the names are shifting your data; the "N" indicates that the name is used when the Shift value is negative; and the "P" indicates that the name is used when the Shift value is positive.
The final dynamic range names are ones we chart and use in our calculations. Because an Excel bug has problems charting range names that begin with "c" (which we would like to use for "chart"), we begin them with "g" (for "graph").
g.Data1 g.Data2 g.DateText1 g.DateText2 =IF(Shift<0,s.Data1N,s.Data1P) =IF(Shift<0,s.Data2N,s.Data2P) =IF(Shift<0,s.DateText1N,s.DateText1P) =IF(Shift<0,s.DateText2N,s.DateText2P)
Now, with the dynamic names defined, you can set up a data table to calculate the cross correlations.
### Set Up the Excel Data Table
This figure shows the full report area. The Data Table in column J and K calculate the cross-correlation values.
To set up the Data Table, first enter the shift values shown in the range J7:J17. Then enter this formula in the cell shown:
K6: =CORREL(g.Data1,g.Data2)
This formula returns the correlation coefficient for the two dynamic ranges shown. These ranges, of course, will shift in time...depending on the value in the Shift cell.
Next, select the range J6:K17 and then choose Data, Data Tools, What If Analysis, Data Table to launch the Data Table dialog. In the Column Input Cell of that dialog, enter...
=Shift
...which is the name of the cell that contains the current value for the number of months that the data is shifted.
Then, after you choose OK, Excel puts each selected value of column J into the Shift cell, calculates the formula in cell K6, and writes the result of the formula in the adjacent cell in column K.
Finally, to assign range names to the Data Table for easy reference, enter the text shown at the bottom of the table; select the range J7:K18; press Ctrl+Shift+F3; in the dialog, make sure that only Bottom Row is checked; and then choose OK.
### Set Up Shift's Data Validation List
The Shift cell uses Excel's Data Validation List feature to allow only the Shift values listed in the Data Table. To set this up, first select cell B1.
Now choose Data, Data Tools, Data Validation, Data Validation. In the Settings tab, choose List in the Allow section. And for the Source, enter...
=ShiftVal
...which is the range name you assigned to the list of shift values in the Data Table.
You can take the next steps with this in three ways. First, in part 2 of this article, you can learn how to create the charts and complete the cross correlation report.
Second, you can . By doing so, you'll also be notified when I post Part 2 of this article.
Tags: #excel, #chart, #cross correlation, #time-shift correlation, #reporting
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Depdendent Variable
Number of equations to solve: 23456789
Equ. #1:
Equ. #2:
Equ. #3:
Equ. #4:
Equ. #5:
Equ. #6:
Equ. #7:
Equ. #8:
Equ. #9:
Solve for:
Dependent Variable
Number of inequalities to solve: 23456789
Ineq. #1:
Ineq. #2:
Ineq. #3:
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cooncob
Registered: 22.10.2004
From: Penguin Paradise
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ameich
Registered: 21.03.2005
From: Prague, Czech Republic
Posted: Sunday 31st of Dec 08:53 Sounds like your concepts are not clear . Mastering in math worksheet combinations and permutations requires that your concepts be strong . I know students who actually start tutoring juniors in their first year. Why don’t you try Algebrator? I am pretty sure, this program will help you.
Sdefom Koopmansshab
Registered: 28.10.2001
From: Woudenberg, Netherlands
Posted: Tuesday 02nd of Jan 11:20 It’s true, even I’ve been using this tool since sometime now and it really helped me in solving problems my queries on math worksheet combinations and permutations and math worksheet combinations and permutations. I also used it to clear my doubts in topics such as difference of squares and difference of squares. If you are short on time , then I would highly recommend this software, and well even if you are not , I still would!
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Registered: 22.07.2004
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Posted: Tuesday 02nd of Jan 14:39 I remember having often faced problems with conversion of units, subtracting fractions and proportions. A really great piece of math program is Algebrator software. By simply typing in a problem homework a step by step solution would appear by a click on Solve. I have used it through many math classes – Basic Math, Pre Algebra and Algebra 1. I greatly recommend the program.
TempnaStoln22
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Mibxrus
Registered: 19.10.2002
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Posted: Friday 05th of Jan 09:11 Sure. It is quite easy to access the program as it is just a click away. Click here : https://mathfraction.com/fractions-2.html. Go through the site and read what the program offers you. Also note that there is a money back promise if you are not pleased . I am sure you will find it as first rate as I did. Good luck to you. | 883 | 3,572 | {"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-2021-31 | latest | en | 0.895357 |
https://9to5answer.com/quick-sort-median-selection | 1,679,676,502,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296945287.43/warc/CC-MAIN-20230324144746-20230324174746-00139.warc.gz | 104,440,845 | 11,577 | # Quick sort median selection
10,891
You should look into the Median of Medians algorithm. It is a linear time algorithm with the following recurrence...
``````T(n) ≤ T(n/5) + T(7n/10) + O(n)
``````
... which is O(n). The algorithm details...
1. divide the list into n/5 subsequences of 5 elements each
2. find the median of each list, by brute force. there will be n/5 of these
3. Let m_1,..., m_n/5 be these medians.
4. recursively find the median of these medians. this will be 1 element, the pivot!
... and some pseudo-code...
``````MedianOfMedians (A[1],...,A[n])
begin
for i=1 to n/5 do {
let m_i be the median of A[5i − 4], A[5i − 3],..., A[5i];
}
pivot = Select(m1,...,m_n/5, n/10); // the pivot
return pivot
end
``````
References
I hope this helps.
Hristo
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### james
Updated on June 04, 2022 | 273 | 835 | {"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-2023-14 | latest | en | 0.820341 |
https://davislivemusic.com/windhorse-farm-wilg/7e1eca-how-long-does-it-take-to-reach-terminal-velocity | 1,627,213,911,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046151672.96/warc/CC-MAIN-20210725111913-20210725141913-00458.warc.gz | 222,198,591 | 20,140 | # how long does it take to reach terminal velocity
Posted on
Keep reading to learn what is velocity formula and what are the most common velocity units. Cliff divers are not in the air for anywhere near 14 seconds. If you want to do it without that option turned on, read on. This velocity is the limit of the acceleration process. Set initial velocity to zero, you're not moving at the beginning of the race. If you have ever wondered how to find velocity, here you can do it in three different ways. (a) Find. The excitement builds as our plane takes you up to 10,000ft before an unbeatable adrenaline rush as you freefall for 30 seconds. The most common example of this is the speed a spacecraft requires to leave Earth for distant planets, which is approximately 11.2 km/s. A 560-g squirrel with a surface area of $930\,{\text{cm}}^{2}$ falls from a 5.0-m tree to the ground. The first velocity is the so-called terminal velocity, which is the highest velocity attainable by a free falling object. For the European sort, it would seem to be roughly 11 m/s, or 24 mph. If you've tried this already, you'll know that the problem with getting this isn't air pressure or Gs, it's that it's very hard to keep falling long enough. 1 (L-4) Free fall, review If we neglect air resistance, all objects, regardless of their mass, fall to earth with the same acceleration Æg ≈10 m/s2 This means that if they start at the same height, they will both hit the ground at the same time. All you'll need to do is type in distance and time. Our online calculators, converters, randomizers, and content are provided "as is", free of charge, and without any warranty or guarantee. Terminal velocity for a human body is not a constant value, it depends heavily on the profile of the falling person. For a velocity of 0.2 m/s, the resistance force on the object is measured to be 1N. We've also prepared a brief but informative article about velocity itself. where g is the acceleration due to gravity and v T is the terminal velocity of the raindrop. With the velocity calculator, you can find that it will be about 59 mph. Limits and Derivatives. Provided an object traveled 500 meters in 3 minutes, to calculate the average velocity you should take the following steps: Let's try another example. . Before we explain how to calculate velocity, we'd like to note that there is a slight difference between velocity and speed. What will be your velocity after 4 seconds? 0.5)) = √(392.266/0.07693) = √5099 = 71 m/s (233 ft/s). Terminal velocity occurs in fluids (e.g., air or water) and depends on the fluid's density. An object dropped from rest will increase its speed until it reaches … Terminal velocity is the maximum velocity attainable by an object as it falls through a fluid. Derivatives. Reach 100% terminal velocity is very difficult, if not impossible, as acceleration drops exponentially as an object approaches its terminal velocity. We've written about it from the point of view of a physicist in the text below. [1] NIST Special Publication 330 (2008) - "The International System of Units (SI)", edited by Barry N.Taylor and Ambler Thompson, p. 52, [2] "The International System of Units" (SI) (2006, 8th ed.). When it approaches light speed, it's kinetic energy becomes unattainable, very large or even infinite. Wikipedia says this about how long it takes a sky diver to reach terminal velocity - about 15 seconds to reach 99% of terminal velocity, that is: "...For example, the terminal velocity of a skydiver in a normal free-fall position with a closed parachute is about 195 km/h (120 mph or 54 m/s). I found the terminal velocity to be -.0196 m/s but I am not sure how to model the velocity equation to solve for time t when the velocity is half of my terminal velocity… When A Skydiver Jumps From A Plane, Gravity Causes Her Downward Velocity To Increase At The Rate Of G9.8 Meters Per Second Squared. Moreover, this is a cause of other phenomena like relativistic velocity addition, time dilation, and length contraction. I understand that finding the time it takes to reach terminal velocity might not be all that useful, so I'm also interested in finding the time needed to reach a certain percentage of terminal velocity. For most of them, they just divided the terminal velocity by acceleration due to gravity, which makes no sense, since we weren't even asked for time taken to reach terminal velocity, but 63% of it. How long will it take for each skydiver to reach the ground (assuming the time to reach terminal velocity is small)? The terminal velocity for a skydiver was found to be in a range from 53 m/s to 76 m/s. However, graphing velocity against time you get a graph that looks like. Our tool will do it all for you! Get an answer to your question “How long does it take for the velocity of the rain drop to reach 99% of its terminal velocity? https://www.gigacalculator.com/calculators/terminal-velocity-calculator.php. You can read more about it in our free fall with air resistance calculator. I hope we've convinced you that velocity plays an essential role in everyday life and not just science, and we hope that you've enjoyed our velocity calculator. Miles per hour ) comes to terminal velocity on any given skydive of. World record for the fastest skydive: ~373 m/s miles per hour.! Initial velocity + acceleration * time prepared a brief but informative article about velocity.... At the beginning of the service one of the raindrop gas calculator velocity - relativistic addition. On from the options the calculator does n't take any of this is a cause of phenomena! The air for anywhere near 14 seconds 2017: this is still way short of the race 0.2,. Net force on the fluid 's density ones, obviously − e −gt/v t ) if v t ( −! May be surprising, but there are many more of them in our!! It would seem to be around 101 m/s or 364 km/h the force. To use the time it takes infinitely long to reach 99 % of terminal velocity on will! Each skydiver to reach terminal velocity with their belly facing the Earth mc2 formula on. Famous e = mc2 formula bases on the relativistic velocity concept the body each... European or African variety of 70 miles in one hour, your average velocity equals 70.... Like relativistic velocity velocity change caused by acceleration over a specific time interval of its velocity... Type in distance and time this into account = 8 m/s and kilometers per hour.. 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A specific time interval improper use of your route and the buoyancy is equal to base. Have how long does it take to reach terminal velocity convert any units by hand when estimating the fuel use of the advantages of using this is. Definition that uses the well-known velocity equation range from 53 m/s to 76 m/s it comes to terminal velocity the! Them below: final velocity = initial velocity + acceleration * time to leave Earth for distant planets which... Fall nearly 10,000 feet ( 3,048 meters ) in one minute easily switch between all them. Expels matter behind it, it will speed up, like a rocket can, of course make... Approaches its terminal velocity is the terminal velocity for a velocity of 0.2 m/s, while acceleration... Will use the average velocity equals 70 mph it occurs when the sum of the service without option... You 'll need to do is type in distance and time n't do without. Do n't have to be very accurate lower terminal velocity occurs when the sum of fundamental. On Earth will prevent you from going more than about 320 km/h, or 24 mph in! A skydiver was found to be very accurate 101 m/s or 364 km/h it may be surprising, but ca... Convert any units by hand not built for super high speeds relativistic velocity addition time... Velocity formula and what it ’ s falling through units for velocity are m/s, while for acceleration they m/s2... How much gas will be used during a particular journey, try our gas calculator 10,000ft before an adrenaline! That we did n't mention, have an explore phenomena like relativistic.... Of terminal velocity velocity for a velocity of the object falling, its area! In this model it takes to travel changes depending on the body balance each other more more! Learn more about it in our free fall with air resistance calculator + acceleration * time the new terminal on! Wall ) will prevent you from going more than about 320 km/h, about! More and more closely as the terminal velocity for the fastest skydive: ~373 m/s, like rocket... And the time to reach half of its terminal velocity with their belly facing how long does it take to reach terminal velocity Earth velocity! About 195 km/h ( 122 miles how long does it take to reach terminal velocity hour ) per hour km/h and g = 9.8 2! Is approximately 11.2 km/s the sum of the average human terminal velocity zero! Feet per second Squared them connected with velocity that we did n't mention have... They would fall nearly 10,000 feet ( 3,048 meters ) in one minute article about velocity.! Freely falling through, if not impossible, as acceleration drops exponentially as an object approaches terminal. The text below objects gravitational pull above examples are just moving in opposite directions type in distance and is... Alcohol and inspect your car regularly be roughly 11 m/s, the force!, head to the downward force of gravity acting on the object to 99. A distance of 70 miles in one hour, your average velocity equals 70 mph a how long does it take to reach terminal velocity tool that you... M/S ( 233 ft/s ) interchangeably, but you ca n't do every... Will it take to reach 99 % of terminal velocity to zero, the force... ( 1 − e −gt/v t ) if v t ( 1 − e − b t / )... An explore ft/s ) 's famous e = mc2 formula bases on the basic velocity that. Meters ) in one hour, your average velocity formula describes the between... Significant digits plane, gravity Causes Her downward velocity to be 1N essential between... Another objects gravitational pull objects gravitational pull drag value of > 0 of tiny oil droplets settles at exceedingly! Units are feet per second Squared skydiving terminal velocity, which is 11.2! 'S list and organize them below: final velocity = initial velocity to be held responsible for resulting. Velocity addition, time dilation, and a mist of tiny oil droplets settles at an exceedingly terminal! Skydiver Jumps from a plane, gravity Causes Her downward velocity to Increase at the beginning of the is! And more closely as the correct one water ) and depends on the to... Only travel about 195 km/h ( 122 miles per hour, note that there is an essential difference between vs! An average, it would seem to be around 101 m/s or km/h. + acceleration * time skydiving terminal velocity where for all practical purposes falling... Fluids ( e.g., air or water ) and depends on the weight of the object 's position as function! Comes to terminal velocity of your car regularly kilometers per hour km/h take the average human approximately 15 seconds reach... Most common example of this is the speed of light km/h ( 122 miles per hour 11.2 km/s you that. That we did n't mention, have an explore long will it to... Remember that you ca n't do it in three different ways velocity against time you get a graph that like! To 10,000ft before an unbeatable adrenaline rush as you freefall for 30 seconds how long does it take to reach terminal velocity a difference! As our plane takes you up to 10,000ft before an unbeatable adrenaline rush as how long does it take to reach terminal velocity... Buoyancy is equal to the speed of an object needs to escape another objects gravitational pull said, about seconds!, of course, make your calculations much easier by using the average velocity formula the. It from the point of view of a physicist in the high region. Free falling object is zero, you 'll only travel about 195 km/h ( 122 miles per km/h. Normal roads and highways are not built for super high speeds fastest skydive: ~373 m/s reach half of terminal... Noticed that we did n't mention, have an explore and organize them below: final velocity = initial +... Keep reading to learn what is velocity change caused by acceleration over a time! The basic velocity definition states that it will take the average human approximately seconds! Than about 320 km/h, or 24 mph, steady speed achieved by an object will also accelerate towards objects! What are the most common velocity units 10,000 feet ( 3,048 meters in! Second m/s and kilometers per hour km/h 101 m/s or 364 km/h unbeatable adrenaline rush as freefall... Distance and time is also needed when estimating the fuel use of your.... Ones, obviously see how dangerous automobile collisions can be 240 kilometres ) per hour calculate. New car that can change its speed with an acceleration of about 6.95 m/s² an unbeatable rush. It takes to travel in many aspects of physics, and length contraction a physicist in the high energy,. The world record for the European or African variety by a free falling object n't! Found to be around 101 m/s or 364 km/h leave Earth for distant planets, which is the acceleration.... What it ’ s changes body position 1,500 feet ) of height before it reaches terminal velocity with belly. Earth for distant planets, which is the highest velocity attainable by a free falling object is to... Explain how to calculate velocity is present in many aspects of physics and! Probably noticed that we use words speed and velocity interchangeably, but are just educational ones obviously..., while for acceleration they are m/s2 10,000 feet ( 3,048 meters ) one... | 3,244 | 14,434 | {"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} | 3.734375 | 4 | CC-MAIN-2021-31 | latest | en | 0.948767 |
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https://ncatlab.org/nlab/show/formal+smooth+infinity-groupoid | 1,534,580,168,000,000,000 | application/xhtml+xml | crawl-data/CC-MAIN-2018-34/segments/1534221213508.60/warc/CC-MAIN-20180818075745-20180818095745-00505.warc.gz | 740,972,427 | 31,311 | # nLab formal smooth infinity-groupoid
### Context
#### Cohesive $\infty$-Toposes
cohesive topos
cohesive (∞,1)-topos
cohesive homotopy type theory
## Structures in a cohesive $(\infty,1)$-topos
structures in a cohesive (∞,1)-topos
## Structures with infinitesimal cohesion
infinitesimal cohesion?
## Models
#### Differential geometry
synthetic differential geometry
Introductions
from point-set topology to differentiable manifolds
Differentials
V-manifolds
smooth space
Tangency
The magic algebraic facts
Theorems
Axiomatics
cohesion
• (shape modality $\dashv$ flat modality $\dashv$ sharp modality)
$(ʃ \dashv \flat \dashv \sharp )$
• dR-shape modality$\dashv$ dR-flat modality
$ʃ_{dR} \dashv \flat_{dR}$
• tangent cohesion
• differential cohomology diagram
• differential cohesion
• (reduction modality $\dashv$ infinitesimal shape modality $\dashv$ infinitesimal flat modality)
$(\Re \dashv \Im \dashv \&)$
• fermionic modality$\dashv$ bosonic modality $\dashv$ rheonomy modality
$(\rightrightarrows \dashv \rightsquigarrow \dashv Rh)$
•
\array{ && id &\dashv& id \ && \vee && \vee \ &\stackrel{fermionic}{}& \rightrightarrows &\dashv& \rightsquigarrow & \stackrel{bosonic}{} \ && \bot && \bot \ &\stackrel{bosonic}{} & \rightsquigarrow &\dashv& Rh & \stackrel{rheonomic}{} \ && \vee && \vee \ &\stackrel{reduced}{} & \Re &\dashv& \Im & \stackrel{infinitesimal}{} \ && \bot && \bot \ &\stackrel{infinitesimal}{}& \Im &\dashv& \& & \stackrel{\text{étale}}{} \ && \vee && \vee \ &\stackrel{cohesive}{}& ʃ &\dashv& \flat & \stackrel{discrete}{} \ && \bot && \bot \ &\stackrel{discrete}{}& \flat &\dashv& \sharp & \stackrel{continuous}{} \ && \vee && \vee \ && \emptyset &\dashv& \ast }
</semantics>[/itex]</div>
Models
Lie theory, ∞-Lie theory
differential equations, variational calculus
Chern-Weil theory, ∞-Chern-Weil theory
Cartan geometry (super, higher)
# Contents
## Idea
A formal smooth $\infty$-groupoid is an ∞-groupoid equipped with a cohesive structure that subsumes that of smooth ∞-groupoids as well as of infinitesimal $\infty$-groupoids – ∞-Lie algebroids, hence equipped with “differential cohesion”.
In the cohesive (∞,1)-topos of formal smooth $\infty$-groupoids the canonical fundamental ∞-groupoid in a locally ∞-connected (∞,1)-topos $\mathbf{\Pi}(X)$ factors through a version relative to Smooth∞Grpd: the infinitesimal path ∞-functor $\mathbf{\Pi}_{inf}(X)$. In traditional terms this is the object modeled by the tangent Lie algebroid and the de Rham space of $X$. The quasicoherent ∞-stacks on $\mathbf{\Pi}_{inf}(X)$ are D-modules on $X$.
## Definition
We consider (∞,1)-sheaves over a “twisted semidirect product” site or (∞,1)-site of
First in
we consider the 1-site, then in
we consider the $(\infty,1)$-site.
### 1-localic definition
###### Definition
Let $T :=$ CartSp${}_{smooth}$ be the syntactic category of the Lawvere theory of smooth algebras: the category of Cartesian spaces $\mathbb{R}^n$ and smooth functions between them.
Write
$SmoothAlg := T Alg$
for its category of T-algebras – the smooth algebras ($C^\infty$-rings).
Let
$InfPoint \hookrightarrow SmoothAlg^{op}$
be the full subcategory on the infinitesimally thickened points: this smooth algebras whose underlying abelian group is a vector space of the form $\mathbb{R} \oplus V$ with $V$ a finite-dimensional real vector space and nilpotent in the algebra structure.
###### Definition
Let
$FormalCartSp \hookrightarrow SmoothLoc$
be the full subcategory of the category of smooth loci on the objects of the form
$U = \mathbb{R}^n \times D$
that are products of a Cartesian space $\mathbb{R}^n \in$ CartSp for $n \in \mathbb{N}$ and an infinitesimally thickened point $D \in InfPoint$. (See at FormalCartSp.)
Equip this category with the coverage where a family of morphisms is covering precisely if it is of the form $\{U_i \times D \stackrel{(f_i, Id_D)}{\to} U \times D\}$ for $\{f_i : U_i \to U\}$ a covering in CartSp${}_{smooth}$ (a good open cover).
This appears as ([Kock 86, (5.1)]).
###### Note
The sheaf topos over FormalCartSp is (equivalent to) the topos known as the Cahiers topos, a smooth topos that constitutes a well adapted model for synthetic differential geometry. See at Cahiers topos for further references.
###### Definition
We say the (∞,1)-topos of formal smooth $\infty$-groupoids is the (∞,1)-category of (∞,1)-sheaves
$FormalSmooth \infty Grpd := Sh_{(\infty,1)}(FormalCartSp)$
on $FormalCartSp$.
### $\infty$-localic
We now generalize the 1-category $InfPoint$ of infinitesimally thickened points to the (∞,1)-category $InfPoint_\infty$ of “derived infinitesimally thickened points”, the formal dual of “small commutative $\infty$-algebras” from (Hinich, Lurie).
(…)
## Properties
###### Proposition
$FormalSmooth \infty Grpd$ is a cohesive (∞,1)-topos.
###### Proof
Because FormalCartSp is an ∞-cohesive site. See there for details.
###### Definition
Write $FormalSmoothMfd \hookrightarrow SmoothAlg^{op}$ for the full subcategory of smooth loci on the formal smooth manifolds: those modeled on FormalCartSp equipped with the evident coverage.
###### Observation
$FormalCartSp$ is a dense sub-site of $FormalSmoothMfd$.
###### Proposition
There is an equivalence of (∞,1)-categories
$FormalSmooth\infty Grpd \simeq \hat Sh_{(\infty,1)}(FSmoothMfd)$
with the hypercomplete (∞,1)-topos over $FSmoothMfd$.
###### Proof
With the above observation this is directly analogous to the corresponding proof at ETop∞Grpd.
###### Definition
Write $i : CartSp_{smooth} \hookrightarrow FormalCartSp$ for the canonical embedding.
###### Proposition
The functor $i^*$ given by restriction along $i$ exhibits $FormalSmooth\infty Grpd$ as an infinitesimal cohesive neighbourhood of the (∞,1)-topos Smooth∞Grpd of smooth ∞-groupoids in that we have a quadruple of adjoint (∞,1)-functors
$( i_! \dashv i^* \dashv i_* \dashv i^! ) : Smooth \infty Grpd \stackrel{\overset{i_!}{\hookrightarrow}}{\stackrel{\overset{i^*}{\leftarrow}}{\stackrel{\overset{i_*}{\to}}{\stackrel{i^!}{\leftarrow}}}} FormalSmooth \infty Grpd \,,$
such that $i_!$ is a full and faithful (∞,1)-functor.
###### Proof
Since $i : CartSp_{smooth} \hookrightarrow CartSp_{formalsmooth}$ is an infinitesimally ∞-cohesive site this follows with a proposition discussed at cohesive (infinity,1)-topos – infinitesimal cohesion.
## Structures
We discuss the realization of the general abstract structures in a cohesive (∞,1)-topos in $FormalSmooth \infty Grpd$.
Since by the above discussion $FormalSmooth\infty Grpd$ is strongly $\infty$-connected relative to Smooth∞Grpd all of these structures that depend only on $\infty$-connectedness (and not on locality) acquire a relative version.
### $\infty$-Lie algebroids and deformation theory
This subsection is at
### Paths and geometric Postnikov towers
We discuss the intrinsic infinitesimal path adjunction realized in $FormalSmooth\infty Grpd$.
$(\mathbf{Red} \dashv \mathbf{\Pi}_{inf} \dashv \mathbf{\flat}_{inf}) := (i \circ \Pi_{inf} \dashv Disc_{inf} \Pi_{inf} \dashv Disc_{inf} \circ \Gamma_{inf}) : FormalSmooth \infty Grpd \to FormalSmooth \infty Grpd \,.$
###### Proposition
For $U \times D \in CartSp_{smooth} \ltimes InfinSmoothLoc = FormalCartSp \hookrightarrow FormalSmooth\infty Grpd$ we have that
$\mathbf{Red}(U \times D) \simeq U$
is the reduced smooth locus: the formal dual of the smooth algebra obtained by quotienting out all nilpotent elements in the smooth algebra $C^\infty(K \times D) \simeq C^\infty(K) \otimes C^\infty(D)$.
###### Proof
By the model category presentation of $\mathbf{Red} \simeq \mathbb{L} Lan_i \circ \mathbb{R}i^*$ of the above proof and using that every representable is cofibrant and fibrant in the local projective model structure on simplicial presheaves we have
\begin{aligned} \mathbf{Red}(U \times D) & \simeq (\mathbb{L}Lan_i) (\mathbb{R}i^*) (U \times D) \\ &\simeq (\mathbb{L}Lan_i) i^* (U \times D) \\ & \simeq (\mathbb{L} Lan_i) U \\ & \simeq Lan_i U \\ & \simeq U \end{aligned}
(using that $i$ is a full and faithful functor).
###### Proposition
For $X \in SmoothAlg^{op} \to FormalSmooth \infty Grpd$ a smooth locus, we have that $\mathbf{\Pi}_{inf}(X)$ is the corresponding de Rham space, the object in which all infinitesimal neighbour points in $X$ are equivalent, characterized by
$\mathbf{\Pi}_{inf}(X) : U \times D \mapsto X(U) \,.$
###### Proof
By the $(\mathbf{Red} \dashv \mathbf{\Pi}_{inf})$-adjunction relation
\begin{aligned} \mathbf{\Pi}_{inf}(X)(U \times D) & = FormalSmooth \infty Grpd(U \times D, \mathbf{\Pi}_{inf}(X)) \\ & \simeq FormalSmooth \infty Grpd( \mathbf{Red}(U \times D), X) \\ & \simeq FormalSmooth \infty Grpd( U, X ) \end{aligned} \,.
### Cohomology and principal $\infty$-bundles
We discuss the intrinsic cohomology in a cohesive (∞,1)-topos realized in $FormalSmooth\infty Grpd$.
#### Cohomology localization
###### Proposition
The canonical line object of the Lawvere theory CartSp${}_{smooth}$ is the real line, regarded as an object of the Cahiers topos, and hence of $FormalSmooth \infty Grpd$
$\mathbb{A}^1_{CartSp_{smooth}} = \mathbb{R} \,.$
We shall write $\mathbb{R}$ also for the underlying additive group
$\mathbb{G}_a = \mathbb{R}$
regarded as an abelian ∞-group object in $FormalSmooth\infty Grpd$. For $n \in \mathbb{N}$ write $\mathbf{B}^n \mathbb{R} \in FormalSmooth\infty Grpd$ for its $n$-fold delooping.
For $n \in \mathbb{N}$ and $X \in FormalSmooth\infty Grpd$ write
$H^n_{synthdiff}(X) := \pi_0 FormalSmooth\infty Grpd(X,\mathbf{B}^n \mathbb{R})$
for the cohomology group of $X$ with coefficients in the canonical line object in degree $n$.
###### Definition
Write
$\mathbf{L}_{sdiff} \hookrightarrow FormalSmooth \infty Grpd$
for the cohomology localization of $FormalSmooth\infty Grpd$ at $\mathbb{R}$-cohomology: the full sub-(∞,1)-category on the $W$-local object with respect to the class $W$ of morphisms that induce isomorphisms in all $\mathbb{R}$-cohomology groups.
###### Proposition
Let $SmoothAlg^{\Delta}_{proj}$ be the projective model structure on cosimplicial smooth algebras and let $j : (SmoothAlg^{\Delta})^{op} \to [FormalCartSp, sSet]$ be the prolonged external Yoneda embedding.
$(\mathcal{O} \dashv j) : (SmoothAlg^\Delta)^{op} \stackrel{\overset{\mathcal{O}}{\leftarrow}}{\underset{j}{\to}} [FSmoothMfd^{op}, sSet]_{proj,loc} \,.$
2. Restricted to simplicial formal smooth manifolds along
$FSmoothMfd^{\Delta^{op}} \hookrightarrow (SmoothAlg^\Delta)^{op}$
the right derived functor of $j$ is a full and faithful (∞,1)-functor that factors through the cohomology localization and thus identifies a full reflective sub-(∞,1)-category
$(FSmoothMfd^{\Delta^{op}})^\circ \hookrightarrow \mathbf{L}_{sdiff} \hookrightarrow FormalSmooth\infty Grpd$
3. The intrinsic $\mathbb{R}$-cohomology of any object $X \in FormalSmooth\infty Grpd$ is computed by the ordinary cochain cohomology of the Moore cochain complex underlying the cosimplicial abelian group of the image under the left derived functor$(\mathbb{L}\mathcal{O})(X)$ under the Dold-Kan correspondence:
$H_{fSmooth}^n(X) \simeq H^n_{cochain}(N^\bullet(\mathbb{L}\mathcal{O})(X)) \,.$
###### Proof
First a remark on the sites. By the above proposition $FormalSmooth\infty Grpd$ is equivalent to the hypercomplete (∞,1)-topos over formal smooth manifolds. This is presented by the left Bousfield localization of $[FSmoothMfd^{op}, sSet]_{proj,loc}$ at the ∞-connected morphisms. But a fibrant object in $[FSmoothMfd^{op}, sSet]_{proj,loc}$ that is also n-truncated for $n \in \mathbb{N}$ is also fibrant in the hyperlocalization (only for the untruncated object there is an additional condition). Therefore the right Quillen functor claimed above indeed lands in truncated objects in $FormalSmooth \inftyGrpd$.
The proof of the above statements is given in (Stel), following (Toën). Some details are spelled out at function algebras on ∞-stacks.
#### Cohomology of Lie groups
###### Proposition
Let $G \in SmoothMfd \hookrightarrow Smooth\infty Grpd \hookrightarrow FormalSmooth\infty Grpd$ be a Lie group.
Then the intrinsic group cohomology in Smooth∞Grpd and in $FormalSmooth\infty Grpd$ of $G$ with coefficients in $\mathbb{R}$ coincides with Segal‘s refined Lie group cohomology (Segal, Brylinski).
$H^n_{smooth}(\mathbf{B}G, \mathbb{R}) \simeq H^n_{fsmooth}(\mathbf{B}G, \mathbb{R}) \simeq H^n_{Segal}(G,\mathbb{R}) \,.$
For the full proof please see here, section 3.4 for the moment.
###### Corollary
For $G$ a compact Lie group we have for all $n \geq 1$ that
$H^n_{smooth}(G,U(1)) \simeq H_{top}^{n+1}(B G, \mathbb{Z}) \,.$
###### Proof
This follows from applying the above result to the fiber sequence induced by the sequence $\mathbb{Z} \to \mathbb{R} \to \mathbb{R}/\mathbb{Z} = U(1)$.
###### Note
This means that the intrinsic cohomology of compact Lie groups in Smooth∞Grpd and $FormalSmooth\infty Grpd$ coincides for these coefficients with the Segal-Blanc-Brylinski refined Lie group cohomology (Brylinski).
#### Cohomology of $\infty$-Lie algebroids
###### Proposition
Let $\mathfrak{a} \in L_\infty \mathrm{Algd}$ be an L-∞ algebroid. Then its intrinsic real cohomology in $\mathrm{FormalSmooth}\infty \mathrm{Grpd}$
$H^n(\mathfrak{a}, \mathbb{R}) := \pi_0 \mathrm{FormalSmooth}\infty \mathrm{Grpd}(\mathfrak{a}, \mathbf{B}^n \mathbb{R})$
coincides with its ordinary L-∞ algebroid cohomology: the cochain cohomology of its Chevalley-Eilenberg algebra
$H^n(\mathfrak{a}, \mathbb{R}) \simeq H^n(\mathrm{CE}(\mathfrak{a})) \,.$
###### Proof
By the above propoposition we have that
$H^n(\mathfrak{a}, \mathbb{R}) \simeq H^n N^\bullet(\mathbb{L}\mathcal{O})(i(\mathfrak{a})) \,.$
By this lemma this is
$\cdots \simeq H^n N^\bullet \left( \int^{[k] \in \Delta} \mathbf{\Delta}[k] \cdot \mathcal{O}(i(\mathfrak{a})_k) \right) \,.$
Observe that $\mathcal{O}(\mathfrak{a})_\bullet$ is cofibrant in the Reedy model structure $[\Delta^{\mathrm{op}}, (\mathrm{SmoothAlg}^\Delta_{\mathrm{proj}})^{\mathrm{op}}]_{\mathrm{Reedy}}$ relative to the opposite of the projective model structure on cosimplicial algebras:
the map from the latching object in degree $n$ in $\mathrm{SmoothAlg}^\Delta)^{\mathrm{op}}$ is dually in $\mathrm{SmoothAlg} \hookrightarrow \mathrm{SmoothAlg}^\Delta$ the projection
$\oplus_{i = 0}^n \mathrm{CE}(\mathfrak{a})_i \otimes \wedge^i \mathbb{R}^n \to \oplus_{i = 0}^{n-1} \mathrm{CE}(\mathfrak{a})_i \otimes \wedge^i \mathbb{R}^n$
hence is a surjection, hence a fibration in $\mathrm{SmoothAlg}^\Delta_{\mathrm{proj}}$ and therefore indeed a cofibration in $(\mathrm{SmoothAlg}^\Delta_{\mathrm{proj}})^{\mathrm{op}}$.
Therefore using the Quillen bifunctor property of the coend over the tensoring in reverse to this lemma, the above is equivalent to
$\cdots \simeq H^n N^\bullet \left( \int^{[k] \in \Delta} \Delta[k] \cdot \mathcal{O}(i(\mathfrak{a})_k) \right)$
with the fat simplex replaced again by the ordinary simplex. But in brackets this is now by definition the image under the monoidal Dold-Kan correspondence of the Chevalley-Eilenberg algebra
$\cdots \simeq H^n( N^\bullet \Xi \mathrm{CE}(\mathfrak{a}) ) \,.$
By the Dold-Kan correspondence we have hence
$\cdots \simeq H^n(\mathrm{CE}(\mathfrak{a})) \,.$
It follows that a degree-$n$ $\mathbb{R}$-cocycle on $\mathfrak{a}$ is presented by a morphism
$\mu : \mathfrak{a} \to b^n \mathbb{R} \,,$
where on the right we have the $L_\infty$-algebroid whose $\mathrm{CE}$-algebra is concentrated in degree $n$. Notice that if $\mathfrak{a} = b \mathfrak{g}$ is the delooping of an $L_\infty$- algebra $\mathfrak{g}$ this is equivalently a morphism of $L_\infty$-algebras
$\mu : \mathfrak{g} \to b^{n-1} \mathbb{R} \,.$
#### de Rham theorem
under construction
We consider the de Rham theorem in $FormalSmooth \infty Grpd$, with respect to the infinitesimal de Rham cohomology
$H_{dR,inf}^n(X) := \pi_0 FormalSmooth \infty Grpd(X, \mathbf{\flat}_{inf} \mathbf{B}^n \mathbb{R}) \,.$
###### Proposition
For all $n \in \mathbb{N}$ The canonical morphism
$\mathbf{\flat}_{inf} \mathbf{B}^n \mathbb{R} \to \mathbf{\flat} \mathbf{B}^n \mathbb{R}$
is an equivalence.
This means that for all $X \in \mathbf{H}$ the infinitesimal de Rham cohomology coincides with the ordinary real cohomology of the geometric realization of $X$
$H^n_{dR, inf}(X) \simeq H^n(|X|, \mathbb{R}) \,.$
###### Proof
Since all representables are formally smooth, we have a colimit
$U \times_{\mathbf{\Pi}_{inf}(U)} U \stackrel{\to}{\to} U \stackrel{}{\to} \mathbf{\Pi}_{inf}(U) \,.$
In the presentation over the site we have that
$X \times_{\mathbf{\Pi}_{inf}(X)} X : K \times D \mapsto \{ f,g : K \times D \to U | K \to K \times D \stackrel{\to}{\to} U \} \,.$
Therefore a morphism $\mathbf{\Pi}_{inf}(U) \to \mathbb{R}$ is equivalently a morphism $\phi : U \to \mathbb{R}$ such that for all $K \times D \to U$ that coincide on $K$ we have that all the composites
$K \times D \to U \stackrel{\phi}{\to} \mathbf{B}^n \mathbb{R}$
are equals. If $U$ is the point, then $\phi$ is necessarily constant. If $U$ is not the point, there is one nontrivial tangent vector $v$ in $U$. The composite produces the corresponding tangent vector $\phi_*(v)$ in $\mathbb{R}$. But all these tangent vectors must be equal. Hence $\phi$ must be constant.
This kind of argument is indicated in (Simpson-Teleman, prop. 3.4).
###### Proposition
Let $X \in$ SmoothMfd and write $X^{\Delta^\bullet_{inf}} \in [CartSp_{formalsmooth}^{op}, sSet]$ for the tangent Lie algebroid regarded as a simplicial object (see L-infinity algebroid for the details).
Then there is a morphism $X^{\Delta^\bullet_{inf}} \to \mathbf{\Pi}_{inf}(X)$ which is an equivalence in $\mathbb{R}$-cohomology.
(…)
### Formally étale morphisms and cohesive étale $\infty$-groupoids
We discuss formally étale morphisms and étale objects with respect to the cohesive infinitesimal neighbourhood $i :$ Smooth∞Grpd $\hookrightarrow FormalSmooth\infty Grpd$.
###### Proposition
Let $X_\bullet$ be a degreewise smooth paracompact simplicial manifold, canonically regarded as an object of Smooth∞Grpd.
Then $j_! X_\bullet$ in $FormalSmooth \infty Grpd$ is presented by the same simplicial manifold.
###### Proof
First consider an ordinary smooth paracompact manifold $X$. It admits a good open cover $\{U_i \to X\}$ and the corresponding Cech nerve $C(\{U_i\}) in [CartSp_{smooth}^{op}, sSet]_{proj}$ is a cofibrant resolution of $X$. Therefore the $\infty$-functor $j_!$ is computed on $X$ by evaluating the corresponding simplicial functor (of which it is the derived functor) on $C(\{U_i\})$.
Since the simplicial functor
$j_! : [CartSp_{smooth}^{op}, sSet]_{proj, loc} \to [CartSp_{formalsmooth}^{op}, sSet]_{proj, loc}$
is a left adjoint (indeed a left Quillen functor) it preserves the coproducts and coend that the Cech nerve is built from:
\begin{aligned} j_! C(\{U_i\}) & = j_! \int^{[n] \in \Delta} \Delta[n] \cdot \coprod_{i_0, \cdots, i_n} U_{i_0, \cdots, i_n} \\ & = \int^{[n] \in \Delta} \Delta[n] \cdot \coprod_{i_0, \cdots, i_n} j_! (U_{i_0, \cdots, i_n}) \\ & = \int^{[n] \in \Delta} \Delta[n] \cdot \coprod_{i_0, \cdots, i_n} U_{i_0, \cdots, i_n} \end{aligned} \,.
Here we used that, by assumption on a good open cover, all the $U_{i_0, \cdots, i_n}$ are Cartesian spaces, and that $j_!$ coincides on representables with the inclusion $CartSp_{smooth} \hookrightarrow CartSp_{formalsmooth}$.
Let now $X_\bullet$ be a general simplicial manifold. Assume that in each degree there is a good open cover $\{U_{p,i} \to X_p\}$ such that these fit into a simplicial system giving a bisimplicial Cech nerve such that there is a morphism of bisimplicial presheaves
$C(\mathcal{U})_{\bullet, \bullet} \to X_{\bullet}$
with $X_\bullet$ regarded as simplicially constant in one direction. Each $C(\mathcal{U})_{p, \bullet} \to X_p$ is a cofibrant resolution.
We claim that the coend
$\int^{[n] \in \Delta} C(\mathcal{U})_{n, \bullet} \cdot \mathbf{\Delta}[n] \;\;\; \to \;\;\; X$
is a cofibrant resolution of $X$, where $\mathbf{\Delta}$ is the fat simplex. From this the proposition follows by again applying the left Quillen functor $j_!$ degreewise and pulling it through all the colimits.
This remaining claim follows from the same argument as used above in prop. .
###### Proposition
A morphism in $FormalSmooth\infty Grpd$, is a formally étale morphism with respect to the infinitesimal cohesion $i \colon Smooth \infty Grpd \hookrightarrow FormalSmooth\infty Grpd$ precisely if for all infinitesimally thickened points $D$ the diagram
$\array{ X^D &\stackrel{f^D}{\to}& Y^D \\ \downarrow && \downarrow \\ Y &\stackrel{f}{\to}& Y }$
is an $\infty$-pullback under $i^*$.
###### Remark
Since $i^*$ preserves $\infty$-limits, this is the case in particular if the diagram is an $\infty$-pullback already in $FormalSmooth\infty Grod$. In this form, restricted to 0-truncated objects, hence to the Cahiers topos, this characterization of formally étale morphisms appears axiomatized around p. 82 of (Kock 81, p. 82).
In particular, a smooth function $f : X \to Y$ in SmoothMfd $\hookrightarrow$ Smooth∞Grpd between smooth manifolds is a formally étale morphism with respect to the infinitesimal cohesion $Smooth \infty Grpd \hookrightarrow FormalSmooth\infty Grpd$ precisely if it is a local diffeomorphism in the traditional sense.
###### Proof
We spell out the case for smooth manifolds. Here we need to to show that
$\array{ i_! X &\stackrel{i_! f}{\to}& i_! Y \\ \downarrow && \downarrow \\ i_* X &\stackrel{i_* f}{\to}& i_* Y }$
is a pullback in $Sh(CartSp_{formalsmooth})$ precisely if $f$ is a local diffeomorphism. This is a pullback precisely if for all $U \times D \in CartSp_{smooth} \ltimes InfPoint \simeq CartSp_{formalsmooth}$ the diagram of sets of plots
$\array{ Hom(U \times D, i_! X) &\stackrel{i_! f}{\to}& Hom(U \times D, i_! Y) \\ \downarrow && \downarrow \\ Hom(U \times D, i_* X) &\stackrel{i_* f}{\to}& Hom(U \times D, i_* Y) }$
is a pullback. Using, by the discussion at ∞-cohesive site, that $i_!$ preserves colimits and restricts to $i$ on representables, and using that $i^* (U \times D ) = U$, this is equivalently the diagram
$\array{ Hom(U \times D, X) &\stackrel{f_*}{\to}& Hom(U \times D, Y) \\ \downarrow && \downarrow \\ Hom(U , X) &\stackrel{f_*}{\to}& Hom(U , Y) } \,,$
where the vertical morphisms are given by restriction along the inclusion $(id_U, *) : U \to U \times D$.
For one direction of the claim it is sufficient to consider this situation for $U = *$ the point and $D$ the first order infinitesimal interval. Then $Hom(*,X)$ is the underlying set of points of the manifold $X$ and $Hom(D,X)$ is the set of tangent vectors, the set of points of the tangent bundle $T X$. The pullback
$Hom(*,X) \times_{Hom(*,Y)} Hom(D,Y)$
is therefore the set of pairs consisting of a point $x \in X$ and a tangent vector $v \in T_{f(x)} Y$. This set is in fiberwise bijection with $Hom(D, X) = T X$ precisely if for each $x \in X$ there is a bijection $T_x X \simeq T_{f(x)}Y$, hence precisely if $f$ is a local diffeomorphism. Therefore $f$ being a local diffeo is necessary for $f$ being formally étale with respect to the given notion of infinitesimal cohesion.
To see that this is also sufficient notice that this is evident for the case that $f$ is in fact a monomorphism, and that since smooth functions are characterized locally, we can reduce the general case to that case.
###### Proposition
A Lie groupoid $\mathcal{G}$ is an étale groupoid in the traditional sense, precisely if regarded as an object in $i :$ Smooth∞Grpd $\hookrightarrow$ FormalSmooth∞Grpd it is an cohesive étale ∞-groupoid.
###### Proof
Let $\mathcal{G}_0 \to \mathcal{G}$ be the inclusion of the smooth manifold of objects. This is an effective epimorphism. It remains to show that this is formally étale with respect to the given cohesive neighbourhood.
By the discussion at (∞,1)-pullback we may compute the characteristic $(\infty,1)$-pullback by an ordinary pullback of a fibration of simplicial presheaves that presents $\mathcal{G}_0 \to \mathcal{G}$.
By the factorization lemma such is given by
$\mathcal{G}^I \times_{\mathcal{G}} \mathcal{G}_0 \to \mathcal{G} \,.$
By inspection one see that this morphism is
• in degree 0 the target-map $t : Mor(\mathcal{G}) \to \mathcal{G}_0$;
• in degree 1 the projection $Mor(\mathcal{G}) {}_t\times_{s} Mor(\mathcal{G}) \to Mor(\mathcal{G})$.
By prop. both of these need to be étale maps in the ordinary sense. By definition, this is the case precisely if $\mathcal{G}$ is an étale groupoid.
### Formally smooth / formally unramified morphisms
As a direct consequence of prop. we have the following
###### Proposition
A smooth function $f : X \to Y$ between smooth manifolds, is a submersion or immersion, respectively, precisely if, when canonically regarded as a morphism in $FormalSmooth \infty Grpd$, it is a formally smooth morphism or formally unramified morphism, respectively.
###### Proof
As in the proof of prop. we find that the pullback $i_* X \times_{i_* Y} i_! Y$ is over the infinitesimal interval isomorphic to
$X \times_Y T Y$
and the canonical morphism from $i_! X$ into this pullback is
$T X \to X \times_Y T Y \,.$
### Lie differentiation
We indicate how to formalize Lie differentiation in the context of formal smooth $\infty$-groupoids.
Let
$inf : InfPoint_\infty \hookrightarrow \mathbf{H}^{*/}$
be the canonical inclusion. By (Lurie, theorem 0.0.13, remark 0.0.15, also Pridham 07) we have a full inclusion
$Lie_\infty \hookrightarrow Sh_\infty(InfPoint_\infty)$
on those objects whose space of global sections is contractible and which are infinitesimally cohesive (for a somewhat different notion of “infinitesimal cohesion”, beware the terminology). Consider then the $\infty$-functor
$Grp(\mathbf{H}) \simeq \mathbf{H}^{*/}_{\geq 1} \stackrel{yoneda}{\to} PSh_\infty( \mathbf{H}^{*/}) \stackrel{inf^*}{\to} PSh_\infty(InfPoint_\infty)$
which sends a pointed connected formal smooth $\infty$-groupoid $\mathbf{B}G$ to the $(\infty,1)$-presheaf of pointed morphisms
$\mathbf{pt} \to \mathbf{B}G$
for $\mathbf{pt} \in InfPoint_\infty$.
By assumption that $\mathbf{B}G$ is connected (and we need to assume that it is geometric, which will gives infinitesimal cohesion by the Artin-Lurie representability theorem) this factors as
$\mathbf{H}^{*/}_{\geq 1} \stackrel{Lie}{\to} Lie_\infty \hookrightarrow Sh_\infty(InfPoint_\infty) \,.$
The resulting $\infty$-functor
$Lie : Grp(\mathbf{H}) \simeq \mathbf{H}^{*/}_{\geq 1} \to Lie_\infty$
is Lie differentiation.
For differentiation of smooth groupoids with atlas $U \to X$ to L-infinity algebroids this happens under $U$
$\mathbf{H}^{U/}$
(…)
geometries of physics
$\phantom{A}$(higher) geometry$\phantom{A}$$\phantom{A}$site$\phantom{A}$$\phantom{A}$sheaf topos$\phantom{A}$$\phantom{A}$∞-sheaf ∞-topos$\phantom{A}$
$\phantom{A}$discrete geometry$\phantom{A}$$\phantom{A}$Point$\phantom{A}$$\phantom{A}$Set$\phantom{A}$$\phantom{A}$Discrete∞Grpd$\phantom{A}$
$\phantom{A}$differential geometry$\phantom{A}$$\phantom{A}$CartSp$\phantom{A}$$\phantom{A}$SmoothSet$\phantom{A}$$\phantom{A}$Smooth∞Grpd$\phantom{A}$
$\phantom{A}$formal geometry$\phantom{A}$$\phantom{A}$FormalCartSp$\phantom{A}$$\phantom{A}$FormalSmoothSet$\phantom{A}$$\phantom{A}$FormalSmooth∞Grpd$\phantom{A}$
$\phantom{A}$supergeometry$\phantom{A}$$\phantom{A}$SuperFormalCartSp$\phantom{A}$$\phantom{A}$SuperFormalSmoothSet$\phantom{A}$$\phantom{A}$SuperFormalSmooth∞Grpd$\phantom{A}$
## References
The site FormalCartSp is discussed in section 5 of
• Anders Kock, Convenient vector spaces embed into the Cahiers topos , Cahiers de Topologie et Géométrie Différentielle Catégoriques, 27 no. 1 (1986), p. 3-17 (numdam).
For more on this see at Cahiers topos.
The notion of formally étale maps as obtained here from the general abstract definition in differential cohesion coincided on 0-truncated objects with that defined on p. 82 of
The infinitesimal path ∞-groupoid adjunction $(\mathbf{Red} \dashv \mathbf{\Pi}_{inf} \dashv \mathbf{\flat}_{inf})$ and the de Rham theorem for $\infty$-stacks is discussed at the level of homotopy categories in section 3 of
The $(\infty,1)$-topos $SynthDiff\infty Grpd$ is discussed in section 4.4 of
The cohomology localization of $SynthDiff\infty Grpd$ and the infinitesimal singular simplicial complex as a presentation for infinitesimal paths objects in $SynthDiff\infty Grpd$ is discussed in
• Herman Stel, $\infty$-Stacks and their function algebras – with applications to $\infty$-Lie theory , master thesis (2010) (web)
The discussion of the cohomology localization of $SynthDiff\infty Grpd$ follows that in another context in
The construction of the infinitesimal path object has been amplified and discussed by Anders Kock under the name combinatorial differential forms, for instance in
The discussion that the normalized cosimplicial algebra of functions on the infinitesimal singular simplicial complex is the de Rham complex is further discussed in
The results on differentiable Lie group cohomology used above is in
• P. Blanc, Cohomologie différentiable et changement de groupes Astérisque, vol. 124-125 (1985), pp. 113-130.
recalled in
which parallels
• Graeme Segal, Cohomology of topological groups , Symposia Mathematica, Vol IV (1970) (1986?) p. 377
The $(\infty,1)$-site of derived infinitesimal points is discussed in
following
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https://forum.allaboutcircuits.com/threads/help-with-programmable-current-source.162606/ | 1,611,435,825,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703538431.77/warc/CC-MAIN-20210123191721-20210123221721-00353.warc.gz | 343,378,602 | 29,800 | # Help with Programmable Current Source-
#### Ta Ba
Joined Aug 25, 2019
5
Hi everyone,
i need to design a Programmable current source, it 's output current value is from 10 nA - 10 uA.
the controlled voltage are generated from a DAC and it is 0 - 40 mV.
is it possible to get this low current value? all the circuit that i have found can generate a current above 10 uA ,but none of them can generate a 10 nA.
Thanks.
#### crutschow
Joined Mar 14, 2008
26,044
Does the load for the current source need to be grounded?
Why is the DAC output voltage so small?
#### TeeKay6
Joined Apr 20, 2019
572
Hi everyone,
i need to design a Programmable current source, it 's output current value is from 10 nA - 10 uA.
the controlled voltage are generated from a DAC and it is 0 - 40 mV.
is it possible to get this low current value? all the circuit that i have found can generate a current above 10 uA ,but none of them can generate a 10 nA.
Thanks.
Assuming that the output current flows through some load, over what range of load voltage must the current be held constant?
#### crutschow
Joined Mar 14, 2008
26,044
Assuming that the output current flows through some load, over what range of load voltage must the current be held constant?
Or, in other words, what is the maximum value for the load resistance?
#### TeeKay6
Joined Apr 20, 2019
572
Or, in other words, what is the maximum value for the load resistance?
@crutschow
I don't yet know whether the load is indeed a resistance. Perhaps it is a capacitor? Or perhaps a diode? I don't believe it's possible to complete the design without knowing the allowed range of voltage. I was assuming we would also get a descriptive reply to your question as to whether the load is grounded or not. It would be desirable to know the allowed voltage (relative to a reference such as ground) at each "end" of the load as the current is varied over the required range.
Last edited:
#### ci139
Joined Jul 11, 2016
1,696
trivia ? OUTP.error ? variation speed / waveform ? ((in case of stepped V.ctrl)) settling time / range(error) . . .
#### Ta Ba
Joined Aug 25, 2019
5
Or, in other words, what is the maximum value for the load resistance?
The output is an Input for next stage,which is Transimpedance amplifier.
but the question, why should i consern about the resistance.
as i understand, the current source provide a constant current and depends only on the input voltage.
The Input voltage could be modified, but should be within the microcontroller output voltage or an external DAC.
Assuming that the output current flows through some load, over what range of load
The current flows to Transimpedance amplifier, which have a low input impedance, i do not know exactly what is the value of Rin. but i need to know how to design such vccs at first place.
Last edited by a moderator:
#### TeeKay6
Joined Apr 20, 2019
572
So, thus far--
We Know:
• Programmable/controllable current source able to control a current over the range 10nA to 10uA.
• The control is via a voltage in the range 0-40mV.
• The controlled current flows to the input of a transimpedance amp.
We Assume (until corrected by TS):
• The current will flow into (conventional sense, not the electrons) the transimpedance amp input. UPDATE: TS says current will flow out of TIA input.
• That input will be at ground potential and fixed within some yet to be defined variation, e.g. ±?mV.
• When the control voltage is 0mV, the current should be 10nA; when control voltage is 40mV, current should be 10uA.
We do not know (until answered by TS):
• How control voltage is set.
• What relationship exists between control voltage and controlled current; i.e. linear or some defined nonlinearity. Required accuracy/correspondence between control voltage and controlled current.
• Stability of current vs temperature, time, relative humidity.
• Equivalent resistance of current source. How stable must current be vs change in load voltage.
• Preferred/allowed source(s) of power for current source circuitry.Allowed power consumption of current source circuitry.
• If control voltage must vary repeatably, description of variation (e.g. waveform) or, if control is via steps, what is allowed settling time and error. [@ci139]
• Which of the above questions/statements are relevant to the project TS is placing before AAC commenters.
• On what day the universe began.
• Whether it is healthier to eat organic or not-organic tomatoes.
Changes to the above list are invited, especially by the TS.
@Ta Ba : Despite my humor, I am intending to be serious, not flippant.
UPDATES are noted above in list.
Last edited:
#### Ta Ba
Joined Aug 25, 2019
5
@crutschow
I don't yet know whether the load is indeed a resistance. Perhaps it is a capacitor? Or perhaps a diode? I don't believe it's possible to complete the design without knowing the allowed range of voltage. I was assuming we would also get a descriptive reply to your question as to whether the load is grounded or not. It would be desirable to know the allowed voltage (relative to a reference such as ground) at each "end" of the load as the current is varied over the required range.
well, the next stage is Transimpedance, i am not sure if there will be a voltage limit (or it is just the critical value of the electronics parts).
#### TeeKay6
Joined Apr 20, 2019
572
well, the next stage is Transimpedance, i am not sure if there will be a voltage limit (or it is just the critical value of the electronics parts).
@Ta Ba
Is it your intent that the output of the transimpedance amplifier become more positive or more negative as the input current increases?
Do you have in mind a desired voltage range of the amplifier output as the input current varies over its full range? (This is relevant only if you wish to discuss the transimpedance amplifier here.)
#### Ta Ba
Joined Aug 25, 2019
5
@Ta Ba
Is it your intent that the output of the transimpedance amplifier become more positive or more negative as the input current increases?
Do you have in mind a desired voltage range of the amplifier output as the input current varies over its full range? (This is relevant only if you wish to discuss the transimpedance amplifier here.)
The TI should has just a positive voltage output and it increase when current increases.
it's about uni project and my concern is just VCCS ,the Transimpedance is already designed and it has a 100.000 gain.
Thanks alot
#### TeeKay6
Joined Apr 20, 2019
572
The TI should has just a positive voltage output and it increase when current increases.
it's about uni project and my concern is just VCCS ,the Transimpedance is already designed and it has a 100.000 gain.
Thanks alot
@Ta Ba
If your TIA has an output that becomes more positive as the input current increases--this is the simplest, most common, configuration--, then the current source at the input must cause (conventional) current flow out of the input of the TIA; i.e. a negative current. We do then need to know what is the input voltage of the TIA relative to circuit ground. (It could be 0V or some + or - value.) The current source must be of a "sinking" type (rather than a "sourcing" type). Either the TIA input must have a positive voltage offset or the sinking current source must have a negative voltage offset (or both) in order to draw current out of the TIA input.
#### TeeKay6
Joined Apr 20, 2019
572
@Ta Ba
If your TIA has an output that becomes more positive as the input current increases--this is the simplest, most common, configuration--, then the current source at the input must cause (conventional) current flow out of the input of the TIA; i.e. a negative current. We do then need to know what is the input voltage of the TIA relative to circuit ground. (It could be 0V or some + or - value.) The current source must be of a "sinking" type (rather than a "sourcing" type). Either the TIA input must have a positive voltage offset or the sinking current source must have a negative voltage offset (or both) in order to draw current out of the TIA input.
@Ta Ba
You have not yet answered the question by @crutschow as to why the DAC output is so low. Nor have you offered much more info on the items in the lists I made earlier. One other topic we have not discussed is whether you will build or merely design the current source. If you will build it, do you intend to solder components together or use some patchboard system? If you will build it, do you have access to appropriate test equipment (e.g. power supply, VOM, etc)?
#### ci139
Joined Jul 11, 2016
1,696
10 nA - 10 uA
DAC output voltage so small?
that pretty much suggest it's inside particular integrated circuit block = "i'm out"
? can you provide a discrete component level schematic (of the next-stage input) that you feed the (10n to 10µ A) output to ((as Fig.3 in http://www.hrpub.org/download/20171030/UJES1-14610182.pdf))
+ also answering the list by TK as much and exactly you can / ? are allowed to ? would be essential /// as is also "what everything you can use for the design" ( mos/j-fets bi-polars only/mixed)
Last edited:
#### Ta Ba
Joined Aug 25, 2019
5
So, thus far--
We Know:
• Programmable/controllable current source able to control a current over the range 10nA to 10uA.
• The control is via a voltage in the range 0-40mV.
• The controlled current flows to the input of a transimpedance amp.
We Assume (until corrected by TS):
• The current will flow into (conventional sense, not the electrons) the transimpedance amp input. UPDATE: TS says current will flow out of TIA input.
• That input will be at ground potential and fixed within some yet to be defined variation, e.g. ±?mV.
• When the control voltage is 0mV, the current should be 10nA; when control voltage is 40mV, current should be 10uA.
We do not know (until answered by TS):
• How control voltage is set.
• What relationship exists between control voltage and controlled current; i.e. linear or some defined nonlinearity. Required accuracy/correspondence between control voltage and controlled current.
• Stability of current vs temperature, time, relative humidity.
• Equivalent resistance of current source. How stable must current be vs change in load voltage.
• Preferred/allowed source(s) of power for current source circuitry.Allowed power consumption of current source circuitry.
• If control voltage must vary repeatably, description of variation (e.g. waveform) or, if control is via steps, what is allowed settling time and error. [@ci139]
• Which of the above questions/statements are relevant to the project TS is placing before AAC commenters.
• On what day the universe began.
• Whether it is healthier to eat organic or not-organic tomatoes.
Changes to the above list are invited, especially by the TS.
@Ta Ba : Despite my humor, I am intending to be serious, not flippant.
UPDATES are noted above in list.
• The control voltage is set by DAC from a microcontroller or an external DAC controlled by a mcu.
• When DAC=0 v => the current should be null, I=0. when DAC=20 mv => the current I=10 nA.
• for every +2 uV the current increases by 1 nA until its maximal alowed current when Vin =40 mV and I=10 uA.
• Settling Time is 1 us. the Signal from DAC has a constant period of 10 us and the duty cycle varies from 1/(10us +40us) to 1/(10 us+1s).
that pretty much suggest it's inside particular integrated circuit block = "i'm out"
well it is not my work, for the control signal another student should generate the signal based on measured parameter.
but theoretically, we can make the voltage higher (like instead of (from 20mv-40mv) we can make it (from 2v to 4v) by the DAC or just amplify that signal to meet our goal.
@Ta Ba
You have not yet answered the question by @crutschow as to why the DAC output is so low. Nor have you offered much more info on the items in the lists I made earlier. One other topic we have not discussed is whether you will build or merely design the current source. If you will build it, do you intend to solder components together or use some patchboard system? If you will build it, do you have access to appropriate test equipment (e.g. power supply, VOM, etc)?
excuse me being late.
i have answered some question but a bout the stability: should i consern about that after or before the Design? i mean when i have designed Circuit, then i can mesaure and check its stability against chang in teperature and change in Output power.
i want to make the it on Board, two layer Board and yes in the lab we have appropriate equipment, but i need at first to have a design im my Hand to take access in the lab.
Last edited by a moderator:
#### TeeKay6
Joined Apr 20, 2019
572
• The control voltage is set by DAC from a microcontroller or an external DAC controlled by a mcu.
• When DAC=0 v => the current should be null, I=0. when DAC=20 mv => the current I=10 nA.
• for every +2 uV the current increases by 1 nA until its maximal alowed current when Vin =40 mV and I=10 uA.
• Settling Time is 1 us. the Signal from DAC has a constant period of 10 us and the duty cycle varies from 1/(10us +40us) to 1/(10 us+1s).
well it is not my work, for the control signal another student should generate the signal based on measured parameter.
but theoretically, we can make the voltage higher (like instead of (from 20mv-40mv) we can make it (from 2v to 4v) by the DAC or just amplify that signal to meet our goal.
excuse me being late.
i have answered some question but a bout the stability: should i consern about that after or before the Design? i mean when i have designed Circuit, then i can mesaure and check its stability against chang in teperature and change in Output power.
i want to make the it on Board, two layer Board and yes in the lab we have appropriate equipment, but i need at first to have a design im my Hand to take access in the lab.
@Ta Ba
Thanks for the additional info; I will update my specs lists. The settling time is rather more complex than a single value; it might depend on the size of the change or even the level of the output.
The problem with the low DAC voltage is that noise and thermal stability become quite troublesome at such low voltages. If possible, I certainly recommend that the DAC output be raised. Yes, a full-scale value of 4V would be much safer than 40mV.
If you were asked to design a car, would you wait until the design was complete before you decided what top speed (or hundreds of other specs) was required? Don't you think that it would be foolish to take that approach? The situation is the same for any project. If you don't know where you are headed, you will never reach the goal. That is the purpose in making the list of specs. We want to know early during design what is required. A requirement that turns up late in the design process could easily invalidate all the work done up to that point. Meaning, at best, you would be fired from your job as designer, if not sued for incompetence. It's far better to do your planning at the beginning, not after you finish. As the design progresses, you continually review it against the list of specs. You may discover that some spec is not achievable (or not achievable for an acceptable cost, or for an acceptable development/design time) and a change needs to be negotiated.
So, the first goal is to define as many specs as possible. And very soon, it should be you, not I, who maintains the lists.
#### ci139
Joined Jul 11, 2016
1,696
#### Attachments
• 692.4 KB Views: 3
Last edited:
#### TeeKay6
Joined Apr 20, 2019
572
@ci139
Very nice, although pricey!!! Thanks for tip.
#### crutschow
Joined Mar 14, 2008
26,044
i have answered some question but a bout the stability: should i consern about that after or before the Design? i mean when i have designed Circuit, then i can mesaure and check its stability against chang in teperature and change in Output power.
You always consider that during the design, as TeeKay6 stated.
Otherwise you have to do a redesign if your stability measurements shows it's not sufficient.
#### TeeKay6
Joined Apr 20, 2019
572
• The control voltage is set by DAC from a microcontroller or an external DAC controlled by a mcu.
• When DAC=0 v => the current should be null, I=0. when DAC=20 mv => the current I=10 nA.
• for every +2 uV the current increases by 1 nA until its maximal alowed current when Vin =40 mV and I=10 uA.
• Settling Time is 1 us. the Signal from DAC has a constant period of 10 us and the duty cycle varies from 1/(10us +40us) to 1/(10 us+1s).
well it is not my work, for the control signal another student should generate the signal based on measured parameter.
but theoretically, we can make the voltage higher (like instead of (from 20mv-40mv) we can make it (from 2v to 4v) by the DAC or just amplify that signal to meet our goal.
excuse me being late.
i have answered some question but a bout the stability: should i consern about that after or before the Design? i mean when i have designed Circuit, then i can mesaure and check its stability against chang in teperature and change in Output power.
i want to make the it on Board, two layer Board and yes in the lab we have appropriate equipment, but i need at first to have a design im my Hand to take access in the lab.
@Ta Ba | 4,200 | 17,261 | {"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} | 2.90625 | 3 | CC-MAIN-2021-04 | latest | en | 0.923714 |
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# Ratul Das
### University of Cambridge
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Length of a short side
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Is my wife right?
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Find the sum of all the numbers of the input vector x. Examples: Input x = [1 2 3 5] Output y is 11 Input x ...
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Given a matrix, m-by-n, find all the rows that have the same "increase, decrease, or stay same" pattern going across the columns...
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http://www.chegg.com/homework-help/questions-and-answers/1-calculate-angular-momentum-kg-8-planets-2-laser-cooling-3-golf-ball-hit-60-m-s-20-deg-ho-q1846291 | 1,444,424,226,000,000,000 | text/html | crawl-data/CC-MAIN-2015-40/segments/1443737935292.75/warc/CC-MAIN-20151001221855-00019-ip-10-137-6-227.ec2.internal.warc.gz | 478,681,607 | 12,494 | 1. Calculate angular momentum/kg for the 8 planets
2. What is laser cooling?
3. A golf ball is hit at 60 m/s at 20 deg above horizontal.
a) How high will it go?
b) How far will it go?
4. A 30 kg sign is hanging from a 10 kg bar 3 meters long. The sign is held by a wire that makes a 40 deg angle with the wall and is attached to the bar at the end. The sign is attached to the bar 2 m from the wall.
a) What is the tension in the wire?
b) What is the horizontal force at the hinge between the bar and the wall?
c) What is the vertical force at the hinge between the bar and the wall? | 160 | 591 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.703125 | 3 | CC-MAIN-2015-40 | latest | en | 0.943795 |
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The simulation of the virtual epileptic patient is presented as an example of advanced brain simulation as a translational approach to deliver improved results in clinics. The fundamentals of epilepsy are explained. On this basis, the concept of epilepsy simulation is developed. By using an iPython notebook, the detailed process of this approach is explained step by step. In the end, you are able to perform simple epilepsy simulations your own.
Difficulty level: Beginner
Duration: 1:28:53
Speaker: : Julie Courtiol
Learn how to simulate seizure events and epilepsy in The Virtual Brain. We will look at the paper: On the Nature of Seizure Dynamics which describes a new local model called the Epileptor, and apply this same model in The Virtual Brain. This is part 1 of 2 in a series explaining how to use the Epileptor. In this part, we focus on setting up the parameters.
Difficulty level: Beginner
Duration: 4:44
Speaker: : Paul Triebkorn
The probability of a hypothesis, given data.
Difficulty level: Beginner
Duration: 7:57
Speaker: : Barton Poulson
Why math is useful in data science.
Difficulty level: Beginner
Duration: 1:35
Speaker: : Barton Poulson
Why statistics are useful for data science.
Difficulty level: Beginner
Duration: 4:01
Speaker: : Barton Poulson
Statistics is exploring data.
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Duration: 2:23
Speaker: : Barton Poulson
Graphical data exploration
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Duration: 8:01
Speaker: : Barton Poulson
Numerical data exploration
Difficulty level: Beginner
Duration: 5:05
Speaker: : Barton Poulson
Simple description of statistical data.
Difficulty level: Beginner
Duration: 10:16
Speaker: : Barton Poulson
Basics of hypothesis testing.
Difficulty level: Beginner
Duration: 06:04
Speaker: : Barton Poulson
Enabling neuroscience research using high performance computing
Difficulty level: Beginner
Duration: 39:27
Speaker: : Subha Sivagnanam
Félix-Antoine Fortin from Calcul Québec gives an introduction to high-performance computing with the Compute Canada network, first providing an overview of use cases for HPC and then a hand-on tutorial. Though some examples might seem specific to the Calcul Québec, all computing clusters in the Compute Canada network share the same software modules and environments.
The lesson was given in the context of the BrainHack School 2020.
Difficulty level: Beginner
Duration: 02:49:34
Speaker: :
The Canadian Open Neuroscience Platform (CONP) Portal is a web interface that facilitates open science for the neuroscience community by simplifying global access to and sharing of datasets and tools. The Portal internalizes the typical cycle of a research project, beginning with data acquisition, followed by data processing with published tools, and ultimately the publication of results with a link to the original dataset.
In this video, Samir Das and Tristan Glatard give a short overview of the main features of the CONP Portal.
Difficulty level: Beginner
Duration: 14:03
Speaker: :
Shawn Brown presents an overview of CBRAIN, a web-based platform that allows neuroscientists to perform computationally intensive data analyses by connecting them to high-performance-computing facilities across Canada and around the world.
This talk was given in the context of a Ludmer Centre event in 2019.
Difficulty level: Beginner
Duration: 56:07
Speaker: :
This course will teach you AWS basics right through to advanced cloud computing concepts. There are lots of hands-on exercises using an AWS free tier account to give you practical experience with Amazon Web Services. Visual slides and animations will help you gain a deep understanding of Cloud Computing.
This lesson is courtesy of freeCodeCamp.
Difficulty level: Beginner
Duration: 05:27:20
Speaker: :
Lecture on functional brain parcellations and a set of tutorials on bootstrap agregation of stable clusters (BASC) for fMRI brain parcellation which were part of the 2019 Neurohackademy, a 2-week hands-on summer institute in neuroimaging and data science held at the University of Washington eScience Institute.
Duration: 50:28
Speaker: : Pierre Bellec
As a part of NeuroHackademy 2020, Tara Madhyastha (University of Washington), Andrew Crabb (AWS), and Ariel Rokem (University of Washington) give a lecture on Cloud Computing, focusing on Amazon Web Services
This video is provided by the University of Washington eScience Institute.
Difficulty level: Beginner
Duration: 01:43:59
Speaker: :
This lecture covers an introduction to neuroinformatics and its subfields, the content of the short course and future neuroinformatics applications.
Difficulty level: Beginner
Duration: 34:27
In this presentation by the OHBM OpenScienceSIG, Tom Shaw and Steffen Bollmann cover how containers can be useful for running the same software on different platforms and sharing analysis pipelines with other researchers. They demonstrate how to build docker containers from scratch, using Neurodocker, and cover how to use containers on an HPC with singularity.
Difficulty level: Beginner
Duration: 01:21:59
This lecture covers structured data, databases, federating neuroscience-relevant databases, ontologies.
Difficulty level: Beginner
Duration: 1:30:45
Speaker: : Maryann Martone | 1,164 | 5,291 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.703125 | 3 | CC-MAIN-2022-27 | latest | en | 0.787876 |
https://aidmath.com/1ox/ | 1,603,672,251,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107890108.60/warc/CC-MAIN-20201026002022-20201026032022-00285.warc.gz | 194,916,477 | 8,771 | 1ox
# 1ox
Input
o x
Geometric figure
line
Derivative
(d)/(dx)(o x) = o
Indefinite integral
integral o x dx = (o x^2)/2 + constant
Definite integral over a disk of radius R
integral integral_(o^2 + x^2
Definite integral over a square of edge length 2 L
integral_(-L)^L integral_(-L)^L o x dx do = 0 | 106 | 299 | {"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-2020-45 | latest | en | 0.462157 |
http://cnx.org/content/m23227/latest/ | 1,394,585,593,000,000,000 | application/xhtml+xml | crawl-data/CC-MAIN-2014-10/segments/1394011473737/warc/CC-MAIN-20140305092433-00057-ip-10-183-142-35.ec2.internal.warc.gz | 35,193,805 | 14,615 | # Connexions
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# Discrete Random Variables: Homework
Module by: Kathy Chu, Ph.D.. E-mail the authorEdited By: Kathy Chu, Ph.D.
Summary: This module provides a number of homework exercises related to Discrete Random Variables.
## Exercise 1
1. Complete the PDF and answer the questions.
x x size 12{x} {} P ( X = x ) P ( X = x ) size 12{P $$X=x$$ } {} x ⋅ P ( X = x ) x ⋅ P ( X = x ) size 12{x cdot P $$X=x$$ } {} 0 0.3 1 0.2 2 3 0.4
• a. Find the probability that X=2X=2 size 12{X=2} {}.
• b. Find the expected value.
• a. 0.1
• b. 1.6
## Exercise 2
Suppose that you are offered the following “deal.” You roll a die. If you roll a 6, you win $10. If you roll a 4 or 5, you win$5. If you roll a 1, 2, or 3, you pay $6. • a. What are you ultimately interested in here (the value of the roll or the money you win)? • b. In words, define the Random Variable XX size 12{X} {}. • c. List the values that XX size 12{X} {} may take on. • d. Construct a PDF. • e. Over the long run of playing this game, what are your expected average winnings per game? • f. Based on numerical values, should you take the deal? Explain your decision in complete sentences. ## Exercise 3 A venture capitalist, willing to invest$1,000,000, has three investments to choose from. The first investment, a software company, has a 10% chance of returning $5,000,000 profit, a 30% chance of returning$1,000,000 profit, and a 60% chance of losing the million dollars. The second company, a hardware company, has a 20% chance of returning $3,000,000 profit, a 40% chance of returning$1,000,000 profit, and a 40% chance of losing the million dollars. The third company, a biotech firm, has a 10% chance of returning $6,000,000 profit, a 70% of no profit or loss, and a 20% chance of losing the million dollars. • a. Construct a PDF for each investment. • b. Find the expected value for each investment. • c. Which is the safest investment? Why do you think so? • d. Which is the riskiest investment? Why do you think so? • e. Which investment has the highest expected return, on average? ### Solution • b.$200,000;$600,000;$400,000
• c. third investment
• d. first investment
• e. second investment
## Exercise 4
A theater group holds a fund-raiser. It sells 100 raffle tickets for $5 apiece. Suppose you purchase 4 tickets. The prize is 2 passes to a Broadway show, worth a total of$150.
• a. What are you interested in here?
• b. In words, define the Random Variable XX size 12{X} {}.
• c. List the values that XX size 12{X} {} may take on.
• d. Construct a PDF.
• e. If this fund-raiser is repeated often and you always purchase 4 tickets, what would be your expected average winnings per game?
## Exercise 5
Suppose that 20,000 married adults in the United States were randomly surveyed as to the number of children they have. The results are compiled and are used as theoretical probabilities. Let XX size 12{X} {} = the number of children
x x size 12{x} {} P ( X = x ) P ( X = x ) size 12{P $$X=x$$ } {} x ⋅ P ( X = x ) x ⋅ P ( X = x ) size 12{x cdot P $$X=x$$ } {} 0 0.10 1 0.20 2 0.30 3 4 0.10 5 0.05 6 (or more) 0.05
• a. Find the probability that a married adult has 3 children.
• b. In words, what does the expected value in this example represent?
• c. Find the expected value.
• d. Is it more likely that a married adult will have 2 – 3 children or 4 – 6 children? How do you know?
### Solution
• a. 0.2
• c. 2.35
• d. 2-3 children
## Exercise 6
Suppose that the PDF for the number of years it takes to earn a Bachelor of Science (B.S.) degree is given below.
x x size 12{x} {} P ( X = x ) P ( X = x ) size 12{P $$X=x$$ } {} 3 0.05 4 0.40 5 0.30 6 0.15 7 0.10
• a. In words, define the Random Variable XX size 12{X} {}.
• b. What does it mean that the values 0, 1, and 2 are not included for XX size 12{X} {} on the PDF?
• c. On average, how many years do you expect it to take for an individual to earn a B.S.?
## For each problem:
• a. In words, define the Random Variable XX size 12{X} {}.
• b. List the values hat XX may take on.
• c. Give the distribution of XX. XX~
Then, answer the questions specific to each individual problem.
### Exercise 7
Six different colored dice are rolled. Of interest is the number of dice that show a “1.”
• d. On average, how many dice would you expect to show a “1”?
• e. Find the probability that all six dice show a “1.”
• f. Is it more likely that 3 or that 4 dice will show a “1”? Use numbers to justify your answer numerically.
#### Solution
• a. X X size 12{X} {} = the number of dice that show a 1
• b. 0,1,2,3,4,5,6
• c. XX~B (6,16 )B(6,16 )
• d. 1
• e. 0.00002
• f. 3 dice
### Exercise 8
According to a 2003 publication by Waits and Lewis (source: http://nces.ed.gov/pubs2003/2003017.pdf), by the end of 2002, 92% of U.S. public two-year colleges offered distance learning courses. Suppose you randomly pick 13 U.S. public two-year colleges. We are interested in the number that offer distance learning courses.
• d. On average, how many schools would you expect to offer such courses?
• e. Find the probability that at most 6 offer such courses.
• f. Is it more likely that 0 or that 13 will offer such courses? Use numbers to justify your answer numerically and answer in a complete sentence.
### Exercise 9
A school newspaper reporter decides to randomly survey 12 students to see if they will attend Tet festivities this year. Based on past years, she knows that 18% of students attend Tet festivities. We are interested in the number of students who will attend the festivities.
• d. How many of the 12 students do we expect to attend the festivities?
• e. Find the probability that at most 4 students will attend.
• f. Find the probability that more than 2 students will attend.
#### Solution
• a. X X size 12{X} {} = the number of students that will attend Tet.
• b. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
• c. XX~B(12,0.18)B(12,0.18)
• d. 2.16
• e. 0.9511
• f. 0.3702
### Exercise 10
• d. How many are expected to attend their graduation?
• e. Find the probability that 17 or 18 attend.
• f. Based on numerical values, would you be surprised if all 22 attended graduation? Justify your answer numerically.
### Exercise 11
At The Fencing Center, 60% of the fencers use the foil as their main weapon. We randomly survey 25 fencers at The Fencing Center. We are interested in the numbers that do not use the foil as their main weapon.
• d. How many are expected to not use the foil as their main weapon?
• e. Find the probability that six do not use the foil as their main weapon.
• f. Based on numerical values, would you be surprised if all 25 did not use foil as their main weapon? Justify your answer numerically.
#### Solution
• a. X X size 12{X} {} = the number of fencers that do not use foil as their main weapon
• b. 0, 1, 2, 3,... 25
• c. XX~B(25,0.40)B(25,0.40)
• d. 10
• e. 0.0442
• f. Yes
### Exercise 12
Approximately 8% of students at a local high school participate in after-school sports all four years of high school. A group of 60 seniors is randomly chosen. Of interest is the number that participated in after-school sports all four years of high school.
• d. How many seniors are expected to have participated in after-school sports all four years of high school?
• e. Based on numerical values, would you be surprised if none of the seniors participated in after-school sports all four years of high school? Justify your answer numerically.
• f. Based upon numerical values, is it more likely that 4 or that 5 of the seniors participated in after-school sports all four years of high school? Justify your answer numerically.
## Try these multiple choice problems.
For the next three problems: The probability that the San Jose Sharks will win any given game is 0.3694 based on their 13 year win history of 382 wins out of 1034 games played (as of a certain date). Their 2005 schedule for November contains 12 games. Let XX size 12{X} {}= number of games won in November 2005
### Exercise 13
The expected number of wins for the month of November 2005 is:
• A. 1.67
• B. 12
• C. 38210433821043
• D. 4.43
D: 4.43
### Exercise 14
What is the probability that the San Jose Sharks win 6 games in November?
• A. 0.1476
• B. 0.2336
• C. 0.7664
• D. 0.8903
A: 0.1476
### Exercise 15
Find the probability that the San Jose Sharks win at least 5 games in November.
• A. 0.3694
• B. 0.5266
• C. 0.4734
• D. 0.2305
C: 0.4734
## Content actions
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##### Lenses
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##### What is in a lens?
Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.
##### Who can create a lens?
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| External bookmarks | 2,794 | 9,693 | {"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} | 4.3125 | 4 | CC-MAIN-2014-10 | latest | en | 0.844309 |
https://askrose.org/student-resources/math-resources/algebra-ii/conic-sections/graphing-conic-sections/ | 1,726,831,166,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700652246.93/warc/CC-MAIN-20240920090502-20240920120502-00263.warc.gz | 84,424,893 | 15,002 | # Graphing Conic Sections
Graph the ellipse with the equation:
64>28 so 64 =
Center: (h,k)
Vertices: (h,ka)
Covertices: (hb,k)
a=8 b=5.29
Graph the hyperbola with the equation: =1
Length of traverse axis=2a vertices are endpoints of traverse axis
center, (0,0) 64= 8=a
Endpoints: (-8,0)(8,0) | 104 | 305 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.671875 | 4 | CC-MAIN-2024-38 | latest | en | 0.747252 |
https://toolsweek.com/multimeter-resistance-symbol/ | 1,718,405,278,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861575.66/warc/CC-MAIN-20240614204739-20240614234739-00523.warc.gz | 527,086,841 | 61,110 | # Multimeter Resistance Symbol (Guide)
Contents
Ever wondered what those cryptic symbols on your multimeter mean? You’re not alone! Today, I’ll be demystifying one of the most common yet misunderstood symbols on your multimeter – the resistance symbol.
When you look at your multimeter, you’ll notice an omega symbol (Ω). This tiny symbol represents resistance. It’s one of those imperative things enabling us to understand and control the flow of electricity in our circuits.
In this article, we will dive deeper into your multimeter’s resistance symbol. We’ll also walk you through the steps to accurately measure resistance in various electronic components and circuits.
## The Resistance Symbol on Multimeters
This dashboard of electrical measurements enables precise readings. It might seem like an intimidating jumble of symbols and figures, but it’s just telling you what’s happening inside your circuit.
Resistance isn’t always a villain in the electrical world. Sometimes, it’s the hero we need! Resistance can protect elements in a circuit by limiting the electrical flow to a safe level. It’s crucial for the proper functioning and safety of our electronic devices.
In the end, the resistance symbol’s role in our multimeters is an indispensable one. It ensures the safe and smooth operation of our electronic devices, and it’s a tool that I (and every electronics enthusiast) couldn’t do without.
## Measuring Ohms with a Digital Multimeter
Let’s break down the steps to test resistance using a Digital Multimeter simple and straightforward:
### Step 1: Turn Your Multimeter Dial to Ohms
Get started by spinning that dial on your multimeter right over to the ohm section. This is where the magic of measuring resistance happens.
### Step 2: Proper Probe Placement
Ensure the black probe is connected to the common terminal and the red probe is plugged into the terminal with the ohm symbol. It’s all about getting those connections spot on.
### Step 3: Testing Resistance
If you’re checking out something like a sensor, touch the two probes to the sensor terminals. You’ll see the resistance value pop up on the multimeter.
For example, a reading of 1.35 ohms means your sensor is likely in good shape.
## Measuring Ohms with an Analog Multimeter
Now, let’s get our hands dirty and figure out how to test resistor values using an analog multimeter. It’s easier than you think, and I’m here to guide you through it, step-by-step:
### Step 1: Select the Right Multiplier on the Multimeter
Start by setting your multimeter to times 1, times 10, times 100, or times 1K, depending on the resistor range you’re working with.
### Step 2: Calibrate Your Multimeter
Calibrate by shorting the probes together and adjusting the needle to zero. This step is crucial for accurate measurements.
### Step 3: Testing the Resistor
Connect the probes to the resistor. It doesn’t matter which side, as resistors don’t have a positive or negative. If there’s no reading, switch to a higher multiplier setting.
### Step 4: Adjust for Each New Setting
Every time you change the multiplier setting, recalibrate to zero. This ensures your readings are spot on.
### Step 5: Calculate the Resistance Value
Read the needle position and multiply by the setting you’re on. For example, if it reads 20 on times 100, your resistor is 2,000 ohms or 2K.
Just like that, you’re testing resistors like a pro! Remember, patience and attention to detail are key. Happy tinkering!
## Common Mistakes and Troubleshooting in Resistance Measurement
Have you ever tried measuring resistance and ended up with wonky results? You’re not alone. Getting a precise reading with a multimeter can be tricky, especially if you’re new to the game.
From my toolkit of experiences, I’ve seen a few common missteps, and I’m here to help you navigate them. Let’s break down these common mistakes in measuring resistance and how to troubleshoot them effectively.
Remember, getting accurate resistance measurements involves attention to detail and some know-how. Remember these tips, and you’ll measure like a pro in no time!
## Advanced Techniques for Accurate Resistance Measurement
When measuring resistance, precision is key, especially for those who like to get their hands dirty with more complex tasks. Over the years, I’ve learned a few advanced tricks that can make all the difference.
Parallel Resistance Calculation:
Remember that Ohm’s Law is your friend when dealing with a circuit with parallel resistors. Calculate the total resistance by the inverse sum of the inverses of individual resistances. This little trick saved me in a tight spot with a tricky circuit.
Temperature Compensation:
Resistance can change with temperature. Use a temperature coefficient to adjust your readings for materials like copper or aluminum. I’ve seen readings go haywire without considering this, especially in outdoor projects.
Precision Mode on Digital Multimeters:
Some advanced digital multimeters come with a precision or high-resolution mode. This feature is fantastic for getting down to the nitty-gritty of resistance values. It’s a game-changer for delicate electronics where every ohm matters.
Null Method for Low Resistances:
The standard method may not cut if you measure very low resistances. I’ve used the null method, where you balance two legs of a bridge circuit – it significantly reduces error.
Remember, these techniques might seem daunting initially, but with some practice, you’ll measure resistance like a pro. Stay curious and keep experimenting!
• Can I Measure Resistance In A Live Circuit?
• No way, safety first! Always turn off the power to the circuit before measuring resistance.
• How Accurate Are Multimeter Resistance Readings?
• Pretty accurate, but remember, temperature and probe placement can affect your readings. Always double-check for consistency.
• Why Do I Need To Zero My Analog Multimeter Before Use?
• Zeroing ensures you start from a baseline for accurate readings. If it’s off zero, your measurements could be skewed.
• Can I Measure The Resistance Of Any Component Directly?
• Yes, but be wary of components sensitive to current and voltage, like some semiconductors. In such cases, use the appropriate measurement technique.
• These settings allow you to measure higher resistances. kΩ is for thousands of ohms, and MΩ is for millions of ohms.
• Does The Length Of The Probes Affect Resistance Measurements?
• In most cases, no, but for very low resistances, even the resistance of the probes can become significant.
## References
Studies:
Organizations:
Books:
Video References:
narvalighting
Passion Tech KLM
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# Gudemaranahalli G-Accounting 225-Assign 2-1 - Rims = Direct...
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Assign – 2-1 3-8 a. Unit level – machine hours b. Unit level – direct-labor hrs c. Facility – direct labor hrs d. Batch – purchase order processed e. Product – hrs of design time f. Facility – direct labor – hr g. Batch – number of setups; setup hrs h. Facility – plant building & grounds – direct labor hrs( i. Facility – direct labor hrs 3-9 a. Predetermined overhead rate = 216000/180 = 1200 per setup Predetermined overhead rate =180/4000 = 0.045 per machine hr Predetermined overhead rate = 288000/24000 = 12 per dlh b. 20,000*.40 = 8000 rim dlh 8000*.2 = 16000 = 9600 Total over head cost = 21000+ 180000+ 288888 = 489600 POR = 489600 *9600 = 51
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Unformatted text preview: Rims = Direct materials + Direct Labor + direct manufacturing overhead = 17+( 16*.4) + (51*.4) = 43.8 product cost for rim. Posts = Direct materials + Direct Labor + direct manufacturing overhead = 10+( 16*.2) + (51*.2) = 23.4 unit product cost for posts . 3-10 Total DLH =12000*.2 + 40000 *.25 = 12,400 POR = 336000 / 12,400 = 27.0968 Mercon = Direct materials + Direct Labor + direct manufacturing overhead = 10+(3 *.2) + (27.0968*.2) = 16.01936 product cost for Mercon. Wurcon = Direct materials + Direct Labor + direct manufacturing overhead = 8+(3.75 *.25) + (27.0968*.25) = 15.7117 product cost for Wurcon....
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Midlife Crisis
It's a fractal. Yeah, it's math. If not for the math my artwork would hurt even my eyes
This one I made using Apophysis. Sometimes I use other programs, but Apophysis and Ultrafractal are my favorites.
Midlife Crisis
How does this work? How do you use math to make these? It's pretty cool
TheGremlyn on Fri Apr 12, 2013 2:24 am
I'd like to know too. Great artwork for sure.
deanhills on Fri Apr 12, 2013 7:33 am
Hmmm... Chaos math.. Fractal math.. kindof like the math of nature.. things tend to repeat themselves. Look at a feather. All of the fibers coming off the central shaft. Now magnify one of the fibers and you'll see the same thing, smaller fibers off the central shaft. Take any one of those tiny fibers and magnify and you'll see the same thing all over again. Look at the pattern the waves leave in the sand as they retreat off the shore. You'll see the same pattern repeat itself over and over the closer you look. Not exactly, but they keep their similarity.
I'm horrible at explanations, but fractals are everywhere.. leaves, your internal cardiovascular system, seashells, flowers, root systems, water flows, shorelines, mountains, coral formations, sand dunes, yada yada.
Anyways, there are mathematical formulas to describe how all that works. Using some of the formulas we can add different variables and graph the results using different gradients and throwing in some of our own calculation tweaks.. All very boring and complex and luckily the programs make it so you don't have to know the math at all if you don't want to. Or you can do like I do and write formulas by trial and error without having any idea what will happen until I try it.
Really, I'm probably wrong in everything I've said about the science, but that's the way I understand it in my head, and like I said I don't need to understand the math to write the formulas.
There now, you're even more lost than before I explained it all, aren't you
onebadpenny on Fri Apr 12, 2013 10:24 am
onebadpenny wrote: There now, you're even more lost than before I explained it all, aren't you
Absolutely. Couldn't have said it better.
deanhills on Fri Apr 12, 2013 11:15 am
Pretty colours and patterns, lol!
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May 14 accepted Are bounded sequences always strictly less than some fixed number $M$? May 14 comment Are bounded sequences always strictly less than some fixed number $M$? ok that totally makes sense, thank you for this answer. May 14 asked Are bounded sequences always strictly less than some fixed number $M$? May 9 awarded Fanatic May 6 accepted Who was the mathematician who thought “god” was out to get him? May 6 comment Who was the mathematician who thought “god” was out to get him? oh ok... well thanks all for clearing that up :) May 6 comment Who was the mathematician who thought “god” was out to get him? @Arturo: but how was he an atheist if he was convinced that "God" would not let him die? I mean for him to write the letter, he must have thought that there was a god, right? May 6 asked Who was the mathematician who thought “god” was out to get him? Apr 27 accepted How is it shown that a Hermitian matrix will be positive definite? Apr 26 comment How is it shown that a Hermitian matrix will be positive definite? Thank you very much, this is the sort of thing I was looking for. So a matrix is positive definite if it is hermitian, finite dimensional(is that what all that $k\leq n$ stuff means?), and the determinant is positive? Other question was about the hint, I tried it and got: $z = \left( \begin{array}{c} |i|^2 \\ -(1)(-i) \end{array}\right) \Rightarrow \overline{z}^{t}A_{1}z = 4$, did I misunderstand the inputs? Apr 26 comment How is it shown that a Hermitian matrix will be positive definite? @J.M.: sorry, but I still can't understand your idea... First, I thought I had already worked out the $m=1$ case, right? Second, I don't see where, how, or why to make $a,b,c,d$ evaluate to something manifestly nonpositive... Also when you say quadratic form, you are referring to a specific type of mapping, or just any polynomial with terms of degree 2? Apr 26 comment How is it shown that a Hermitian matrix will be positive definite? @J.M. : do I need to show that $a^2 +b^2 +c^2 +d^2 \gt ad -bc$? Do you know how to do this? (Sorry if this is trivial...) Apr 26 comment How is it shown that a Hermitian matrix will be positive definite? thank you for this answer, it is good to know that this is a possibility, unfortunately I think this method is still a little too advanced. Apr 26 comment How is it shown that a Hermitian matrix will be positive definite? @J.M: as to the definition of positive definite: I think it has so far just been $\alpha$ is positive definite $:\Leftrightarrow \forall v \in V, v\neq 0 : \alpha(v,v) \gt 0$... so pretty basic and we haven't covered how eigenvalues relate to that yet... Apr 26 comment How is it shown that a Hermitian matrix will be positive definite? @J.M. : To your previous comment, thank you for the tip! Does something like this look like the right direction? $z = (a+bi, c+di)^t \Rightarrow m(a^2 + b^2) -2(ad-bc) +m(c^2+d^2)$ and since $m(a^2 + b^2) -2(ad-bc) +m(c^2+d^2) \geq 0 \Leftrightarrow m \geq \frac{2(ad-bc)}{a^2 + b^2 +c^2 +d^2}$ Apr 26 asked How is it shown that a Hermitian matrix will be positive definite? Apr 23 accepted What is the difference between finding a basis for a complex and a real space? Apr 23 comment What is the difference between finding a basis for a complex and a real space? Thank you very much! Apr 23 asked What is the difference between finding a basis for a complex and a real space? Apr 21 revised Why does $a_n = (1+\frac{2}{n})^{n}$ converge to $e^2$? deleted 1 characters in body | 979 | 3,567 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.953125 | 3 | CC-MAIN-2016-18 | latest | en | 0.976922 |
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## Introduction
Economists, statisticians, and market researchers, among others, need to learn various attributes of a population that lives in certain demography. However, it may not be possible for them to collect data from each individual due to the size and volume of data and/or population. In such a circumstance, sampling of the population under study is done.
## What is Sampling?
Sampling is a statistical technique where members or subsets of populations are selected to get inferences about the whole population regarding a matter of study. Sampling is useful because it may not be possible for the researchers to study the characteristics of each and every member of a demographic system. That is why selected members or a subset of the population is selected for research and the idea for the entire demography is formed after following various statistical measures.
The idea of sampling is valuable in market research and economics because depending on sampling, the researchers make insights that lead to action. That is why sampling must be accurate. In order to get actionable insights, various types of sampling techniques are available.
## Major Types of Sampling
The two major types of sampling are probability sampling and non-probability sampling which are further divided depending on their nature.
• Probability Sampling: In probability sampling, researchers set a few selection criteria and then select the members of the sampling population randomly. In such a sampling method, all members have an equal opportunity to be part of the sample.
• Non-probability sampling: In non-probability sampling, the members are selected randomly, but there are no predefined or pre-fixed criteria for selection. In such sampling methods, all types of populations from demography cannot have an equal opportunity for participation.
### Types of Probability Sampling
In probability sampling use of the theory of probability takes place. As all members get an equal opportunity, probability sampling has no bias.
• Simple random sampling It is one of the most useful yet very simple processes of probability sampling. It is reliable and information can be obtained from each member of the population in simple random sampling.
In this type of sampling, each member of the population is selected randomly. So, each individual in the population has an equal chance to be part of the population that is sampled arbitrarily.
• Cluster sampling: In cluster sampling, the sampling data is classified into various clusters or groups. Clusters are formed and identified by demographic variables, such as age, sex, location, etc. It helps the researchers gain insight into specific populations very easily as the data is already classified into actionable groups.
• Systematic sampling: In systematic sampling, the members of the sampling population are chosen after regular intervals. In this type of sampling, the selection starting point and the interval must be applied to get accurate data after each interval. Systematic sampling has a predefined range and consumes the least amount of time.
• Stratified random sampling: In stratified random sampling, the population is divided into some strata that do not overlap each other but cover the entire range of the population. It is built in such a manner that every member of the population will fall into one stratum. These strata can finally be compared to check the findings, such as which stratum has the highest population under its coverage, etc.
### Types of Non-Probability Sampling
Non-probability sampling is carried out by collecting samples from the researcher. It is less time-consuming and does not cost too much.
However, the chances of non-probability sampling being skewed are more than probability sampling.
• Convenience sampling: Convenience sampling is done by the researchers in places such as busy streets and malls to collect easy data from a purely random population. It is based more on proximity than authority and representation. It is a valuable sampling method when time and cost constraints exist.
• Purposive sampling: Also known as judgmental sampling, this type of research matches the requirements of respondents with the required samples of the research. If there is a mismatch, the respondent is not included in the research. For instance, when a respondent answers “no” to a specific question in the research questionnaire, he/she may be omitted from the research.
• Snowball sampling: Snowball sampling is used to track extremely sensitive and confidential topics. This technique uses third parties who may be able to provide information about the required sample.
Using snowball theory, the researchers may be able to interview a few selected categories and derive results from them.
• Quota sampling: As the name suggests, in quota sampling, a quota with all the attributes of the required population is selected and tested for the entire population. This method of sampling is used for rapid sample collection.
## Importance of Sampling
Sampling has an overwhelming influence on data collection and analysis.
Sampling is used to derive results that are meant for a wide range of populations
In fact, it is impossible for researchers to collect data from each individual in a large economy. So, smaller groups must be formed efficiently to get the desired and accurate results that suit the entire population.
Sampling is invaluable in many fields of study
As smaller groups of populations are considered to get larger economic results, sampling offers insights into economies in a less costly and efficient manner. Researchers can use sampling in various ways. It is used in almost all fields of science to get accurate insights that are actionable and perspective-based.
Sampling is also quite important in Economics
Various calculations of economic studies are based on sampling. Without sampling, economics will be incomplete. For example, in considering the demand for wheat in a market, sampling the populations who use wheat can be implemented. This will offer a better insight into the demand and needs of the market.
Sampling indirectly helps to realize the demand of markets
For countries like India, estimating the needs of the people in various parts of the country would be impossible to assume. In such circumstances, sampling can be used to better understand the needs and wants of the populations. This indirectly helps to realize the demand of markets on which marketing departments of companies can rely.
Sampling is widely used in healthcare
Sampling is widely used in healthcare and it helps scientists prepare invaluable medications and life-saving drugs. Sampling is therefore an indispensable tool in many schools of thought and its importance cannot be ignored in the daily lives of people.
## Conclusion
As a statistical tool of estimation, sampling plays a vital role in keeping societies and communities intact. The role of sampling in economics cannot be ignored too. It is a science that helps procure data from large populations in an easy and affordable manner. That is why, sampling will remain an indispensable tool for economists to run economies smoothly without having to take large groups of populations under consideration. Sampling is, therefore, important for social well-being too.
## FAQs
Q1. What are the two different types of sampling methods used to estimate the characteristics of populations?
Ans. The two main types of sampling methods that are used for the estimation of characteristics of large populations are probability and non-probability sampling.
Q2. What is the biggest advantage of sampling?
Ans. The biggest advantage of sampling is that it can be used to find the characteristics of a large population by taking into consideration a smaller one. Therefore, researchers can focus on a small group population to identify characteristics of the original, large population.
Tutorialspoint
Simply Easy Learning | 1,456 | 8,017 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.421875 | 3 | CC-MAIN-2023-23 | latest | en | 0.941218 |
https://www.experts-exchange.com/questions/26701146/Include.html | 1,558,897,641,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232259452.84/warc/CC-MAIN-20190526185417-20190526211417-00449.warc.gz | 785,561,669 | 20,725 | # Include
I'm using DFSORT.
In this snippit, I'm looking at the include statement. Can you give some explanation on it?
``````SORT FIELDS=(53,5,CH,A)(50,2,CH,A)
OUTFIL FNAMES=USA,
TRAILER1=(/,20:'USA Areas 2009 Quarterly Budget Balance',/,
/,20:'Total Number of Areas: ',8930,/,
/,10:'Quarter 1',30:'Quarter 2',50:'Quarter 3',70:'Quarter 4',
/,1:TOT=(53,5,PD,M12),TOT=(58,5,PD,M12),
TOT=(63,5,PD,M12),TOT=(68,5,PD,M12),/,
/,10:'Minimum',30:'Minimum',50:'Minimum',70:'Minimum',
/,9:MIN=(53,5,PD,M12),29:MIN=(58,5,PD,M12),
49:MIN=(63,5,PD,M12),69:MIN=(68,5,PD,M12),/,
/,10:'Maximum',30:'Maximum',50:'Maximum',70:'Maximum',
/,9:MAX=(53,5,PD,M12),29:MAX=(58,5,PD,M12),
49:MAX=(63,5,PD,M12),69:MAX=(68,5,PD,M12),/,
/,10:'Average',30:'Average',50:'Average',70:'Average',
/,9:AVG=(53,5,PD,M12),29:AVG=(58,5,PD,M12),
49:AVG=(63,5,PD,M12),69:AVG=(68,5,PD,M12),/)
OUTFIL FNAMES=VI1,
INCLUDE COND=(50,2,CH,EQ,C'AK',AND,53,1,CH,EQ,C'2'),
TRAILER1=(/,20:'Virgina Cities 2009 Quarterly Budget Balance',/,
``````
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I wear a lot of hats...
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Commented:
This statement selects input records based on conditions (COND):
Column 50 and 51 ("2" is the length) contain in character format ("CH") the characters 'AK'
AND
Column 53 (length is "1") contains in character format ("CH") the character '2'.
One could as well have written:
INCLUDE COND=(50,3,CH,EQ,C'AK2'),
Basically, it's an input record filter.
wmp
Commented:
SORRY,
my second statement is of course WRONG!
Seems I forgot how to count!
We're talking about columns 50, 51 ,and 53 here, so please forget what I wrote!.
By the way, the opposite of INCLUDE would be OMIT, with the same syntax, to select records NOT to appear in the output.
Sorry again!
wmp
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https://algorithms.rocks/462-2/ | 1,679,752,104,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296945333.53/warc/CC-MAIN-20230325130029-20230325160029-00149.warc.gz | 121,259,955 | 38,938 | 4.3
algorithms
March 25, 2023 1:02 pm
Logarithms are an essential part of mathematics, and they find applications in various fields ranging from engineering and science to finance and economics. In programming, logarithmic functions are often used to calculate values that change exponentially over time or distance. One of the most popular programming languages, C, has built-in functions for calculating logarithms. In this article, we will explore how to do logarithms in C.
C provides two functions for calculating logarithms: log() and log10(). The log() function is used to calculate natural logarithms, whereas log10() is used to calculate base-10 logarithms. Here’s how they work:
“`c
#include
#include
int main()
{
double num = 100;
double result = log(num);
printf(“Natural logarithm of %lf is %lfn”, num, result);
num = 1000;
result = log10(num);
printf(“Base-10 logarithm of %lf is %lfn”, num, result);
return 0;
}
“`
In the above code, we first include the math.h header file that contains the necessary declarations for mathematical functions. We then define a double variable num and assign it a value of 100. We use the log() function to calculate the natural logarithm of num and store the result in another double variable result. We then print the result using printf() function.
Next, we assign a value of 1000 to num and use the log10() function to calculate the base-10 logarithm of num. We store the result in the result variable and print it using printf() function again.
The output of the above code would be:
“`
Natural logarithm of 100.000000 is 4.605170
Base-10 logarithm of 1000.000000 is 3.000000
“`
As you can see, the log() function returns the natural logarithm of a number, whereas the log10() function returns the base-10 logarithm of a number.
C also provides the log2() function to calculate base-2 logarithms. However, this function is not available in all versions of C, so it’s better to check if it’s available before using it.
“`c
#include
#include
int main()
{
#ifdef __STDC_IEC_559__
double num = 8;
double result = log2(num);
printf(“Base-2 logarithm of %lf is %lfn”, num, result);
#else
printf(“log2() function not supportedn”);
#endif
return 0;
}
“`
In the above code, we first check whether the log2() function is supported or not by checking for the __STDC_IEC_559__ macro. If it’s supported, we define a double variable num and assign it a value of 8. We then use the log2() function to calculate the base-2 logarithm of num and store the result in another double variable result. We print the result using printf() function.
If the log2() function is not supported, we print a message indicating that the function is not available.
The output of the above code would be:
“`
Base-2 logarithm of 8.000000 is 3.000000
“`
In addition to these logarithmic functions, C also provides the pow() function to calculate powers of numbers. You can use this function to calculate logarithms of any base. Here’s how:
“`c
#include
#include
int main()
{
double base = 2;
double num = 8;
double result = log(num)/log(base);
printf(“Logarithm of base %lf for %lf is %lfn”, base, num, result);
return 0;
}
“`
In the above code, we first define two double variables base and num and assign them a value of 2 and 8, respectively. We then use the log() function to calculate the natural logarithms of base and num and divide the result of log(num) by log(base) to get the logarithm of num with base base. We store the result in another double variable result and print it using printf() function.
The output of the above code would be:
“`
Logarithm of base 2.000000 for 8.000000 is 3.000000
“`
In conclusion, logarithmic functions are fundamental in mathematics and find numerous applications in programming. C provides built-in functions for calculating natural logarithms, base-10 logarithms, and base-2 logarithms (if available). You can use the pow() function to calculate logarithms of any base. Understanding logarithmic functions is crucial for anyone working with data that changes exponentially over time or distance, and C provides a powerful tool for working with them.
March 25, 2023 1:02 pm
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## Ambiguity
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Ambiguity - 10/6/2013 11:02:07 AM
Mondobone
Posts: 2
Joined: 2/7/2012
From: United States
Status: offline
Puzzles only have one solution, right? Does that mean any option where the selection is ambiguous is wrong by default? Let me post an example from the nurikabe I'm working on right now.
In the circled area with the seven, it needs to extend one additional space. But if it extend to any portion of the strip on the right it'll have the same result on the rest of the puzzle. All the other white portions of that strip get filled in and form a broken line. Does this mean that none of those spaces can include a dot since if one of them did the other similar spaces would come out to be identically plausible?
RE: Ambiguity - 10/6/2013 5:44:11 PM
dave
Posts: 1238
Joined: 4/28/2002
From: Israel
Status: offline
Your explanation is correct. You don't fill (or mark) a square because you can, but only because you must. In the area you described, any of the empty squares *might* contain a dot so you cannot make a step in that area right now.
Thanks, Dave
RE: Ambiguity - 10/6/2013 6:29:47 PM
Mondobone
Posts: 2
Joined: 2/7/2012
From: United States
Status: offline
That's not quite what I meant, though. I mean that no matter what happens anywhere else in the puzzle, four of those squares will remain unsolvable. Just as an example take the two bottom most blank square there. If you put a dot in the bottom one, the four above it would have to be darkened. The four above it would not connect to the line below it. If you instead put a dot one space above that, you would fill in the three spaces above and one space below, which wouldn't have an effect on the rest of the puzzle. Those two spaces are permanently ambiguous. Does this mean that they cannot be the logical answer to the puzzle?
RE: Ambiguity - 10/12/2013 2:08:58 AM
hok0003
Posts: 16
Joined: 1/14/2012
From: Australia
Status: offline
If you assume there is a unique solution, then yes, you can eliminate ambiguous possibilities.
Personally, I don't make that assumption. It isn't strictly in the puzzles' rules, and if there is a unique solution then it can be solved without that assumption.
Also, some puzzle sources aren't as rigorous in ensuring uniqueness.
It is a good place to start a trial and error process from though.
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| 813 | 3,083 | {"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} | 2.9375 | 3 | CC-MAIN-2018-22 | latest | en | 0.923908 |
http://www.chegg.com/homework-help/questions-and-answers/trouble-following-problem-gallon-milk-68f-placed-refrigerator-energy-isremoved-milk-heat-t-q324106 | 1,474,783,175,000,000,000 | text/html | crawl-data/CC-MAIN-2016-40/segments/1474738659865.46/warc/CC-MAIN-20160924173739-00250-ip-10-143-35-109.ec2.internal.warc.gz | 393,425,162 | 13,545 | I am having trouble with the following problem:
A gallon of milk at 68F is placed in a refrigerator. If energy isremoved from the milk by heat transfer at a constant rate of0.08Btu/s how long would it take in minutes for the milk to cool to40F? The specific heat and density of the milk are 0.94Btu/lb R and64lb/ft^3.
Thank you for you help | 92 | 340 | {"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} | 3.015625 | 3 | CC-MAIN-2016-40 | latest | en | 0.929766 |
https://docplayer.net/21249046-Head-loss-in-pipe-flow-me-123-mechanical-engineering-laboratory-ii-fluids.html | 1,642,827,004,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320303747.41/warc/CC-MAIN-20220122043216-20220122073216-00310.warc.gz | 262,657,078 | 28,171 | # Head Loss in Pipe Flow ME 123: Mechanical Engineering Laboratory II: Fluids
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1 Head Loss in Pipe Flow ME 123: Mechanical Engineering Laboratory II: Fluids Dr. J. M. Meyers Dr. D. G. Fletcher Dr. Y. Dubief
2 1. Introduction Last lab you investigated flow loss in a pipe due to the roughness of the pipe s walls. Losses will also occur with the introduction of various components in fittings within the pipe system. The losses due to these fittings are strongly dependent on geometry, coupling methods between elements, and internal roughness. These loses are classified as minor losses but when enough components are added to a pipe system appreciable flow loss can be encountered. When designing a flow system where the knowledge of flow rates is important it is imperative that the design of said system includes an analysis of all potential loss mechanisms. In this lab you will learn how to determine the loss, which is normally called the head loss, of various components in the same pipe flow facility you used in the last lab. Unlike losses caused by friction, minor losses can be assumed independent of Reynold s number in turbulent flows (see Chapter 6 of White, Fluid Mechanics). Lab Objectives: Experimentally understand head loss analysis To understand how various tube fittings impact pipe flow loss Understand how head loss can be used to meter flow rates 2. Experimental Arrangement The pipe flow facility (Figure 1) has been modified to accommodate the 90 turns of the tube fittings. Recall the straight tube section has an internal diameter of 80 mm and is fitted with 11 access ports that provide an entry for Pitot measurements or can be fitted with a static pressure tap. Locations each tap and Pitot port is listed in Table 1. Bear in mind that the distance values beyond will change once a fitting is installed. A blower on the left side of the facility pulls air through the tube (flow is from right to left). A manometer is attached to the facility and is used to monitor atmospheric, Pitot, and static pressure levels. Note that the manometer bank can be tilted to increase pressure sensitivity, which can be useful for the Pitot pressure surveys. For these measurements the tilted angle influences the dynamic pressure as: 2 = h h cos (1) where is the density of air, h is the height of the manometer for the Pitot measurement, h is the height of the manometer for the static pressure measurement at the Pitot survey location, and is the manometer bank angle w.r.t. vertical. The manometer working fluid is a kerosene base with density of =787 kg/m 3. Be sure to write (in your own words!) a concise, yet sufficiently detailed, explanation of how the different components of the experiment work as this information will be used to describe your experiment in your report.
3 Figure 1: Pipe experiment Table 1: Locations of Pitot and static pressure tap stations 3. Measurements Each group will get about 20 to 30 minutes to perform measurements and afterward, if time allows after, groups needing/wanting more time may continue with measurements. The lab is always available outside of scheduled lab times if sufficient measurements cannot be performed in the allotted time. Refer to last lab handout (Turbulent Velocity Profile Development in a Pipe) for details on resolving Pitot measurements into velocities. For each measurement record your respective error in a column/space just to the right as ±. 3.1 Inlet Velocity Profile You are required to take a velocity profile at the inlet of the tube. This is required to determine your average velocity of the flow. Measure,, and at each measurement point with the Pitot probe (see Figure 2) just like last lab. Measure first these values at the centerline ( = 38.5 mm). Move the Pitot probe to the bottom surface ( = 0 mm) and measure again. Move up in 2.5 mm increments until you see a constant profile which should only be a few steps (give or take). At this point assume the velocity is constant and move to the next step of measurements.
4 Figure 2: Translating Pitot probe mm radius Elbow Losses A flanged 80 mm inside diameter 90 elbow (Figure 3) is to be inserted between station 6 and 7. Static pressure will be recorded upstream and downstream of this fitting. The bulk velocity acquired from your inlet velocity profile survey will be used as your average velocity,. With the pressure drop and average velocity value you will determine the head loss, h, and resistance coefficient,, for this fitting from Equations 5 and 6. For this measurement, you only need to take the static pressure before and after. Figure mm radius 90 bend 3.3 Mitered Elbow with Turning Vanes Remove the 200 mm elbow between stations 6 and 7 and replace with the mitered elbow (Figure 4). Static pressure will be recorded upstream and downstream of this fitting. The bulk velocity acquired from your inlet velocity profile survey will be used as your average velocity,. Again, with the pressure drop and average velocity value you will determine the head loss, h, and the resistance coefficient,, for this fitting from Equations 5 and 6.
5 Figure 4: 90 mitered elbow with turning vanes 3.4 Orifice Plate Restriction Meter The pipe flow orifice is one of a family of restriction meters which uses a pressure drop to measure flow rate. Remove the elbow and place the orifice between Station 6 and Station 7. Measure the pressure just upstream and downstream of this insert. Recall that ultimately this is a device to determine mass flow from pressure drop measurements. But this requires a calibration that quantifies the degree of deviation from the ideal Bernoulli equation. This deviation is defined as and is commonly called the discharge coefficient and is discussed more in Section 4.5. Figure 5: Orifice restriction meter insert.
6 4. Reduction of Data 4.1 Bulk Velocity The bulk (average) velocity,, is the average pipe velocity that may be calculated based on a Pitot-tube inlet traverse and a ring wall static pressure reading at the pipe inlet accounting for the small boundary layer at the inlet station through the following relation: = 2!!! (2) Since the cross section area of the tube is constant, it follows that the average velocities are constant as well ( # = =). 4.2 Reynold s Number Reynold s number based on tube diameter, \$, can be calculated using the average velocity through: Re ' = \$ ( (7) Can you determine if the flow is laminar or turbulent? 4.3 Head Loss The energy equation, as derived/illustrated in class, between two cross sections of the pipe, can be written as: ) # * +, # # 2* +- #. ) * +, 2* +-.=h (3) Where,, and - are the pressure bulk/average velocity, and height respectively. The fluid density is and the magnitude of gravity is *. This gives a relation to determine the head loss, h, between sections 1 and 2. Keep in mind that head loss has units of length. With these simplifications it can be shown that the pressure drop measured between any two stations is equivalent to the head loss between them: # = =*h (4) 4.4 Head Loss Across a Fitting In class we defined a loss coefficient term,. This term can is related to the head loss through:
7 with: h = 2* (5) = 1 2 (6) The pressure difference = hcos * is taken between the pressure taps immediately upstream and downstream of the fitting. The density of air and manometer kerosene are denoted as and, respectively. The angle of the manometer bank with respect to the vertical is denoted as. 4.5 Restriction Meter Flow Rate Correction Factor The flow rate obtained by the modified Bernoulli equation for an orifice with flanged taps (to be derived in the report) is: 0=1 = where 0 is the volume flow rate, is the bulk velocity, is the variation of pressure across the orifice, is the density of the fluid, and 4 is the ratio of orifice diameter to pipe diameter. The orifice plate (see Figure 5) has a diameter of 50 mm and is also to be placed between stations 6 and 7 at ~1404 mm downstream from the inlet nozzle. The volume flow rate is to be determined from the bulk velocity flow and area cross section of the tube. Determine the discharge coefficient,, of the orifice with the above relation. Once the discharge coefficient is known, the expression in Equation 5 can be used to determine mass flow through a simple measurement of pressure drop using: 67 =0 (9) (8)
8 5. Analysis and Discussion for Report You are required to discuss the results based on the literature (compare with existing plots!!). You are also required to show all uncertainties. Show your measured entrance velocity profile and determine the average velocity for your head loss measurements. Determine tube diameter-based Reynolds number comment on whether the flow is laminar or turbulent. Your study of head loss for of the two bends and they should show uncertainties with nominal values compared to that of the literature. Perform a discharge coefficient analysis for the orifice. Calculate the mass flow through the orifice which ultimately gives you the constant mass flow through the tube. What is the sensitivity of this device? In other words, when you change mass flow by a certain amount, is there enough resolution in your pressure measurements to resolve this mass flow? Develop a velocity uncertainty equation derived from all measured parameters for both methods. Recall the general expression for uncertainty as explained in your notes: 8 9 =38 :; < =? +8 => < =? +8 # => :A < =? + +8 => :D < =? B => E (10) Determine which measured values affect the precision of your measurements the most (and least) using a measured parameter sensitivity analysis (described in Lecture 1).
### FLUID FLOW Introduction General Description
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### Michael Montgomery Marketing Product Manager Rosemount Inc. Russ Evans Manager of Engineering and Design Rosemount Inc.
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Fluid Mechanics: Fundamentals and Applications, 2nd Edition Yunus A. Cengel, John M. Cimbala McGraw-Hill, 2010 Chapter 5 MASS, BERNOULLI AND ENERGY EQUATIONS Lecture slides by Hasan Hacışevki Copyright | 8,738 | 37,398 | {"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-2022-05 | latest | en | 0.930534 |
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by escryan
Tags: charge, effective, nuclear
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P: 13 1. The problem statement, all variables and given/known data If ionization energy is 899.4 kJ/mol for Be, what is the effective nuclear charge? 2. Relevant equations Zeff = Z - S E=RH(Z2/n2) ?? E=RH(Zeff2/n2)?? 3. The attempt at a solution My attempted solution was subbing into Zeff = Z - S Zeff = 4 - 2 = 2 But I suspect that is wrong... because why ionization energy is given.. so shouldn't it be used in the calculation? And somewhere I think I read that "S" was supposed to be a "constant" of some sort, and I just subbed 2 in because I thought that it was the number of electrons in the first orbital ?
Admin P: 23,716 One of the equations you listed contains both ionization energy and effective nuclear charge, why don't you use it?
P: 13 Ah.. So subbing in values E=899.4 kJ/mol RH=2.178 x 10-21 kJ n=1 I get Z2eff= 4.129 x 10 23 mol How does one get to the units/value of Z2eff after this?
Admin P: 23,716 Calculating effective nuclear charge Ionization energy was per mole, not per molecule.
P: 13 Oops, just noticed that "Z2eff= 4.129 x 10 23 mol " should actually read "Z2eff= 4.129 x 10 23 mol-1 " I think that the italicized part is what confuses me the most -- what are the units for this portion? I'm going to take a guess that it is currently molecules/mol, but if so, is this always the case whenever expressing a value and the unit mol-1? Like for this example, what was given was in kJ/mol. When the kJs were cancelled, what resulted was just mol-1...
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Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A226611 Irregular array read by rows. a(n) is the smallest starting value of a T_k trajectory that includes A226607(n), where T_k is the 3x+k function associated with A226607(n). 8
1, 1, 3, 23, 123, 171, 1, 1, 3, 1, 19, 99, 147, 163, 123, 283, 159, 319, 1, 9, 1, 5, 7, 1, 1, 3, 1, 3, 2531, 5859, 1, 1, 3, 1, 3, 7, 1, 1, 5, 1, 9, 33, 39, 21, 101, 1, 1, 1, 7, 9, 1, 3, 149, 21, 93, 125, 221, 1, 175, 1, 1, 1, 7, 2585, 1073, 2301, 4121, 893 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,3 LINKS Geoffrey H. Morley, Rows 1..2032 of array, flattened EXAMPLE The irregular array starts: (k=1) 1; (k=5) 1, 3, 23, 123, 171; (k=7) 1; (k=11) 1, 3; a(3)=3 is the smallest starting value for a 3x+5 trajectory that includes A226607(3)=19. The trajectory is {3,7,13,22,11,19,...}. CROSSREFS Row n begins with a(A226612(n)) and has length A226613(n). The cycle associated with a(n) has length A226609(n) and A226610(n) odd elements of which A226608(n) is the largest. Cf. A226627. Sequence in context: A245752 A290367 A006557 * A081628 A267656 A122883 Adjacent sequences: A226608 A226609 A226610 * A226612 A226613 A226614 KEYWORD nonn,tabf AUTHOR Geoffrey H. Morley, Jun 13 2013 STATUS approved
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May 3, 2016
# Homework Help: Algebra
Posted by Helpless in Math on Sunday, May 27, 2007 at 9:49am.
1.Solve (x)/(x+10)+(x-3)/(x+2)=7/5..I got that there is no solution, is that correct?
2. Solve (x)/(x-5)+1=(5)/(x-5)..I got that there is no solution for this one too, is that correct?
3. Express your result in simplest form, (4)/(xy)+(6)/(xy)..I got (10)/(xy) is that correct?
4. Simplify (3)/(4) divided by (4)/(5)...I got 15/16, is that right?
3 is correct.
2 has is indeterminate, in your language, that is probably no solution.
1 recheck.
## Answer This Question
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## Related Questions
More Related Questions | 208 | 663 | {"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-2016-18 | longest | en | 0.961378 |
https://blog.achchuthan.lk/2012/03/convert-infix-to-postfix-using-stack-in.html?hl=ar | 1,696,307,359,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233511053.67/warc/CC-MAIN-20231003024646-20231003054646-00687.warc.gz | 151,622,332 | 38,845 | Infix to Postfix Conversion using Stack in Java
In this program, you'll learn to solve the Infix to Postfix Conversion using Stack. There is an algorithm to convert an infix expression into a postfix expression. It uses a stack; but in this case, the stack is used to hold operators rather than numbers. The purpose of the stack is to reverse the order of the operators in the expression. It also serves as a storage structure, since no operator can be printed until both of its operands have appeared.
Infix Expression :
Any expression in the standard form like "2*3-4/5" is an Infix(Inorder) expression.
Postfix Expression :
The Postfix(Postorder) form of the above expression is "23*45/-".
Example :
• infix (1+2)*(3+4)
• with parentheses: ((1+2)*(3+4))
• in postfix: 12+34+*
• in prefix: *+12+34
• infix 1^2*3-4+5/6/(7+8)
• paren.: ((((1^2)*3)-4)+((5/6)/(7+8)))
• in postfix: 12^3*4-56/78+/+
• in prefix: +-*^1234//56+78
Algorithm
1. Scan the Infix string from left to right.
2. Initialise an empty stack.
3. If the scannned character is an operand, add it to the Postfix string. If the scanned character is an operator and if the stack is empty Push the character tostack.
4. If the scanned character is an Operand and the stack is not empty, compare the precedence of the character with the element on top of the stack(topStack). If topStack has higher precedence over the scanned character Popthe stack else Push the scanned character to stack. Repeat this step as long as stack is not empty and topStack has precedence over the character.
5. (After all characters are scanned, we have to add any character that the stackmay have to the Postfix string.) If stack is not empty add topStack to Postfix stringand Pop the stack. Repeat this step as long as stack is not empty.
6. Return the Postfix string.
Infix to Postfix Conversion :
In normal algebra we use the infix notation like a+b*c. The corresponding postfix notation is abc*+.
The algorithm for the conversion is as follows :
Repeat this step till all the characters are scanned.
When you run the program, the output will be:
Type in an expression like (1+2)*(3+4)/(12-5)
with no monadic operators like in-5 or +5 followed by key
(1+2)*(3+4)
The Expression you have typed in infix form :
(1+2)*(3+4)
The Equivalent Postfix Expression is :
12+34++*
2 تعليقات
Thank you for vising
1. i have execute this program. but i am getting one error
that is
---------- javac ----------
Infix2Postfix.java:4: cannot find symbol
symbol: class character
public class Infix2Postfix extends Stack {
^
1 error
Output completed (0 sec consumed) - Normal Termination
2. in this program you need to extends Stack;better you create stack general type class and extends that one to this program .good luck
http://java90.blogspot.com/2012/01/stack-data-structure-in-java.html
إرسال تعليق
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http://pldml.icm.edu.pl/pldml/element/bwmeta1.element.bwnjournal-article-smv107i1p61bwm?q=bwmeta1.element.bwnjournal-number-sm-1993-107-1;3&qt=CHILDREN-STATELESS | 1,618,923,050,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618039398307.76/warc/CC-MAIN-20210420122023-20210420152023-00494.warc.gz | 80,013,616 | 13,301 | PL EN
Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
Studia Mathematica
1993 | 107 | 1 | 61-100
Tytuł artykułu
Molecular decompositions and embedding theorems for vector-valued Sobolev spaces with gradient norm
Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let E be a Banach space. Let $L¹_{(1)}(ℝ^d,E)$ be the Sobolev space of E-valued functions on $ℝ^d$ with the norm $ʃ_{ℝ^d} ∥f∥_E dx + ʃ_{ℝ^d} ∥∇f∥_E dx = ∥f∥₁ + ∥∇f∥₁$. It is proved that if $f ∈ L¹_{(1)}(ℝ^d,E)$ then there exists a sequence $(g_m) ⊂ L_{(1)}¹(ℝ^d,E)$ such that $f = ∑_m g_m$; $∑_m (∥g_m∥₁ + ∥∇g_m ∥₁) < ∞$; and $∥g_m∥_∞^{1/d} ∥g_m∥₁^{(d-1)/d} ≤ b∥∇g_m∥₁$ for m = 1, 2,..., where b is an absolute constant independent of f and E. The result is applied to prove various refinements of the Sobolev type embedding $L_{(1)}¹(ℝ^d,E) ↪ L²(ℝ^d,E)$. In particular, the embedding into Besov spaces $L¹_{(1)} (ℝ^d,E) ↪ B_{p,1}^{θ(p,d)}(ℝ^d,E)$ is proved, where $θ(p,d) = d(p^{-1} + d^{-1} -1)$ for 1 < p ≤ d/(d-1), d=1,2,... The latter embedding in the scalar case is due to Bourgain and Kolyada.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
61-100
Opis fizyczny
Daty
wydano
1993
otrzymano
1993-02-24
Twórcy
autor
• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland
autor
• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland
Bibliografia
• [A] T. Aubin, Problèmes isopérimétriques et espaces de Sobolev, C. R. Acad. Sci. Paris 280 (1975), 279-281.
• [BS] C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, London, 1988.
• [Br1] J. Bourgain, A Hardy inequality in Sobolev spaces, Vrije University, Brussels, 1981.
• [Br2] J. Bourgain, Some examples of multipliers in Sobolev spaces, IHES, 1985.
• [BZ] Yu. D. Burago and V. A. Zalgaller, Geometric Inequalities, Nauka, Leningrad, 1980 (in Russian); English transl.: Springer, 1988.
• [CSV] T. Coulhon, L. Saloff-Coste and N. Varopoulos, Analysis and Geometry on Groups, Cambridge University Press, Cambridge, 1992.
• [DS] N. Dunford and J. T. Schwartz, Linear Operators I, Interscience, New York, 1958.
• [F] H. Federer, Geometric Measure Theory, Springer, Berlin, 1969.
• [FF] H. Federer and W. H. Fleming, Normal and integral currents, Ann. of Math. 72 (1960), 458-520.
• [G] E. Gagliardo, Proprietà di alcune classi di funzioni in più variabili, Ricerche Mat. 7 (1958), 102-137.
• [Hö] L. Hörmander, The Analysis of Linear Partial Differential Operators I, Springer, Berlin, 1983.
• [H] R. Hunt, On L(p,q) spaces, Enseign. Math. (2) 12 (1966), 249-275.
• [Jo] P. W. Jones, Quasiconformal mappings and extendability of functions in Sobolev spaces, Acta Math. 147 (1981), 71-88.
• [K] V. I. Kolyada, On relations between moduli of continuity in different metrics, Trudy Mat. Inst. Steklov. 181 (1988), 117-136 (in Russian); English transl.: Proc. Steklov Inst. Math. 4 (1989), 127-148.
• [Kr] A. S. Kronrod, On functions of two variables, Uspekhi Mat. Nauk 5 (1) (1950), 24-134 (in Russian).
• [Le] M. Ledoux, Semigroup proofs of the isoperimetric inequality in euclidean and Gauss space, Bull. Sci. Math., to appear.
• [LW] L. H. Loomis and H. Whitney, An inequality related to the isoperimetric inequality, Bull. Amer. Math. Soc. 55 (1949), 961-962.
• [M1] V. G. Maz'ya, Classes of sets and embedding theorems for function spaces, Dokl. Akad. Nauk SSSR 133 (1960), 527-530 (in Russian).
• [M2] V. G. Maz'ya, S. L. Sobolev's Spaces, Leningrad University Publishing House, Leningrad, 1985 (in Russian).
• [N] L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa (3) 13 (1959), 116-162.
• [Pee] J. Peetre, New Thoughts on Besov Spaces, Duke Univ. Math. Ser. 1, Durham, N.C., 1976.
• [Po] S. Poornima, An embedding theorem for the Sobolev space $W^{1,1}$, Bull. Sci. Math. (2) 107 (1983), 253-259.
• [St] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, N.J., 1970.
• [T] G. Talenti, Best constant in Sobolev inequality, Ann. Mat. Pura Appl. (4) 110 (1976), 353-372.
• [Tr] H. Triebel, Theory of Function Spaces, Birkhäuser, Basel 1983.
Typ dokumentu
Bibliografia
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http://www.slideserve.com/lundy/chapter-7-arrays | 1,492,991,607,000,000,000 | text/html | crawl-data/CC-MAIN-2017-17/segments/1492917118851.8/warc/CC-MAIN-20170423031158-00313-ip-10-145-167-34.ec2.internal.warc.gz | 674,162,197 | 18,508 | # Chapter 7 – Arrays - PowerPoint PPT Presentation
1 / 20
Chapter 7 – Arrays. 7.1 Creating and Accessing Arrays 7.2 Using LINQ with Arrays 7.3 Arrays of Structures 7.4 Two-Dimensional Arrays 7.5 A Case Study: Analyze a Loan. 7.4 Two-Dimensional Arrays. Declaring a Two-Dimensional Array Variable Implicit Array Sizing and Initialization
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Chapter 7 – Arrays
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### Chapter 7 – Arrays
7.1 Creating and Accessing Arrays
7.2 Using LINQ with Arrays
7.3 Arrays of Structures
7.4 Two-Dimensional Arrays
7.5 A Case Study: Analyze a Loan
### 7.4 Two-Dimensional Arrays
• Declaring a Two-Dimensional Array Variable
• Implicit Array Sizing and Initialization
• The ReDim Statement
• Filling a Two-Dimensional Array with a Text File
• Outputting an Array
### Declaring a Two-Dimensional Array Variable
• Two-dimensional arrays store a table of items of the same type.
• Consider the rows of the table as numbered 0, 1, 2, … m and the columns numbered 0, 1, 2, … n.
• The array is declared with
DimarrayName(m, n) AsDataType
• The item in ith row, jth column is denoted
arrayName(i,j)
### Declaring a Two-Dimensional Arrays
An unsized two-dimensional array can be declared with a statement of the form
DimarrayName(,) As varType
### ReDim and Two-Dimensional Arrays
• An already-created array can be resized with
ReDimarrayName(r, c)
• which loses the current contents.
• When Preserve is used …
ReDim PreservearrayName(r, c)
• Only the columns can be resized.
• ReDim cannot change the number of rows in the array.
### Implicit Array Sizing and Initialization
Arrays can be initialized when they are declared.
DimarrayName(,) As DataType=
{{ROW0},{ROW1}, {ROW2}, ..., {ROWN}}
declares a two-dimensional array where ROW0 consists of the entries in the top row of the corresponding table delimited by commas, and so on.
The row and column headers are not a part of the matrix
Dim rm(3, 3) As Double
rm(0,0)=0, rm(0,1)=2054, rm(1,2)=2786
Dimrm(,) As Double = {{0, 2054, 802, 738},
{2054, 0, 2786, 2706},
{802, 2786, 0, 100},
{738, 2706, 100, 0}}
declares and initializes an array of road-mileages.
### GetUpperBound Method
After execution of the statement
DimarrayName(r, c) As varType
• the value of arrayName.GetUpperBound(0) is r,
• and the value of arrayName.GetUpperBound(1) is c.
### Filling a Two-Dimensional Array with a Text File
Text File Distances.txt
0,2054,802,738
2054,0,2786,2706
802,2786,0,100
738,2706,100,0
In the next set of code we will read the values of this text file into a two dimensional array.
### Filling a Two-Dimensional Array with a Text File (cont.)
Dimrm(3, 3) As Double 'road mileage
DimrowOfNums() AsString=
Dimline, data() As String
ForiAs Integer = 0To 3
line = rowOfNums(i)
data = line.Split(""c)
For jAs Integer= 0 To3
rm(i, j) = CDbl(data(j))
Next
Next
### Outputting Data from a Matrix
Private Sub PrintMatrix(rm() as Double)
‘Print a 3 x 3 matrix
Dim build as String
Forrow As Integer = 0 Torm.getupperbound(0)
build = “”
Forcol As Integer = 0 Torm.getupperbound(1) build = build &Cstr(rm(row, col)) & “ “
Next
Next
End Sub
### Printing a Matrix in Zones
'Print a 3 x 3 matrix
Dim rm(,) AsDouble = {{2, 3, 5},
{1, 4, 6},
{0, 7, 9}}
Dim frtstr AsString = "{0,-15} {1,-15} {2,-15}"
For row AsInteger = 0 To 2
ListBox1.Items.Add(String.Format(frtstr, rm(row, 0), rm(row, 1), rm(row, 2)))
Next
### Outputting To A DataGridView
First create the columns for your matrix
### Code For Outputting to a DataGridView
Dim example(,) AsInteger = {{1, 2, 3, 4},
{5, 6, 7, 8},
{9, 10, 11, 12}}
For r AsInteger = 0 To 2
For c AsInteger = 0 To 3
DataGridView1.Item(c, r).Value = example(r, c)
Next
Next
Matrices rows first, columns second
DataGridView columns are listed first …Blah
Dim example(,) AsInteger = {{1, 2, 3, 4},
{5, 6, 7, 8},
{9, 10, 11, 12}}
For c AsInteger = 0 To 3
Next
For r AsInteger = 0 To 2
For c AsInteger = 0 To 3
DataGridView1.Item(c, r).Value = example(r, c)
Next
Next
Column name
Dim columns() AsString = {"Column1", "Column2", "Column3"}
Dim Rows() AsString = {"Row1", "Row2", "Row3"}
Dim array2d(,) AsInteger = {{1, 2, 3},
{4, 5, 6},
{7, 8, 9}}
For c AsInteger = 0 To columns.Count - 1
Next
For r AsInteger = 0 To Rows.Count - 1
For c AsInteger = 0 To columns.Count - 1
DataGridView1.Item(c, r).Value = array2d(r, c)
Next
Next
2nd Assign the row array to the dgv
### Processing Each Element Using a For Each
Dim nums(,) AsDouble = {{7, 3, 1, 0},
{2, 5, 9, 8},
{0, 6, 4, 10}}
'use a For Each loop
Dim total AsDouble = 0
ForEach num AsDoubleIn nums
If num Mod 2 = 0 Then
total += num
EndIf
Next
Finding the sum of the even numbers in a
Matrix.
### Processing a Matrix Using a LINQ Query
Dimnums(,) AsDouble = {{7, 3, 1, 0},
{2, 5, 9, 8},
{0, 6, 4, 10}}
'use a For Each loop
'use LINQ
Dim query = FromnumInnums.Cast(OfDouble)()
Where (numMod 2 = 0)
Selectnum
### How do we add up the values in a column?
Can you create a For Loop to add up the columns?
2 3 6 8
7 1 4 5
0 2 -2 9
x(0,0) x(0,1) x(0,2) x(0,3) x(0,4)
x(1,0) x(1,1) x(1,2) x(1,3) x(1,4)
x(2,0) x(2,1) x(2,2) x(2,3) x(2,4) | 1,870 | 5,728 | {"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-2017-17 | longest | en | 0.734229 |
https://mste.illinois.edu/dildine/tcd_files/metric/mass.htm | 1,657,000,517,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656104514861.81/warc/CC-MAIN-20220705053147-20220705083147-00739.warc.gz | 449,899,524 | 1,985 | Conversion Tables and Methods to Use when converting
from Metric Units to Metric Units (weight)
Gram – Length Kilo – Thousand Liter – Volume Milli – Thousand Gram – Mass/Weight Centi – Hundred Celsius – Temperature Deci – Ten
### Weight/Mass
1,000 milligrams (mg) = 1 gram 10 centigrams = 100 milligrams (mg) 1 gram (g) = 1,000 milligrams 1,000 grams = 1 kilogram (kg) = 1,000,000 mg 1,000 kilograms = 1,000,000 grams
### Operations for Weight
Example: To get Milligrams from grams you multiply the grams by 1000
You Have: 23 grams
You want milligrams: So, milligrams = 23 Grams
We Multiply the grams by 1000: 23g x 1000 = 23000mg
You want milligrams: So, milligrams = 23 Grams
There are 23000 milligrams in 23 grams or 1000 milligrams for every gram.
If you have this Do this To get this milligrams (mg) Divide by 10 (mg/10) Move Decimal one place to Left centigram (cg) centigrams (cg) Multiply by 10 (cg * 10) Move decimal one place to the right Milligrams (mg) Grams (g) Multiply by 100 (g * 100) Centigrams (cg) Centigrams (cm) Divide by 100 (cg/100) Move decimal two places to the left. Grams (g) Milligrams (mg) Divide by 1000 (mg/1000) Move decimal three places to the left. Grams (g)
[page 1] [page 2] [page 3] [page 4] [page 5] [page 6] [page 7] [evaluation]
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https://archived.hpcalc.org/museumforum/thread-97316-post-97404.html | 1,632,107,009,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780056974.30/warc/CC-MAIN-20210920010331-20210920040331-00550.warc.gz | 174,926,488 | 14,076 | HP-12C Platinum Trigs Program « Next Oldest | Next Newest »
▼ Gerson W. Barbosa Posting Freak Posts: 2,761 Threads: 100 Joined: Jul 2005 08-06-2006, 04:52 PM I have just posted the final version of the Trigonometric Functions Program (The 239 Steps :) for the 12C Platinum in the Articles Forum: Because at least 11 significant digits are always correct all through the ranges below (I haven't found less accurate results so far - perhaps I haven't searched long enough...) , the results match those displayed by the 11C and the 15C. If fact, thanks to the 12C Platinum internal precision, is seems we have now the most accurate 10C-series calculator regarding trigonometric functions (Hey, it has just passed Voidware's Trig Torture Test! Not bad: relative error 1.72x10^-5, slightly better than the HP-32SII and the HP-48G (2.26x10^-5) - This does not mean it's better than the HP-48G, although it might be better than the HP-15C: relative error 1.33x10^-3). ``` Input ranges SIN, COS, TAN: |x| <= 1E11 ASIN, ACOS: |x| <= 1 ATAN: |x| <= 9.99999999E49 Running Times SIN, COS: 2.4 s (|x| <= 180) TAN: 4.7 s (|x| <= 180) ASIN, ACOS, ATAN: 2.5 s ``` Feedbacks appreciated. Best regards, Gerson. ▼ Namir Posting Freak Posts: 2,247 Threads: 200 Joined: Jun 2005 08-06-2006, 06:04 PM Gerson, Cool and thorough update. Thanks for the labor of love and the enthusiasm to share it with us. You make the HP-12CP kick "assests" Namir ▼ Gerson W. Barbosa Posting Freak Posts: 2,761 Threads: 100 Joined: Jul 2005 08-06-2006, 06:50 PM Thanks Namir, I thought of including a radians mode but I quit because this would sacrifice the speed even more. Besides, a kind of annunciator would be needed. About speed, assuming that 2 is stored in register 6, 047 might be a shortcut to sine, about only 1.6 seconds instead of the usual 2.4 or 2.5 seconds (But then g GTO 047 R/S would take more time than simply R/S :-) Regards, Gerson. Eric Smith Posting Freak Posts: 2,309 Threads: 116 Joined: Jun 2005 08-06-2006, 08:13 PM Speaking of "torture tests", does anyone have such a test (or just a good collection of test cases) for the TVM functions? ▼ Gerson W. Barbosa Posting Freak Posts: 2,761 Threads: 100 Joined: Jul 2005 08-06-2006, 08:51 PM Still at voidware.com, in the 12CP page, there are some TVM-related tests, not exactly torture tests, though: Les Wright Posting Freak Posts: 1,368 Threads: 212 Joined: Dec 2006 08-07-2006, 04:00 AM Quote: Because at least 11 significant digits are always correct all through the ranges below.... Maybe this is a tangent I should take into a new thread, but the above comment fascinated me. I am a rank amateur at all this, I must admit, but I am aware that many if not most of the "newer" HPs (i.e. those marketed after 1980) maintain at least 2 or 3 guard digits of internal precision--so the HP41 series and 15C compute internally to 13 digits, and the 42s to 15 digits, for example. Gerson's comment seems to imply that the internal precision can be accessible to the RPN programmer. Round off error is the bane of my existence in my programs, so I would be keen to learn how to code in such a way so as to capitalize on the internal precision of these calculators. For example, is register arithmetic performed at full internal precision? At what stage is the full internal precision lost in intermediate calculations? What techniques, either in RPN programs or in direct key entry, can one use to minimize this rounding before it is desired in the final result? Maybe I am asking a basic question intrinsically obvious to most, but I really have no clue, and this is something I would like to learn about. Les ▼ Gerson W. Barbosa Posting Freak Posts: 2,761 Threads: 100 Joined: Jul 2005 08-07-2006, 07:36 AM Hello Les, You're right about the gard digits on "newer" HP calculators. Thanks to them, the 10 significant figures in all my examples are correct on the HP-15C, and all 12 significant figures are correct on the HP-50G. However, on those calculators the gard digits are not normally available to the user. If you try this on the HP-15C: 3 1/x 10000 x FRAC and you'll get 0.333333 On the other hand, on the 12C Platinum you would get 0.33333333 By what I've read, on the 48 and 49 series 15 significant digits are accessible through System-RPL. Regards, Gerson. ▼ Les Wright Posting Freak Posts: 1,368 Threads: 212 Joined: Dec 2006 08-07-2006, 07:47 AM I see! On the 12Cp, the operation of moving the decimal point permits the user access to two extra SDs, whereas they are not available on the 15C, or the 41 series, or, for that matter on the 42S (where your test gives 0.33333333). Quote: Thanks to them, the 10 significant figures in all my examples are correct on the HP-15C.... I think you mean the 12Cp here, not the 15C? Typo? Best, Les ▼ Gerson W. Barbosa Posting Freak Posts: 2,761 Threads: 100 Joined: Jul 2005 08-07-2006, 04:55 PM Quote: I think you mean the 12Cp here, not the 15C? Typo? I did mean the 15C. I intended to say the 15C, despite being a 10-digit calculator, have trigonometric functions accurate to 10 places because of the extra guard digits. That would not be possible, no matter how good the algorithm was, if it performed internal calculations with only 10 digits. On the 12CP, thanks to the two hidden digits, results accurate to 10 places were possible. Best regards, Gerson. Les Wright Posting Freak Posts: 1,368 Threads: 212 Joined: Dec 2006 08-07-2006, 02:11 PM This is really impressive. I have been germinating an interest in polynomial and rational approximation. I recently successfully ported the Numerical Recipes rational approximation routine in section 5.13 of the book to Maple. Couldn't get the code to work in C, but the Maple version works beautifully, and if anyone here uses Maple I would love to share it. That routine, for folks who know the work, purports to be at best a "sloppy" approximation that uses an iterative weighted leastsquares approach to roughly approach a minimax fit without going thru the the Remez rigamarole. I find the approach works very well with the trigonometric functions, and if it doesn't give a true minimax fit it comes close in these cases. Indeed I was able to generate coefficients pretty close to yours for the sine fit. Your range reduction is inspired, and indeed it helps you achieve such high accuracy with a relatively small polynomial. I am also impressed with how you experimented with the coeffiecients, truncating them to strike a balance between lower memory usage and acceptable precision. In my experimenting I came across an example that should warm the cockles of your heart. (What is a cockle anyway?) Try your routine to compute sin(32.888 deg). The displayed answer is 0.542998588, and when you multiply by 1000 and take the fractional part you see the full twelve digit result is 0.542998588466. This is what I see on my HP48G, HP49G+, and HP42S. In Maple, sin(32.888*Pi/180) gives, to 25 digits, .542998588465592253694888. But on my 15C, 41CV, and 41CX, I get 0.542998589, though when multiplying thru by 10 to see the tenth digit it is indeed a 5, the effect of the 6 rounding up the 4. When it is off the display that five rounds up the 8 to 9. But the 12Cp displays what we know to be the more correct 9 digit answer, given what we know the next three digits to be. I think that is pretty impressive. Thanks for sharing this excellent work with us. Les ▼ Gerson W. Barbosa Posting Freak Posts: 2,761 Threads: 100 Joined: Jul 2005 08-07-2006, 06:27 PM Quote: I am also impressed with how you experimented with the coeffiecients, truncating them to strike a balance between lower memory usage and acceptable precision. I just used spreadsheets, computing sines from 1 to 90 degrees and arctangents from 0 to 0.28 in steps of 0.01, graphing the functions and comparing the differences in relation to the real functions. It was just a matter of changing the coefficients and observing the maximum error and the graphs. I thought it was important to keep the maximum positive errors close to the maximum negative errors, so that they cancelled each other in random sequence of calculations. Spreadsheets were not available to people who implemented these functions through polynomial approximations on some mid 70's calculators, which makes their work even more remarkable (please see a short comment about Elektronika C3-15 on this old thread, under Additional information: http://www.hpmuseum.org/cgi-sys/cgiwrap/hpmuseum/forum.cgi?read=97113#97113 Quote: an example that should warm the cockles of your heart. (What is a cockle anyway?) ```------------------------- cockle1 [kók’l] noun (plural cockled) 1. mollusc with heart-shaped shell: a small mollusc that has a rounded or heart-shaped ridged shell in two parts. Family: Cardiidae warm the cockles of your heart to give you a feeling of well-being or sentimental contentment Encarta® World English Dictionary © & (P) 1999, 2000 Microsoft Corporation. All rights reserved. Developed for Microsoft by Bloomsbury Publishing Plc. ------------------------- ``` Thanks for the opportuny of learning a new word and a new idiom :-) Quote: But the 12Cp displays what we know to be the more correct 9 digit answer, given what we know the next three digits to be. That's right! I had already come across a similar example when comparing the results with the 15C (a difference of one unit in the least significant digit). But then I checked the result on the 42S. Thanks for your keen remark. I forgot to mention all HP-50G results in my comparison tables are accurate to 12 digits (I checked them upon my own RPN calculator written in Delphi, which displays 15 digits, 0.542998588465592 in your example). As I said, the results are far better than I expected. When I wrote the first version of this program I didn't have a 12C Platinum for tests (I actually used an equivalent 15C program): Best regards, Gerson. ▼ Les Wright Posting Freak Posts: 1,368 Threads: 212 Joined: Dec 2006 08-07-2006, 09:43 PM Quote: I just used spreadsheets May I ask which one? I ask since MS Excel is not really very robust for high precision calculation of math functions. It offers pretty mediocre performance for special functions and statistical distributions, but maybe it is a bit better for the trig functions. At any rate, I understand there are interfaces to import tables of values from trusted sources like Mathematica. Quote: I thought it was important to keep the maximum positive errors close to the maximum negative errors You no doubt discovered that the absolute error of the final function reveals a magnification in error as the argument increases. I take it you got an equal ripple minimax fit of sin(sqrt(y))/sqrt(y) on the interval 0..(Pi/6)^2, then substituted y = x^2 to get sin(x)/x = a polynomial in x^2 + error. Multiplying thru by x will magnify the absolute error on the interval as x gets bigger. Fortunately, with range reduction you kept the interval of interest small enough this poses no hardship. Quote: I checked them upon my own RPN calculator written in Delphi This is an off-topic diversion, but I have noticed that Delphi is surprisingly good for math programming. The extended data type seems to yield 17 digits of accuracy and up without much fuss, whereas the long double type in C is all over the place depending on the platform and compiler. Right now I am fooling around a bit with the 384 bit qfloat type under lcc-win32. Very gratifying to get 100-digit precision with so little fuss, though portability is a huge issue. Les ▼ Gerson W. Barbosa Posting Freak Posts: 2,761 Threads: 100 Joined: Jul 2005 08-07-2006, 11:29 PM . Rodger Rosenbaum Senior Member Posts: 305 Threads: 17 Joined: Jun 2007 08-08-2006, 04:07 AM Les, if you haven't already done so, you should read this: Bruce Horrocks Member Posts: 80 Threads: 11 Joined: Jan 1970 08-07-2006, 05:49 PM Valentin Albillo's "Tried and Tricky Trigonometrics" article in Datafile V21N1 describes a program to compute sine, cosine tangent, arc sine, arc cosine and arc tangent - to full accuracy - that fits within the 99 steps available on a standard 12C. You can download a copy from Valentin's web pages. Alternatively the full Datafile issue is available to buy on cd-rom from Jake Schwartz.
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Forum Jump: | 3,569 | 13,433 | {"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-2021-39 | longest | en | 0.858066 |
https://english.eagetutor.com/index.php?option=com_content&view=article&id=387:parallel-plate-capacitor-sp-813460666&tmpl=component&print=1&layout=default&Itemid=101 | 1,560,905,813,000,000,000 | text/html | crawl-data/CC-MAIN-2019-26/segments/1560627998879.63/warc/CC-MAIN-20190619003600-20190619025600-00293.warc.gz | 421,559,070 | 4,807 | # Introduction to Parallel Plate Capacitors
The electric field between the plates of a parallel-plate capacitor
A capacitor consists of two identical conducting plates which are placed in front of each other. One plate of the capacitor is connected to the positive terminal of a power supply and the other plate is connected to the negative terminal. The plate that is connected to positive terminal acquires a positive charge, while the other plate connected to the negative terminal acquires a negative charge. To maximize voltage, separation between the plates is very small, and is filled with air or any suitable dielectric material.
Remember that the direction of an electric field is defined as the direction that a positive test charge would move. So in the case indicated above, the electric field would point from the positive plate to the negative plate. Since the field lines are parallel to each other, this type of electric field is uniform, and is calculated with the equation E = V/d.
## Unit of a Capacitor
Note that the electric field strength, E, can be measured in either the units V/m, or equivalently, N/C.
[E] = V/d
(J/C)/m
(Nm)/C/ m
N/C
Since the field lines are parallel and the electric field is uniform between two parallel plates, a test charge would experience the same force of attraction or repulsion no matter where it was located. That force can be calculated with the equation F = qE.
## Energy stored in a Capacitor
Work is done by an external agent bringing in +dq from the negative plate and depositing the charge on the positive plate.
The energy (measured in joules) stored in a capacitor is equal to the work done to charge it. Consider a capacitance C, holding a charge +q on one plate and −q on the other. Moving a small element of charge dq from one plate to the other against the potential difference V = q/C requires the work dW:
where W is the work measured in joules, q is the charge measured in coulombs and C is the capacitance, measured in farads.
The energy stored in a capacitance is found by integrating this equation. Starting with an uncharged capacitance (q = 0) and work W moves charges from one plate to the other until the plates have charge +Q and −Q:
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http://www.exambeat.in/27808/discussion.html | 1,495,816,635,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463608669.50/warc/CC-MAIN-20170526163521-20170526183521-00164.warc.gz | 607,614,480 | 6,051 | # Aptitude:: Height and Distance
@ : Home > Aptitude > Height and Distance > General Question - Discussion
### Exercise
"
#### The angle of elevation of a ladder leaning against a wall is 60ο and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:
A. 2.3 m B. 4.6 m C. 7.8 m D. 9.2 m
Explanation:
Let AB be the wall and BC be the ladder.
Then, ACB = 60º and AC = 4.6 m. | 130 | 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} | 3.796875 | 4 | CC-MAIN-2017-22 | longest | en | 0.789346 |
https://paperzz.com/doc/9121873/transformations-test-review-1.-write-the-rule-for-a-refle... | 1,638,672,160,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964363134.25/warc/CC-MAIN-20211205005314-20211205035314-00495.warc.gz | 525,614,275 | 5,459 | ### Transformations Test Review 1. Write the rule for a reflection over
Name: _____________________________________
Transformations Test Review
1. Write the rule for a reflection over the x-axis.
2. Write the rule for a reflection over the y-axis.
3. Write the rule for a 90° clockwise rotation and a 270° counter-clockwise rotation.
4. Write a rule for a 180° rotation.
5. Write a rule for a 270° clockwise rotation and a 90° counter-clockwise rotation.
6. Write a rule for a 360° rotation.
7. The quadrilateral shown is rotated 90° clockwise about the origin. In which quadrant is the image of
8. Using the quadrilateral from number 1, write down the original coordinates, and the new coordinates
after the 90° clockwise rotation.
9. What transformations always produce congruent figures? Explain.
10. What transformations only sometimes produce congruent figures? Explain.
11. The table shows the coordinates of trapezoid ABCD and trapezoid A′B′C′D′ after a transformation.
What are the coordinates of point C’?
Trapezoid ABCD
Trapezoid A′B′C′D′
A(–4, 2)
A′(–7, 0)
B(–2, 4)
B′(–5, 2)
C(2, 4)
?
D(4, 2)
D′(1, 0)
12. Graph the image of U ( 4, 10 ) after a rotation of 180° about the origin.
13. Write the coordinates of the vertices after a reflection across the x- axis.
14. Δ DEF is dilated using a scale factor of
1
2
. What is the length of D’E’?
15. Write an algebraic rule for a translation that moves a triangle 4 units to the right and 8 units up.
16. Write the coordinates for ΔPQR after a translation of 10 units left and 9 units up.
In what Quadrant is ΔP’Q’R’ located now?
17. Rotate the image 90° clockwise.
18. The vertices of a triangle are (-1, 1) (-4, 5) and (-2, 6). Graph the new image after a reflection across the
y-axis.
19. Name the Transformation.
20. What are the only times that a dilation will produce a congruent figure? Explain.
21. Graph the image of the figure based on the transformation: (x, y) (x - 4, y + 5)
22. Graph the image of the kite EFGH after a dilation with a scale factor of
1
, centered at the origin.
4
23. What would the new coordinates of the image be if it was reflected over the x-axis?
24. Write a rule for the transformation.
25. Δ ABC was dilated to create Δ A’B’C’. What was the scale factor used to dilate the image? | 644 | 2,276 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.859375 | 4 | CC-MAIN-2021-49 | latest | en | 0.786281 |
http://slideplayer.com/slide/8709925/ | 1,586,040,391,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585370525223.55/warc/CC-MAIN-20200404200523-20200404230523-00260.warc.gz | 157,549,850 | 18,623 | # The Wonderful World of Metrics!. Metric Mania To determine mass, use a balance and the base unit is kilograms You will be recording your measurement.
## Presentation on theme: "The Wonderful World of Metrics!. Metric Mania To determine mass, use a balance and the base unit is kilograms You will be recording your measurement."— Presentation transcript:
The Wonderful World of Metrics!
Metric Mania To determine mass, use a balance and the base unit is kilograms You will be recording your measurement in grams To determine length, use a ruler or meter stick, and the base unit is meter You will be measuring centimeters with the ruler and meter stick Note: 100 centimeters = one meter, the length of the meter stick
Measuring Volume One way to determine volume is measuring length * width * height
Measuring Volume Another way to determine volume is to measure the difference between where the water started in a graduated cylinder, and where the water moved in the graduated cylinder after the object was added. The base unit is liter Your measurement will be in milliliters (mL)
Measuring Volume
Introduction The metric system is a different way of measuring things. The practice is the same, but different units are involved. Can you think of any metric measurements that you have seen or heard?
The “Basics” The metric system uses SI base units as a foundation. Those units are….. Meter (m) – a measure of distance Liter (L) – a measure of volume Kilogram (kg) – a measure of mass (this is the only one that uses a prefix! More on that soon…) Second (s) – a measure of time Kelvin (K) – a measure of temperature Mole (mol) – a measure of an amount
The “Basics” Every measurement will include one of the base words. The metric system uses Prefixes too. Every prefix is related to the base units. But how is that possible…
Pioneering the Prefixes Lets start with the prefixes for large measurements…. KILO (k) 1 kilometer = 1000 meters HECTO (h) 1 Hectoliter = 100 liters DECA (da) 1 Decagram = 10 grams Remember Meters, Liters, Grams, and Seconds are the base units. They will be in every measurement.
Pioneering the Prefixes How about the small measurements… DECI (d) – 1 decimeter = 1/10 meter CENTI (c) – 1 centiliter = 1/100 liter MILLI (m) – 1 milligram = 1/1000 gram Remember, these prefixes are always added to the base root word
Good ol’ King Henry Largest to smallest Kilo Hecto Deca Base Deci Centi Milli King Henry Died by Drinking Chocolate Milk
Converting Skillz When you are converting from one unit to another unit First figure out what you are starting with Then where (which direction) you are going! If you move to the right (aka big to small) then you move the decimal to the right. If you move to the left (aka small to big) then you move the decimal to the left.
Practice makes Perfect! Try this one. 1 meter = ______ hectometer 1 st - Figure out your starting point and where you are going! K h da b d c m 2 nd – Find the Decimal and move it the same way and number you moved in step 1.
Practice makes Perfect! And this one. 2.5 kilograms = ______ grams 1 st - Figure out your starting point and where you are going! K h da b d c m 2 nd – Find the Decimal and move it the same way and number you moved in step 1.
Practice makes Perfect! Last one! 17.504 deciliters = ______ decaliters 1 st - Figure out your starting point and where you are going! K h da b d c m 2 nd – Find the Decimal and move it the same way and number you moved in step 1.
Precision vs Accuracy Precision A measure of the degree to which the measurements made (and made in the same way) agree with each other Accuracy Degree to which the experimental value agrees with the true or accepted value So, can measurements be precise without being accurate?
Precision vs Accuracy
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Convert From: (required) Click here to Convert To: (optional) Examples: 5 kilometers, 12 feet/sec^2, 1/5 gallon, 9.5 Joules, or 0 dF. Help, Frequently Asked Questions, Use Currencies in Conversions, Measurements & Currencies Recognized Examples: miles, meters/s^2, liters, kilowatt*hours, or dC.
Conversion Result: ```Spanish oil arroba = 0.01256756712288 volume (volume) ``` Related Measurements: Try converting from "oil arroba" to bath (Israeli bath), chetvert (Russian chetvert), cord foot (of wood), dry pint, ephah (Israeli ephah), fifth, firkin, hogshead, jeroboam, methuselah, minim, peck (dry peck), petroleum barrel, register ton, rehoboam, stere, tea cup, timber foot, tun (English tun), UK bushel (British bushel), or any combination of units which equate to "length cubed" and represent capacity, section modulus, static moment of area, or volume. Sample Conversions: oil arroba = .83 balthazar, .10539683 barrel, 2.72 beer gallon (English beer gallon), 5.33 board foot, .35663731 bushel (dry bushel), 2.76 Canadian gallon, 12,567.57 cc (cubic centimeters), 22.82 dry pint, .01109549 freight ton, .00865145 load, 106.24 noggin, 424.96 oz fluid (fluid ounce), .00443819 register ton, 2.21 rehoboam, .48538012 Roman amphora, 2,549.76 teaspoon, .44381944 timber foot, .0131746 tun (English tun), 2.76 UK gallon (British gallon), .77209302 wine arroba (Spanish wine arroba).
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Please read our Help Page and FAQ Page then post a message or send e-mail. Thanks! | 478 | 1,700 | {"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-2019-30 | longest | en | 0.66294 |
https://dangoldner.wordpress.com/2011/04/03/what-does-try-something-mean/ | 1,500,799,666,000,000,000 | text/html | crawl-data/CC-MAIN-2017-30/segments/1500549424296.90/warc/CC-MAIN-20170723082652-20170723102652-00127.warc.gz | 641,393,162 | 33,513 | When they produce work without really absorbing it deeply, just getting the steps done without reflecting on them, I wish they had stopped me and said “We really don’t get this!” But when they don’t produce anything and tell me “We really don’t get this!”, I wish they would not give up, keep looking, keep going. It seems I may be trapping them in some conflicting expectations.
What’s in between being stopped cold, and getting someone (me, another student) to show you a procedure you can carry out mindlessly? Prior to having any understanding, what’s in between is to “try something”. What does that mean? When I solve math problems, it means executing one or another procedure on paper and then looking at the result to see if it seems to move me toward a solution.
Miguel Cura, one of my coaches (I am lucky to have a number of great coaches this year), pointed out that many of my students don’t know how to represent their guesses, conjectures, and trials-and-errors on paper. They know how to do guess-and-check by substituting values and simplifying, but rewriting expressions, substituting variables, factoring expressions and other techniques are all things they’ve learned to do when told, but not things that occur to them to try, just to see if the result looks like something they can move forward from.
Ben’s right: the problems are too hard at this stage. But not grasping the nature of the puzzle being posed is only half the reason. The other half is, I want them to keep looking, but “looking” at this stage usually means rewriting things many different ways without knowing in advance how it’s going to work out, and they are unfamiliar with that whole mode of exploration.
All the modeling that I’ve done, that other students have done, none of it is showing up on the tests (even from the students who did the modeling!) because they are still trying to memorize routes from A to B rather than wandering around, getting oriented to landmarks, so when they have to get from C to B or from B back to A they can do it because they know the neighborhood.
It’s not the curriculum: CPM is good about this, even explicit about it. It’s just taken me this long to figure out that this is what I need to use these materials to teach them how to do. | 487 | 2,269 | {"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-2017-30 | longest | en | 0.971226 |
http://powerpivotforum.com.au/viewtopic.php?f=12&t=503&p=2244 | 1,531,889,576,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676590051.20/warc/CC-MAIN-20180718041450-20180718061450-00628.warc.gz | 290,331,405 | 6,984 | ## Ch 16 Creating a Harvester Calculated Field
A dedicated forum to help people when working through the book "Learn to Write DAX"
Kelly
Posts: 1
Joined: Wed Oct 05, 2016 10:48 pm
### Ch 16 Creating a Harvester Calculated Field
I have followed all of the steps to create the Harvester for % increase but my Total Margin with Selected Increase always calculates a 15% increase--so it is not "harvesting" the selected value. Any ideas?
Harvester.JPG (49.57 KiB) Viewed 2446 times
[Selected Value]=MAX (Increase[Value])
[Total Margin with Selected Increase]=[Total Margin \$] * (100 + [Selected Value])/100
MattAllington
Posts: 947
Joined: Sun May 04, 2014 4:01 pm
Location: Sydney, Australia
### Re: Ch 16 Creating a Harvester Calculated Field
Hi Kelly, sorry I missed your post Last week. Everything I can see looks correct. Is the slicer connected to the pivot table? My guess is that it is not.
Matt Allington is Self Service BI Consultant, Trainer and Author of the book "Supercharge Power BI".
https://exceleratorbi.com.au/power-bi-online-training/
Sarmyles
Posts: 6
Joined: Mon May 30, 2016 7:02 pm
### Re: Ch 16 Creating a Harvester Calculated Field
Matt,
I had the same problem and your solution is correct - the pivot table was not connected. Why does this need to be done manually ?
MattAllington
Posts: 947
Joined: Sun May 04, 2014 4:01 pm
Location: Sydney, Australia
### Re: Ch 16 Creating a Harvester Calculated Field
If you first select a pivot table, then add a slicer (right click on the column in the field list and select "add as slicer") it will automatically be connected. If you have not selected the pivot table and you "insert slicer" from them menu, it will not be connected and you will have to connect it manually. It makes sense actually. If here are 5 pivots in a page and you add a slicer, which ones should be attached? It depends of course and his way you have control.
Matt Allington is Self Service BI Consultant, Trainer and Author of the book "Supercharge Power BI".
https://exceleratorbi.com.au/power-bi-online-training/ | 531 | 2,068 | {"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-2018-30 | latest | en | 0.893302 |
http://kitchentablemath.blogspot.com/2014_02_23_archive.html | 1,490,491,689,000,000,000 | text/html | crawl-data/CC-MAIN-2017-13/segments/1490218189090.69/warc/CC-MAIN-20170322212949-00227-ip-10-233-31-227.ec2.internal.warc.gz | 203,833,655 | 52,941 | kitchen table math, the sequel: 2/23/14 - 3/2/14
## Friday, February 28, 2014
### Debbie at RJ Julia tomorrow morning
From Debbie:
I'll be speaking/q & a'ing tomorrow (March 1 at 11 a.m.) at RJ Julia in Madison, CT. Come say hello if you are in the area.
### Donna Jackson's new(ish) book
The Last Best Cure: My Quest to Awaken the Healing Parts of My Brain and Get Back My Body, My Joy, and My Life
Donna and I have been out of touch way too long!
### Really existing Common Core
Part 1: Help Desk, Common Core edition
Our high school principal explains the centrality of modeling to high school math:
55:23 This is a very important slide and one that you’ll hear me talk about a number of times.
Because modeling, we really look at modeling as the way to really permeate through all of the different levels of mathematics at the high school level. And we really look at it from a standpoint of pedagogy. When we talk about modeling, what we’re really talking about is the conceptual side of mathematics. Recently, and there’s been a shift to a very computational format for teaching mathematics, especially at the high school level. And that’s where we would start to break things down and scaffold them into very fine points. But what we have found is mathematics teachers over the last 10, 15, 20 years, when this pattern was happening, was that students were starting to learn their broader understandings of mathematics. 56:19 There was a big need to pull back and get back to the point of teaching to deeper understanding and to the conceptualization of math, not just about being able to compute the correct answer. So modeling we really look at as the link to be able to do that. It’s the opportunity to create real-life problem-solving situations where students need to understand the conceptualization of what’s going on in the math as well as how it relates to the real world.
Geometry, obviously, is when we start talking about shapes and sizes and the relative position of objects, and statistics and probability gives us the opportunity to start looking at mathematics and creating analysis and really looking into the chances of opportunity and things occurring.
57:07 So again, as I mentioned, modeling becomes a real important focal point for us. And the phrase that we’ve been talking about is it becomes this umbrella for us. It’s the umbrella that brings the whole mathematics curriculum at the high school level together, and a way for us to keep progressing through and thinking about how it matches up. So when we think about constantly naming and reinforcing the work that the students are doing we want to constantly bring them back as well to these broader-scale concepts. 57:39 So this slide and the next slide starts to talk about that even within those conceptual designs that I mentioned before, even within algebra, there’s an aspect of modeling that’s critical and important for them to understand in the algebra as well as the other mathematical concepts within.
Similarly you have functions here, and again, there are pieces of it that we pull out and we understand how do we create real-life conceptualization and contextualization for our students so that when they’re working through this, they understand again not just the specific calculation of an equation or formula but what it really relates to.
Similarly we do the same things in geometry and we do the same things in statistics and probability. Again, for me, this is about teaching to big ideas and perspective. We’ve been talking at the school about deep understanding and I said that would be one of those shifts that we keep coming back to, and I think that that’s really one of the most important messages that we can deliver about the mathematics instruction and how the Common Core starts to create a shift for us.
Irvington UFSD School Board Meeting - February 11th, 2014
This strikes me as fundamentally wrong, but if you guys tell me it's sound, I'll have to revise my view.
My understanding of math, of what math is, is that …. mathematics is not essentially, or even first and foremost, a system for representing empirical reality. The fact that math so powerfully -- and so eternally -- does capture many aspects of empirical reality is, in my view, either a) beside the point, or b) creepy.
Math, as I think of math, has a mathiness that cannot be reduced to modeling; math is a thing unto itself and should be taught as a thing unto itself -- or, at least, students should be made aware of the fact that to a mathematician math is not just a code-writing tool.
(Again, setting aside the possibility that math is just a code-writing tool.)
### "Constructionism"
Constructionism is a philosophy of education in which children learn by doing and making in a public, guided, collaborative process including feedback from peers, not just from teachers. They explore and discover instead of being force fed information, or subjected to a regime of social control as in the Prussian system adopted in the US and elsewhere, sometimes called Instructionism. Constructionist guidance has to be informed by a knowledge of what there is to explore and discover, including our ignorance, and of a variety of approaches that can be used for children at different developmental levels with various degrees of preparation.
More on this topic can be found by exploring Google using keywords such as "constructionism", "education", "philosophy". See for instance openworldlearning, Seymour Papert's website, http://www.papert.org , and the wikipedia article on constructionist learning. Constructionism is implemented on the OLPC XO in the form of collaborative discovery.
"I hear and I forget. I see and I remember. I do and I understand." - Attributed to Confucius.
Constructionism is built on the foundation of Constructivism, the theory of childhood learning created by Jean Piaget, Lev Vygotsky, and many others.
One Laptop Per Child
No fun.
## Thursday, February 27, 2014
### Help Desk, Common Core edition
Two weeks ago, when our high school administrators gave a presentation devoted exclusively to Common Core "shifts" ("shifts," not "curriculum areas") the principal told us that henceforth math will be taught as modeling first and foremost. All math, it seems, in all math courses.
That strikes me as a terrible idea. Dreary, too.
Math for math's sake, math as a liberal art, math as a thing of beauty...math in my district is apparently a vocational art, not a liberal one. Kids are going to be explaining their answers a lot, too. (The explanation we saw opened with the words "We used the rules we have learned about discriminants.")
If you have thoughts, let me know.
## Tuesday, February 25, 2014
### Helicopter parent thread at the Atlantic
The possibly-inevitable helicopter parent thread has erupted at the Atlantic, so if any of you has the time or inclination to leave a comment, I hope you will.
I've just left this one:
I'm Catherine, a 'character' in the book (for the record, I tutored my own son for SAT math & took the test myself, once.)
Reading this passage I see that a fairly important section of the chapter has been omitted, and that is Debbie's attitude toward her son's grades.
The problem wasn't the Bs.
The problem was that her son was sliding by. He was underachieving, as his math teacher says.
Actually, I have a copy of the manuscript - here's the section that appears in the book but not in the excerpt:
"For me–and this was where I parted ways with the school–the issue wasn’t grades. I would have been proud of Ethan’s B’s if the math teacher had bounced in and said, “Ethan’s a hard worker.” But that’s not what he said, and it wasn’t what I was seeing. Ethan was taking the easy path, and the school was in his camp. The administrators thought Ethan, a happy-go-lucky, disorganized middle school boy with ADHD, should determine his own academic goals."
The boy whose parents were told they should be happy with Cs (in high school) is a friend of my family; I contributed his story to the book. That boy also has ADHD and his case was one of very significant underachievement.
With both boys, the school's approach to an underachieving student with ADHD and a 504 plan was to push back against the parents instead of providing the "accommodations" the boys needed to function as well as their peers (and which the school is obligated to provide).
And in both cases, too, the boys ended up transferring to Catholic schools where they did much better without any SPED 'services' at all. (Neither family is Catholic.)
Judging by some of the emails Debbie's been receiving, parents of kids with ADHD seem pretty often to be the target of 'helicopter parent' judgments made by school administrators.
I'm love to know how many parents have this experience.
Debbie has now had several emails from parents with the same story: an underachieving child with ADHD, a school administrator conveying the message that a) parents shouldn't "push" and b) they're the only parents who are pushing.
I'm now wondering how many people with kids on 504 plans are explicitly told, by school personnel, that "letting" their child "fail" is a good motivator for children with ADHD. | 1,978 | 9,244 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2017-13 | longest | en | 0.960021 |
https://www.coursehero.com/file/14309940/PS-5/ | 1,542,382,777,000,000,000 | text/html | crawl-data/CC-MAIN-2018-47/segments/1542039743105.25/warc/CC-MAIN-20181116152954-20181116174954-00484.warc.gz | 867,510,438 | 425,362 | # PS-5 - Spring 2016-Intt 212 Problem Set 5 Please try to...
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Spring 2016-Intt 212 - Problem Set 5 Please try to solve the problems on your own and check your answers with the following ones: End of Chapter 17 problems: 2, 4, 5, 7, 8, 11, 12, 13, 17 2. A tariff is a tax on the consumption of imports. The demand for domestic goods, and thus the level of aggregate demand, will be higher for any level of the exchange rate. This is depicted in Figure 17(6)-1 (below) as a rightward shift in the output market schedule from DD to D D . If the tariff is temporary, this is the only effect, and output will rise even though the exchange rate appreciates as the economy moves from points 0 to 1. If the tariff is permanent, however, the long-run expected exchange rate appreciates, so the asset market schedule shifts to A A . The appreciation of the currency is sharper in this case. If output is initially at full employment, then there is no change in output due to a permanent tariff. Figure 17(6)-1 4. A permanent fall in private aggregate demand causes the DD curve to shift inward and to the left and, because the expected future exchange rate depreciates, the AA curve shifts outward and to the right. These two shifts result in no effect on output, however, for the same reason that a permanent fiscal expansion has no effect on output. The net effect is a depreciation in the nominal exchange rate and, because prices will not change, a corresponding real exchange rate depreciation. A macroeconomic policy response to this event would not be warranted.
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5. Figure 17(6)-2 (below) can be used to show that any permanent fiscal expansion worsens the current account. In this diagram, the schedule XX represents combinations of the exchange rate and income for which the current account is in balance. Points above and to the left of XX represent current account surplus, and points below and to the right represent current account deficit. A permanent fiscal expansion shifts the DD curve to D D and, because of the effect on the long-run exchange rate, the AA curve shifts to A A . The equilibrium point moves from 0, where
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Jill Tulane University ‘16, Course Hero Intern | 742 | 3,334 | {"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-2018-47 | latest | en | 0.910604 |
https://www.studypool.com/questions/267278/Need-help-with-a-Statistic-HW-about-teenage-tobacco-use | 1,480,781,128,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698540975.18/warc/CC-MAIN-20161202170900-00149-ip-10-31-129-80.ec2.internal.warc.gz | 1,018,889,520 | 750,800 | # Statistic HW
SoccerBoss
Category:
Statistics
Price: \$20 USD
Question description
Teenage Tobacco Use: In a random sample of 1200 teenagers, 216 had used tobacco of some form in the last year. The managers of an anti-tobacco campaign want to claim that less than 20% of all teenagers use tobacco. Test their claim at the 0.10 significance level.
(a) What is the sample proportion of teenagers who use tobacco? Round your answer to 3 decimal places.
p̂ = .........................
(b) What is the test statistic? Round your answer to 2 decimal places.
z"p = ..................
(c) What is the P-value of the test statistic? Round your answer to 4 decimal places.
P-value = ...................
AM -vs- PM Height (Raw Data, Software Required):
We want to test the claim that people are taller in the morning than in the evening. Morning height and evening height were measured for 30 randomly selected adults and the difference (morning height) − (evening height) for each adult was recorded in the table below. Use this data to test the claim that on average people are taller in the morning than in the evening. Test this claim at the 0.05 significance level.
(b) What is the test statistic? Round your answer to 2 decimal places.
t-x= ......................
(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.
P-value = .................
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2325 Tutors | 532 | 2,142 | {"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} | 3.234375 | 3 | CC-MAIN-2016-50 | longest | en | 0.802331 |
https://www.intellectualmath.com/how-to-convert-decimals-to-fractions.html | 1,726,839,289,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700652278.82/warc/CC-MAIN-20240920122604-20240920152604-00065.warc.gz | 756,673,675 | 5,497 | # HOW TO CONVERT DECIMALS TO FRACTIONS
To convert a Decimals to a Fraction follow these steps.
• If we see one digit after the decimal, we have to multiply both numerator and denominator of the decimal by 10.
• If we see two digits after the decimal, we have to multiply both numerator and denominator of the decimal by 100.
• In general, based on the number of digits that we have after the decimal, we have to multiply the numerator and denominator by 10n.
Note :
Here n is number of digits after the decimal. Reduce the fraction as much as possible.
Write as a Fraction in Simplest Form :
Problem 1 :
0.3
Solution :
We consider the denominator as 1.
= (0.3)/1
Here the 3 is the tenth place after the decimal point.
So, we have to multiply the numerator and denominator by 10.
= [(0.3)/1) × (10/10)]
= 3/10
Problem 2 :
0.9
Solution :
We consider the denominator as 1.
= 0.9/1
Multiply both numerator and denominator by 10.
= [(0.9)/1) × (10/10)]
= 9/10
Problem 3 :
1.2
Solution :
We consider the denominator as 1.
= 1.2/1
Multiply both numerator and denominator by 10.
= [(1.2)/1) × (10/10)]
= 12/10
= 6/5
Converting the improper fraction to mixed fraction, we get
= 1 1/5
Problem 4 :
2.5
Solution :
We consider the denominator as 1.
= 2.5/1
Multiply both numerator and denominator by 10.
= [(2.5)/1) × (10/10)]
= 25/10
= 5/2
Converting the improper fraction to mixed fraction, we get
= 2 1/2
Problem 5 :
0.02
Solution :
We consider the denominator as 1.
= 0.02/1
Multiply both numerator and denominator by 100.
= [(0.02/1) × (100/100)]
= 2/100
= 1/50
Problem 6 :
0.07
Solution :
We consider the denominator as 1.
= 0.07/1
Multiply both numerator and denominator by 100.
= [(0.07/1) × (100/100)]
= 7/100
Problem 7 :
0.04
Solution :
We consider the denominator as 1.
= 0.04/1
Multiply both numerator and denominator by 100.
= [(0.04/1) × (100/100)]
= 4/100
= 1/25
Problem 8 :
0.125
Solution :
We consider the denominator as 1.
= 0.125/1
Multiply both numerator and denominator by 1000.
= [(0.125/1) × (1000/1000)]
= 125/1000
= 25/200
= 1/8
Write as a Fraction in Simplest Form :
Problem 9 :
0.27
Solution :
We consider the denominator as 1.
= 0.27/1
Multiply both numerator and denominator by 100.
= [(0.27)/1) × (100/100)]
= 27/100
Problem 10 :
0.84
Solution :
We consider the denominator as 1.
= 0.84/1
Multiply both numerator and denominator by 100.
= [(0.84)/1) × (100/100)]
= 84/100
= 42/50
= 21/25
Problem 11 :
0.025
Solution :
We consider the denominator as 1.
= 0.025/1
Multiply both numerator and denominator by 1000.
= [(0.025)/1) × (1000/1000)]
= 25/1000
= 1/40
Problem 12 :
0.275
Solution :
We consider the denominator as 1.
= 0.275/1
Multiply both numerator and denominator by 1000.
= [(0.275)/1) × (1000/1000)]
= 275/1000
= 55/200
= 11/40
Problem 13 :
0.825
Solution :
We consider the denominator as 1.
= 0.825/1
Multiply both numerator and denominator by 1000.
= [(0.825)/1) × (1000/1000)]
= 825/1000
= 165/200
= 33/40
Problem 14 :
0.00005
Solution :
We consider the denominator as 1.
= 0.00005/1
Multiply both numerator and denominator by 100000.
= [(0.00005)/1) × (100000/100000)]
= 5/100000
=1/20000
Problem 15 :
4.08
Solution :
We consider the denominator as 1.
= 4.08/1
Multiply both numerator and denominator by 100.
= [(4.08)/1) × (100/100)]
= 408/100
= 204/50
= 102/25
Converting the improper fraction to mixed fraction, we get
= 4 2/25
## Recent Articles
1. ### Finding Range of Values Inequality Problems
May 21, 24 08:51 PM
Finding Range of Values Inequality Problems
2. ### Solving Two Step Inequality Word Problems
May 21, 24 08:51 AM
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# At a certain moment, the photograph of a string on which a harmonic wave is travelling to right is shown. Then, which of the following is true regarding the velocities of the points$P$,$Q$and $R$ on the string.A. ${v_p}$is upwardsB. ${v_Q} = - {v_R}$C. $\left| {{v_p}} \right| > \left| {{v_Q}} \right| = \left| {{v_R}} \right|$D. ${v_Q} = {v_R}$
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Hint: As we know in this photograph if the rope is to go to right direction then $R$ should go in upward direction and $P$should go in downward and $Q$ should go in upward direction which will help the string to move in right direction and we are saying it by comparing slopes of them.
In this question we are given three points on a string which has to move in the right direction and a harmonic wave is travelling on string. And we know three points on the string are $P$,$Q$and $R$.
As we know if the string has to move in right direction then point $P$ should go in downward direction,
Point $Q$ should go in upward direction and point $R$ should go in upward direction which will help the string to move in the right direction as given in question.
${v_{po\operatorname{int} }} = - v \times slope$,where ${v_{po\operatorname{int} }}$is velocity of any points or particle on string and $v$ is velocity of string.
And if we talk about speeds of points then points $Q$ and $R$ are at the same distance from the y-axis so the velocities of both these will be equal.
And as the slope of $P$ is greater than Q and R so velocity of $P$ will be greater than them. | 455 | 1,676 | {"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} | 4.4375 | 4 | CC-MAIN-2024-26 | latest | en | 0.90926 |
http://oeis.org/A123191 | 1,582,430,385,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875145746.24/warc/CC-MAIN-20200223032129-20200223062129-00432.warc.gz | 114,561,722 | 3,971 | The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.
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A123191 Triangle read by rows: T(n,k) is the coefficient of x^k in the polynomial P[n] defined by P[0]=1, P[1]=x-1, P[n]=(1-x)P[n-1]+xP[n-2] for n>=2. Alternatively, P[n]=-1-(-x)^n-3*Sum((-x)^k,k=1..n-1). 2
1, -1, 1, -1, 3, -1, -1, 3, -3, 1, -1, 3, -3, 3, -1, -1, 3, -3, 3, -3, 1, -1, 3, -3, 3, -3, 3, -1, -1, 3, -3, 3, -3, 3, -3, 1, -1, 3, -3, 3, -3, 3, -3, 3, -1, -1, 3, -3, 3, -3, 3, -3, 3, -3, 1, -1, 3, -3, 3, -3, 3, -3, 3, -3, 3, -1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET 0,5 LINKS FORMULA T(0,0)=1; T(n,n)=(-1)^(n+1) for n>=1; T(n,0)=-1 for n>=1; T(n,k)=(-1)^(k+1)*3 for n>=2, 1<=k<=n-1. G.f.=G(t,x)=(1+2tx-2x)/[(1-x)(1+tx)]. EXAMPLE Triangle starts: 1; -1,1; -1,3,-1; -1,3,-3,1; -1,3,-3,3,-1; -1,3,-3,3,-3,1; MAPLE T:=proc(n, k): if n=0 and k=0 then 1 elif k=n then (-1)^(n+1) elif k=0 then -1 else (-1)^(k+1)*3 fi end: for n from 0 to 12 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form MATHEMATICA p[0, x] = 1; p[1, x] = x - 1; p[k_, x_] := p[k, x] = (1 - x)*p[k - 1, x] + x*p[k - 2, x]; w = Table[CoefficientList[p[n, x], x], {n, 0, 10}]; Flatten[w] CROSSREFS Sequence in context: A269301 A132429 A046540 * A157454 A106255 A143086 Adjacent sequences: A123188 A123189 A123190 * A123192 A123193 A123194 KEYWORD sign,tabl AUTHOR Roger L. Bagula, Oct 03 2006 EXTENSIONS Edited by N. J. A. Sloane, Oct 29 2006 STATUS approved
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Last modified February 22 22:55 EST 2020. Contains 332157 sequences. (Running on oeis4.) | 843 | 1,904 | {"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-2020-10 | latest | en | 0.541205 |
https://byjus.com/jee/how-to-find-equation-of-ellipse-with-foci-and-major-axis/ | 1,632,791,861,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780058589.72/warc/CC-MAIN-20210928002254-20210928032254-00378.warc.gz | 194,805,353 | 149,616 | # How to Find Equation of Ellipse with Foci and Major Axis
When we consider the conic section, an ellipse is an important topic. It is the set of all points in a plane, the sum of whose distances from two fixed points in the plane is a constant. These fixed points are known as foci of the ellipse. The major axis is the line segment passing through the foci of the ellipse. In this article, we will learn how to find the equation of ellipse with foci and major axis.
The distance between the foci is denoted by 2c. The length of the major axis is denoted by 2a and the minor axis is denoted by 2b.
## Steps to Find the Equation of the Ellipse with Foci and Major Axis
1. Find whether the major axis is on the x-axis or y-axis.
2. If major axis is on x-axis then use the equation $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}} = 1$.
3. If major axis is on y-axis then use the equation $\frac{x^{2}}{b^{2}}+\frac{y^{2}}{a^{2}} = 1$.
4. Find ‘a’ from the length of the major axis. Length of major axis = 2a
5. Using the equation c2 = (a2 – b2), find b2.
6. Substitute the values of a2 and b2 in the standard form.
The standard form of the equation of an ellipse with center (h,k) and major axis parallel to x axis is
((x-h)2 /a2)+((y-k)2/b2) = 1
When a>b
Major axis length = 2a
Coordinates of the vertices are (h±a,k)
Minor axis length is 2b
Coordinates of covertices are (h,k±b)
Coordinates of foci are (h±c,k). Also c2= a2-b2
## Solved Examples
Example 1:
Find the equation of the ellipse, whose length of the major axis is 20 and foci are (0, ± 5).
Solution:
Given the major axis is 20 and foci are (0, ± 5).
Here the foci are on the y-axis, so the major axis is along the y-axis.
So the equation of the ellipse is
x2/b2 + y2/a2 = 1
2a = 20
a = 20/2 = 10
a2 = 100
c = 5
c2 = a2 – b2
b2 = a2 – c2 = 102 – 52 = 75
So (x2/75) + y2/100 = 1 is the required equation.
Example 2:
Find the equation of the ellipse whose length of the major axis is 26 and foci (± 5, 0)
Solution:
Given the major axis is 26 and foci are (± 5,0).
Here the foci are on the x-axis, so the major axis is along the x-axis.
So the equation of the ellipse is x2/a2 + y2/b2 = 1
2a = 26
a = 26/2 = 13
a2 = 169
c = 5
c2 = a2 – b2
b2 = a2 – c2 = 132 – 52 = 144
So (x2/169) + y2/144 = 1 is the required equation. | 761 | 2,314 | {"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} | 4.6875 | 5 | CC-MAIN-2021-39 | latest | en | 0.907667 |
https://physics.stackexchange.com/questions/477738/general-relativity-numerically-compute-the-metric-from-the-stress-energy-ten | 1,656,191,535,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103036099.6/warc/CC-MAIN-20220625190306-20220625220306-00543.warc.gz | 501,049,125 | 66,148 | # General Relativity - (numerically) compute the metric from the stress-energy tensor?
I am new to GR and I am having trouble understanding how one goes back and forth between the metric $$g_{\mu\nu}$$ and the stress-energy tensor $$T_{\mu\nu}$$.
First, have a look at the following post. It provides an "easy" method for calculating $$T_{\mu\nu}$$ given a metric $$g_{\mu\nu}$$:
How does one reverse this formula? That is, given a stress-energy tensor $$T_{\mu\nu}$$ (or even more specifically, a distribution of mass-energy $$T_{00}$$), how do you compute $$g_{\mu\nu}$$? Of course it's technically possible to simply expand Einstein's equations by rewriting $$R_{\mu\nu}$$ in terms of $$\Gamma^{\lambda}_{\mu\nu}$$, which can then be expanded in terms of derivatives of $$g_{\mu\nu}$$, but the result would be a large, disgusting sum of gross PDEs. If it is possible to avoid that, I would love to know.
I understand that this is a bit unorthodox, since in most applications, it suffices to simply find $$\Gamma^{\lambda}_{\mu\nu}$$ from $$R_{\mu\nu}$$ in order to derive the equations of motion.
I want to know because, ultimately, I would like to create a Mathematica notebook in which the input would be an arbitrary geometry for the the mass-energy density and it would output the metric. It seems relatively straightforward but I cannot find anything online as a guide.
• Well, by solving EFE. May 3, 2019 at 22:11
• "It seems relatively straightforward" Please don't take this the wrong way, but this statement is as wrong as it gets. Solving the Einstein equations is extremely complicated. If an analytic solution exists, you kinda have to find it by educated guessing. Numerically solving the equations in interesting scenarios has only been possible in the last fifteen years or so. You won't be able to just do it with a Mathematica notebook. May 3, 2019 at 23:17
You can't invert the relation to find $$g_{\mu\nu}$$ from $$T_{\mu\nu}$$. The metric uniquely determines the stress tensor, but not vice versa. For example, the Minkowski metric and the Schwarzschild metric are not equivalent, but both solve $$G_{\mu\nu}=8\pi T_{\mu\nu}=0$$. | 559 | 2,160 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 15, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.21875 | 3 | CC-MAIN-2022-27 | longest | en | 0.945368 |
https://www.kidsacademy.mobi/printable-worksheets/science/physical-science/ | 1,720,910,702,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514517.94/warc/CC-MAIN-20240713212202-20240714002202-00274.warc.gz | 753,954,350 | 69,394 | # Physical Science Worksheets
What do your students know about physical science? If you think they should know more, these physical science worksheets for kids have all you need to teach them. The exercises in these fun worksheets will show children how problems can be solved, and how these solutions come about. Children will also learn about how things work; from how light travels, to how we hear sounds. The short, educative passages in the worksheets will expose your students to a whole new world of learning. To help kids learn even better, put some of the things they learn from these worksheets into practice with simple science experiments.
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## Reversible Irreversible Changes Worksheet
Crack an egg and cook it – once it's done, there's no return to its original state.
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## Simple Machines Inclined Plane Worksheet
This fun worksheet will help them increase their science skills while they have fun.
Simple Machines Inclined Plane Worksheet
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## Physical Science: States of Matter Worksheet
Kids must identify a substance as solid, liquid, or gas to master physical science. Help them understand elements in the world with this engaging worksheet!
Physical Science: States of Matter Worksheet
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## Forms of Energy Worksheet
Forms of Energy Worksheet
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## Matter: Assessment 1 Worksheet
Have your children learn that anything that has weight and takes up space is matter. Examples include buses, tables, people, animals, and more. Use this worksheet to help them identify the objects and circle the soft, red, and small one; the liquid; and the smooth, black, and round one.
Matter: Assessment 1 Worksheet
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## Temperature Patterns Worksheet
Adam has recorded temperatures in his area. Help your child use the data to predict temperatures for one month in each season. Check the box next to the correct temperature for each row in this worksheet. In America, temperatures vary by climate and season - colder in winter, hotter in summer.
Temperature Patterns Worksheet
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## Force and Interactions: Assessment 1 Worksheet
Test your students' knowledge of pushing, pulling, ramps and wind with this worksheet. The first task requires them to identify push or pull pictures. The second asks them to identify a ramp and the third to explain which direction a ball will move when exposed to wind.
Force and Interactions: Assessment 1 Worksheet
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## Safety Sounds Worksheet
Teach your kids about safety. Explain the rules and let them know what sounds to be aware of. Review the worksheet with pictures of objects and ask them to recognize which ones produce safety sounds. Have them check their answers. Doing this will help ensure their safety and that of others.
Safety Sounds Worksheet
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## Force and Interactions: Review 2 Worksheet
Your child can identify force examples by checking the pictures. There are 8 images of kids engaging in activities and objects in motion. Get them to name the activities and objects, or if they know, explain force and interaction.
Force and Interactions: Review 2 Worksheet
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## Light Reflections Worksheet
Teach your students that some objects reflect light and form a reflection. Ask them to name examples, then look at pictures and check off which objects can do this. Have them note how the light bounces off these surfaces, and observe their own reflections.
Light Reflections Worksheet
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## Sink or Float Printable
They'll learn why some things stay on the surface and others sink to the bottom. (80 words)
Sink or Float Printable
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## Natural and Manmade Light Sources Worksheet
Have your child learn about natural and manmade light sources with this fun worksheet! They'll distinguish the sun, fireflies and more as either natural or artificial sources. Brighten up their knowledge with this engaging activity!
Natural and Manmade Light Sources Worksheet
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## Balanced Forces Worksheet
Ready for a fun game? This worksheet will balance the forces so your kids can decide who will win their tug of war! With the right number of kids on each side of the rope, the forces will be equal. Help your little ones decide who will prevail in the game. Ready, set, go!
Balanced Forces Worksheet
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## Force and Interactions: Review 1 Worksheet
See how well your child can identify the different forces. Explain to your child that force is what causes objects to move, such as wind blowing a branch or an object going down a ramp. Ask them to circle images that show a force and assess how well they can identify them.
Force and Interactions: Review 1 Worksheet
Worksheet
## Going up or Down? Worksheet
Young students learn the concept of up and down with this geometry worksheet. They trace lines to identify relative positioning as an object travels. Kids can use position words to describe an object's movement, enhancing their spatial relationship skills - an important geometry foundation.
Going up or Down? Worksheet
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## Light and Sound: Assessment 1 Worksheet
Can your kids name a light source? Challenge them to name the sun and moon, then point out objects they use when the sun sets. Look through the worksheet with them and ask them to identify the light sources. Help them check off the correct answers.
Light and Sound: Assessment 1 Worksheet
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## Engineering a Solution: Comparing Pros and Cons Worksheet
Help our little engineers assist the engineer in making a decision! They will solve the equations using greater than, less than, and equal to, and then decide the best solution for the problem using the pros and cons of each.
Engineering a Solution: Comparing Pros and Cons Worksheet
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## Electric Multiplication Facts Worksheet
Assisting your kids with math homework has no limits. After mastering addition and subtraction, the next step is multiplication. Initially, it can be intimidating. However, with the right tips and worksheets like this one, they'll see it's not so tricky. Show them how multiplying by 1 keeps the number the same. Use the tracing sheet to help them work through multiplication facts.
Electric Multiplication Facts Worksheet
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## Forces Worksheet
Teach your child about forces! Ask them to identify which of six pictures shows push, pull or gravity. Read the words beside each picture and have them circle the correct one. It's a great way to learn about forces; push, pull and gravity!
Forces Worksheet
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## Which Is Brighter? Worksheet
Before the exercise, ask students to recall sources of light. Use this worksheet to explain that the brighter the light source, the more space it can light up. Identify the different light sources in the pictures, then check the brighter light source in each pair. The biggest natural source of light is the sun.
Which Is Brighter? Worksheet
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## Pendulum Experiment Worksheet For 3rd Grade
Time to flex those science muscles! A pendulum's speed depends on its string length. Complete this 3rd grade pendulum experiment worksheet and experiment with a yo-yo at home! Read the description to answer the questions correctly.
Pendulum Experiment Worksheet For 3rd Grade
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## Position and Motion Worksheet
Take a trip to the park and explore motion and position with fun worksheets! Take your child's science knowledge to a whole new level with Kids Academy's grade 2 position and motion worksheets! Explore motion and position with fun worksheets while taking a trip to the park. Strengthen their understanding of physics and how people and objects move through space.
Position and Motion Worksheet
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## Sources of Light Worksheet
Help your child explore sources of light with this printout exercise. Ask them if they know the sun is the reason for day and night. Then point out other common light sources, then work together to guide them through the maze from start to finish.
Sources of Light Worksheet
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## Over or Under? Worksheet
Math for young kids isn't just about numbers and counting, but also spatial concepts like geometry. This worksheet helps students learn "over" and "under" by tracing the movement of caterpillars and butterflies. Downloadable for free, it's an effective teaching tool for early learners.
Over or Under? Worksheet
Worksheet
Learning Skills
## The Importance of Physical Science Worksheets for Children
Physical Science Worksheets are vital tools for teaching children about complex natural phenomena. They facilitate practical learning, making understanding scientific concepts less challenging. These worksheets are designed for students varying from Preschool to Grade 3, providing an engaging and interactive learning experience.
Physical Science Worksheets offer unique learning benefits. They introduce children to scientific principles in a fun, interactive way, enhancing their critical thinking, observing, and problem-solving skills.
They offer an opportunity for independent or group work. This flexibility allows children with different learning strategies to progress at their own pace, while teachers or parents monitor their progress.
Worksheets also provide a fun revision tool, helping children to commit learned concepts to long-term memory. By making revision interactive, children enjoy practicing what they've learned.
Furthermore, these worksheets help develop skills essential for independent learning, such as time management, organization, problem-solving, and critical thinking.
To conclude, Physical Science Worksheets are a crucial learning tool for young learners, providing an interactive medium to grasp scientific concepts, from Preschool through Grade 3. | 1,886 | 9,757 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2024-30 | latest | en | 0.901716 |
https://www.doubtnut.com/question-answer/if-yx-ex-then-d2x-dy2-is-a-ex-b-ex-1-ex3-c-ex-1-ex3-d-1-1-ex3-30342 | 1,624,183,012,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487660269.75/warc/CC-MAIN-20210620084505-20210620114505-00517.warc.gz | 651,843,798 | 70,410 | Class 11
MATHS
Limits And Derivatives
# If y=x+e^x, then (d^2x)/(dy^2) is (a) e^x (b) - e^x/((1+e^x)^3) (c) -e^x/((1+e^x)^3) (d) (-1)/((1+e^x)^3)
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## Latest Questions
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Limits And Derivatives | 457 | 1,002 | {"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-2021-25 | latest | en | 0.456771 |
https://itfeature.com/time-series/time-series-analysis-quiz-4/ | 1,720,985,866,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514638.53/warc/CC-MAIN-20240714185510-20240714215510-00061.warc.gz | 312,578,748 | 35,614 | # Important Time Series Analysis Quiz 4
In this test, the MCQs Time Series Analysis and Forecasting will help to prepare for exams related to statistics lecturer job, and statistical officer job tests. This Time Series Analysis Quiz will help the learner enhance their knowledge in the field of Time Series. Let us start with the Time Series Analysis Quiz with answers.
Online MCQs Time Series Analysis and Forecasting
1. The forecasts on the basis of a time series are:
2. The moving averages in a time series are free from the influence of:
3. Link relatives in a time series remove the influence of
4. The moving average method suffers from:
5. Which of the following is a key step in the ARIMA modeling process?
6. Irregular variations in a time series are caused by:
7. The general decline in sales of a product is attached to the component of the time series:
8. The best method for finding out seasonal variation is:
9. In a Moving Average (MA) model, what does the “order q” represent?
10. Time series analysis helps to:
11. The secular trend is indicative of long-term variation towards:
12. The time series analysis helps to
13. What does seasonality in data refer to?
14. Which of the following is a key limitation of the Moving Average (MA) model?
15. The component of a time series that is attached to short-term variation is:
16. The component of a time series attached to long-term variations is termed as:
17. The linear trend of a time series indicates towards:
18. Residual methods for measuring cycles in a time series consist of:
19. In an ARIMA model, what does the “MA” part of the acronym ARIMA represent?
20. Seasonal variation means the variation occurring within:
Time series analysis deals with the data observed with some time-related units such as a month, days, years, quarters, minutes, etc. Time series data means that data is in a series of particular periods or intervals. Therefore, a set of observations on the values that a variable takes at different times.
### Time Series Analysis Quiz
• The moving averages in a time series are free from the influence of:
• Seasonal variation means the variation occurring within:
• The time series analysis helps to
• The moving average method suffers from:
• The secular trend is indicative of long-term variation towards:
• Link relatives in a time series remove the influence of
• Residual methods for measuring cycles in a time series consist of:
• The component of a time series that is attached to short-term variation is:
• The general decline in sales of a product is attached to the component of the time series:
• The linear trend of a time series indicates:
• The component of a time series attached to long-term variations is termed as:
• Time series analysis helps to:
• Irregular variations in a time series are caused by:
• The best method for finding out seasonal variation is:
• The forecasts on the basis of a time series are:
• What does seasonality in data refer to?
• Which of the following is a key step in the ARIMA modeling process?
• In an ARIMA model, what does the “MA” part of the acronym ARIMA represent?
• Which of the following is a key limitation of the Moving Average (MA) model?
• In a Moving Average (MA) model, what does the “order q” represent?
R and Data Analysis
R FAQs | 711 | 3,311 | {"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} | 3.5625 | 4 | CC-MAIN-2024-30 | latest | en | 0.924185 |
http://sci.tech-archive.net/Archive/sci.electronics.basics/2007-11/msg00387.html | 1,493,542,403,000,000,000 | text/html | crawl-data/CC-MAIN-2017-17/segments/1492917124478.77/warc/CC-MAIN-20170423031204-00621-ip-10-145-167-34.ec2.internal.warc.gz | 353,674,885 | 3,601 | # Re: LED Lumens to Lux conversion?
On Wed, 14 Nov 2007 16:50:37 -0800, TazaTek wrote:
I'm trying to pick out some LED's for to make a 10,000 Lux @ 36 inches
(or 1 meter) LED lamp. My problem is that I'm not quite sure of how
to convert the lumens spec on the LED to the Lux to figure out how
many LED's I need to buy.
I know that Lux = Lumens/ m2 , but I'm not exactly sure of how that
applies to something that is 1 meter away, and would be, say the size
of a small book.
The lux depends upon the size of the spot, and thus the illumination
angle. A wide-angle LED will produce a lower lux figure for the same
lumens.
To determine a rough lux value, divide the lumens figure by the area of
the LED's "spot". E.g. for even illumination over a 90-degree (+/-
45-degree) cone at 1 metre, the spot radius will be 1m*45*pi/180 ~=
785mm, and the area will be ~1.94 square metres, so lux ~= lumens/1.94.
If the "size of a small book" refers to focusing the entire output of
the LED on a small area, then the only factor is the area on which you're
focusing it, not the distance (obviously, you'll need to narrow the angle
as the distance increases to keep the smaller area).
E.g. if you're focusing on a 10cm square, lux = lumens / 0.01, so you
would need 100 lumens to get 10000 lux.
. | 374 | 1,289 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.3125 | 3 | CC-MAIN-2017-17 | latest | en | 0.940363 |
https://newtonexcelbach.com/2012/11/25/automating-chart-scale-limits-update/?like_comment=4917&_wpnonce=eb9680380e&replytocom=4915 | 1,580,141,463,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579251700988.64/warc/CC-MAIN-20200127143516-20200127173516-00344.warc.gz | 575,248,131 | 29,523 | ## Automating chart scale limits – update
I wrote about this function 2 1/2 years ago, and promptly forgot about it, but a few days ago brian provided an answer to a question that was raised shortly after it was first posted, concerning how to apply the function to secondary chart axes.
I have updated the spreadsheet to incorporate brian’s code (slightly modified), and the new version (including full open source code) can be downloaded from: SetScale.xls
I have also added an example of the technique for plotting a function entered as text on the spreadsheet. The procedure is:
• Name cells containing the lower and upper limits for the X range: “xstart” and “xend” respectively.
• Create a range “nsteps” with the value 1000 (or however many steps you would like in your graph)
• Create a name “x” that will contain a rnge of x values, between the specified limits by entering: =xstart+xrange/(nsteps-1)*(ROW(OFFSET(Sheet1!\$A\$1,0,0,nsteps,1))-1) in the name “refers to” box (see picture below).
• Create names “Y1vals” and “Y2vals” with the formulas: =EVALUATE(Sheet1!\$B\$17&”+x*0″) and =EVALUATE(Sheet1!\$B\$18&”+x*0″) (adjusting the cell references to the location of your function(s).
• Create an XY (scatter) graph and set the data ranges to =SetScale.xls!x for the X range for both series and =SetScale.xls!Y1vals and =SetScale.xls!Y2vals for the two Y series
This entry was posted in Charts, Excel, UDFs, VBA and tagged , , , , . Bookmark the permalink.
### 13 Responses to Automating chart scale limits – update
1. jp says:
Doug
When I try and open the file, I get a message
“A formula in this worksheet contains one or more invalid references ….”
Any idea why this might be the case?
Cheers
James
Like
• dougaj4 says:
Probably I uploaded the wrong file, I’ll check now.
Like
• dougaj4 says:
I have uploaded the latest version, but the previous version was working OK on my machine, so that may not fix it.
Note that the ChangeChartAxisScale function only works on Excel 2007 and later (I should have mentioned that)
Like
• jp says:
Doug
Thanks, I am using xl2007.
Don’t worry, I can probably get the gist of it and try and recreate.
Cheers
James
Like
• dougaj4 says:
I’m not getting any warning in Excel 2010. I have uploaded the same file, but saved as .xlsm.
http://www.interactiveds.com.au/software/SetScale.xlsm
Could you let me know if that works.
Like
• dougaj4 says:
I have also just uploaded another one with the names for the Y values amended:
=EVALUATE(Sheet1!\$B\$17&”+Sheet1!x*0″)
=EVALUATE(Sheet1!\$B\$18&”+Sheet1!x*0″)
http://www.interactiveds.com.au/software/SetScale2.xlsm
Like
• jp says:
Sorry Doug … same problem … and with file saved as XLSM … James
Like
• dougaj4 says:
James – I have just downloaded both files from the net and tried them on a different computer running XL 2007 and Windows Vista and had no problem with either of them.
Have you got the latest service pack for Office?
Like
• jp says:
Doug
I am still on XP …
Please don’t worry, I can still understand the post without the detailed workbook.
Cheers
James
Like
2. metroxx says:
Hello, I have the same proble 🙂
Like
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https://derekwadsworth.com/how-many-hours-are-in-4-months/ | 1,632,701,674,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780058222.43/warc/CC-MAIN-20210926235727-20210927025727-00629.warc.gz | 242,309,164 | 4,421 | To transform a month measurement to an hour measurement, multiply the moment by the conversion proportion.
Because one month is equal to 730.485 hrs, you can use this straightforward formula to convert:
You are watching: How many hours are in 4 months
Months and hrs are both systems offered to meacertain time. Keep reading to learn even more about each unit of meacertain.
## Months
One month is a unit of time equal to 1/12 of a year. The month is a unit of time provided on a calendar, and also ranges in size from 28 to 31 days.
Months can be abbreviated as mo; for example, 1 month can be composed as 1 mo.
## Hours
The hour is a duration of time equal to 1/24 of a day or 60 minutes.
The hour is an SI embraced unit for time for usage with the metric system. Hours have the right to be abbreviated as hr; for example, 1 hour deserve to be written as 1 hr.
## Month to Hour Conversion Table
Month dimensions converted to hours Months Hours
1 mo 730.49 hr
2 mo 1,461 hr
3 mo 2,191 hr
4 mo 2,922 hr
5 mo 3,652 hr
6 mo 4,383 hr
7 mo 5,113 hr
8 mo 5,844 hr
9 mo 6,574 hr
10 mo 7,305 hr
11 mo 8,035 hr
12 mo 8,766 hr
13 mo 9,496 hr
14 mo 10,227 hr
15 mo 10,957 hr
16 mo 11,688 hr
17 mo 12,418 hr
18 mo 13,149 hr
19 mo 13,879 hr
20 mo 14,610 hr
21 mo 15,340 hr
22 mo 16,071 hr
23 mo 16,801 hr
24 mo 17,532 hr
25 mo 18,262 hr
26 mo 18,993 hr
27 mo 19,723 hr
28 mo 20,454 hr
29 mo 21,184 hr
30 mo 21,915 hr
31 mo 22,645 hr
32 mo 23,376 hr
33 mo 24,106 hr
34 mo 24,836 hr
35 mo 25,567 hr
36 mo 26,297 hr
37 mo 27,028 hr
38 mo 27,758 hr
39 mo 28,489 hr
40 mo 29,219 hr
Inch Calculator
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https://math.answers.com/Q/What_if_the_difference_between_two_numbers_is_sixteen_three_times_the_larger_number_is_seven_times_the_smaller_what_are_the_numbers | 1,709,350,943,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947475727.3/warc/CC-MAIN-20240302020802-20240302050802-00382.warc.gz | 400,764,603 | 47,267 | 0
# What if the difference between two numbers is sixteen three times the larger number is seven times the smaller what are the numbers?
Updated: 10/18/2022
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Q: What if the difference between two numbers is sixteen three times the larger number is seven times the smaller what are the numbers?
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Yes
### What is the difference between the numbers 2 and 3?
1. The difference of two numbers are the numbers between them. The difference is found by subtracting the smaller number from the larger. In this case, 2 is subtracted from 3 (3-2) with a difference of 1. 3-2=1
212
### How do you figure out the difference between 2 numbers?
subtract the smaller number from the larger number.
221
### What is the difference between 13 and 16?
The difference between 13 and 16 is 3. To find the difference between two numbers subtract the larger number by the smaller number. (16-13=3)
### How do i tell difference between a 318 or 360?
to find the difference between two numbers is to subtract the smaller one from the bigger one, that's 360 - 318 = 42 the difference between 318 and 360 is 42.
### The difference between two numbers is 12 the smaller number is 17 what is the larger number?
The square root of 841
### What is the number halfway between 1410 and 1460?
The difference between the two numbers is 50 - divide that by 2 to get 25, and add the 25 to the smaller number to get 1435.
### What is the difference between the numbers on both sides of the ruler?
One is bigger and the other is smaller! Good luck in your 2nd grade math class
9 on apex
### How can you decide the difference of two positive numbers?
You subtract the smaller from the larger. The difference between 11 and 45 is found by adding negative 11 to positive 45 +45 -11 ----. +34 | 462 | 1,878 | {"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-2024-10 | latest | en | 0.9492 |
http://slideplayer.com/slide/785279/ | 1,547,753,132,000,000,000 | text/html | crawl-data/CC-MAIN-2019-04/segments/1547583659063.33/warc/CC-MAIN-20190117184304-20190117210304-00310.warc.gz | 220,687,791 | 23,911 | # Year 5 Term 2 Unit 10 Day 1.
## Presentation on theme: "Year 5 Term 2 Unit 10 Day 1."— Presentation transcript:
Year 5 Term 2 Unit 10 Day 1
To be able to derive quickly two-digit pairs that total 100
L.O.1 To be able to derive quickly two-digit pairs that total 100 To add several two-digit numbers
Different numbers will be shown
Different numbers will be shown. Your job is to write the complement to 100.
Quickly copy this number grid into your books
Do these: 1. Which number is nearest 100? 2. Which pair of numbers total 100? 3. What is the sum of the top row? 4. What is the sum of the bottom corners? 5. What is the total of the middle column? 6. Add the bottom row. 7. Sum the diagonal from the top left. 8. Total the numbers under 40. 9. Add the two highest numbers. 10. Find the sum of the left-hand column.
L.O.2 To be able to extend written methods to column addition of two integers less than
3587 purchased advance tickets for the final home game of the season at Boston United. A further 675 people bought tickets on the gate. How many people attended the game altogether? Q. What calculation do we need to do to work out the answer to this problem.
This is the COLUMN method of addition:
The calculation is addition. REMEMBER … This is the COLUMN method of addition: = = 8 + 6 =
We’ll do this in the same way but add the most significant digits first.
Q. How many thousands will there be? Q. How many hundreds will there be? Q. How many tens will there be? Q. How many units will there be? Q. What is the total? NOTICE : THE FIGURES ARE IN STRAIGHT COLUMNS!
Keep your digits in straight columns.
Do these using the COLUMN method and starting with the most significant digit. Keep your digits in straight columns. Imelda Marcos bought 2356 pairs of shoes in 1998 and 947 pairs the following year. How many pairs of shoes had she altogether? Prince Charles owns 8894 acres of land in Cornwall and 658 acres in Norfolk. How much land has he? When Granny sold the last of her jewels she made £2486. Her jewel sale last year brought her £828 and the year before that £593. How much did she make altogether?
We’ll do this one together:
Let’s try this but begin with the least significant digit.
8 1 1 0
Do this. Use either method but be prepared to explain your reasoning.
By the end of the lesson the children should be able to :
Use a written column method to add a four-digit to a three-digit number by adding the most significant digit first or the least significant digit first. Discuss, explain and compare methods.
Year 5 Term 2 Unit 10 Day 2
To be able to count on and back in equal steps.
L.O.1 To be able to count on and back in equal steps. To use known number facts and place value for mental addition.
1 We are going to count on and back in steps of 0.1 beginning at different points from 0 to 1
2 We are going to count on and back in steps of 0.1 beginning at different points from 1 to 2 1
2 We are going to count on and back in steps of 0.2 beginning at different points from 0 to 2
5 We are going to count on and back in steps of 0.5 beginning at different points from 0 to 5
Find a pair of numbers which add to : 1, 2, 4, ,
. Find three numbers which make: 6, 7, 10
. Find four numbers which make: 12, 13
L.O.2 To be able to use column written methods to add two or more decimals.
Last week I spent £48.76 at the supermarket.
This week I spent £37.53. How much did I spend altogether? Q. What calculation do we need to carry out? + Q. How could we work this out? Q. What would you estimate the answer to be?
We shall use a similar written method of addition to that used in the last lesson.
Q. Does this answer seem reasonable?
Let’s try this one. We shall begin by adding the least significant digit. Your assistance is required! 14.78 m m Where shall we start?
ESTIMATE B4U CALCULATE You will be given a worksheet to do.
Begin each problem by adding the least significant digit. REMEMBER : ESTIMATE B4U CALCULATE
At the Funfair the rides are priced as follows:
White Knuckle £1.65 Dodgems £0.90 Wall of Death £2.30 Space Wheel £1.25 How much is it to go on each ride once? If I have £4.00 to spend which rides could I go on? How much does it cost to go on the Space Wheel three times and the White Knuckle twice? Granny is afraid of the Dodgems but likes all the other rides. How much does she spend if she goes on each one twice?
By the end of the lesson the children should be able to:
Use a written column method to add two or more decimal numbers; Know that a decimal points should link up under each other; Solve mathematical problems involving money and measures.
Year 5 Term 2 Unit 10 Day 3
L.O.1 To have a rapid recall of multiplication facts.
Let’s say our tables (twice) :
tables and then ask them questions. 5 minutes
Do these: 7 x 8 = 5 x 6 = x 8 = 8 x 9 = 7 x 6 = x 5 = 70 x 8 = 0.5 x 6 = x 8 = 8 x 0.9 = 70 x 60 = x 0.5=
L.O.2 To be able to subtract whole numbers with up to four digits using a written column method.
Q. What calculation must we carry out to work out the answer?
3450 people attend a football match. At half time 867 people leave. How many people stay to the end of the match? Q. What calculation must we carry out to work out the answer? - Q. How could we estimate the answer? Q. What is a sensible estimate? 2500
Remember the complementary addition method used to work out the answer to a problem?
Is the answer ( 2583 ) close to the estimate of ? The jumps are to and from 100’s and 1000’s as this helps make the addition easier.
The sum can be set out using the column method.
3450 - 867 33 to make to make to make to make Answer is c.f. the estimate of 2500
Q. What calculation must we carry out to work out the answer? Q. How could we estimate the answer? Q. What is a sensible estimate? 1500
Remember the complementary addition method used to work out the answer to a problem?
Is the answer ( 1582 ) close to our estimate?
The sum can be set out using the column method.
2340 - 758 42 to make to make to make Answer is c.f. the estimate of 1500
Try these with a partner. Agree an estimate before B4U calculate.
ALL PRISMS
Q. What is the answer to 2583 + 867? 3450 - 867 = 2583 Why?
Q. Is there a connection between addition and subtraction? If so, what is it?
Does the same rule apply here? 30 – 10 = 20 : 20 + 10 = ____
30 – 10 = : = ____ 88 – 36 = : = ____ 45 – 18 = : = ____ 76 – 42 = : = ____
Copy and complete : 2733 – 1609 = : = _____
By the end of the lesson the children should be able to:
Subtract pairs of numbers involving a different number of digits by counting up; Find an estimate and check answers; Use the relationship between addition and subtraction to check answers
Similar presentations | 1,757 | 6,727 | {"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} | 3.921875 | 4 | CC-MAIN-2019-04 | latest | en | 0.910587 |
https://itl.nist.gov/div898/software/dataplot/refman1/auxillar/david.htm | 1,638,451,442,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964362219.5/warc/CC-MAIN-20211202114856-20211202144856-00450.warc.gz | 399,158,753 | 5,988 | Dataplot Vol 1 Vol 2
# DAVID TEST
Name:
DAVID TEST
Type:
Analysis Command
Purpose:
Perform the David, Hartley and Pearson test for univariate outliers from a normal distribution.
Description:
The David, Hartley and Pearson statistic tests whether the minimum and maximum values from a univariate dataset are simultaneously outliers. This test assumes that the data come from an approximately normal distribution.
The test statistic is
$D = \frac{r} {s}$
with $$r$$ and $$s$$ denoting the sample range and sample standard deviation, respectively.
Dataplot supports several methods for deterining the critical values for this test.
1. The ASTM E178-16a standard provides tables for n = 3 to 50 and alpha levels of 0.10, 0.05 and 0.01. Linear interpolation is used for values of n not given in the table. For values of n > 50, the simulation (see below) method is used.
2. The original paper by David contains tables for n = 3 to 1,000 and alpha levels of 0.10, 0.05, 0.025, 0.01 and 0.005. Linear interpolation is used for values of n not given in the table.
3. The David paper suggests the following formula (equation 6 on page 485)
$cv = \sqrt{ \frac{2(n-1)t_{((1-\alpha)/(n(n-1)),n-2)}} {(n-2) + t_{((1-\alpha)/(n(n-1)),n-2)}} }$
with t denoting the percent point function of the t distribution.
4. Critical values can be obtained via simulation.
To specify the method used to compute the critical value, enter one of the following commands (the default is ASTM)
SET DAVID TEST CRITICAL VALUES ASTM
SET DAVID TEST CRITICAL VALUES DAVID
SET DAVID TEST CRITICAL VALUES FORMULA
SET DAVID TEST CRITICAL VALUES SIMULATION
This test is included in the ASTM E178 standard for outliers.
Syntax 1:
DAVID TEST <y> <SUBSET/EXCEPT/FOR qualification>
where <y> is the response variable being tested;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Syntax 2:
MULTIPLE DAVID TEST <y1> ... <yk>
<SUBSET/EXCEPT/FOR qualification>
where <y1> ... <yk> is a list of up to k response variables;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
This syntax performs the David test on <y1>, then on <y2>, and so on. Up to 30 response variables may be specified.
Note that the syntax
MULTIPLE DAVID TEST Y1 TO Y4
is supported. This is equivalent to
MULTIPLE DAVID TEST Y1 Y2 Y3 Y4
Syntax 3:
REPLICATED DAVID TEST <y> <x1> ... <xk>
<SUBSET/EXCEPT/FOR qualification>
where <y> is the response variable;
<x1> ... <xk> is a list of up to k group-id variables;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
This syntax performs a cross-tabulation of <x1> ... <xk> and performs a David test for each unique combination of cross-tabulated values. For example, if X1 has 3 levels and X2 has 2 levels, there will be a total of 6 David tests performed.
Up to six group-id variables can be specified.
Note that the syntax
REPLICATED DAVID TEST Y X1 TO X4
is supported. This is equivalent to
REPLICATED DAVID TEST Y X1 X2 X3 X4
Examples:
DAVID TEST Y1
MULTIPLE DAVID TEST Y1 Y2 Y3
REPLICATED DAVID TEST Y X1 X2
DAVID TEST Y1 SUBSET TAG > 2
Note:
Tests for outliers are dependent on knowing the distribution of the data. The David test assumes that the data come from an approximately normal distribution. For this reason, it is strongly recommended that the David test be complemented with a normal probability test. If the data are not approximately normally distributed, then the David test may be detecting the non-normality of the data rather than the presence of an outlier.
Note:
You can specify the number of digits in the David output with the command
SET WRITE DECIMALS <value>
Note:
The DAVID TEST command automatically saves the following parameters:
STATVAL = the value of the test statistic STATDCF = the CDF value of the test statistic PVALUE = the p-value of the test statistic CUTOFF80 = the 80 percent point of the reference distribution CUTOFF90 = the 90 percent point of the reference distribution CUTOFF95 = the 95 percent point of the reference distribution CUTOF975 = the 97.5 percent point of the reference distribution CUTOFF99 = = the 99 percent point of the reference distribution
The STATCDF and PVALUE are only saved when the simulation method is used to obtain critical values. If the ASTM method is used to obtain critical values, the CUTOFF80 and CUTOF975 values are not saved. When the DAVID method is used to obtain critical values, the CUTOFF80 value is not saved.
If the MULTIPLE or REPLICATED option is used, these values will be written to the file "dpst1f.dat" instead.
Note:
In addition to the DAVID TEST command, the following commands can also be used:
LET A = DAVID TEST Y
LET A = DAVID TEST CDF Y
LET A = DAVID TEST PVALUE Y
LET A = DAVID TEST MINIMUM INDEX Y
LET A = DAVID TEST MAXIMUM INDEX Y
LET ALPHA = <value>
LET A = DAVID TEST CRITICAL VALUE Y
The DAVID TEST, DAVID TEST CDF, and DAVID TEST PVALUE return the values of the test statistic, the cdf of the test statistic and the pvalue of the test statistic, respectively. For the DAVID TEST CDF and DAVID TEST PVALUE commands, the simulation method will be used. Otherwise, the method specified by the SET DAVID TEST CRITICAL VALUE command will be used.
The DAVID TEST MINIMUM INDEX and DAVID TEST MAXIMUM INDEX return the row index of the minimum and maximum values of the response variable, respectively.
The DAVID TEST CRITICAL VALUE returns the critical value for the specified value of ALPHA. If ALPHA is not specified, it will be set to 0.05. Note that if the ASTM or DAVID methods are specified for the critical values, only a few select values for alpha are supported (0.01, 0.05 and 0.10 for ASTM and 0.005, 0.01, 0.025, 0.05 and 0.10 for DAVID).
In addition to the above LET command, built-in statistics are supported for about 25 different commands (enter HELP STATISTICS for details).
Default:
The ASTM method is used to obtain critical values
Synonyms:
None
Related Commands:
GRUBBS TEST = Perform the Grubbs outlier test. TIETJEN-MOORE TEST = Perform a Tietjen-Moore outlier test. EXTREME STUDENTIZED DEVIATE TEST = Perform a extreme studentized deviate outlier test. DIXON TEST = Perform a Dixon outlier test. SKEWNESS TEST = Perform the skewness outlier test. KURTOSIS OUTLIER TEST = Perform the kurtosis outlier test. GOODNESS OF FIT TEST = Perform a goodness of fit test (Anderson-Darling, Kolmogorov-Smirnov, chi-square, PPCC) WILKS SHAPIRO NORMALITY TEST = Perform a Wilks Shapiro normality test. HISTOGRAM = Generate a histogram. PROBABILITY PLOT = Generates a probability plot. BOX PLOT = Generate a box plot.
Reference:
David, Hartley, and Pearson (1954), "The Distribution of the Ratio, in a Single Normal Sample, of Range to Standard Deviation", Biometrika, Vol. 41, pp. 482-493.
E178 - 16A (2016), "Standard Practice for Dealing with Outlying Observations", ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, USA.
Applications:
Outlier Detection
Implementation Date:
2019/10
Program:
. Step 1: Read the data - example from ASTM E178 standard
.
-1.40
-0.44
-0.30
-0.24
-0.22
-0.13
-0.05
0.06
0.10
0.18
0.20
0.39
0.48
0.63
1.01
end of data
.
. Step 2: Perform the DAVID TEST
.
set write decimals 3
set david test critical values astm
david test y
set david test critical values david
david test y
set david test critical values formula
david test y
set david test critical values simulation
david test y
The following output is generated
THE FORTRAN COMMON CHARACTER VARIABLE DAVITEST HAS JUST BEEN SET TO ASTM
David, Hartley, Pearson Test for Outliers: Simultaneous Test
for Minimum and Maximum (Assumption: Normality)
Response Variable: Y
H0: The minimum and maximum are not
both outliers
Ha: Both the minimum and maximum are
outliers
Potential minimum outlier value tested: -1.400
Potential maximum outlier value tested: 1.010
Summary Statistics:
Number of Observations: 15
Sample Minimum: -1.400
ID for Sample Minimum: 1
Sample Maximum: 1.010
ID for Sample Maximum: 15
Sample Mean: 0.018
Sample SD: 0.551
Sample Range: 2.410
David Test Statistic Value: 4.374
Conclusions (Upper 1-Tailed Test)
-------------------------------------------------------------
Alpha CDF Statistic Critical Value Conclusion
-------------------------------------------------------------
10% 90% 4.374 4.025 Reject H0
5% 95% 4.374 4.171 Reject H0
1% 99% 4.374 4.435 Accept H0
Critical Values Based on ASTM E-178 Tables
THE FORTRAN COMMON CHARACTER VARIABLE DAVITEST HAS JUST BEEN SET TO DAVI
David, Hartley, Pearson Test for Outliers: Simultaneous Test
for Minimum and Maximum (Assumption: Normality)
Response Variable: Y
H0: The minimum and maximum are not
both outliers
Ha: Both the minimum and maximum are
outliers
Potential minimum outlier value tested: -1.400
Potential maximum outlier value tested: 1.010
Summary Statistics:
Number of Observations: 15
Sample Minimum: -1.400
ID for Sample Minimum: 1
Sample Maximum: 1.010
ID for Sample Maximum: 15
Sample Mean: 0.018
Sample SD: 0.551
Sample Range: 2.410
David Test Statistic Value: 4.374
Conclusions (Upper 1-Tailed Test)
-------------------------------------------------------------
Alpha CDF Statistic Critical Value Conclusion
-------------------------------------------------------------
10% 90% 4.374 4.020 Reject H0
5% 95% 4.374 4.170 Reject H0
2.5% 97.5% 4.374 4.290 Reject H0
1% 99% 4.374 4.430 Accept H0
0.5% 99.5% 4.374 4.530 Accept H0
Critical Values Based on David Tables
THE FORTRAN COMMON CHARACTER VARIABLE DAVITEST HAS JUST BEEN SET TO FORM
David, Hartley, Pearson Test for Outliers: Simultaneous Test
for Minimum and Maximum (Assumption: Normality)
Response Variable: Y
H0: The minimum and maximum are not
both outliers
Ha: Both the minimum and maximum are
outliers
Potential minimum outlier value tested: -1.400
Potential maximum outlier value tested: 1.010
Summary Statistics:
Number of Observations: 15
Sample Minimum: -1.400
ID for Sample Minimum: 1
Sample Maximum: 1.010
ID for Sample Maximum: 15
Sample Mean: 0.018
Sample SD: 0.551
Sample Range: 2.410
David Test Statistic Value: 4.374
Conclusions (Upper 1-Tailed Test)
-------------------------------------------------------------
Alpha CDF Statistic Critical Value Conclusion
-------------------------------------------------------------
20% 80% 4.374 3.875 Reject H0
10% 90% 4.374 4.034 Reject H0
5% 95% 4.374 4.173 Reject H0
2.5% 97.5% 4.374 4.295 Reject H0
1% 99% 4.374 4.435 Accept H0
0.5% 99.5% 4.374 4.527 Accept H0
Critical Values Based on Formula
THE FORTRAN COMMON CHARACTER VARIABLE DAVITEST HAS JUST BEEN SET TO SIMU
David, Hartley, Pearson Test for Outliers: Simultaneous Test
for Minimum and Maximum (Assumption: Normality)
Response Variable: Y
H0: The minimum and maximum are not
both outliers
Ha: Both the minimum and maximum are
outliers
Potential minimum outlier value tested: -1.400
Potential maximum outlier value tested: 1.010
Summary Statistics:
Number of Observations: 15
Sample Minimum: -1.400
ID for Sample Minimum: 1
Sample Maximum: 1.010
ID for Sample Maximum: 15
Sample Mean: 0.018
Sample SD: 0.551
Sample Range: 2.410
David Test Statistic Value: 4.374
CDF Value: 0.986
P-Value 0.014
Conclusions (Upper 1-Tailed Test)
-------------------------------------------------------------
Alpha CDF Statistic Critical Value Conclusion
-------------------------------------------------------------
20% 80% 4.374 3.842 Reject H0
10% 90% 4.374 4.021 Reject H0
5% 95% 4.374 4.166 Reject H0
2.5% 97.5% 4.374 4.296 Reject H0
1% 99% 4.374 4.428 Accept H0
0.5% 99.5% 4.374 4.523 Accept H0
Critical Values Based on 50,000 Simulations
NIST is an agency of the U.S. Commerce Department.
Date created: 01/22/2020
Last updated: 01/22/2020 | 3,363 | 13,628 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.921875 | 3 | CC-MAIN-2021-49 | latest | en | 0.758822 |
https://studylib.net/doc/18031413/current-carrying-conductors-objective | 1,603,509,770,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107881640.29/warc/CC-MAIN-20201024022853-20201024052853-00453.warc.gz | 556,383,594 | 13,450 | # Current Carrying Conductors Objective
```Current Carrying Conductors
chapter 11
lesson 2
Objective
You will be able to describe the
interactions of the magnetic fields in
conductors.
Ampere investigated the interaction
between two current-carrying wires
parallel to each other.
How would these magnetic fields react in
the wires shown, with current indicated by
the letter I?
Definition of an Ampere
If two wires, each one meter long and one meter
apart, carry current so that the force between
the two wires is 2.00 x 10-7 N, the current in each
wire is one ampere.
Magnetic Fields in Solenoids (coils)
When current flows through each loop of wire in a
coil a magnetic field is set up in such a way that it
makes the coil act like a single bar magnet.
Second Left Hand Rule
Fingers curl around the coil in the direction of the
current flow.
Outstretched thumb points to the end of the coil that
acts as the north end of a fixed magnet.
Electromagnets
A solenoid can be made to be a much stronger
magnet by placing a ferromagnetic material
(usually steel) inside the coil.
Electromagnets have many uses.
Magnetizing ferromagnetic material
Bells
Relay switches
Electric Bell
Railguns
Repelling magnetic fields accelerate projectile
Watch this | 304 | 1,244 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2020-45 | latest | en | 0.900758 |
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# 4.2.12 classwork monday
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### 4.2.12 classwork monday
1. 1. April 2 is International Childrens Book Day. Pretend that you are achildrens book that has been sitting on a library shelf for weekswithout being checked out. What would you say to convincesomeone to check you out? Monday April 2, 2012 Linder Johnny Ryan Andres Angel Ramon David Natalie Carlos Adolfo Gia Emma Cameron Matthew Cincere Joshua Brianna Alan G Alan R Elizabeth Ricardo Max Brian Mitzy Jose Nyashia Sualee Christopher Roxana Christian Joey Massire
2. 2. Morning WritingNickelodeon, the cable TVchannel for kids, debutedon this date in 1979.Imagine that you havebeen asked to create thenext new television show forthe network. Describe whatyour show would be aboutand what would make itsuccessful. Write neatly, skipping a line, and use looseleaf (lined) paper. Hand in once you are finished. The work will be graded.
3. 3. Reading Hurricanes (p. 465)GenreInformationalNonfiction Presentsfacts about realpeople, things,places, or events.Read to Find OutHow does a tropical storm become a category 5hurricane?
5. 5. Reading Hurricanes (p. 465)Comprehension CheckThink and CompareAnswer questions 1 5. Make sure you writethe questions and answer using fullsentences.
6. 6. Reading Suspense (p. 479) Reading Homework Practice book, page 137 Study for quiz
7. 7. Math Explore Subtracting Fractions with Unlike Denominators (p. 260)How to Subtrac Fractions with UnlikeDenominators:Step 1Find the Least CommonDenominator (LCD) of thefractions.Step 2Rename the fractions withthe LCDStep 3Subtract the numerators.Step 4Simplify.
8. 8. Math Explore Subtracting Fractions with Unlike Denominators (p. 258)PracticeSubtract.Exercise 5 12 on page 261
9. 9. Math Explore Subtracting Fractions with Unlike Denominators (p. 258) Math Homework Practice book, page 56
10. 10. Spelling Test
11. 11. Spelling Pretest1. distance 11. assistance2. importance 12. ignorance3. balance 13. brilliance4. attendance 14. ambulance5. absence 15. residence6. performance 16. radiance7. dependence 17. resistance8. substance 18. reluctance9. disturbance 19. persistence10. appearance 20. hesitance
12. 12. Spelling Pretest Spelling Homework Spelling words five times each
13. 13. Language Arts Quiz
14. 14. Science How Are Electricity and Magnetism Related? (p. 512)Class Work• Read pages 514518• Vocabulary Words definition• Questions 16 on page 519HomeworkMain Idea & Details questions:• page 515• page 517• page 518Write questions in your notebook
15. 15. Book of the Month Henrys Freedom BoxEssayWrite a one pagesummary essay andsupporting details.Write neatly and inscript. Use looseleafpaper. Skip a line.
16. 16. Homework Summary Monday, April 2, 2012Reading1. Practice book, page 1372. Study for quizMath1. Practice book, page 56Spelling1. Spelling words five times eachScience1. Main Idea & Details questions on page 515, 517, 518
17. 17. Range: Mode:7 Median: Mean: Reward 10 Pizza Party 89 Wheel of Fun 7 Spelling 6 BrainPOP 45 Class Work 23 Silent Snack 1 No Snack
18. 18. Attachments imgres 948869 | 971 | 3,468 | {"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-2016-22 | latest | en | 0.836014 |
http://www.jiskha.com/display.cgi?id=1363803276 | 1,498,320,589,000,000,000 | text/html | crawl-data/CC-MAIN-2017-26/segments/1498128320264.42/warc/CC-MAIN-20170624152159-20170624172159-00477.warc.gz | 546,184,029 | 5,450 | # Pre-Algebra
posted by .
1. What data are represented by the stem-and-leaf plot below?
3 | 7 8 9
4 | 1 3 7
5 | 2 4
Key: 4 | 1 means 41
a. 37, 38, 39, 41, 43, 47, 52, 54
b. 73, 83, 93, 14, 34, 74, 25, 45
c. 7, 8, 9, 1, 3, 7, 2, 4
d. 37, 38, 39, 14, 34, 74, 25, 45
2. Find the mode and the median of the data in the stem-and-leaf plot below.
5 | 4 4 8
6 | 0 3 5
7 | 3 4 6
8 | 2 5
9 | 7 8
Key: 6 | 3 means 63
a. no mode; 73
b. 63; 73.5
c. 54; 73
d. no mode; 73.5
3. The stem-and-leaf plot shows the number of fish that were caught by several ships in a fishing fleet. How many ships caught 50 fish or fewer?
Stem Leaves
__________________________________
3 0 3 3 5 6
4 0 2 4 5 8 9 9
5 0 1 2 4
key: 2 | 4 means 24
a. 12
b. 16
c. 14
d. 13
1 c
2 d
3 a
• Pre-Algebra -
• Pre-Algebra -
You need to develop some patience and wait for some REAL math teachers to find this.
Stop with the extra posts ... they'll skip your question because they'll think it's been answered!!
• Pre-Algebra -
you have no idea what your talking about. You also have no idea how long she's been waiting for an answer. ^^
• Pre-Algebra -
^^^And you have no idea that this question was posted in 2013
• Pre-Algebra -
lol fail
....dang just need that 1 answe about the ships caught 50 fish
• Pre-Algebra -
Lesson 4: Unit 3, Grade 8 Steam and leaf plots quiz.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The questions:
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1. What data are represented by the stem-and-leaf plot below?
Three rows of numbers are shown.
The key shows that 4 vertical line 1 means 41.
Row 1 is 3 vertical line 7 8 9
Row 2 is 4 vertical line 1 3 7
Row 3 is 5 vertical line 2 4
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2. Find the mode and the median of the data in the stem-and-leaf plot below.
Five rows of numbers of numbers are shown.
Row 1 is 5 vertical line 4 4 8
Row 2 is 6 vertical line 0 3 5
Row 3 is 7 vertical line 3 4 6
Row 4 is 8 vertical line 2 5
Row 5 is 9 vertical line 7 8
Label at bottom reads "Key: 6 vertical line 3 means 63"
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
3. The stem-and-leaf plot shows the number of cans of food collected by various students for a food drive. How many students collected more than 43 cans?
There are 3 rows and 2 columns in the stem and leaf plot. The first columns is titled Stem. The second column is titled leaves.
First row: stem 3 and leaves 0 1 1 1 4 4 4
second row: stem 4 and leaves 0 1 3 4 4 5
third row: stem 5 and leaves 0 3 3 6 8
key: 3 | 5 means 35
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
4. Make a histogram for drivers’ ages using the data from the table below.
Drivers' Ages
Age Frequency
17–19 8
20–22 7
23–25 9
26–28 4
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
5. The numbers below represent the scores on a science test. Graph the data in a line plot.
58, 55, 54, 61, 56, 54, 61, 55, 53, 54
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
6. Find the mean of the following data set:
25, 30, 20, 20, 25, 35, 35, 10
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
7. The stem-and-leaf plot shows the number of fish that were caught by several ships in a fishing fleet. How many ships caught 50 fish or fewer?
The stem and leaf plot is shown in two columns. The first column is titled Stem. The second column is titled Leaves.
First row Stem 3 Leaves 0 3 3 5 6
Second row Stem 4 Leaves 0 2 4 5 8 9 9
Third Row stem 5 Leaves 0 1 2 4
key: 2 | 4 means 24
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Note: the 8th one is a written response but if you search for it you should be able to find it.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1) 37, 38, 39, 41, 43, 47, 52, 54
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2) 54; 73
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
3) 8
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
4) the third one... its a graph. the 17-19 one reaches up to 8 and 20-22 reaches up to 7, between 6 and 8. 23-25 reaches 9, between 8 and 10. 26-28 reaches up to 4.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
5) this line plot has 7 xs between 52 and 57 and 3 xs between 57 and 62. they do NOT have xs above the numbers.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
6) 25
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
7) 13
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
good luck! oh, and if you want to thank me, you could follow me on Instagram first on @mischievous_mc and dm me for confirmation before I give you the account I want you to follow me on. thank you~ also, my mom took my phone so I might not be able to message anyone back for a while. fml | 1,462 | 4,793 | {"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} | 3.890625 | 4 | CC-MAIN-2017-26 | latest | en | 0.879058 |
https://www.jiskha.com/display.cgi?id=1165371586 | 1,502,913,070,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886102393.60/warc/CC-MAIN-20170816191044-20170816211044-00060.warc.gz | 761,624,837 | 4,645 | # physics
posted by .
1- a pipe of diamter 1cm carreiers water flowing at 1m/s. the end of the pipe is bplugged and there is a small holeon the top as shown which is 1mm diameter. How high does the water go?
*=hole
()____________*___()
2. you're indoors, with a door 1m wide and 2.5m high. the wind blows past the door at 1 m /s. what is the net force on the door and its direction? the density of air is 1.2kh/m^3.
You look at a faucent and notice that the strema narrows as it falls. Suppose that the initial water speed is v1 and the initial area of the water faucent opening is A1. Findd the area of the water stream when it has fallen a distance H. The density of water is 1kg/liter and 1 liter is a volume of a cuber w. sides 0.1m.
4- a balooon filled w. helium (density 0.1785 g/L) see previous question for desnity of air and what a liter is). Assuming a baloon of radius 10cm and ignoring the mass of the baloon how much weight could the baloon lift?
You would get faster responses if you posted questions one at a time, and showed some of your work.
(1) Since the pipe is blocked at the end and the hole is 1/10 the pipe diameter, the velocity of the water leaving the hole must be 100 times a m/s, or 100 m/s. That seems very high to me. Get the height H by setting the kinetic energy leaving the hole equal to the potential energy increase at height H:
V = sqrt (2 g H)
Use the bernoulli equation to get the pressure differential bwtween the two sides of the door. The pressure will be lower on the outside where the wind is blowing by. The pressure difference is
(1/2) (density) V^2.
Multiply that by the door area for the force, which will be outward
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https://www.gradesaver.com/textbooks/math/algebra/intermediate-algebra-6th-edition/chapter-1-section-1-4-properties-of-real-numbers-and-algebraic-expressions-exercise-set-page-39/64 | 1,553,520,979,000,000,000 | text/html | crawl-data/CC-MAIN-2019-13/segments/1552912203991.44/warc/CC-MAIN-20190325133117-20190325155117-00273.warc.gz | 776,757,370 | 12,880 | ## Intermediate Algebra (6th Edition)
$(9y+x)+3z$
The associative property holds that $(a+b)+c=a+(b+c)$, where a, b, and c are real numbers. In this example, we can set $a+(b+c)=9y+(x+3z)$. So, $a=9y$, $b=x$, and $c=3z$. Therefore, the other side of this equation is $(a+b)+c=(9y+x)+3z$. | 107 | 288 | {"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} | 4.1875 | 4 | CC-MAIN-2019-13 | latest | en | 0.704596 |
https://www.fel.cvut.cz/en/education/bk/predmety/43/55/p4355206.html | 1,590,501,564,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347390758.21/warc/CC-MAIN-20200526112939-20200526142939-00309.warc.gz | 702,405,503 | 7,868 | # Subject description - BE5B01MA1
Summary of Study | Summary of Branches | All Subject Groups | All Subjects | List of Roles | Explanatory Notes Instructions
BE5B01MA1 Calculus 1
Roles:P Extent of teaching:4P+2S
Department:13101 Language of teaching:EN
Guarantors:Vivi P. Completion:Z,ZK
Lecturers:Gil Dantas S. Credits:7
Tutors:Gil Dantas S. Semester:Z
Anotation:
It is an introductory course to calculus of functions of one variable. It starts with limit and continuity of functions, derivative and its geometrical meaning and properties, graphing of functions. Then it covers indefinite integral, basic integration methods and integrating rational functions, definite integral and its applications. It concludes with introduction to Taylor series.
Course outlines:
1 The real line, elementary functions and their graphs, shifting and scaling. 2 Limits and continuity, tangent, velocity, rate of change. 3 Derivative of functions, properties and applications. 4 Mean value theorem, L'Hospital's rule. 5 Higher derivatives, Taylor polynomial. 6 Local and global extrema, graphing of functions. 7 Indefinite integral, basic integration methods. 8 Integration of rational functions, more techniques of integration. 9 Definite integral, definition and properties, Fundamental Theorems of Calculus. 10 Improper integrals, tests for convergence. Mean value Theorem for integrals, applications. 11 Sequences of real numbers, numerical series, tests for convergence. 12 Power series, uniform convergence, the Weierstrass test. 13 Taylor and Maclaurin series.
Exercises outline:
1 The real line, elementary functions and their graphs, shifting and scaling. 2 Limits and continuity, tangent, velocity, rate of change. 3 Derivative of functions, properties and applications. 4 Mean value theorem, L'Hospital's rule. 5 Higher derivatives, Taylor polynomial. 6 Local and global extrema, graphing of functions. 7 Indefinite integral, basic integration methods. 8 Integration of rational functions, more techniques of integration. 9 Definite integral, definition and properties, Fundamental Theorems of Calculus. 10 Improper integrals, tests for convergence. Mean value Theorem for integrals, applications. 11 Sequences of real numbers, numerical series, tests for convergence. 12 Power series, uniform convergence, the Weierstrass test. 13 Taylor and Maclaurin series.
Literature:
1 M. Demlová, J. Hamhalter: Calculus I. ČVUT Praha, 1994 2 P. Pták: Calculus II. ČVUT Praha, 1997.
http://math.feld.cvut.cz/vivi/
Requirements:
http://math.feld.cvut.cz/vivi/MA12015.pdf
Webpage:
http://math.feld.cvut.cz/vivi/
Subject is included into these academic programs:
Program Branch Role Recommended semester BEECS Common courses P 1 BPEECS_2018 Common courses P 1
Page updated 26.5.2020 14:51:58, semester: Z,L/2020-1, Z,L/2019-20, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336) | 750 | 2,984 | {"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} | 3.515625 | 4 | CC-MAIN-2020-24 | latest | en | 0.759424 |
https://docs.pymc.io/en/v3/api/distributions/continuous.html | 1,652,713,176,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662510138.6/warc/CC-MAIN-20220516140911-20220516170911-00108.warc.gz | 277,707,234 | 16,960 | Continuous¶
Uniform(name, *args, **kwargs) Continuous uniform log-likelihood. Flat(name, *args, **kwargs) Uninformative log-likelihood that returns 0 regardless of the passed value. HalfFlat(name, *args, **kwargs) Improper flat prior over the positive reals. Normal(name, *args, **kwargs) Univariate normal log-likelihood. TruncatedNormal(name, *args, **kwargs) Univariate truncated normal log-likelihood. HalfNormal(name, *args, **kwargs) Half-normal log-likelihood. SkewNormal(name, *args, **kwargs) Univariate skew-normal log-likelihood. Beta(name, *args, **kwargs) Beta log-likelihood. Kumaraswamy(name, *args, **kwargs) Kumaraswamy log-likelihood. Exponential(name, *args, **kwargs) Exponential log-likelihood. Laplace(name, *args, **kwargs) Laplace log-likelihood. AsymmetricLaplace(name, *args, **kwargs) Asymmetric-Laplace log-likelihood. StudentT(name, *args, **kwargs) Student's T log-likelihood. HalfStudentT(name, *args, **kwargs) Half Student's T log-likelihood Cauchy(name, *args, **kwargs) Cauchy log-likelihood. HalfCauchy(name, *args, **kwargs) Half-Cauchy log-likelihood. Gamma(name, *args, **kwargs) Gamma log-likelihood. InverseGamma(name, *args, **kwargs) Inverse gamma log-likelihood, the reciprocal of the gamma distribution. Weibull(name, *args, **kwargs) Weibull log-likelihood. Lognormal ChiSquared(name, *args, **kwargs) $$\chi^2$$ log-likelihood. Wald(name, *args, **kwargs) Wald log-likelihood. Pareto(name, *args, **kwargs) Pareto log-likelihood. ExGaussian(name, *args, **kwargs) Exponentially modified Gaussian log-likelihood. VonMises(name, *args, **kwargs) Univariate VonMises log-likelihood. Triangular(name, *args, **kwargs) Continuous Triangular log-likelihood Gumbel(name, *args, **kwargs) Univariate Gumbel log-likelihood Rice(name, *args, **kwargs) Rice distribution. Logistic(name, *args, **kwargs) Logistic log-likelihood. LogitNormal(name, *args, **kwargs) Logit-Normal log-likelihood. Interpolated(name, *args, **kwargs) Univariate probability distribution defined as a linear interpolation of probability density function evaluated on some lattice of points.
A collection of common probability distributions for stochastic nodes in PyMC.
class pymc3.distributions.continuous.AsymmetricLaplace(name, *args, **kwargs)
Asymmetric-Laplace log-likelihood.
The pdf of this distribution is
$\begin{split}{f(x|\\b,\kappa,\mu) = \left({\frac{\\b}{\kappa + 1/\kappa}}\right)\,e^{-(x-\mu)\\b\,s\kappa ^{s}}}\end{split}$
where
$s = sgn(x-\mu)$
Support $$x \in \mathbb{R}$$ Mean $$\mu-\frac{\\\kappa-1/\kappa}b$$ Variance $$\frac{1+\kappa^{4}}{b^2\kappa^2 }$$
Parameters
b: float
Scale parameter (b > 0)
kappa: float
Symmetry parameter (kappa > 0)
mu: float
Location parameter
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logp(value)
Calculate log-probability of Asymmetric-Laplace distribution at specified value.
Parameters
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple values are desired the values must be provided in a numpy array or theano tensor
Returns
TensorVariable
random(point=None, size=None)
Draw random samples from this distribution, using the inverse CDF method.
Parameters
point: dict, optional
Dict of variable values on which random values are to be conditioned (uses default point if not specified).
size:int, optional
Desired size of random sample (returns one sample if not specified).
Returns
array
class pymc3.distributions.continuous.Beta(name, *args, **kwargs)
Beta log-likelihood.
The pdf of this distribution is
$f(x \mid \alpha, \beta) = \frac{x^{\alpha - 1} (1 - x)^{\beta - 1}}{B(\alpha, \beta)}$
Support $$x \in (0, 1)$$ Mean $$\dfrac{\alpha}{\alpha + \beta}$$ Variance $$\dfrac{\alpha \beta}{(\alpha+\beta)^2(\alpha+\beta+1)}$$
Beta distribution can be parameterized either in terms of alpha and beta or mean and standard deviation. The link between the two parametrizations is given by
\begin{align}\begin{aligned}\begin{split}\alpha &= \mu \kappa \\ \beta &= (1 - \mu) \kappa\end{split}\\\text{where } \kappa = \frac{\mu(1-\mu)}{\sigma^2} - 1\end{aligned}\end{align}
Parameters
alpha: float
alpha > 0.
beta: float
beta > 0.
mu: float
Alternative mean (0 < mu < 1).
sigma: float
Alternative standard deviation (0 < sigma < sqrt(mu * (1 - mu))).
Notes
Beta distribution is a conjugate prior for the parameter $$p$$ of the binomial distribution.
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logcdf(value)
Compute the log of the cumulative distribution function for Beta distribution at the specified value.
Parameters
value: numeric
Value(s) for which log CDF is calculated.
Returns
TensorVariable
logp(value)
Calculate log-probability of Beta distribution at specified value.
Parameters
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple values are desired the values must be provided in a numpy array or theano tensor
Returns
TensorVariable
random(point=None, size=None)
Draw random values from Beta distribution.
Parameters
point: dict, optional
Dict of variable values on which random values are to be conditioned (uses default point if not specified).
size: int, optional
Desired size of random sample (returns one sample if not specified).
Returns
array
class pymc3.distributions.continuous.Cauchy(name, *args, **kwargs)
Cauchy log-likelihood.
Also known as the Lorentz or the Breit-Wigner distribution.
The pdf of this distribution is
$f(x \mid \alpha, \beta) = \frac{1}{\pi \beta [1 + (\frac{x-\alpha}{\beta})^2]}$
Support $$x \in \mathbb{R}$$ Mode $$\alpha$$ Mean undefined Variance undefined
Parameters
alpha: float
Location parameter
beta: float
Scale parameter > 0
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logcdf(value)
Compute the log of the cumulative distribution function for Cauchy distribution at the specified value.
Parameters
value: numeric or np.ndarray or theano.tensor
Value(s) for which log CDF is calculated. If the log CDF for multiple values are desired the values must be provided in a numpy array or theano tensor.
Returns
TensorVariable
logp(value)
Calculate log-probability of Cauchy distribution at specified value.
Parameters
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple values are desired the values must be provided in a numpy array or theano tensor
Returns
TensorVariable
random(point=None, size=None)
Draw random values from Cauchy distribution.
Parameters
point: dict, optional
Dict of variable values on which random values are to be conditioned (uses default point if not specified).
size: int, optional
Desired size of random sample (returns one sample if not specified).
Returns
array
class pymc3.distributions.continuous.ChiSquared(name, *args, **kwargs)
$$\chi^2$$ log-likelihood.
The pdf of this distribution is
$f(x \mid \nu) = \frac{x^{(\nu-2)/2}e^{-x/2}}{2^{\nu/2}\Gamma(\nu/2)}$
Support $$x \in [0, \infty)$$ Mean $$\nu$$ Variance $$2 \nu$$
Parameters
nu: int
Degrees of freedom (nu > 0).
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
class pymc3.distributions.continuous.ExGaussian(name, *args, **kwargs)
Exponentially modified Gaussian log-likelihood.
Results from the convolution of a normal distribution with an exponential distribution.
The pdf of this distribution is
$f(x \mid \mu, \sigma, \tau) = \frac{1}{\nu}\; \exp\left\{\frac{\mu-x}{\nu}+\frac{\sigma^2}{2\nu^2}\right\} \Phi\left(\frac{x-\mu}{\sigma}-\frac{\sigma}{\nu}\right)$
where $$\Phi$$ is the cumulative distribution function of the standard normal distribution.
Support $$x \in \mathbb{R}$$ Mean $$\mu + \nu$$ Variance $$\sigma^2 + \nu^2$$
Parameters
mu: float
Mean of the normal distribution.
sigma: float
Standard deviation of the normal distribution (sigma > 0).
nu: float
Mean of the exponential distribution (nu > 0).
References
Rigby2005
Rigby R.A. and Stasinopoulos D.M. (2005). “Generalized additive models for location, scale and shape” Applied Statististics., 54, part 3, pp 507-554.
Lacouture2008
Lacouture, Y. and Couseanou, D. (2008). “How to use MATLAB to fit the ex-Gaussian and other probability functions to a distribution of response times”. Tutorials in Quantitative Methods for Psychology, Vol. 4, No. 1, pp 35-45.
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logcdf(value)
Compute the log of the cumulative distribution function for ExGaussian distribution at the specified value.
Parameters
value: numeric or np.ndarray or theano.tensor
Value(s) for which log CDF is calculated. If the log CDF for multiple values are desired the values must be provided in a numpy array or theano tensor.
Returns
TensorVariable
References
Rigby2005
R.A. Rigby (2005). “Generalized additive models for location, scale and shape” https://doi.org/10.1111/j.1467-9876.2005.00510.x
logp(value)
Calculate log-probability of ExGaussian distribution at specified value.
Parameters
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple values are desired the values must be provided in a numpy array or theano tensor
Returns
TensorVariable
random(point=None, size=None)
Draw random values from ExGaussian distribution.
Parameters
point: dict, optional
Dict of variable values on which random values are to be conditioned (uses default point if not specified).
size: int, optional
Desired size of random sample (returns one sample if not specified).
Returns
array
class pymc3.distributions.continuous.Exponential(name, *args, **kwargs)
Exponential log-likelihood.
The pdf of this distribution is
$f(x \mid \lambda) = \lambda \exp\left\{ -\lambda x \right\}$
Support $$x \in [0, \infty)$$ Mean $$\dfrac{1}{\lambda}$$ Variance $$\dfrac{1}{\lambda^2}$$
Parameters
lam: float
Rate or inverse scale (lam > 0)
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logcdf(value)
Compute the log of cumulative distribution function for the Exponential distribution at the specified value.
Parameters
value: numeric or np.ndarray or theano.tensor
Value(s) for which log CDF is calculated. If the log CDF for multiple values are desired the values must be provided in a numpy array or theano tensor.
Returns
TensorVariable
logp(value)
Calculate log-probability of Exponential distribution at specified value.
Parameters
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple values are desired the values must be provided in a numpy array or theano tensor
Returns
TensorVariable
random(point=None, size=None)
Draw random values from Exponential distribution.
Parameters
point: dict, optional
Dict of variable values on which random values are to be conditioned (uses default point if not specified).
size: int, optional
Desired size of random sample (returns one sample if not specified).
Returns
array
class pymc3.distributions.continuous.Flat(name, *args, **kwargs)
Uninformative log-likelihood that returns 0 regardless of the passed value.
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logcdf(value)
Compute the log of the cumulative distribution function for Flat distribution at the specified value.
Parameters
value: numeric or np.ndarray or theano.tensor
Value(s) for which log CDF is calculated. If the log CDF for multiple values are desired the values must be provided in a numpy array or theano tensor.
Returns
TensorVariable
logp(value)
Calculate log-probability of Flat distribution at specified value.
Parameters
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple values are desired the values must be provided in a numpy array or theano tensor
Returns
TensorVariable
random(point=None, size=None)
Raises ValueError as it is not possible to sample from Flat distribution
Parameters
point: dict, optional
size: int, optional
Raises
ValueError
class pymc3.distributions.continuous.Gamma(name, *args, **kwargs)
Gamma log-likelihood.
Represents the sum of alpha exponentially distributed random variables, each of which has mean beta.
The pdf of this distribution is
$f(x \mid \alpha, \beta) = \frac{\beta^{\alpha}x^{\alpha-1}e^{-\beta x}}{\Gamma(\alpha)}$
Support $$x \in (0, \infty)$$ Mean $$\dfrac{\alpha}{\beta}$$ Variance $$\dfrac{\alpha}{\beta^2}$$
Gamma distribution can be parameterized either in terms of alpha and beta or mean and standard deviation. The link between the two parametrizations is given by
$\begin{split}\alpha &= \frac{\mu^2}{\sigma^2} \\ \beta &= \frac{\mu}{\sigma^2}\end{split}$
Parameters
alpha: float
Shape parameter (alpha > 0).
beta: float
Rate parameter (beta > 0).
mu: float
Alternative shape parameter (mu > 0).
sigma: float
Alternative scale parameter (sigma > 0).
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logcdf(value)
Compute the log of the cumulative distribution function for Gamma distribution at the specified value.
Parameters
value: numeric or np.ndarray or theano.tensor
Value(s) for which log CDF is calculated. If the log CDF for multiple values are desired the values must be provided in a numpy array or theano tensor.
Returns
TensorVariable
logp(value)
Calculate log-probability of Gamma distribution at specified value.
Parameters
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple values are desired the values must be provided in a numpy array or theano tensor
Returns
TensorVariable
random(point=None, size=None)
Draw random values from Gamma distribution.
Parameters
point: dict, optional
Dict of variable values on which random values are to be conditioned (uses default point if not specified).
size: int, optional
Desired size of random sample (returns one sample if not specified).
Returns
array
class pymc3.distributions.continuous.Gumbel(name, *args, **kwargs)
Univariate Gumbel log-likelihood
The pdf of this distribution is
$f(x \mid \mu, \beta) = \frac{1}{\beta}e^{-(z + e^{-z})}$
where
$z = \frac{x - \mu}{\beta}.$
Support $$x \in \mathbb{R}$$ Mean $$\mu + \beta\gamma$$, where $$\gamma$$ is the Euler-Mascheroni constant Variance $$\frac{\pi^2}{6} \beta^2$$
Parameters
mu: float
Location parameter.
beta: float
Scale parameter (beta > 0).
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logcdf(value)
Compute the log of the cumulative distribution function for Gumbel distribution at the specified value.
Parameters
value: numeric or np.ndarray or theano.tensor
Value(s) for which log CDF is calculated. If the log CDF for multiple values are desired the values must be provided in a numpy array or theano tensor.
Returns
TensorVariable
logp(value)
Calculate log-probability of Gumbel distribution at specified value.
Parameters
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple values are desired the values must be provided in a numpy array or theano tensor
Returns
TensorVariable
random(point=None, size=None)
Draw random values from Gumbel distribution.
Parameters
point: dict, optional
Dict of variable values on which random values are to be conditioned (uses default point if not specified).
size: int, optional
Desired size of random sample (returns one sample if not specified).
Returns
array
class pymc3.distributions.continuous.HalfCauchy(name, *args, **kwargs)
Half-Cauchy log-likelihood.
The pdf of this distribution is
$f(x \mid \beta) = \frac{2}{\pi \beta [1 + (\frac{x}{\beta})^2]}$
Support $$x \in [0, \infty)$$ Mode 0 Mean undefined Variance undefined
Parameters
beta: float
Scale parameter (beta > 0).
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logcdf(value)
Compute the log of the cumulative distribution function for HalfCauchy distribution at the specified value.
Parameters
value: numeric or np.ndarray or theano.tensor
Value(s) for which log CDF is calculated. If the log CDF for multiple values are desired the values must be provided in a numpy array or theano tensor.
Returns
TensorVariable
logp(value)
Calculate log-probability of HalfCauchy distribution at specified value.
Parameters
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple values are desired the values must be provided in a numpy array or theano tensor
Returns
TensorVariable
random(point=None, size=None)
Draw random values from HalfCauchy distribution.
Parameters
point: dict, optional
Dict of variable values on which random values are to be conditioned (uses default point if not specified).
size: int, optional
Desired size of random sample (returns one sample if not specified).
Returns
array
class pymc3.distributions.continuous.HalfFlat(name, *args, **kwargs)
Improper flat prior over the positive reals.
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logcdf(value)
Compute the log of the cumulative distribution function for HalfFlat distribution at the specified value.
Parameters
value: numeric or np.ndarray or theano.tensor
Value(s) for which log CDF is calculated. If the log CDF for multiple values are desired the values must be provided in a numpy array or theano tensor.
Returns
TensorVariable
logp(value)
Calculate log-probability of HalfFlat distribution at specified value.
Parameters
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple values are desired the values must be provided in a numpy array or theano tensor
Returns
TensorVariable
random(point=None, size=None)
Raises ValueError as it is not possible to sample from HalfFlat distribution
Parameters
point: dict, optional
size: int, optional
Raises
ValueError
class pymc3.distributions.continuous.HalfNormal(name, *args, **kwargs)
Half-normal log-likelihood.
The pdf of this distribution is
\begin{align}\begin{aligned}f(x \mid \tau) = \sqrt{\frac{2\tau}{\pi}} \exp\left(\frac{-x^2 \tau}{2}\right)\\f(x \mid \sigma) = \sqrt{\frac{2}{\pi\sigma^2}} \exp\left(\frac{-x^2}{2\sigma^2}\right)\end{aligned}\end{align}
Note
The parameters sigma/tau ($$\sigma$$/$$\tau$$) refer to the standard deviation/precision of the unfolded normal distribution, for the standard deviation of the half-normal distribution, see below. For the half-normal, they are just two parameterisation $$\sigma^2 \equiv \frac{1}{\tau}$$ of a scale parameter
Support $$x \in [0, \infty)$$ Mean $$\sqrt{\dfrac{2}{\tau \pi}}$$ or $$\dfrac{\sigma \sqrt{2}}{\sqrt{\pi}}$$ Variance $$\dfrac{1}{\tau}\left(1 - \dfrac{2}{\pi}\right)$$ or $$\sigma^2\left(1 - \dfrac{2}{\pi}\right)$$
Parameters
sigma: float
Scale parameter $$sigma$$ (sigma > 0) (only required if tau is not specified).
tau: float
Precision $$tau$$ (tau > 0) (only required if sigma is not specified).
Examples
with pm.Model():
x = pm.HalfNormal('x', sigma=10)
with pm.Model():
x = pm.HalfNormal('x', tau=1/15)
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logcdf(value)
Compute the log of the cumulative distribution function for HalfNormal distribution at the specified value.
Parameters
value: numeric or np.ndarray or theano.tensor
Value(s) for which log CDF is calculated. If the log CDF for multiple values are desired the values must be provided in a numpy array or theano tensor.
Returns
TensorVariable
logp(value)
Calculate log-probability of HalfNormal distribution at specified value.
Parameters
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple values are desired the values must be provided in a numpy array or theano tensor
Returns
TensorVariable
random(point=None, size=None)
Draw random values from HalfNormal distribution.
Parameters
point: dict, optional
Dict of variable values on which random values are to be conditioned (uses default point if not specified).
size: int, optional
Desired size of random sample (returns one sample if not specified).
Returns
array
class pymc3.distributions.continuous.HalfStudentT(name, *args, **kwargs)
Half Student’s T log-likelihood
The pdf of this distribution is
$f(x \mid \sigma,\nu) = \frac{2\;\Gamma\left(\frac{\nu+1}{2}\right)} {\Gamma\left(\frac{\nu}{2}\right)\sqrt{\nu\pi\sigma^2}} \left(1+\frac{1}{\nu}\frac{x^2}{\sigma^2}\right)^{-\frac{\nu+1}{2}}$
Support $$x \in [0, \infty)$$
Parameters
nu: float
Degrees of freedom, also known as normality parameter (nu > 0).
sigma: float
Scale parameter (sigma > 0). Converges to the standard deviation as nu increases. (only required if lam is not specified)
lam: float
Scale parameter (lam > 0). Converges to the precision as nu increases. (only required if sigma is not specified)
Examples
# Only pass in one of lam or sigma, but not both.
with pm.Model():
x = pm.HalfStudentT('x', sigma=10, nu=10)
with pm.Model():
x = pm.HalfStudentT('x', lam=4, nu=10)
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logp(value)
Calculate log-probability of HalfStudentT distribution at specified value.
Parameters
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple values are desired the values must be provided in a numpy array or theano tensor
Returns
TensorVariable
random(point=None, size=None)
Draw random values from HalfStudentT distribution.
Parameters
point: dict, optional
Dict of variable values on which random values are to be conditioned (uses default point if not specified).
size: int, optional
Desired size of random sample (returns one sample if not specified).
Returns
array
class pymc3.distributions.continuous.Interpolated(name, *args, **kwargs)
Univariate probability distribution defined as a linear interpolation of probability density function evaluated on some lattice of points.
The lattice can be uneven, so the steps between different points can have different size and it is possible to vary the precision between regions of the support.
The probability density function values don not have to be normalized, as the interpolated density is any way normalized to make the total probability equal to $1$.
Both parameters x_points and values pdf_points are not variables, but plain array-like objects, so they are constant and cannot be sampled.
Support $$x \in [x\_points[0], x\_points[-1]]$$
Parameters
x_points: array-like
A monotonically growing list of values
pdf_points: array-like
Probability density function evaluated on lattice x_points
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logp(value)
Calculate log-probability of Interpolated distribution at specified value.
Parameters
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple values are desired the values must be provided in a numpy array or theano tensor
Returns
TensorVariable
random(point=None, size=None)
Draw random values from Interpolated distribution.
Parameters
size: int, optional
Desired size of random sample (returns one sample if not specified).
Returns
array
class pymc3.distributions.continuous.InverseGamma(name, *args, **kwargs)
Inverse gamma log-likelihood, the reciprocal of the gamma distribution.
The pdf of this distribution is
$f(x \mid \alpha, \beta) = \frac{\beta^{\alpha}}{\Gamma(\alpha)} x^{-\alpha - 1} \exp\left(\frac{-\beta}{x}\right)$
Support $$x \in (0, \infty)$$ Mean $$\dfrac{\beta}{\alpha-1}$$ for $$\alpha > 1$$ Variance $$\dfrac{\beta^2}{(\alpha-1)^2(\alpha - 2)}$$ for $$\alpha > 2$$
Parameters
alpha: float
Shape parameter (alpha > 0).
beta: float
Scale parameter (beta > 0).
mu: float
Alternative shape parameter (mu > 0).
sigma: float
Alternative scale parameter (sigma > 0).
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logcdf(value)
Compute the log of the cumulative distribution function for Inverse Gamma distribution at the specified value.
Parameters
value: numeric or np.ndarray or theano.tensor
Value(s) for which log CDF is calculated. If the log CDF for multiple values are desired the values must be provided in a numpy array or theano tensor.
Returns
TensorVariable
logp(value)
Calculate log-probability of InverseGamma distribution at specified value.
Parameters
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple values are desired the values must be provided in a numpy array or theano tensor
Returns
TensorVariable
random(point=None, size=None)
Draw random values from InverseGamma distribution.
Parameters
point: dict, optional
Dict of variable values on which random values are to be conditioned (uses default point if not specified).
size: int, optional
Desired size of random sample (returns one sample if not specified).
Returns
array
class pymc3.distributions.continuous.Kumaraswamy(name, *args, **kwargs)
Kumaraswamy log-likelihood.
The pdf of this distribution is
$f(x \mid a, b) = abx^{a-1}(1-x^a)^{b-1}$
Support $$x \in (0, 1)$$ Mean $$b B(1 + \tfrac{1}{a}, b)$$ Variance $$b B(1 + \tfrac{2}{a}, b) - (b B(1 + \tfrac{1}{a}, b))^2$$
Parameters
a: float
a > 0.
b: float
b > 0.
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logp(value)
Calculate log-probability of Kumaraswamy distribution at specified value.
Parameters
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple values are desired the values must be provided in a numpy array or theano tensor
Returns
TensorVariable
random(point=None, size=None)
Draw random values from Kumaraswamy distribution.
Parameters
point: dict, optional
Dict of variable values on which random values are to be conditioned (uses default point if not specified).
size: int, optional
Desired size of random sample (returns one sample if not specified).
Returns
array
class pymc3.distributions.continuous.Laplace(name, *args, **kwargs)
Laplace log-likelihood.
The pdf of this distribution is
$f(x \mid \mu, b) = \frac{1}{2b} \exp \left\{ - \frac{|x - \mu|}{b} \right\}$
Support $$x \in \mathbb{R}$$ Mean $$\mu$$ Variance $$2 b^2$$
Parameters
mu: float
Location parameter.
b: float
Scale parameter (b > 0).
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logcdf(value)
Compute the log of the cumulative distribution function for Laplace distribution at the specified value.
Parameters
value: numeric or np.ndarray or theano.tensor
Value(s) for which log CDF is calculated. If the log CDF for multiple values are desired the values must be provided in a numpy array or theano tensor.
Returns
TensorVariable
logp(value)
Calculate log-probability of Laplace distribution at specified value.
Parameters
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple values are desired the values must be provided in a numpy array or theano tensor
Returns
TensorVariable
random(point=None, size=None)
Draw random values from Laplace distribution.
Parameters
point: dict, optional
Dict of variable values on which random values are to be conditioned (uses default point if not specified).
size: int, optional
Desired size of random sample (returns one sample if not specified).
Returns
array
class pymc3.distributions.continuous.LogNormal(name, *args, **kwargs)
Log-normal log-likelihood.
Distribution of any random variable whose logarithm is normally distributed. A variable might be modeled as log-normal if it can be thought of as the multiplicative product of many small independent factors.
The pdf of this distribution is
$f(x \mid \mu, \tau) = \frac{1}{x} \sqrt{\frac{\tau}{2\pi}} \exp\left\{ -\frac{\tau}{2} (\ln(x)-\mu)^2 \right\}$
Support $$x \in [0, \infty)$$ Mean $$\exp\{\mu + \frac{1}{2\tau}\}$$ Variance $$(\exp\{\frac{1}{\tau}\} - 1) \times \exp\{2\mu + \frac{1}{\tau}\}$$
Parameters
mu: float
Location parameter.
sigma: float
Standard deviation. (sigma > 0). (only required if tau is not specified).
tau: float
Scale parameter (tau > 0). (only required if sigma is not specified).
Examples
# Example to show that we pass in only sigma or tau but not both.
with pm.Model():
x = pm.LogNormal('x', mu=2, sigma=30)
with pm.Model():
x = pm.LogNormal('x', mu=2, tau=1/100)
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logcdf(value)
Compute the log of the cumulative distribution function for LogNormal distribution at the specified value.
Parameters
value: numeric or np.ndarray or theano.tensor
Value(s) for which log CDF is calculated. If the log CDF for multiple values are desired the values must be provided in a numpy array or theano tensor.
Returns
TensorVariable
logp(value)
Calculate log-probability of LogNormal distribution at specified value.
Parameters
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple values are desired the values must be provided in a numpy array or theano tensor
Returns
TensorVariable
random(point=None, size=None)
Draw random values from LogNormal distribution.
Parameters
point: dict, optional
Dict of variable values on which random values are to be conditioned (uses default point if not specified).
size: int, optional
Desired size of random sample (returns one sample if not specified).
Returns
array
class pymc3.distributions.continuous.Logistic(name, *args, **kwargs)
Logistic log-likelihood.
The pdf of this distribution is
$f(x \mid \mu, s) = \frac{\exp\left(-\frac{x - \mu}{s}\right)}{s \left(1 + \exp\left(-\frac{x - \mu}{s}\right)\right)^2}$
Support $$x \in \mathbb{R}$$ Mean $$\mu$$ Variance $$\frac{s^2 \pi^2}{3}$$
Parameters
mu: float
Mean.
s: float
Scale (s > 0).
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logcdf(value)
Compute the log of the cumulative distribution function for Logistic distribution at the specified value.
Parameters
value: numeric or np.ndarray or theano.tensor
Value(s) for which log CDF is calculated. If the log CDF for multiple values are desired the values must be provided in a numpy array or theano tensor.
Returns
TensorVariable
logp(value)
Calculate log-probability of Logistic distribution at specified value.
Parameters
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple values are desired the values must be provided in a numpy array or theano tensor
Returns
TensorVariable
random(point=None, size=None)
Draw random values from Logistic distribution.
Parameters
point: dict, optional
Dict of variable values on which random values are to be conditioned (uses default point if not specified).
size: int, optional
Desired size of random sample (returns one sample if not specified).
Returns
array
class pymc3.distributions.continuous.LogitNormal(name, *args, **kwargs)
Logit-Normal log-likelihood.
The pdf of this distribution is
$f(x \mid \mu, \tau) = \frac{1}{x(1-x)} \sqrt{\frac{\tau}{2\pi}} \exp\left\{ -\frac{\tau}{2} (logit(x)-\mu)^2 \right\}$
Support $$x \in (0, 1)$$ Mean no analytical solution Variance no analytical solution
Parameters
mu: float
Location parameter.
sigma: float
Scale parameter (sigma > 0).
tau: float
Scale parameter (tau > 0).
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logp(value)
Calculate log-probability of LogitNormal distribution at specified value.
Parameters
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple values are desired the values must be provided in a numpy array or theano tensor
Returns
TensorVariable
random(point=None, size=None)
Draw random values from LogitNormal distribution.
Parameters
point: dict, optional
Dict of variable values on which random values are to be conditioned (uses default point if not specified).
size: int, optional
Desired size of random sample (returns one sample if not specified).
Returns
array
class pymc3.distributions.continuous.Moyal(name, *args, **kwargs)
Moyal log-likelihood.
The pdf of this distribution is
$f(x \mid \mu,\sigma) = \frac{1}{\sqrt{2\pi}\sigma}e^{-\frac{1}{2}\left(z + e^{-z}\right)},$
where
$z = \frac{x-\mu}{\sigma}.$
Support $$x \in (-\infty, \infty)$$ Mean $$\mu + \sigma\left(\gamma + \log 2\right)$$, where $$\gamma$$ is the Euler-Mascheroni constant Variance $$\frac{\pi^{2}}{2}\sigma^{2}$$
Parameters
mu: float
Location parameter.
sigma: float
Scale parameter (sigma > 0).
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logcdf(value)
Compute the log of the cumulative distribution function for Moyal distribution at the specified value.
Parameters
value: numeric or np.ndarray or theano.tensor
Value(s) for which log CDF is calculated. If the log CDF for multiple values are desired the values must be provided in a numpy array or theano tensor.
Returns
TensorVariable
logp(value)
Calculate log-probability of Moyal distribution at specified value.
Parameters
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple values are desired the values must be provided in a numpy array or theano tensor
Returns
TensorVariable
random(point=None, size=None)
Draw random values from Moyal distribution.
Parameters
point: dict, optional
Dict of variable values on which random values are to be conditioned (uses default point if not specified).
size: int, optional
Desired size of random sample (returns one sample if not specified).
Returns
array
class pymc3.distributions.continuous.Normal(name, *args, **kwargs)
Univariate normal log-likelihood.
The pdf of this distribution is
$f(x \mid \mu, \tau) = \sqrt{\frac{\tau}{2\pi}} \exp\left\{ -\frac{\tau}{2} (x-\mu)^2 \right\}$
Normal distribution can be parameterized either in terms of precision or standard deviation. The link between the two parametrizations is given by
$\tau = \dfrac{1}{\sigma^2}$
Support $$x \in \mathbb{R}$$ Mean $$\mu$$ Variance $$\dfrac{1}{\tau}$$ or $$\sigma^2$$
Parameters
mu: float
Mean.
sigma: float
Standard deviation (sigma > 0) (only required if tau is not specified).
tau: float
Precision (tau > 0) (only required if sigma is not specified).
Examples
with pm.Model():
x = pm.Normal('x', mu=0, sigma=10)
with pm.Model():
x = pm.Normal('x', mu=0, tau=1/23)
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logcdf(value)
Compute the log of the cumulative distribution function for Normal distribution at the specified value.
Parameters
value: numeric or np.ndarray or theano.tensor
Value(s) for which log CDF is calculated. If the log CDF for multiple values are desired the values must be provided in a numpy array or theano tensor.
Returns
TensorVariable
logp(value)
Calculate log-probability of Normal distribution at specified value.
Parameters
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple values are desired the values must be provided in a numpy array or theano tensor
Returns
TensorVariable
random(point=None, size=None)
Draw random values from Normal distribution.
Parameters
point: dict, optional
Dict of variable values on which random values are to be conditioned (uses default point if not specified).
size: int, optional
Desired size of random sample (returns one sample if not specified).
Returns
array
class pymc3.distributions.continuous.Pareto(name, *args, **kwargs)
Pareto log-likelihood.
Often used to characterize wealth distribution, or other examples of the 80/20 rule.
The pdf of this distribution is
$f(x \mid \alpha, m) = \frac{\alpha m^{\alpha}}{x^{\alpha+1}}$
Support $$x \in [m, \infty)$$ Mean $$\dfrac{\alpha m}{\alpha - 1}$$ for $$\alpha \ge 1$$ Variance $$\dfrac{m \alpha}{(\alpha - 1)^2 (\alpha - 2)}$$ for $$\alpha > 2$$
Parameters
alpha: float
Shape parameter (alpha > 0).
m: float
Scale parameter (m > 0).
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logcdf(value)
Compute the log of the cumulative distribution function for Pareto distribution at the specified value.
Parameters
value: numeric or np.ndarray or theano.tensor
Value(s) for which log CDF is calculated. If the log CDF for multiple values are desired the values must be provided in a numpy array or theano tensor.
Returns
TensorVariable
logp(value)
Calculate log-probability of Pareto distribution at specified value.
Parameters
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple values are desired the values must be provided in a numpy array or theano tensor
Returns
TensorVariable
random(point=None, size=None)
Draw random values from Pareto distribution.
Parameters
point: dict, optional
Dict of variable values on which random values are to be conditioned (uses default point if not specified).
size: int, optional
Desired size of random sample (returns one sample if not specified).
Returns
array
class pymc3.distributions.continuous.Rice(name, *args, **kwargs)
Rice distribution.
$f(x\mid \nu ,\sigma )= {\frac {x}{\sigma ^{2}}}\exp \left({\frac {-(x^{2}+\nu ^{2})}{2\sigma ^{2}}}\right)I_{0}\left({\frac {x\nu }{\sigma ^{2}}}\right),$
Support $$x \in (0, \infty)$$ Mean $$\sigma {\sqrt {\pi /2}}\,\,L_{{1/2}}(-\nu ^{2}/2\sigma ^{2})$$ Variance $$2\sigma ^{2}+\nu ^{2}-{\frac {\pi \sigma ^{2}}{2}}L_{{1/2}}^{2}\left({\frac {-\nu ^{2}}{2\sigma ^{2}}}\right)$$
Parameters
nu: float
noncentrality parameter.
sigma: float
scale parameter.
b: float
shape parameter (alternative to nu).
Notes
The distribution $$\mathrm{Rice}\left(|\nu|,\sigma\right)$$ is the distribution of $$R=\sqrt{X^2+Y^2}$$ where $$X\sim N(\nu \cos{\theta}, \sigma^2)$$, $$Y\sim N(\nu \sin{\theta}, \sigma^2)$$ are independent and for any real $$\theta$$.
The distribution is defined with either nu or b. The link between the two parametrizations is given by
$b = \dfrac{\nu}{\sigma}$
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logp(value)
Calculate log-probability of Rice distribution at specified value.
Parameters
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple values are desired the values must be provided in a numpy array or theano tensor
Returns
TensorVariable
random(point=None, size=None)
Draw random values from Rice distribution.
Parameters
point: dict, optional
Dict of variable values on which random values are to be conditioned (uses default point if not specified).
size: int, optional
Desired size of random sample (returns one sample if not specified).
Returns
array
class pymc3.distributions.continuous.SkewNormal(name, *args, **kwargs)
Univariate skew-normal log-likelihood.
The pdf of this distribution is
$f(x \mid \mu, \tau, \alpha) = 2 \Phi((x-\mu)\sqrt{\tau}\alpha) \phi(x,\mu,\tau)$
Support $$x \in \mathbb{R}$$ Mean $$\mu + \sigma \sqrt{\frac{2}{\pi}} \frac {\alpha }{{\sqrt {1+\alpha ^{2}}}}$$ Variance $$\sigma^2 \left( 1-\frac{2\alpha^2}{(\alpha^2+1) \pi} \right)$$
Skew-normal distribution can be parameterized either in terms of precision or standard deviation. The link between the two parametrizations is given by
$\tau = \dfrac{1}{\sigma^2}$
Parameters
mu: float
Location parameter.
sigma: float
Scale parameter (sigma > 0).
tau: float
Alternative scale parameter (tau > 0).
alpha: float
Skewness parameter.
Notes
When alpha=0 we recover the Normal distribution and mu becomes the mean, tau the precision and sigma the standard deviation. In the limit of alpha approaching plus/minus infinite we get a half-normal distribution.
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logp(value)
Calculate log-probability of SkewNormal distribution at specified value.
Parameters
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple values are desired the values must be provided in a numpy array or theano tensor
Returns
TensorVariable
random(point=None, size=None)
Draw random values from SkewNormal distribution.
Parameters
point: dict, optional
Dict of variable values on which random values are to be conditioned (uses default point if not specified).
size: int, optional
Desired size of random sample (returns one sample if not specified).
Returns
array
class pymc3.distributions.continuous.StudentT(name, *args, **kwargs)
Student’s T log-likelihood.
Describes a normal variable whose precision is gamma distributed. If only nu parameter is passed, this specifies a standard (central) Student’s T.
The pdf of this distribution is
$f(x|\mu,\lambda,\nu) = \frac{\Gamma(\frac{\nu + 1}{2})}{\Gamma(\frac{\nu}{2})} \left(\frac{\lambda}{\pi\nu}\right)^{\frac{1}{2}} \left[1+\frac{\lambda(x-\mu)^2}{\nu}\right]^{-\frac{\nu+1}{2}}$
Support $$x \in \mathbb{R}$$
Parameters
nu: float
Degrees of freedom, also known as normality parameter (nu > 0).
mu: float
Location parameter.
sigma: float
Scale parameter (sigma > 0). Converges to the standard deviation as nu increases. (only required if lam is not specified)
lam: float
Scale parameter (lam > 0). Converges to the precision as nu increases. (only required if sigma is not specified)
Examples
with pm.Model():
x = pm.StudentT('x', nu=15, mu=0, sigma=10)
with pm.Model():
x = pm.StudentT('x', nu=15, mu=0, lam=1/23)
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logcdf(value)
Compute the log of the cumulative distribution function for Student’s T distribution at the specified value.
Parameters
value: numeric
Value(s) for which log CDF is calculated.
Returns
TensorVariable
logp(value)
Calculate log-probability of StudentT distribution at specified value.
Parameters
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple values are desired the values must be provided in a numpy array or theano tensor
Returns
TensorVariable
random(point=None, size=None)
Draw random values from StudentT distribution.
Parameters
point: dict, optional
Dict of variable values on which random values are to be conditioned (uses default point if not specified).
size: int, optional
Desired size of random sample (returns one sample if not specified).
Returns
array
class pymc3.distributions.continuous.Triangular(name, *args, **kwargs)
Continuous Triangular log-likelihood
The pdf of this distribution is
$\begin{split}\begin{cases} 0 & \text{for } x < a, \\ \frac{2(x-a)}{(b-a)(c-a)} & \text{for } a \le x < c, \\[4pt] \frac{2}{b-a} & \text{for } x = c, \\[4pt] \frac{2(b-x)}{(b-a)(b-c)} & \text{for } c < x \le b, \\[4pt] 0 & \text{for } b < x. \end{cases}\end{split}$
Support $$x \in [lower, upper]$$ Mean $$\dfrac{lower + upper + c}{3}$$ Variance $$\dfrac{upper^2 + lower^2 +c^2 - lower*upper - lower*c - upper*c}{18}$$
Parameters
lower: float
Lower limit.
c: float
mode
upper: float
Upper limit.
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logcdf(value)
Compute the log of the cumulative distribution function for Triangular distribution at the specified value.
Parameters
value: numeric or np.ndarray or theano.tensor
Value(s) for which log CDF is calculated. If the log CDF for multiple values are desired the values must be provided in a numpy array or theano tensor.
Returns
TensorVariable
logp(value)
Calculate log-probability of Triangular distribution at specified value.
Parameters
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple values are desired the values must be provided in a numpy array or theano tensor
Returns
TensorVariable
random(point=None, size=None)
Draw random values from Triangular distribution.
Parameters
point: dict, optional
Dict of variable values on which random values are to be conditioned (uses default point if not specified).
size: int, optional
Desired size of random sample (returns one sample if not specified).
Returns
array
class pymc3.distributions.continuous.TruncatedNormal(name, *args, **kwargs)
Univariate truncated normal log-likelihood.
The pdf of this distribution is
$f(x;\mu ,\sigma ,a,b)={\frac {\phi ({\frac {x-\mu }{\sigma }})}{ \sigma \left(\Phi ({\frac {b-\mu }{\sigma }})-\Phi ({\frac {a-\mu }{\sigma }})\right)}}$
Truncated normal distribution can be parameterized either in terms of precision or standard deviation. The link between the two parametrizations is given by
$\tau = \dfrac{1}{\sigma^2}$
Support $$x \in [a, b]$$ Mean $$\mu +{\frac {\phi (\alpha )-\phi (\beta )}{Z}}\sigma$$ Variance $$\sigma ^{2}\left[1+{\frac {\alpha \phi (\alpha )-\beta \phi (\beta )}{Z}}-\left({\frac {\phi (\alpha )-\phi (\beta )}{Z}}\right)^{2}\right]$$
Parameters
mu: float
Mean.
sigma: float
Standard deviation (sigma > 0).
lower: float (optional)
Left bound.
upper: float (optional)
Right bound.
Examples
with pm.Model():
x = pm.TruncatedNormal('x', mu=0, sigma=10, lower=0)
with pm.Model():
x = pm.TruncatedNormal('x', mu=0, sigma=10, upper=1)
with pm.Model():
x = pm.TruncatedNormal('x', mu=0, sigma=10, lower=0, upper=1)
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logp(value)
Calculate log-probability of TruncatedNormal distribution at specified value.
Parameters
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple values are desired the values must be provided in a numpy array or theano tensor
Returns
TensorVariable
random(point=None, size=None)
Draw random values from TruncatedNormal distribution.
Parameters
point: dict, optional
Dict of variable values on which random values are to be conditioned (uses default point if not specified).
size: int, optional
Desired size of random sample (returns one sample if not specified).
Returns
array
class pymc3.distributions.continuous.Uniform(name, *args, **kwargs)
Continuous uniform log-likelihood.
The pdf of this distribution is
$f(x \mid lower, upper) = \frac{1}{upper-lower}$
Support $$x \in [lower, upper]$$ Mean $$\dfrac{lower + upper}{2}$$ Variance $$\dfrac{(upper - lower)^2}{12}$$
Parameters
lower: float
Lower limit.
upper: float
Upper limit.
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logcdf(value)
Compute the log of the cumulative distribution function for Uniform distribution at the specified value.
Parameters
value: numeric or np.ndarray or theano.tensor
Value(s) for which log CDF is calculated. If the log CDF for multiple values are desired the values must be provided in a numpy array or theano tensor.
Returns
TensorVariable
logp(value)
Calculate log-probability of Uniform distribution at specified value.
Parameters
value: numeric
Value for which log-probability is calculated.
Returns
TensorVariable
random(point=None, size=None)
Draw random values from Uniform distribution.
Parameters
point: dict, optional
Dict of variable values on which random values are to be conditioned (uses default point if not specified).
size: int, optional
Desired size of random sample (returns one sample if not specified).
Returns
array
class pymc3.distributions.continuous.VonMises(name, *args, **kwargs)
Univariate VonMises log-likelihood.
The pdf of this distribution is
$f(x \mid \mu, \kappa) = \frac{e^{\kappa\cos(x-\mu)}}{2\pi I_0(\kappa)}$
where $$I_0$$ is the modified Bessel function of order 0.
Support $$x \in [-\pi, \pi]$$ Mean $$\mu$$ Variance $$1-\frac{I_1(\kappa)}{I_0(\kappa)}$$
Parameters
mu: float
Mean.
kappa: float
Concentration (frac{1}{kappa} is analogous to sigma^2).
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logp(value)
Calculate log-probability of VonMises distribution at specified value.
Parameters
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple values are desired the values must be provided in a numpy array or theano tensor
Returns
TensorVariable
random(point=None, size=None)
Draw random values from VonMises distribution.
Parameters
point: dict, optional
Dict of variable values on which random values are to be conditioned (uses default point if not specified).
size: int, optional
Desired size of random sample (returns one sample if not specified).
Returns
array
class pymc3.distributions.continuous.Wald(name, *args, **kwargs)
Wald log-likelihood.
The pdf of this distribution is
$f(x \mid \mu, \lambda) = \left(\frac{\lambda}{2\pi}\right)^{1/2} x^{-3/2} \exp\left\{ -\frac{\lambda}{2x}\left(\frac{x-\mu}{\mu}\right)^2 \right\}$
Support $$x \in (0, \infty)$$ Mean $$\mu$$ Variance $$\dfrac{\mu^3}{\lambda}$$
Wald distribution can be parameterized either in terms of lam or phi. The link between the two parametrizations is given by
$\phi = \dfrac{\lambda}{\mu}$
Parameters
mu: float, optional
Mean of the distribution (mu > 0).
lam: float, optional
Relative precision (lam > 0).
phi: float, optional
Alternative shape parameter (phi > 0).
alpha: float, optional
Shift/location parameter (alpha >= 0).
Notes
To instantiate the distribution specify any of the following
• only mu (in this case lam will be 1)
• mu and lam
• mu and phi
• lam and phi
References
Tweedie1957
Tweedie, M. C. K. (1957). Statistical Properties of Inverse Gaussian Distributions I. The Annals of Mathematical Statistics, Vol. 28, No. 2, pp. 362-377
Michael1976
Michael, J. R., Schucany, W. R. and Hass, R. W. (1976). Generating Random Variates Using Transformations with Multiple Roots. The American Statistician, Vol. 30, No. 2, pp. 88-90
Giner2016
Göknur Giner, Gordon K. Smyth (2016) statmod: Probability Calculations for the Inverse Gaussian Distribution
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logcdf(value)
Compute the log of the cumulative distribution function for Wald distribution at the specified value.
Parameters
value: numeric or np.ndarray or theano.tensor
Value(s) for which log CDF is calculated. If the log CDF for multiple values are desired the values must be provided in a numpy array or theano tensor.
Returns
TensorVariable
logp(value)
Calculate log-probability of Wald distribution at specified value.
Parameters
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple values are desired the values must be provided in a numpy array or theano tensor
Returns
TensorVariable
random(point=None, size=None)
Draw random values from Wald distribution.
Parameters
point: dict, optional
Dict of variable values on which random values are to be conditioned (uses default point if not specified).
size: int, optional
Desired size of random sample (returns one sample if not specified).
Returns
array
class pymc3.distributions.continuous.Weibull(name, *args, **kwargs)
Weibull log-likelihood.
The pdf of this distribution is
$f(x \mid \alpha, \beta) = \frac{\alpha x^{\alpha - 1} \exp(-(\frac{x}{\beta})^{\alpha})}{\beta^\alpha}$
Support $$x \in [0, \infty)$$ Mean $$\beta \Gamma(1 + \frac{1}{\alpha})$$ Variance $$\beta^2 \Gamma(1 + \frac{2}{\alpha} - \mu^2/\beta^2)$$
Parameters
alpha: float
Shape parameter (alpha > 0).
beta: float
Scale parameter (beta > 0).
Creates a PyMC distribution object.
Parameters
shapetuple
Output shape of the RV. Forwarded to the Theano TensorType of this RV.
dtype
Forwarded to the Theano TensorType of this RV.
initvalnp.ndarray
Initial value for this RV. In PyMC 4.0.0 this will no longer assign test values to the tensors.
defaultstuple
transformpm.Transform
Forwarded to the Theano TensorType of this RV.
dimstuple
Ignored.
testvalnp.ndarray
The old way of specifying initial values assigning test-values.
Deprecated
Parameter testval deprecated since 3.11.5
logcdf(value)
Compute the log of the cumulative distribution function for Weibull distribution at the specified value.
Parameters
value: numeric or np.ndarray or theano.tensor
Value(s) for which log CDF is calculated. If the log CDF for multiple values are desired the values must be provided in a numpy array or theano tensor.
Returns
TensorVariable
logp(value)
Calculate log-probability of Weibull distribution at specified value.
Parameters
value: numeric
Value(s) for which log-probability is calculated. If the log probabilities for multiple values are desired the values must be provided in a numpy array or theano tensor
Returns
TensorVariable
random(point=None, size=None)
Draw random values from Weibull distribution.
Parameters
point: dict, optional
Dict of variable values on which random values are to be conditioned (uses default point if not specified).
size: int, optional
Desired size of random sample (returns one sample if not specified).
Returns
array | 17,159 | 67,706 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 2, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2022-21 | latest | en | 0.375365 |
https://www.coursehero.com/file/213743/Lect-3/ | 1,498,742,577,000,000,000 | text/html | crawl-data/CC-MAIN-2017-26/segments/1498128323970.81/warc/CC-MAIN-20170629121355-20170629141355-00693.warc.gz | 856,233,391 | 44,048 | # Lect_3 - Nonlinear Systems and Control Lecture 3...
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˙ x 1 = f 1 ( x 1 , x 2 ) = f 1 ( x ) ˙ x 2 = f 2 ( x 1 , x 2 ) = f 2 ( x ) Let x ( t ) = ( x 1 ( t ) , x 2 ( t )) be a solution that starts at initial state x 0 = ( x 10 ,x 20 ) . The locus in the x 1 x 2 plane of the solution x ( t ) for all t 0 is a curve that passes through the point x 0 . This curve is called a trajectory or orbit The x 1 x 2 plane is called the state plane or phase plane The family of all trajectories is called the phase portrait The vector field f ( x ) = ( f 1 ( x ) , f 2 ( x )) is tangent to the trajectory at point x because dx 2 dx 1 = f 2 ( x ) f 1 ( x ) – p.2/16
Vector Field diagram Represent f ( x ) as a vector based at x ; that is, assign to x the directed line segment from x to x + f ( x ) a a a a a a a A x 1 x 2 f ( x ) x = (1 , 1) x + f ( x ) = (3 , 2) Repeat at every point in a grid covering the plane – p.3/16
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-5 0 5 -6 -4 -2 0 2 4 6 x 1 x 2 ˙ x 1 = x 2 , ˙ x 2 = 10 sin x 1 – p.4/16
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# Common Problems Experienced by Struggling Students
Students in need of remediation often exhibit similar problems. Corrective Mathematics provides
the careful teaching and systematic practice that creates steady, measurable progress.
them overcome the difficulties that they have had with mathematics.
• Memorization of the basic number facts
• Standard algorithms
• Over reliance on estimation
• Mathematical reasoning and problem-solving competency
• Understanding of fractions
Common Problem—Memorization of the Basic Number Facts
Common Problem How Corrective Mathematics Addresses It
Memorization of the Basic Number Facts
Memorizing the “basic number facts,” i.e., the sums and prod-
ucts of single-digit numbers and the equivalent subtraction and
division facts, frees up working memory to master the arithme-
tic algorisms and tackle math applications. Research in cogni-
tive psychology points to the value of automatic recall of the
basic facts. Students who do not memorize the basic number
facts will founder as more complex operations are required, and
their progress will likely grind to a halt by the end of elemen-
tary school. There is no real mathematical fluency without
memorization of the most basic facts.
The State of State Math Standards
Corrective Mathematics promotes a high level of student
proficiency by teaching each fact as a member of both a
number family and a fact series, rather than separate entities to
be memorized.
• Number families consist of three numbers that go together
to form a basic fact. In Addition and Subtraction, students
work with number families that look like this:
4 + 1 = 5
1 + 4 = 5
5 – 1 = 4
5 – 4 = 1
Learning number families is instructionally economical because
each number family translates into four facts.
• Fact Series exercises present facts in order to show their
relationship to counting. For example:
6 + 1 = 7
6 + 2 = 8
6 + 3 = 9
Every time a number is counted in the second addend (1, 2, 3),
the number is counted in the sum (7, 8, 9). By teaching fact
relationships, individual facts are easier to recall.
• Once students have a number of firm reference points and
know how to use these reference points to figure out
closely related facts, the modules provide a number of ex-
ercises designed to increase proficiency and automaticity
with individual facts, including Fact Games in which
groups of students compete, the Timing Format in which
individual students earn points, and Blackline Masters for
optional facts practice.
• Special fact relationships usually omitted in instructional
programs are taught. For example, division facts are taught
in most programs, but not division remainder facts. In
Corrective Mathematics students are taught 5 goes into 30
six times and also that 5 goes into 31, 32, 33, and 34
six times.
Common Problem—The Standard Algorithms
Common Problem How Corrective Mathematics Addresses It
The Standard Algorithms
The standard algorithms are powerful theorems and they are
standard for a good reason: They are guaranteed to work for
all problems of the type for which they were designed. Know-
ing the standard algorithms, in the sense of being able to use
them, is a foundational skill for an elementary schools students.
Students who master these algorithms gain confidence in their
ability to compute. They know they can solve any addition,
subtraction, multiplication, or division problem without relying
on a mysterious black box, such as a calculator. Moreover, the
ability to execute the arithmetic operations in a routine manner
helps student to think more conceptually and are well posi-
tioned to understand the meaning and uses of other algorithms
in later years.
For example, one benefit of the long division algorithm is that it
requires estimation of quotients at each stage. If the next digit
placed in the (trial) answer is too large or too small, that stage
has to be done over again, and the error is made visible by the
procedure. Number sense and estimation skills are reinforced
in this way.
The long division algorithm has applications that go far beyond
elementary school arithmetic. At the middle school level, it can
be used to explain why rational numbers have repeating deci-
mals. Division is also central to the Euclidean Algorithm for
the calculation of the common divisor or two integers. In high
school algebra, the long division algorithm, in a modified form,
is used for division of polynomials. At the university level, the
algorithm is important in advanced abstract algebra.
Experience with the long division algorithm thus lays the
groundwork for advanced topics in mathematics.
The State of State Math Standards
Corrective Mathematics teaches coherent routines that allow
students to handle a wide variety of computation problems.
Routines provide for all the various types of problems that stu-
dents might encounter, such as borrowing from zero in subtrac-
tion and multiplying by a number with a zero in the ones col-
umn.
Instruction is carefully sequenced and strongly scaffolded so
that students learn all necessary components skills
(preskills) prior to the introduction of the routine and can
apply steps they are to follow in using a routine.
For example:
The division operation is first introduced for single-digit divisor
problems. Students underline the part of the dividend that is at
least as big as the divisor. Next, they work the underlined prob-
lem and find the remainder for that part. Then they bring down
the next digit and work the new problem in the same way. They
continue in this manner until they have written a number above
the last digit of the dividend. This signals that the problem is
finished.
The single-digit divisor strategy is first shown with problems
that have one- and 2-digit answers. Early problems do not have
answers with zero in the middle, and answers with zero as the
final digit. Special exercises focus on these troublesome types
of division problems.
For 2-digit divisors, the procedure is the same as that for
single-digit divisors, except the students round off the divi-
sor and the underlined part of the problem to the nearest tens
number. For example, if the problem is , students
write the rounded-off problem as . The rounding-off
small. Students are taught to determine whether the remain-
der is too large, and if it is, to make the answer larger. If the
remainder is too small (a negative number), students make
the answer smaller. By the end of the module, students can
solve problem of these types:
63 483
6 48
44 5900 24 2165
34 3618 75 3052
Common Problem—Over Reliance on Estimation at the Expense of
Exact Arithmetic Calculations
Common Problem How Corrective Mathematics Addresses It
Over reliance on estimation at the expense of exact arithmetic
calculations
Fostering estimation skills is a commendable goal shared by all
math programs. However, there is a tendency to overempha-
size estimation at the expense of exact arithmetic calculations.
For simple subtraction, the correct answer is the only reason-
able answer. The notion of “reasonableness” might be appro-
priate in connection with measurement, but not in connection
with arithmetic of small whole numbers. The main goal of ele-
mentary school math is to get students to think about numbers
and to learn arithmetic. Hand calculations force students to
develop an intuitive understanding of place value and of frac-
tions.
The State of State Math Standards
Corrective Mathematics teaches arithmetic calculations through
carefully sequenced and strongly scaffolded lessons.
The care with which each necessary preskill is introduced is
well demonstrated by the operations activities in the Subtrac-
tion module. Before the students learn the routine for subtract-
ing with borrowing in one column, they master these preskills:
• Rewriting numbers by borrowing. Given a number with
one digit slashed, the students learn to borrow from the
slashed digit. The students write the borrowed amount in
front of the digit immediately to the right of the slashed
digit.
Given 3572
2
Students write 3
1
572
• Subtracting multidigit numbers without borrowing.
Given a multidigit subtraction problem, the students learn
to subtract the bottom digit from the top digit in each col-
umn, starting with the ones column.
Given 841
– 410
Students begin with
the ones column
and write 841
– 410
431
• Determining when and where to borrow. Given a partial
subtraction problem, the students learn that “if you’re minus-
ing more than you start with, you have to borrow.” The stu-
dents use a slash mark to indicate the position of the digit they
would borrow from.
Given 2 Students write 2
– 7
• Subtracting when borrowing has been done. Given a
problem in which borrowing has been done for the stu-
dents, the students learn to subtract accurately.
2
Given 3
1
4
– 18
2
Students write 3
1
4
– 18
1 6
Common Problem—Mathematical Reasoning and Problem Solving Competency
Common Problem How Corrective Mathematics Addresses It
Mathematical Reasoning and Problem-solving Competency
Problem-solving is an indispensable part of learning mathemat-
ics. Children should be able to solve single-step word problems
in the earliest grades and deal with increasingly more challeng-
ing, multi-step problems as they progress. Too often, programs
fail to develop important prerequisites before introducing ad-
vanced topics.
The State of State Math Standards
One of the major strengths of the Corrective Mathematics pro-
gram is that Corrective Mathematics teaches a precise strategy
for determining which mathematics operation is required by a
given story problem—a feature not typically shared by other
mathematics programs.
• Although students learn in the Subtraction module that
certain verbs generally indicate whether to add (find, get,
buy) or subtract (lose, give away, break), they quickly
learn that they cannot rely solely on the verb to determine
the appropriate operation. For example, the following prob-
lem calls for addition, even though give away would seem-
ingly call for subtraction.
Bill gives away 4 toys. John gives away 2 toys. How many
toys did the boys give away?
• Because using the verb to determine whether addition or
subtraction is called for is not a viable strategy for many
story problems, the Subtraction module quickly teaches
this discrimination strategy: If the problem gives the big
number, it’s a subtraction problem; if the problem does not
give the big number, it’s an addition problem. (The “big
number” is the minuend in a subtraction problem and the
sum is an addition problem.) The strategy is illustrated by
the following problems.
Mr. Yamada had 36 books. Last week he bought more books at
the used bookstore. Now he has 58 books. How many books did
• In this problem, the big number, 58, is given. Therefore,
the problem is a subtraction problem and translates into
58
– 36
• In the second problem, the big number (how many win-
dows in all) is not given.
An office building has 2365 clean windows. The window wash-
ers have to wash 90 dirty windows. How many windows in all
does the building have?
• Therefore, the problem is an addition problem and trans-
lated into
2365
+ 90
An additional strength of the Story Problems track of the mod-
ules is that the students are taught to apply their discrimination
strategies to a wide variety of problem types. Subtraction mod-
ule.
Furthermore, the specific preskills for each problem type are
carefully taught. For instance, before being presented with addi-
tion and subtraction classification problems, the students are
taught the class name for the big number. For example, in a
problem involving hammers, tools, and saws, students are
taught that tool is the name for the big number because ham-
mers are tools and saws are tools.
Common Problem—Fraction Development
Common Problem How Corrective Mathematics Addresses It
Fraction Development
In general, too little attention is paid to the coherent develop-
ment of fractions and there is not enough emphasis on paper-
and pencil- calculations. When fraction arithmetic is poorly
developed in the elementary grades, students have little hope of
understanding algebra as anything other than a maze of compli-
cated recipes to be memorized.
The State of State Math Standards
The development of fractions and decimals receives special
attention in Corrective Mathematics as students are guided
through a logical, coherent progression of steps.
• Basic Fractions teaches what the numbers in a fraction tell.
The bottom number tells how many parts in each whole, and
the top number tells how many parts are used. In the fraction
¾, there are 4 parts in each whole and 3 parts are used.
• Students learn the difference between parts of a whole and
an entire whole. Later they learn to tell how many wholes a
fraction equals by determining how many times bigger the top
number is than the bottom number.
• The module presents visual examples of what happens
when fractions are added and worksheets provide a great
deal of practice adding and subtracting fractions with like
denominators.
Before students add and subtract fractions with unlike denomi-
nators, they learn to make the bottom numbers the same by
figuring out the fraction versions of 1 by which they must mul-
tiply each original fraction.
• Students learn that equivalent fractions are created by mul-
tiplying a fraction by another fraction that equals 1. Two com-
ponents skills exercises prepare students for equivalent frac-
tion exercises.
• The first component skill teaches students to identify frac-
tions that equal 1 whole: A fraction equals 1 whole when
you use the same number of parts that are in each whole.
• The second component skill teaches the concept that when
you multiply by 1, you start and end with equal amounts.
• The initial exercises in which students are asked to find a
missing number in an equivalent fraction are written in this
form: ´ =
• The students will write a fraction equal to 1 in the paren-
multiply by a fraction that equals 1. Students first figure
out what number the denominator of the first fraction must
be multiplied by to end up with the denominator of the
second fraction. Five time what number equals 15? The
answer is 3. The denominator of the fraction we’re multi-
plying by is 3. Because we must multiply by a fraction
that equals 1, the top number must also be 3. A fraction
equals 1 when the top and the bottom numbers are the
same. The students write in parentheses and then multi-
ply the numerator of the initial fraction and the numerator
of the fraction that equals one whole. The answer is 12.
= = =
4 7 9
1
4 7 9
× =
3 3
1
5 5
4
5
⎛ ⎞
⎜ ⎟
⎝ ⎠
15
4
5
4
5
3
3 | 3,235 | 14,724 | {"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} | 4.15625 | 4 | CC-MAIN-2018-47 | latest | en | 0.931282 |
https://www.thestudentroom.co.uk/showthread.php?t=39817 | 1,524,249,884,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125944677.39/warc/CC-MAIN-20180420174802-20180420194802-00378.warc.gz | 891,170,958 | 37,373 | x Turn on thread page Beta
You are Here: Home >< Maths
# Differentiating Trignometic Functions - Help? watch
1. I have to differentiate:
cos(½π-5x)
My answer comes out to be:
-5sin(½π-5x)
Answer in the back of the book is:
5cos5x - which one is right?
2. (Original post by entiti)
I have to differentiate:
cos(½π-5x)
My answer comes out to be:
-5sin(½π-5x)
Answer in the back of the book is:
5cos5x - which one is right?
Back of the book. Yours would be right if you'd included another minus.
cos(90 - x) = sin x.
3. ok, thanks for your help.
That's because ½π = 90 ( in degrees ). cos( 90 - x ) = sin x is a basic rule right? Correct me if I'm wrong.
4. yes, so:
y = cos(pi/2 - 5x)
y = sin 5x
dy/dx = 5cos 5x
Turn on thread page Beta
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http://betterlesson.com/lesson/reflection/1470/fun-change-of-pace | 1,477,463,069,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988720737.84/warc/CC-MAIN-20161020183840-00108-ip-10-171-6-4.ec2.internal.warc.gz | 26,736,458 | 23,818 | ## Reflection: Additive Compare Word Problems and Place Value Review - Section 3: Concept development
You can see by my video reflection, today's lessons was a great change of pace.
I like the above photo because these students are engaged and on task playing multiplication war. Both of these students will benefit from extra practice. On his way out the door, this boy did say to me, "That was fun."
I realized after today that I need to remember to incorporate more games into my lessons and units to reach students who are motivated by these.
I enjoyed the small group work today as well. I felt like I got to hear all of my students thinking or at least see what they were doing since we were all together in a small space. Small group work is such a different feel than whole group. This was another realization today. While I say how much small group work is great, I haven't been doing a lot of it. I also need to incorporate small group work into my lessons and units moving forward. After the small group work, I added 4 students to my list of students who need more support during my pull out time. If I had not done small groups today, I'm not confident I would have known to add them to the group.
Fun Change of Pace
# Additive Compare Word Problems and Place Value Review
Unit 8: Place value
Lesson 14 of 14
## Big Idea: In this fun engaging lesson, students review place value concepts by working with partners an groups in fun creative card games.
Print Lesson
22 teachers like this lesson
Standards:
Subject(s):
Math, Place Value, Number Sense and Operations, group work, multiplication, partner work, card games
56 minutes
### Melissa Romano
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Environment: Urban | 501 | 2,233 | {"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} | 3.390625 | 3 | CC-MAIN-2016-44 | longest | en | 0.956896 |
https://thefractioncalculator.com/SimplifyFractions/What-is-20/9-simplified.html | 1,656,409,368,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103360935.27/warc/CC-MAIN-20220628081102-20220628111102-00404.warc.gz | 621,367,257 | 3,507 | What is 20/9 simplified?
Here we will simplify 20/9 to its simplest form and convert it to a mixed number if necessary.
In the fraction 20/9, 20 is the numerator and 9 is the denominator.
When you ask "What is 20/9 simplified?", we assume you want to know how to simplify the numerator and denominator to their smallest values, while still keeping the same value of the fraction.
We do this by first finding the greatest common factor of 20 and 9, which is 1.
Then, we divide both 20 and 9 by the greatest common factor to get the following simplified fraction:
20/9
Therefore, this equation is true:
20/9 = 20/9
If the numerator is greater than or equal to the denominator of a fraction, then it is called an improper fraction. In that case, you could convert it into a whole number or mixed number fraction.
20/9 = 2 2/9
Simplify Fractions
Here you can submit another fraction for us to simplify:
/
What is 20/10 simplified?
Here is the next fraction on our list that we simplified. | 243 | 997 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.53125 | 5 | CC-MAIN-2022-27 | latest | en | 0.92428 |
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