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https://bjlkeng.github.io/posts/autoregressive-autoencoders/ | 1,656,206,388,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103036363.5/warc/CC-MAIN-20220626010644-20220626040644-00509.warc.gz | 197,102,617 | 14,171 | # Autoregressive Autoencoders
You might think that I'd be bored with autoencoders by now but I still find them extremely interesting! In this post, I'm going to be explaining a cute little idea that I came across in the paper MADE: Masked Autoencoder for Distribution Estimation. Traditional autoencoders are great because they can perform unsupervised learning by mapping an input to a latent representation. However, one drawback is that they don't have a solid probabilistic basis (of course there are other variants of autoencoders that do, see previous posts here, here, and here). By using what the authors define as the autoregressive property, we can transform the traditional autoencoder approach into a fully probabilistic model with very little modification! As usual, I'll provide some intuition, math and an implementation.
#### Vanilla Autoencoders
The basic autoencoder is a pretty simple idea. Our primary goal is take an input sample $x$ and transform it to some latent dimension $z$ (encoder), which hopefully is a good representation of the original data. As usual, we need to ask ourselves: what makes a good representation? An autoencoder's answer: "A good representation is one where you can reconstruct the original input!". The process of transforming the latent dimension $z$ back to a reconstructed version of the input $\hat{x}$ is called the decoder. It's an "autoencoder" because it's using the same value $x$ value on the input and output. Figure 1 shows a picture of what this looks like.
Figure 1: Vanilla Autoencoder (source: Wikipedia)
From Figure 1, we typically will use a neural network as the encoder and a different (usually similar) neural network as the decoder. Additionally, we'll typically put a sensible loss function on the output to ensure $x$ and $\hat{x}$ are as close as possible:
\begin{align*} \mathcal{L_{\text{binary}}}({\bf x}) &= \sum_{i=1}^D -x_i\log \hat{x}_i - (1-x_i)\log(1-\hat{x_i}) \tag{1} \\ \mathcal{L_{\text{real}}}({\bf x}) &= \sum_{i=1}^D (x_i - \hat{x}_i)^2 \tag{2} \end{align*}
Here we assume that our data point ${\bf x}$ has $D$ dimensions. The loss function we use will depend on the form of the data. For binary data, we'll use cross entropy and for real-valued data we'll use the mean squared error. These correspond to modelling $x$ as a Bernoulli and Gaussian respectively (see the box).
Negative Log-Likelihoods (NLL) and Loss Functions
The loss functions we typically use in training machine learning models are usually derived by an assumption on the probability distribution of each data point (typically assuming identically, independently distributed (IID) data). It just doesn't look that way because we typically use the negative log-likelihood as the loss function. We can do this because we're usually just looking for a point estimate (i.e. optimizing) so we don't need to worry about the entire distribution, just a single point that gives us the highest probability.
For example, if our data is binary, then we can model it as a Bernoulli with parameter $p$ on the interval $(0,1)$. The probability of seeing a given 0/1 $x$ value is then:
\begin{equation*} P(x) = p^x(1-p)^{(1-x)} \tag{3} \end{equation*}
If we take the logarithm and negate it, we get the binary cross entropy loss function:
\begin{equation*} \mathcal{L_{\text{binary}}}(x) = -x\log p - (1-x)\log(1-p) \tag{4} \end{equation*}
This is precisely the expression from Equation 1, except we replace $x=x_i$ and $p=\hat{x_i}$, where the former is the observed data and latter is the estimate of the parameters that our model gives.
Similarly, we can do the same trick with a normal distribution. Given an observed real-valued data point $x$, the probability density for parameters $\mu, \sigma^2$ is given by:
\begin{equation*} p(x) = \frac{1}{\sqrt{2\pi \sigma^2}} e^{-\frac{(x-\mu)^2}{2\sigma^2}} \tag{5} \end{equation*}
Taking the negative logarithm of this function, we get:
\begin{equation*} -\log p(x) = \frac{1}{2}\log(2\pi \sigma^2) + \frac{1}{2\sigma^2} (x-\mu)^2 \tag{6} \end{equation*}
Now if we assume that the variance is the same fixed value for all our data points, then the only parameter we're optimizing for is $\mu$. So adding and multiplying a bunch of constants to our main expression doesn't change the optimal (highest probability) point so we can just simplify it (when optimizing) and still get the same point solution:
\begin{align*} \underset{\mu}{\operatorname{argmax}} -\log p(x) = \underset{\mu}{\operatorname{argmax}} \mathcal{L_{\text{real}}}(x) = \underset{\mu}{\operatorname{argmax}} (x-\mu)^2 \\ \tag{7} \end{align*}
Here our observation is $x$ and our model would produce an estimate of the parameter $\mu$ i.e. $\hat{x}$ in this case. I have some more details on this in one of my previous posts on regularization.
##### Losing Your Identity
Now this is all well and good but an astute observer will notice that unless we put some additional constraints, our autoencoder can just set $z=x$ (i.e. the identity function) and generate a perfect reconstruction. What better representation for a reconstruction than exactly the original data? This is not desirable because we originally wanted to find a good latent representation for $z$, not just regurgitate $x$! We can easily solve this though by making it difficult to learn just the identity function.
The easiest method is to just make the dimensions of $z$ smaller than $x$. For example, if your image has 900 pixels (30 x 30) then make the dimensions of $z$, say 100. In this way, you're "forcing" the autoencoder to learn a more compact representation.
Another method used in denoising autoencoders is to artificially introduce noise on the input $x' = \text{noise}(x)$ (e.g. Gaussian noise) but still compare the output of the decoder with the clean value of $x$. The intuition here is that a good representation is robust to any noise that you might give it. Again, this prevents the autoencoder from just learning the identify mapping (because your input is not the same as your output anymore).
In both cases, you will eventually end up with a pretty good latent representation of $x$ that can be used in all sorts of applications such as semi-supervised learning.
##### Proper Probability Distributions
Although vanilla autoencoders do pretty well in learning a latent representation of data in an unsupervised manner, they don't have a proper probabilistic interpretation. We put a loss function on the outputs of the autoencoder in Equation 1 and 2 but that doesn't automatically mean our autoencoder will generate a proper distribution of the data! Let me explain.
Ideally, we would like the unsupervised autoencoder to learn the distribution of the data. That is, for each one of our $\bf x$ values, we would like to be able to evaluate the probability $P({\bf x})$ to see how often we would expect to see this data point. Implicitly this means that if we sum over all possible $\bf x$ values, we should get $1$, i.e. $\sum_{\bf x} P({\bf x}) = 1$. For traditional autoencoders, we can show that this property is not guaranteed.
Consider two samples $\bf x_1$, and $\bf x_2$. Let's say (regardless of what type of autoencoder we use) our neural network "memorizes" these two samples and is able to reconstruct them perfectly. That is, pass $\bf x_1$ into the autoencoder and get exactly $\bf x_1$ back; pass $\bf x_2$ into the autoencoder and get exactly $\bf x_2$ back. If this happened, it would be a good thing (as long as we had a bottleneck or a denoising autoencoder) because we have a learned a really powerful latent representation that can reconstruct the data perfectly! However, this implies the loss from Equation 1 (or 2 in the continuous case) is $0$. If we negate and take the exponential to translate it to a probability this means both $P({\bf x_1})=1$ and $P({\bf x_2})=1$, which of course is not a valid probability distribution. In contrast, if our model did model the data distribution properly, then we would end up with a fully generative model, where we could do nice things like sample from it (e.g. generate new images).
For vanilla autoencoders, we started with some neural network and then tried to apply some sort of probabilistic interpretation that didn't quite work out. I like it the other way around: start with a probabilistic model and then figure out how to use neural networks to help you add more capacity and scale it.
#### Autoregressive Autoencoders
So vanilla autoencoders don't quite get us to a proper probability distribution but is there a way to modify them to get us there? Let's review the product rule:
\begin{equation*} p({\bf x}) = \prod_{i=1}^{D} p(x_i | {\bf x}_{<i}) \tag{8} \end{equation*}
where ${\bf x}_{<i} = [x_1, \ldots, x_{i-1}]$. Basically, component $i$ of ${\bf x}$ only depends on the dimensions of $j < i$.
So how does this help us? In vanilla autoencoders, each output $\hat{x_i}$ could depend on any of the components input $x_1,\ldots,x_n$, as we saw before, this resulted in an improper probability distribution. If we start with the product rule, which guarantees a proper distribution, we can work backwards to map the autoencoder to this model.
For example, let's consider binary data (say a binarized image). $\hat{x_1}$ does not depend on any other components of ${\bf x}$, therefore our implementation should just need to estimate a single parameter $p_1$ for this pixel. How about $\hat{x_2}$ though? Now we let $\hat{x_2}$ depend only on $x_1$ since we have $p(x_2|x_1)$. This dependency can be modelled using a non-linear function... say maybe a neural network? So we'll have some neural net that maps $x_1$ to the $\hat{x_2}$ output. Now consider the general case of $\hat{x_j}$, we can have a neural net that maps $\bf x_{<j}$ to the $\hat{x_j}$ output. Lastly, there's no reason that each step needs to be a separate neural network, we can just put it all together in a single shared neural network so long as we follow a couple of rules:
1. Each output of the network $\hat{x}_i$ represents the probability distribution $p(x_i|{\bf x_{<i}})$.
2. Each output $\hat{x_i}$ can only have connections (recursively) to smaller indexed inputs $\bf x_{<i}$ and not any of the other ones.
Said another way, our neural net first learns $p(x_1)$ (just a single parameter value in the case of binarized data), then iteratively learns the function mapping from ${\bf x_{<j}}$ to $x_j$. In this view of the autoencoder, we are sequentially predicting (i.e. regressing) each dimension of the data using its previous values, hence this is called the autoregressive property of autoencoders.
Now that we have a fully probabilistic model that uses autoencoders, let's figure out how to implement it!
##### Masks and the Autoregressive Network Structure
The autoregressive autoencoder is referred to as a "Masked Autoencoder for Distribution Estimation", or MADE. "Masked" as we shall see below and "Distribution Estimation" because we now have a fully probabilistic model. ("Autoencoder" now is a bit looser because we don't really have a concept of encoder and decoder anymore, only the fact that the same data is put on the input/output.)
From the autoregressive property, all we want to do is ensure that we only have connections (recursively) from inputs $i$ to output $j$ where $i < j$. One way to accomplish this is to not make the unwanted connections in the first place, but that's a bit annoying because we can't easily use our existing infrastructure for neural networks.
The main observation here is that a connection with weight zero is the same as no connection at all. So all we have to do is zero-out the weights we don't want. We can do that easily with a "mask" for each weight matrix which says which connections we want and which we don't.
This is a simple modification to our standard neural networks. Consider a one hidden layer autoencoder with input $x$:
\begin{align*} {\bf h}({\bf x}) &= {\bf g}({\bf b} + {\bf (W \odot M^W)x}) \\ {\hat{\bf x}} &= \text{sigm}({\bf c} + {\bf (V \odot M^V)h(x)}) \tag{9} \end{align*}
where:
• $\odot$ is an element wise product
• $\bf x, \hat{x}$ is our vectors of input/output respectively
• $\bf h(x)$ is the hidden layer
• $\bf g(\cdot)$ is the activation function of the hidden layer
• $\text{sigm}(\cdot)$ is the sigmoid activation function of the output layer
• $\bf b, c$ are the constant biases for the hidden/output layer respectively
• $\bf W, V$ are the weight matrices for the hidden/output layer respectively
• $\bf M^W, M^V$ are the weight mask matrices for the hidden/output layer respectively
So long as our masks are set such that the autoregressive property is satisfied, the network can produce a proper probability distribution. One subtlety here is that for each hidden unit, we need to define an index that says which inputs it can be connected to (which also determines which index/output in the next layer it can be connected to). We'll use the notation in the paper of $m^l(k)$ to denote the index assigned to hidden node $k$ in layer $l$. Our general rule for our masks is then:
\begin{align*} M^{W^l}_{k', k} = \left\{ \begin{array}{ll} 1 \text{ if } m^l(k') \geq m^{l-1}(k) \\ 0 \text{ otherwise} \end{array} \right. \\ \tag{10} \end{align*}
Basically, for a given node, only connect it to nodes in the previous layer that have an index less than or equal to its index. This will guarantee that a given index will recursively obey our auto-regressive property.
The output mask has a slightly different rule:
\begin{align*} M^{V}_{d, k} = \left\{ \begin{array}{ll} 1 \text{ if } d > m^{L}(k) \\ 0 \text{ otherwise} \end{array} \right. \\ \tag{11} \end{align*}
which replaces the less than equal with just an equal. This is important because the first node should not depend on any other ones so it should not have any connections (will only have the bias connection), and the last node can have connections (recursively) to every other node except its respective input.
Finally, one last topic to discuss is how to assign $m^l(k)$. It doesn't really matter too much as long as you have enough connections for each index. The paper did a natural thing and just sampled from a uniform distribution with range $[1, D-1]$. Why only up to $D-1$? Recall, we should never assign index $D$ because it will never be used so there's no use in connecting anything to $D$ (nothing can ever depend on the $D^{\text{th}}$ input). Figure 2 (from the original paper) shows this whole process pictorially.
A few things to notice:
• Output 1 is not connected to anything. It will just be estimated with a single constant parameter derived from the bias node.
• Input 3 is not connected to anything because no node should depend on it (autoregressive property).
• $m^l(k)$ are more or less assigned randomly.
• If you trace back from output to input, you will see that the autoregressive property is maintained.
So then implementing MADE is as simple as providing a weight mask and doing an extra element-wise product. Pretty simple, right?
##### Ordering Inputs, Masks, and Direct Connections
A few other minor topics that can improve the performance of the MADE. The first is the ordering of the inputs. We've been taking about "Input 1, 2, 3, ..." but usually there is no natural ordering of the inputs. We can arbitrarily pick any ordering that we want just by shuffling ${\bf m^0}$, the selection layer for the input. This can even be performed at each mini-batch to get an "average" over many different models.
The next idea is also very similar, instead of just resampling the input selection, resample all ${\bf m^L}$ selections. In the paper, they mention the best results are having a fixed number of configurations for these selections (and their corresponding masks) and rotating through them in the mini-batch training.
The last idea is just to add a direct connection path from input to output like so:
\begin{equation*} {\hat{\bf x}} = \text{sigm}\big({\bf c} + {\bf (V \odot M^V)h(x)}\big) + \big({\bf A} \odot {\bf M^A}\big){\bf x} \tag{12} \end{equation*}
where ${\bf A}$ is the weight matrix that directly connects inputs to outputs, and ${\bf M^A}$ is the corresponding mask matrix that follows the autoregressive property.
##### Generating New Samples
One final idea that isn't explicitly mentioned in the paper is how to generate new samples. Remember, we now have a fully generative probabilistic model for our autoencoder. It turns out it's quite easy but a bit slow. The main idea (for binary data):
1. Randomly generate vector ${\bf x}$, set $i=1$.
2. Feed ${\bf x}$ into autoencoder and generate outputs $\hat{\bf x}$ for the network, set $p=\hat{x_i}$.
3. Sample from a Bernoulli distribution with parameter $p$, set input $x_{i}=\text{Bernoulli}(p)$.
4. Increment $i$ and repeat steps 2-4 until i > D.
Basically, we're iteratively calculating $p(x_i|{\bf x_{<i}})$ by doing a forward pass on the autoencoder each time. Along the way, we sample from the Bernoulli distribution and feed the sampled value back into the autoencoder to compute the next parameter for the next bit. It's a bit inefficient but MADE is also a relatively small modification to the vanilla autoencoder so you can't ask for too much.
I implemented a MADE layer and built a network using a binarized MNIST dataset similar to what they used in the original paper (notebook).
My implementation is a lot simpler than the one used in the paper. I used Keras and created a custom "MADE" layer that took as input the number of layers, number of hidden units per layer, whether or not to randomize the input selection, as well as standard stuff like dropout and activation function. I didn't implement any of the randomized masks for minibatchs because it was a bit of a pain. I did implement the direct connection though.
(As an aside: I'm really a big fan of higher-level frameworks like Keras, it's quite wonderful. The main reason is that for most things I have the nice Keras frontend, and then occasionally I can dip down into the underlying primitives when needed via the Keras "backend". I suspect when I eventually get around to playing with RNNs it's not going to be as wonderful but for now I quite like it.)
I was able to generate some new digits that are not very pretty, shown in Figure 3.
Figure 3: Generated MNIST images using Autoregressive Autoencoder
It's a bit hard to make out any numbers here. If you squint hard enough, you can make out some "4"s, "3"s, "6"s, maybe some "9"s? The ones in the paper look a lot better (although still not perfect, there were definitely some that were hard to make out).
The other thing is that I didn't use their exact version of binarized MNIST, I just took the one from Keras and did a round() on each pixel. This might also explain why I was unable to get as good of a negative log-likelihood as them. In the paper they report values $< 90$ (even with a single mask) but the lowest I was able to get on my test set was around $99$, and that was after a bunch of tries tweaking the batch and learning rate (more typical was around $120$). It could be that their test set was easier, or the fact that they did some hyper-parameter tuning for each experiment, whereas I just did some trial and error tuning.
##### Implementation Notes
Here are some random notes that I came across when building this MADE:
• Adding a direct (auto-regressive) connection between inputs and outputs seemed to make a huge difference (150 vs. < 100 loss). For me, this basically was the make-or-break piece for implementing a MADE. It's funny that it's just a throw-away paragraph in the actual paper. Probably because the idea was from an earlier paper in 2000 and not the main contribution of the paper. For some things, you really have to implement it to understand the important parts, papers don't tell the whole story!
• I had to be quite careful when coding up layers since getting the indexes for selection exactly right is important. I had a few false starts because I mixed up the indexes. When using the high-level Keras API, there's not much of this detailed work, but when implementing your own layers it's important!
• I tried a random ordering (just a single one for the entire training, not one per batch) and it didn't really seem to do much.
• In their actual implementation, they also add dropout to all their layers. I added it too but didn't play around with it much except to try to tune it to get a lower NLL. One curious thing I found out was about using the set_learning_phase() API. When implementing dropout, I basically just took the code from the dropout layer and inserted into my custom layer. However, I kept getting an error, it turns out that I had to use set_learning_phase(1) during training, and set_learning_phase(0) during prediction because the Keras dropout implementation uses in_train_phase(<train_input>, <test_input>), which switches between two behaviours for training/testing based on the status of this bit. For some reason when using the regular dropout layer you don't have to do this but when doing it in a custom layer you do? I suspect I missed something in my custom layer that happens in the dropout layer.
#### Conclusion
So yet another post on autoencoders, I can't seem to get enough of them! Actually I still find them quite fascinating, which is why I'm following this line of research about fully probabilistic generative models. There's still at least one or two more papers in this area that I'm really excited to dig into (at which point I'll have approached the latest published work), so expect more to come!
I'm Brian Keng, a former academic, current data scientist and engineer. This is the place where I write about all things technical.
Signup for Email Blog Posts | 5,359 | 21,846 | {"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} | 3.3125 | 3 | CC-MAIN-2022-27 | latest | en | 0.875942 |
http://hismath.blogspot.com/2005/05/jsh-sft-is-not-easy.html | 1,502,969,972,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886103270.12/warc/CC-MAIN-20170817111816-20170817131816-00597.warc.gz | 197,794,040 | 6,301 | JSH: SFT is not easy
Well actually verifying the SFT equations myself was very useful in multiple ways.
For one thing, it revealed the role of experimentation, and convinced me that the theorem itself is just a step along the path to a practical factoring method.
That is good and it probably means that it's not trivial to figure out all the in's and out's to getting it to work, but there are simple reasons why it must be possible to find a way to get it to work.
In trying to explain before I ran into a flurry of hostile and disparaging postings from people who were making it their business to try and distract from the actual issues.
Now that I realize that it takes some time to figure out how to get from the SFT to a practical factoring algorithm, I realize just how dangerous those people are.
It is quite reasonable that there has been a delay up until now, and it's possible that there will be an indefinite delay while the mechanics of using the SFT are figured out.
So, why do I know it must work?
Well, given
ab = M
where 'a' and 'b' are rationals, and M is an integer with, say, two prime factors, the number of factors that will give a non-trivial factorization is infinite, as is the number of factors that will give a trivial factorization.
For some odd reason, posters have gotten away with arguing a relative size difference between these twin infinities, to push the argument that as M gets larger and its prime factors get larger, you have a lower probability of getting 'a' and 'b' such that M is non-trivially factored.
That makes no sense though, as in even a small range, like from 1/2 to 1 in rationals, you have an infinity of solutions to 'a' that would non-trivially factor M, without regard to the size of M.
That's important. So, say, if M is the largest public key known, there are an *infinite* number of rationals in the range from 1/2 to 1 that will factor M non-trivially.
There are an infinite number that will trivially factor it as well.
The reality is that the SFT allows you to do what has never been possible before, which is, if you wished, check in the range from 1/2 to 1, to get one of your factors of the surrogate, and see what happens.
You can experiment.
That means that the people who check may figure out what the people who do not, can't.
And someone might just get lucky and stumble across something.
It's already clear that using integer factors of the surrogate doesn't work well--so easiest is out--and I'll probably research that area as I'm curious.
But who knows when I'll move on to fractions.
I kind of like you people. You're so...calm...and as you're calm, things can progress slowly, which I think may just save us all.
Eventually, yeah, I think that RSA is toast, but it might take a few months, as the research progresses.
It's about time and mental effort, and luck, at this point.
And everybody has a chance. | 672 | 2,904 | {"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} | 3.375 | 3 | CC-MAIN-2017-34 | longest | en | 0.97719 |
http://www.docstoc.com/docs/123633510/RCC-DESIGN | 1,405,262,410,000,000,000 | text/html | crawl-data/CC-MAIN-2014-23/segments/1404776438296.25/warc/CC-MAIN-20140707234038-00097-ip-10-180-212-248.ec2.internal.warc.gz | 260,202,060 | 17,169 | # RCC DESIGN
Document Sample
``` As per RCC design ( B.C. punmia ) page 184 example 7.6
DESIGN OF CANTILEVER CHAJJA
A cantilever slab bends down wards, with the result that tension is devloped at
the upper face. Hence reiforcement is provided at upper face, The span of slab is taken equal to
the actual length.or over hang plus half the effective depth If the width of cantilever is long, 1meter
length of the cantilever is taken for the design purpose. However, if the the width of cantilever is
short, whole width may be taken as the width of slab for design purpose.
As per RCC design ( B.C. punmia ) page 184 example 7.6
DESIGN OF CANTILEVER CHAJJA
Name of work :- pkn
1 Cear Span 1.25 mtr 1250 mm
2 Wall width 0.30 mtr 300 mm
3 Super imposed loads (with finishing) 1800 N/m2 or 1.80 kN/m2
4 Concrete M- 20 wt.of concrete 25000
scbc 7 m 13.3
5 Steel fy 415 Tensile stress 230
6 Assume average thickness 100 mm 0.10 mtr
7 Nominal Cover 20 mm Effective Cover 30
8 Reinforcement
Main Top bars 8 mm F 300 mm
Distribution bars 8 mm F 300 mm
300
1250
8 mm f .bars 300 mm c/c
8 mm f bars 300 mm c/c
100
mm
150
mm
(A) X - section
pk_nandwana @yahoo.co.in
A
N/m3
2
N/mm
mm
15 115 20 45 33 44 18 40 20 41 20 40 18 40 16 34 # 34 26
As per RCC design ( B.C. punmia ) page 184 example 7.6
#VALUE!
Cear Span 1.25 mtr 1250 mm
Wall width 0.30 mtr 300 mm
Super imposed loads (with finishing) 1800 N/m2 or Or 1.80 kN/m2
Assume average thickness 100 mm Or 0.10 mtr
Concrete M 20
Steel fy 415 N/mm2 Tensile stess = 230 N/mm2
Nominal cover 20 mm
Effective cover 30 mm
1 Design Constants:- For HYSD Bars Cocrete M = 20
sst = = 230 N/mm2 wt. of concrete = 25000 N/mm
2
scbc = = 7 N/mm3
m = 13.33
m*c 13.33 x 7
k= = = 0.289
m*c+sst 13.33 x 7 + 230
j=1-k/3 = 1 - 0.289 / 3 = 0.904
R=1/2xc x j x k = 0.5 x 7 x 0.904 x 0.289 = 0.9130
2 Caculcation of B.M. :-
Dead weight, per m2 = 0.10 x 1x 1 x #### = 2500 N
Super imposed loads (with finishing) = = 1800 N
= Total weight = 4300 N
Max. possible wL2 4300 x( 1.25 )2 3359
Bending moment
= = = 3.359 x 10 6 K N-m
2 2 .= N m
Vmax. = wL = 4300 x 1.25 = 5375 N
2 Design of setion :-
Effective depth 3.359 x 10 6
Rxb = = 61 mm
required = 0.913 x 1000
From stiffness (i.e. deflection) point of view, L/d = 7for a cantilever where L=l+d/2 =
= 1250 + 50 = 1300 mm say For M20-Fe415 combination p1.lim'=0.44%
Hence modification factore for HYSD bars W 1.30 mm
Hence d = L/ 1.300 x 7 = 1300 /( 1.30 x 7 )W 143 mm
However, this is a structure of minor importance keep D = 150 mm at the support.
Keeping nominal cover of = 20 mm
and using 8 mm F bars, D = 150 - 20 - 4 = 126 mm
Reduce D = 100 mm at free end
4 Steel Reiforcement :-
BM 3.36 x 10 6
Ast = = = 128 mm2
sst x j x D 230 x 0.904 x 126
2
using 8 mm bars A = 3.14xdia = 3.14 x 8 x 8
= 50.2 mm2
4 x100 4 x 100
Nomber of Bars = Ast/A = 128 / 50 = 2.55 say = 3 No.
Maximum permissble spacing = 3 x d = 3 x 150 = 450 mm or 300 mm
which ever is smaller.
Hence Provided 8 mm F bar, @ 300 mm c/c .
1000 x 50.2
Actual Ast= = 167 mm2
300
pk_nandwana@yahoo.co.in
5 Embeded of reinforcement in supports.:-
In order to devlopfull tensile strength at face of support, each bars should be embeded
into support by a length equal to Ld = 45 F = 45 x 8= 360 mm.
0
This could be best achieved by providing one bend of 90 where anchor value of this bend=8F
= 8 x 8 = 64 mm. Thus total anchorage achieved value
= 300 - 20 + 64 +( 150 - 2.00 x 20 - 4 )'= 450 mm
= 450 > Ld Hence O.K. Ld = 360
6 Check for shear :-
Neglecting the taper and taking an average d=( 150 + 100 )- 20 = 105 mm
2
V = 5375 N b= 1000 mm d = 105 mm
V 5375
tv = = = 0.051 N/mm2
bxd 1000 x 105
Permissible value of t c = 0.18 x 1.30 = 0.234 N/mm2
For M 20 grade concrete and
100Ast 100 x 167
p' = = = 0.16 %
bd 1000 x 105
Hence from Table permissible shear (tc)for M 20 concrete, for 0.16 % steel = 0.18 N/mm2
here tv < tc Hence safe
7 Distribution reinforcement:- Avrage depth = 125 mm
Asd = 0.12 x bxD 0.12 x 1000 x D
= = 1.20 D
100 100
"= 1.20 x 125 = 150 mm
3.14 x 8 x 8
Using 8 mm F bars each having = = 50.2 mm2
4 x 100
1000 x As 1000 x 50.2 = 335 mm
pitch s= =
Asd 150
However, provied these @ 300 mm c/c .
7 Details of reinforcement:- Shown in drawing
pk_nandwana@yahoo.co.in
W
W
Name of work :- pkn
wall width
300
1250
8 mm bars @ 300 C/C 8 mm bars @ 300 C/C
100
150
VALUES OF DESIGN CONSTANTS
Grade of concrete M-15 M-20 M-25 M-30 M-35 M-40 Grade of concrete
Modular Ratio 18.67 13.33 10.98 9.33 8.11 7.18 tbd (N / mm2)
scbc N/mm2 5 7 8.5 10 11.5 13
m scbc 93.33 93.33 93.33 93.33 93.33 93.33
(a) sst = kc 0.4 0.4 0.4 0.4 0.4 0.4
140 jc 0.867 0.867 0.867 0.867 0.867 0.867
N/mm2 Rc 0.867 1.214 1.474 1.734 1.994 2.254
(Fe 250) Pc (%) 0.714 1 1.214 1.429 1.643 1.857
kc 0.329 0.329 0.329 0.329 0.329 0.329
(b) sst = jc 0.89 0.89 0.89 0.89 0.89 0.89
190
Rc 0.732 1.025 1.244 1.464 1.684 1.903
N/mm2
Pc (%) 0.433 0.606 0.736 0.866 0.997 1.127
(c ) sst = kc 0.289 0.289 0.289 0.289 0.289 0.289
230 jc 0.904 0.904 0.904 0.904 0.904 0.904
N/mm2 Rc 0.653 0.914 1.11 1.306 1.502 1.698
(Fe 415) Pc (%) 0.314 0.44 0.534 0.628 0.722 0.816
(d) sst = kc 0.253 0.253 0.253 0.253 0.253 0.253
275 jc 0.916 0.916 0.916 0.914 0.916 0.916
N/mm2 Rc 0.579 0.811 0.985 1.159 1.332 1.506
(Fe 500) Pc (%) 0.23 0.322 0.391 0.46 0.53 0.599
Permissible shear stress Table tv in concrete (IS : 456-2000)
100As Permissible shear stress in concrete tv N/mm2
bd M-15 M-20 M-25 M-30 M-35 M-40
< 0.15 0.18 0.18 0.19 0.2 0.2 0.2
0.25 0.22 0.22 0.23 0.23 0.23 0.23
0.50 0.29 0.30 0.31 0.31 0.31 0.32
0.75 0.34 0.35 0.36 0.37 0.37 0.38
1.00 0.37 0.39 0.40 0.41 0.42 0.42
1.25 0.40 0.42 0.44 0.45 0.45 0.46
1.50 0.42 0.45 0.46 0.48 0.49 0.49
1.75 0.44 0.47 0.49 0.50 0.52 0.52
2.00 0.44 0.49 0.51 0.53 0.54 0.55
2.25 0.44 0.51 0.53 0.55 0.56 0.57
2.50 0.44 0.51 0.55 0.57 0.58 0.60
2.75 0.44 0.51 0.56 0.58 0.60 0.62
3.00 and above 0.44 0.51 0.57 0.6 0.62 0.63
Maximum shear stress tc.max in concrete (IS : 456-2000)
Grade of concrete M-15 M-20 M-25 M-30 M-35 M-40
tc.max 1.6 1.8 1.9 2.2 2.3 2.5
Shear stress tc Reiforcement %
100As 100As
M-20 M-20
bd bd
0.15 0.18 0.18 0.15
0.16 0.18 0.19 0.18
0.17 0.18 0.2 0.21
0.18 0.19 0.21 0.24
0.19 0.19 0.22 0.27
0.2 0.19 0.23 0.3
0.21 0.2 0.24 0.32
0.22 0.2 0.25 0.35
0.23 0.2 0.26 0.38
0.24 0.21 0.27 0.41
0.25 0.21 0.28 0.44
0.26 0.21 0.29 0.47
0.27 0.22 0.30 0.5
0.28 0.22 0.31 0.55
0.29 0.22 0.32 0.6
0.3 0.23 0.33 0.65
0.31 0.23 0.34 0.7
0.32 0.24 0.35 0.75
0.33 0.24 0.36 0.82
0.34 0.24 0.37 0.88
0.35 0.25 0.38 0.94
0.36 0.25 0.39 1.00
0.37 0.25 0.4 1.08
0.38 0.26 0.41 1.16
0.39 0.26 0.42 1.25
0.4 0.26 0.43 1.33
0.41 0.27 0.44 1.41
0.42 0.27 0.45 1.50
0.43 0.27 0.46 1.63
0.44 0.28 0.46 1.64
0.45 0.28 0.47 1.75
0.46 0.28 0.48 1.88
0.47 0.29 0.49 2.00
0.48 0.29 0.50 2.13
0.49 0.29 0.51 2.25
0.5 0.30
0.51 0.30
0.52 0.30
0.53 0.30
0.54 0.30
0.55 0.31
0.56 0.31
0.57 0.31
0.58 0.31
0.59 0.31
0.6 0.32
0.61 0.32
0.62 0.32
0.63 0.32
0.64 0.32
0.65 0.33
0.66 0.33
0.67 0.33
0.68 0.33
0.69 0.33
0.7 0.34
0.71 0.34
0.72 0.34
0.73 0.34
0.74 0.34
0.75 0.35
0.76 0.35
0.77 0.35
0.78 0.35
0.79 0.35
0.8 0.35
0.81 0.35
0.82 0.36
0.83 0.36
0.84 0.36
0.85 0.36
0.86 0.36
0.87 0.36
0.88 0.37
0.89 0.37
0.9 0.37
0.91 0.37
0.92 0.37
0.93 0.37
0.94 0.38
0.95 0.38
0.96 0.38
0.97 0.38
0.98 0.38
0.99 0.38
1.00 0.39
1.01 0.39
1.02 0.39
1.03 0.39
1.04 0.39
1.05 0.39
1.06 0.39
1.07 0.39
1.08 0.4
1.09 0.4
1.10 0.4
1.11 0.4
1.12 0.4
1.13 0.4
1.14 0.4
1.15 0.4
1.16 0.41
1.17 0.41
1.18 0.41
1.19 0.41
1.20 0.41
1.21 0.41
1.22 0.41
1.23 0.41
1.24 0.41
1.25 0.42
1.26 0.42
1.27 0.42
1.28 0.42
1.29 0.42
1.30 0.42
1.31 0.42
1.32 0.42
1.33 0.43
1.34 0.43
1.35 0.43
1.36 0.43
1.37 0.43
1.38 0.43
1.39 0.43
1.40 0.43
1.41 0.44
1.42 0.44
1.43 0.44
1.44 0.44
1.45 0.44
1.46 0.44
1.47 0.44
1.48 0.44
1.49 0.44
1.50 0.45
1.51 0.45
1.52 0.45
1.53 0.45
1.54 0.45
1.55 0.45
1.56 0.45
1.57 0.45
1.58 0.45
1.59 0.45
1.60 0.45
1.61 0.45
1.62 0.45
1.63 0.46
1.64 0.46
1.65 0.46
1.66 0.46
1.67 0.46
1.68 0.46
1.69 0.46
1.70 0.46
1.71 0.46
1.72 0.46
1.73 0.46
1.74 0.46
1.75 0.47
1.76 0.47
1.77 0.47
1.78 0.47
1.79 0.47
1.80 0.47
1.81 0.47
1.82 0.47
1.83 0.47
1.84 0.47
1.85 0.47
1.86 0.47
1.87 0.47
1.88 0.48
1.89 0.48
1.90 0.48
1.91 0.48
1.92 0.48
1.93 0.48
1.94 0.48
1.95 0.48
1.96 0.48
1.97 0.48
1.98 0.48
1.99 0.48
2.00 0.49
2.01 0.49
2.02 0.49
2.03 0.49
2.04 0.49
2.05 0.49
2.06 0.49
2.07 0.49
2.08 0.49
2.09 0.49
2.10 0.49
2.11 0.49
2.12 0.49
2.13 0.50
2.14 0.50
2.15 0.50
2.16 0.50
2.17 0.50
2.18 0.50
2.19 0.50
2.20 0.50
2.21 0.50
2.22 0.50
2.23 0.50
2.24 0.50
2.25 0.51
2.26 0.51
2.27 0.51
2.28 0.51
2.29 0.51
2.30 0.51
2.31 0.51
2.32 0.51
2.33 0.51
2.34 0.51
2.35 0.51
2.36 0.51
2.37 0.51
2.38 0.51
2.39 0.51
2.40 0.51
2.41 0.51
2.42 0.51
2.43 0.51
2.44 0.51
2.45 0.51
2.46 0.51
2.47 0.51
2.48 0.51
2.49 0.51
2.50 0.51
2.51 0.51
2.52 0.51
2.53 0.51
2.54 0.51
2.55 0.51
2.56 0.51
2.57 0.51
2.58 0.51
2.59 0.51
2.60 0.51
2.61 0.51
2.62 0.51
2.63 0.51
2.64 0.51
2.65 0.51
2.66 0.51
2.67 0.51
2.68 0.51
2.69 0.51
2.70 0.51
2.71 0.51
2.72 0.51
2.73 0.51
2.74 0.51
2.75 0.51
2.76 0.51
2.77 0.51
2.78 0.51
2.79 0.51
2.80 0.51
2.81 0.51
2.82 0.51
2.83 0.51
2.84 0.51
2.85 0.51
2.86 0.51
2.87 0.51
2.88 0.51
2.89 0.51
2.90 0.51
2.91 0.51
2.92 0.51
2.93 0.51
2.94 0.51
2.95 0.51
2.96 0.51
2.97 0.51
2.98 0.51
2.99 0.51
3.00 0.51
3.01 0.51
3.02 0.51
3.03 0.51
3.04 0.51
3.05 0.51
3.06 0.51
3.07 0.51
3.08 0.51
3.09 0.51
3.10 0.51
3.11 0.51
3.12 0.51
3.13 0.51
3.14 0.51
3.15 0.51
Permissible Bond stress Table tbd in concrete (IS : 456-2000)
Grade of concreteM-10 M-15 M-20 M-25 M-30 M-35 M-40 M-45
tbd (N / mm2) -- 0.6 0.8 0.9 1 1.1 1.2 1.3
Development Length in tension
Grade of Plain M.S. Bars H.Y.S.D. Bars
concrete tbd (N / mm2) kd = Ld F tbd (N / mm2) k d = Ld F
M 15 0.6 58 0.96 60
M 20 0.8 44 1.28 45
M 25 0.9 39 1.44 40
M 30 1 35 1.6 36
M 35 1.1 32 1.76 33
M 40 1.2 29 1.92 30
M 45 1.3 27 2.08 28
M 50 1.4 25 2.24 26
Permissible stress in concrete (IS : 456-2000)
Permission stress in compression (N/mm 2) Permissible stress in bond (Average) for
Bending acbc Direct (acc) plain bars in tention (N/mm2)
concrete
(N/mm2) Kg/m2 (N/mm2) Kg/m2 (N/mm2) in kg/m2
M 10 3.0 300 2.5 250 -- --
M 15 5.0 500 4.0 400 0.6 60
M 20 7.0 700 5.0 500 0.8 80
M 25 8.5 850 6.0 600 0.9 90
M 30 10.0 1000 8.0 800 1.0 100
M 35 11.5 1150 9.0 900 1.1 110
M 40 13.0 1300 10.0 1000 1.2 120
M 45 14.5 1450 11.0 1100 1.3 130
M 50 16.0 1600 12.0 1200 1.4 140
00)
M-50
1.4
```
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## You must determine the length of a long, thin wire that is suspended from the ceiling in the atrium of a tall building. A 2.00-cm-long piece of the wire is left over from its installation. Using an analytical balance, you determine that the mass of the spare piece is 14.5 mg. You then hang a 0.400 kg mass from the lower end of the long, suspended wire. When a small-amplitude transverse wave pulse is sent up that wire, sensors at both ends measure that it takes the wave pulse 26.7 ms to travel the length of the wire. (a) Use these measurements to calculate the length of the wire. Assume that the weight of the wire has a negligible effect on the speed of the transverse waves. (b) Discuss the accuracy of the approximation made in part (a).
You must determine the length of a long, thin wire that is suspended
from the ceiling in the atrium of a tall building. A 2.00-cm-long
piece of the wire is left over from its installation. Using an analytical
balance, you determine that the mass of the spare piece is 14.5 mg.
You then hang a 0.400 kg mass from the lower end of the long, suspended
wire. When a small-amplitude transverse wave pulse is sent up
that wire, sensors at both ends measure that it takes the wave pulse 26.7 ms
to travel the length of the wire. (a) Use these measurements to calculate the
length of the wire. Assume that the weight of the wire has a negligible effect
on the speed of the transverse waves. (b) Discuss the accuracy of the approximation
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# Einstein's Relativity Coffin nail # 9
## Year 2006 Case NV CMa binary stars apsidal motion
By Professor Joe Nahhas
joenahhas1958@yahoo.com
1973.
## Here is me in year 2009 showing my 1979 thermo book with my
picture stapled next to most notable Physicists of past 350 years
whispering; it is not only Einstein is wrong but physics is wrong for past
350 years. It is time for change; regime change. It is time to end the
western Royals Imperials and Corporate Physicists monopoly on
physics taught and learned in past 350 years is at least 51 % wrong
and Modern Physics is at least 88.88 % silly and because there is
better physics and better physics is real time physics.
The elimination of relativity theory and annexation of quantum mechanics to classical
mechanics is a matter of time and not a matter of science because time is a scale and not a
dimension. A measurement is an event taken in present time of an event that happened in
the past. We measure what is happening live in present time of what had already
happened in past time.
Present time = present time
Present time = past time + [present time - past time]
Present time = past time + the difference between past time and present time
Measurement time = event time + time delays
Experiment = theory + corrections
Real time physics = event time physics + delay time physics
## An event: r (θ, 0) = [a (1-ε²)/ (1+ ε cosine θ)] Planet motion Event
Time factor {e [λ (r) + ỉ ω (r)] t}
Physics live: r (θ, t) = [a (1-ε²)/ (1+ε cosine θ)] {e [λ (r) + ỉ ω (r)] t}
Perihelion advance corrections:
W" (ob) = (-720x36526x3600/T) {[√ (1-ε²)]/ (1-ε) ²} [(v* + v°)/c] ²
= 43.11” of an arc per century for mercury
## "The silly notion of time as a dimension can be sent back to sender"
Abstract: This is the solution to the 150 years apsidal motion puzzle solution that is not
solvable by space-time physics or any said or published physics including 109 years of
noble prize winner physics and 400 years of astronomy. Binary stars apsidal motion or
"Apparent" rate of orbital axial rotation is projected light aberrations visual effects along
the line of sight of moving objects applied to the angular velocity at Apses. From the
thousands of close binary stars astronomers picked a dozen sets of binary stars systems
that would be a good test of relativity theory and collected data for all past century and
relativity theory failed every one of them. This rate of "apparent" axial rotation is given
by this new equation
W° (ob) = (-720x36526/T) {[√ (1-ε²)]/ (1-ε) ²]} [(v° + v*)/c] ² degrees/100 years
T = period; ε = eccentricity; v° = spin velocity effect; v*= orbital velocity effect
When applied to NV Canis Majoris binary stars
Apsidal period of U = 1757.5 years
## Real time universal mechanics solution
All there is in the Universe is objects of mass m moving in space (x, y, z) at a location
r = r (x, y, z). The state of any object in the Universe can be expressed as the product
S = m r; State = mass x location:
## P = d S/d t = m (d r/d t) + (dm/d t) r = Total moment
= change of location + change of mass
= m v + m' r; v = velocity = d r/d t; m' = mass change rate
## F = d P/d t = d²S/dt² = Total force
= m (d²r/dt²) +2(dm/d t) (d r/d t) + (d²m/dt²) r
= m γ + 2m'v +m" r; γ = acceleration; m'' = mass acceleration rate
## In polar coordinates system
We Have r = r r (1) ;v = r' r(1) + r θ' θ(1) ; γ = (r" - rθ'²)r(1) + (2r'θ' + r θ")θ(1)
r = location; v = velocity; γ = acceleration
F = m γ + 2m'v +m" r
F = m [(r"-rθ'²) r (1) + (2r'θ' + r θ") θ (1)] + 2m'[r' r (1) + r θ' θ (1)] + (m" r) r (1)
= [d² (m r)/dt² - (m r) θ'²] r (1) + (1/mr) [d (m²r²θ')/d t] θ (1)
= [-GmM/r²] r (1) ------------------------------- Newton's Gravitational Law
Proof:
First r = r [cosine θ î + sine θ Ĵ] = r r (1)
Define r (1) = cosine θ î + sine θ Ĵ
Define v = d r/d t = r' r (1) + r d[r (1)]/d t
= r' r (1) + r θ'[- sine θ î + cosine θĴ]
= r' r (1) + r θ' θ (1)
## Define θ (1) = -sine θ î +cosine θ Ĵ;
And with r (1) = cosine θ î + sine θ Ĵ
## Then d [θ (1)]/d t= θ' [- cosine θ î - sine θ Ĵ= - θ' r (1)
And d [r (1)]/d t = θ' [-sine θ î + cosine θ Ĵ] = θ' θ (1)
## Define γ = d [r' r (1) + r θ' θ (1)] /d t
= r" r (1) + r'd [r (1)]/d t + r' θ' r (1) + r θ" r (1) +r θ'd [θ (1)]/d t
γ = (r" - rθ'²) r (1) + (2r'θ' + r θ") θ (1)
## With d² (m r)/dt² - (m r) θ'² = -GmM/r² Newton's Gravitational Equation (1)
And d (m²r²θ')/d t = 0 Central force law (2)
(2): d (m²r²θ')/d t = 0
Then m²r²θ' = constant
= H (0, 0)
= m² (0, 0) h (0, 0); h (0, 0) = r² (0, 0) θ'(0, 0)
= m² (0, 0) r² (0, 0) θ'(0, 0); h (θ, 0) = [r² (θ, 0)] [θ'(θ, 0)]
= [m² (θ, 0)] h (θ, 0); h (θ, 0) = [r² (θ, 0)] [θ'(θ, 0)]
= [m² (θ, 0)] [r² (θ, 0)] [θ'(θ, 0)]
= [m² (θ, t)] [r² (θ, t)] [θ' (θ, t)]
= [m²(θ, 0) m²(0,t)][ r²(θ,0)r²(0,t)][θ'(θ, t)]
= [m²(θ, 0) m²(0,t)][ r²(θ,0)r²(0,t)][θ'(θ, 0) θ' (0, t)]
## With m²r²θ' = constant
Differentiate with respect to time
Then 2mm'r²θ' + 2m²rr'θ' + m²r²θ" = 0
Divide by m²r²θ'
Then 2 (m'/m) + 2(r'/r) + θ"/θ' = 0
This equation will have a solution 2 (m'/m) = 2[λ (m) + ì ω (m)]
And 2(r'/r) = 2[λ (r) + ì ω (r)]
And θ"/θ' = -2{λ (m) + λ (r) + ỉ [ω (m) + ω (r)]}
## Then (m'/m) = [λ (m) + ì ω (m)]
Or d m/m d t = [λ (m) + ì ω (m)]
And dm/m = [λ (m) + ì ω (m)] d t
[λ (m) + ì ω (m)] t
Then m = m (0) e
[λ (m) + ì ω (m)] t
m = m (0) m (0, t); m (0, t) e
With initial spatial condition that can be taken at t = 0 anywhere then m (0) = m (θ, 0)
[λ (m) + ì ω (m)] t
And m = m (θ, 0) m (0, t) = m (θ, 0) e
[λ (m) + ì ω (m)] t
And m (0, t) = e
Similarly we can get
[λ (r) + ì ω (r)] t
Also, r = r (θ, 0) r (0, t) = r (θ, 0) e
[λ (r) + ì ω (r)] t
With r (0, t) = e
-2{[λ(m) + λ(r)] + ì [ω(m) + ω(r)]}t
Then θ'(θ, t) = {H(0, 0)/[m²(θ,0) r(θ,0)]}e -----I
-2{[λ (m) + λ(r)] + ì [ω (m) + ω (r)]} t
And θ'(θ, t) = θ' (θ, 0)] e ------------------------I
And, θ'(θ, t) = θ' (θ, 0) θ' (0, t)
-2{[λ (m) + λ (r)] + ì [ω (m) + ω(r)]} t
And θ' (0, t) = e
Also θ'(θ, 0) = H (0, 0)/ m² (θ, 0) r² (θ, 0)
And θ'(0, 0) = {H (0, 0)/ [m² (0, 0) r (0, 0)]}
## With (1): d² (m r)/dt² - (m r) θ'² = -GmM/r² = -Gm³M/m²r²
And d² (m r)/dt² - (m r) θ'² = -Gm³ (θ, 0) m³ (0, t) M/ (m²r²)
Let m r =1/u
Then d (m r)/d t = -u'/u² = - (1/u²) (θ') d u/d θ = (- θ'/u²) d u/d θ = -H d u/d θ
And d² (m r)/dt² = -Hθ'd²u/dθ² = - Hu² [d²u/dθ²]
## -Hu² [d²u/dθ²] - (1/u) (Hu²)² = -Gm³ (θ, 0) m³ (0, t) Mu²
[d²u/ dθ²] + u = Gm³ (θ, 0) m³ (0, t) M/ H²
t = 0; m³ (0, 0) = 1
u = Gm³ (θ, 0) M/ H² + A cosine θ =Gm (θ, 0) M (θ, 0)/ h² (θ, 0)
## And m r = 1/u = 1/ [Gm (θ, 0) M (θ, 0)/ h (θ, 0) + A cosine θ]
= [h²/ Gm (θ, 0) M (θ, 0)]/ {1 + [Ah²/ Gm (θ, 0) M (θ, 0)] [cosine θ]}
= [h²/Gm (θ, 0) M (θ, 0)]/ (1 + ε cosine θ)
## Then m (θ, 0) r (θ, 0) = [a (1-ε²)/ (1+ ε cosine θ)] m (θ, 0)
Dividing by m (θ, 0)
Then r (θ, 0) = a (1-ε²)/ (1+ ε cosine θ)
This is Newton's Classical Equation solution of two body problem which is the equation
of an ellipse of semi-major axis of length a and semi minor axis b = a √ (1 - ε²) and focus
length c = ε a
And m r = m (θ, t) r (θ, t) = m (θ, 0) m (0, t) r (θ, 0) r (0, t)
[λ (r) + ì ω (r)] t
Then, r (θ, t) = [a (1-ε²)/ (1+ ε cosine θ)] e --------------------------- II
This is Newton's time dependent equation that is missed for 350 years
If λ (m) ≈ 0 fixed mass and λ(r) ≈ 0 fixed orbit; then
ì ω (r) t
Then r (θ, t) = r (θ, 0) r (0, t) = [a (1-ε²)/ (1+ε cosine θ)] e
+ ì ω (m) t ì ω (m) t
And m = m (θ, 0) e = m (θ, 0) e
## We Have θ'(0, 0) = h (0, 0)/r² (0, 0) = 2πab/ Ta² (1-ε) ²
= 2πa² [√ (1-ε²)]/T a² (1-ε) ²
= 2π [√ (1-ε²)]/T (1-ε) ²
Then θ'(0, t) = {2π [√ (1-ε²)]/ T (1-ε) ²} Exp {-2[ω (m) + ω (r)] t
= {2π [√ (1-ε²)]/ (1-ε) ²} {cosine 2[ω (m) + ω (r)] t - ỉ sin 2[ω (m) + ω (r)] t}
= θ'(0, 0) {1- 2sin² [ω (m) + ω (r)] t}
- 2i θ'(0, 0) sin [ω (m) + ω (r)] t cosine [ω (m) + ω (r)] t
## Then θ'(0, t) = θ'(0, 0) {1 - 2sine² [ω (m) t + ω (r) t]}
- 2ỉ θ'(0, 0) sin [ω (m) + ω(r)] t cosine [ω (m) + ω(r)] t
## Δ θ' (0, t) = Real Δ θ' (0, t) + Imaginary Δ θ (0, t)
Real Δ θ (0, t) = θ'(0, 0) {1 - 2 sine² [ω (m) t ω(r) t]}
## Let W (cal) = Δ θ' (0, t) (observed) = Real Δ θ (0, t) - θ'(0, 0)
= -2θ'(0, 0) sine² [ω (m) t + ω(r) t]
= -2[2π [√ (1-ε²)]/T (1-ε) ²] sine² [ω (m) t + ω(r) t]
And W (cal) = -4π [√ (1-ε²)]/T (1-ε) ²] sine² [ω (m) t + ω(r) t]
## If this apsidal motion is to be found as visual effects, then
With, v ° = spin velocity; v* = orbital velocity; v°/c = tan ω (m) T°; v*/c = tan ω (r) T*
Where T° = spin period; T* = orbital period
And ω (m) T° = Inverse tan v°/c; ω (r) T*= Inverse tan v*/c
W (ob) = -4 π [√ (1-ε²)]/T (1-ε) ²] sine² [Inverse tan v°/c + Inverse tan v*/c] radians
Multiplication by 180/π
W (ob) = (-720/T) {[√ (1-ε²)]/ (1-ε) ²} sine² {Inverse tan [v°/c + v*/c]/ [1 - v° v*/c²]}
degrees and multiplication by 1 century = 36526 days and using T in days
## W° (ob) = (-720x36526/Tdays) {[√ (1-ε²)]/ (1-ε) ²} x
sine² {Inverse tan [v°/c + v*/c]/ [1 - v° v*/c²]} degrees/100 years
Approximations I
## With v° << c and v* << c, then v° v* <<< c² and [1 - v° v*/c²] ≈ 1
Then W° (ob) ≈ (-720x36526/Tdays) {[√ (1-ε²)]/ (1-ε) ²} x sine² Inverse tan [v°/c + v*/c]
degrees/100 years
Approximations II
With v° << c and v* << c, then sine Inverse tan [v°/c + v*/c] ≈ (v° + v*)/c
W° (ob) = (-720x36526/Tdays) {[√ (1-ε²)]/ (1-ε) ²} x [(v° + v*)/c] ² degrees/100 years
This is the equation that gives the correct apsidal motion rates -----------------------III
The circumference of an ellipse: 2πa (1 - ε²/4 + 3/16(ε²)²- --.) ≈ 2πa (1-ε²/4); R =a (1-ε²/4)
Where v (m) = √ [GM²/ (m + M) a (1-ε²/4)]
And v (M) = √ [Gm² / (m + M) a (1-ε²/4)]
Looking from top or bottom at two stars they either spin in clock (↑) wise or counter
clockwise (↓)
Looking from top or bottom at two stars they either approach each other coming from the
top (↑) or from the bottom (↓)
Knowing this we can construct a table and see how these two stars are formed. There are
many combinations of velocity additions and subtractions and one combination will give
the right answer.
1- Advance of Perihelion of mercury. [No spin factor] Because data are given with no
spin factor
30
G=6.673x10^-11; M=2x 10 kg; m=.32x1024kg; ε = 0.206; T=88days
And c = 299792.458 km/sec; a = 58.2km/sec; 1-ε²/4 = 0.989391
With v° = 2meters/sec
And v *= √ [GM/a (1-ε²/4)] = 48.14 km/sec
Calculations yields: v = v* + v° = 48.14km/sec (mercury)
And [√ (1- ε²)] (1-ε) ² = 1.552
W" (ob) = (-720x36526x3600/T) {[√ (1-ε²)]/ (1-ε) ²} (v/c) ²
W" (ob) = (-720x36526x3600/88) x (1.552) (48.14/299792)² = 43.0”/century
This is the rate of for the advance of perihelion of planet mercury explained as "apparent"
without the use of fictional forces or fictional universe of space-time confusions of
physics of relativity.
## Venus Advance of perihelion solution:
W" (ob) = (-720x36526x3600/T) {[√ (1-ε²)]/ (1-ε) ²} [(v°+ v*)/c] ² seconds/100 years
Calculations
## 1-ε = 0.0068; (1-ε²/4) = 0.99993; [√ (1-ε²)] / (1-ε) ² = 1.00761
G=6.673x10^-11; M (0) = 1.98892x19^30kg; R = 108.2x10^9m
## V* (p) = √ [GM²/ (m + M) a (1-ε²/4)] = 41.64 km/sec
Advance of perihelion of Venus motion is given by this formula:
W" (ob) = (-720x36526x3600/T) {[√ (1-ε²)]/ (1-ε) ²]} [(v° + v*)/c] ² seconds/100 years
W" (ob) = (-720x36526x3600/T) {[√ (1-ε²)]/ (1-ε) ²} sine² [Inverse tan 41.64/300,000]
= (-720x36526x3600/224.7) (1.00762) (41.64/300,000)²
## W" (observed) = 8.2"/100 years; observed 8.4"/100years
This is a proof that not only space-time physicists are incompetent liars but it does not
require fictional forces or universes to example an insignificant issue of advance of
perihelion which says that every 301395.3488 years Mercury does one extra run around
mother sun
Looking from top or bottom at two stars they either spin in clock (↑) wise or counter
clockwise (↓)
Looking from top or bottom at two stars they either approach each other coming from the
top (↑) or from the bottom (↓)
Knowing this we can construct a table and see how these two stars are formed. There are
many combinations of velocity additions and subtractions and one combination will give
the right answer.
NV CMa Binary stars apsidal motion table
Primary → v°(p) ↑ v* (p)↑ v° (p) ↑v* (p)↓ v° (p) ↓ v* (p) ↑ v° (p) ↓V* (p) ↓
Secondary ↓
v°(s) ↑ v* (s)↑ Spin=[↑,↑] [↑,↑][↓,↑] [↓,↑][↑,↑] [↓,↑][↓,↑]
[↑,↑]=orbit
Spin results v°(p) + v°(s) v°(p) + v°(s) - v°(p) + v°(s) -v°(p) + v°(s)
Orbit results v*(p) + v*(s) -v*(p) + v*(s) v* (p) + v*(s) -v* (p) + v* (s)
Examples NV CMa
v° (s) ↑v* (s)↓ [↑,↑][↑,↓] [↑,↑][↓,↓] [↓,↑][↑,↓] [↓,↑][↓,↓]
Spin results v°(p) + v°(s) v°(p) + v°(s) -v°(p) + v°(s) -v°(p) + v°(s)
Orbit results v*(p) - v*(s) -v*(p) - v*(s) v*(p) - v*(s) -v* (p) - v* (s)
Examples
v° (p) ↓ v*(s) ↑ [↑,↓][↑,↑] [↑,↓][↓,↑] [↓,↓][↑,↑] [↓,↓][↓,↑]
Spin results v°(p) - v°(s) v°(p) - v°(s) -v°(p) - v°(s) -v°(p) - v°(s)
Orbit results v*(p) + v*(s) -v*(p) + v*(s) v*(p) + v*(s) -v* (p) + v* (s)
Examples
v° (s) ↓V*(s) ↓ [↑,↓][↑,↓] [↑,↓][↓,↓] [↓,↓][↑,↓] [↓,↓][↓,↓]
Spin results v°(p) - v°(s) v°(p) - v°(s) -v°(p) - v°(s) -v°(p) - v°(s)
Orbit results v*(p) - v*(s) -v*(p) - v*(s) v*(p) - v*(s) -v* (p) - v* (s)
Examples NV CMa
## Data: T=1.885159 days; ε = 0; v* (p) = 128.55 km/sec; v* (s) = 130.87 km/sec
[√ (1-ε²)] / (1-ε) ² = 3.33181; v° (p) = 51.7 km/sec and v° (s) = 52.4 km/sec
## Apsidal motion is given by this formula:
W° (ob) = (-720x36526/T) {[√ (1-ε²)]/ (1-ε) ²]} [(v° + v*)/c] ² degrees/100 years
With v* = v* (p) + v*(s) = 259.42 km/sec and v° = v° (p) + v° (s) = 104.1
And v* + v° = 363.52 km/sec
W° (observed) = (-720x36526/T) {[√ (1-ε²)]/ (1-ε) ²} sine² [Inverse tan 363.52/300,000]
= (-720x36526/1.885159) (1) (363.52/300,000)²
= 20.48333818°/century = 0.2048333818°/year
U = 360°/0.2048333818°/year;
U = 1757. 5 years
## References: Go to Smithsonian/NASA website SAO/NASA and type:
Absolute dimensions NV CMa; Kaluzny, J; Pych, W; Rucinski, S. M; Thompson, I.B | 6,248 | 13,846 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2019-13 | latest | en | 0.917119 |
http://www.riddlesandanswers.com/tag/hard-riddles/7/ | 1,580,322,494,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579251801423.98/warc/CC-MAIN-20200129164403-20200129193403-00334.warc.gz | 256,720,072 | 26,504 | # HARD RIDDLES
### Fun Facts (Hints)
Hard riddles are universal, and continue to leave a lasting impression on many different cultures across the globe. Here are some interesting facts:
• The mere definition of what a riddle is, is something that has drawn a large amount of debate between scholars for centuries.
• Complex riddles have been used since ancient times, and extensively in ancient/medieval literature.
• There is only one riddle in the Bible appearing in the book of Judges. It is known as "Samson's riddle."
• Charades is a popular contemporary game created with the use of riddle.
• In author J. R. R. Tolkien's 'The Hobbit' Bilbo Baggins is given a challenging riddle by Gollum, and his life was dependent upon getting the correct answer.
#### Popular Searches
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## Eight Eights
Hint:
888 + 88 + 8 + 8 + 8 = 1000.
Did you answer this riddle correctly?
YES NO
Solved: 60%
## 2 Fathers And 2 Sons Riddle
Hint:
One of the 'fathers' is also a grandfather. Therefore the other father is both a son and a father to the grandson.
In other words, the one father is both a son and a father.
Did you answer this riddle correctly?
YES NO
Solved: 78%
## Who Owns The Fish?
Hint:
The German sits in his Green House, smoking his Prince cigars, drinking coffee, and watching his FISH.
The rest go like this-
1st House: Yellow, Norwegian, Water, Cats, Dunhill
2nd House: Blue, Dane, Tea, Horse, Blends
3rd House: Red, Brit, Milk, Birds, Pall Malls
4th House: Green, German, Coffee, FISH, Prince
5th House: White, Swede, Beer, Dogs, Bluemasters
Did you answer this riddle correctly?
YES NO
Solved: 67%
## How Many Pieces Of Chicken?
Hint:
After 6 all numbers divisible by 3 can be ordered (because they can all be expressed as a sum of 6's and 9's). After 26, all numbers divisible by three when subtracted by 20 can be obtained. After 46, all numbers divisible by three when subtracted by 40 can be obtained. After 46, all numbers fit into one of these 3 categories, so all numbers can be obtained. 43 is the last number that doesn't fall into one of these categories (44 = 20 + 6 * 4, 45 = 6 * 6 + 9).
Did you answer this riddle correctly?
YES NO
Solved: 17%
## A Man In New York City
Hint:
When he gets on the subway it is 6 stops away from the end of the line (end of the track). So when it reaches this point it begins to work backwards. So when it goes back one stop he has traveled 7 stops but is only 5 away from where he began.
Did you answer this riddle correctly?
YES NO
Solved: 43%
## Closed Areas Riddle
Hint:
4
Look at how many closed areas there are.
9999 has 4 closed areas (the top of the '9')
8888 has 8 closed areas, the top and bottom parts of the 8 and there are no other digits
1816 has 3 closed areas, (top and bottom of 8 and bottom of 6, and it has 2 other digits ( 3*2=6)
1212 has 0 closed areas,(0*4=0)
Did you answer this riddle correctly?
YES NO
Solved: 45%
## I Have Keys But No Lock
Hint:
A keyboard.
Did you answer this riddle correctly?
YES NO
Solved: 57%
## Post Your Hard Riddles Below
Can you come up with a cool, funny or clever Hard Riddles of your own? Post it below (without the answer) to see if you can stump our users.
Prev 1 ... 2 3 4 5 6 7 | 908 | 3,253 | {"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-2020-05 | latest | en | 0.947873 |
https://ge-spark.com/electrical-energy/your-question-what-is-the-difference-between-electric-force-and-electricity.html | 1,656,873,394,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656104248623.69/warc/CC-MAIN-20220703164826-20220703194826-00286.warc.gz | 328,923,014 | 19,016 | # Your question: What is the difference between electric force and electricity?
Contents
Charges that are different attract each other. The interaction between electric charges is called electricity. The force between charged objects is called electric force.
## Is electricity a form of electric force?
Electric force exists between charges, as described by Coulomb’s Law. Worked example: a line of charge with q off the end. Written by Willy McAllister. Our study of electricity begins with electrostatics and the electrostatic force, one of the four fundamental forces of nature.
## What is an electric force?
The attractive or repulsive interaction between any two charged objects is an electric force. Like any force, its effect upon objects is described by Newton’s laws of motion. The electric force – Felect – joins the long list of other forces that can act upon objects.
## What is electric force example?
Electrical Force Examples
The charge in a bulb. Electric circuits. Static friction between cloth when rubbed by a dryer. The shock that is felt after touching a doorknob.
The electrostatic force is an attractive and repulsive force between particles are caused due to their electric charges. The electric force between stationary charged bodies is conventionally known as the electrostatic force. It is also referred to as Columb’s force.
THIS IS UNIQUE: Quick Answer: Why is argon gas used along with tungsten wire in an electric bulb?
## What is electric force Class 12?
Electric field is a force produced by a charge near its surroundings. This force is exerted on other charges when brought in the vicinity of this field. SI unit of electric field is N/C (Force/Charge).
## What is electric force formula?
The electrostatic force exerted by a point charge on a test charge at a distance r depends on the charge of both charges, as well as the distance between the two. The electric field E is defined to be E=Fq E = F q , where F is the Coulomb or electrostatic force exerted on a small positive test charge q.
## What is the difference between static electricity and current electricity?
The most significant difference between the static electricity and the current electricity is that in that static electricity the charges are at rest and they are accumulated on the surface of the insulator, whereas, in current electricity the electrons are in state of motion inside the conductor.
## What is the law of electric force?
Coulomb’s law states that the electrical force between two charged objects is directly proportional to the product of the quantity of charge on the objects and inversely proportional to the square of the separation distance between the two objects.
## What is the symbol for electric force?
Symbols for physical quantities and their international units
symbol quantity symbol
FE, FE electric force, electrostatic force N
E, E electric field N/C, V/m
ΦE electric flux N m2/C, V m
U, UE potential energy, electric potential energy J
## Who is the father of voltage?
The Father of Voltage – Alessandro Volta
Discovering that electrical potential stored in a capacitor is proportional to its electrical charge. Volta was also credited with creating the first electric battery, called the Voltaic Pile, which allowed scientists of the time to create a steady flow of electrons.
THIS IS UNIQUE: What is the best climate for solar panels?
## Who invented phones?
Alexander Graham Bell is often credited with being the inventor of the telephone since he was awarded the first successful patent. However, there were many other inventors such as Elisha Gray and Antonio Meucci who also developed a talking telegraph. First Bell Telephone, June 1875.
## Is electricity made of water?
Flowing water creates energy that can be captured and turned into electricity. This is called hydroelectric power or hydropower. … Water released from the reservoir flows through a turbine, spinning it, which in turn activates a generator to produce electricity. | 803 | 4,013 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.96875 | 4 | CC-MAIN-2022-27 | latest | en | 0.963381 |
http://mathhelpforum.com/calculus/64688-finding-examples-functions-print.html | 1,526,901,874,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794864063.9/warc/CC-MAIN-20180521102758-20180521122758-00537.warc.gz | 186,613,821 | 3,051 | # finding examples for functions
• Dec 12th 2008, 11:45 AM
omert
finding examples for functions
I wanted to find an example for a function that maintains the following conditions:
1. f(x)=? if all the following conditions are correct.
2. if all the following conditions are correct: f(x) is a function that defined in a split domain. I need to find examples for f(x);x>=0 and for f(x);x<0.
• Dec 12th 2008, 06:45 PM
Ziaris
For the first one, one example is $\displaystyle f(x) = \delta(x)$ with $\displaystyle \delta(x)$ being the delta function defined as
$\displaystyle \delta(x) = \begin{cases} \infty, & x = 0 \\ 0, & x \ne 0 \end{cases}.$
I'm not quite understanding what you're asking for in your second problem. A piecewise function that satisfies the limits provided is
$\displaystyle f(x) = \begin{cases}\frac{1}{x+1/2}, & x\geq 0 \\ x+6, & x<0 \end{cases}.$
Hopefully that's what you meant.
• Dec 12th 2008, 11:04 PM
omert
thanks for the second example! but in the first one I need a function that not defined in a split domain!!!
l
• Dec 12th 2008, 11:11 PM
Mathstud28
Quote:
Originally Posted by omert
thanks for the second example! but in the first one I need a function that not defined in a split domain!!!
l
$\displaystyle f(x)=\frac{1}{\sqrt{|x|}}$. You can find a million examples, all they need to do is fill three criterion: they are dominated by x as x goes to zero, they are even, and obviously the second criterion you set. Some other examples would be $\displaystyle f(x)=\ln\left(\frac{1}{|x|}\right)$ or $\displaystyle \ln\left(\frac{1}{x^{2n}}\right)~n\in\mathbb{N}$ | 483 | 1,600 | {"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} | 4.0625 | 4 | CC-MAIN-2018-22 | latest | en | 0.854242 |
https://optionsphqc.web.app/spino45441mogo/variable-interest-rate-bonds-quizlet-1228.html | 1,642,754,000,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320302740.94/warc/CC-MAIN-20220121071203-20220121101203-00407.warc.gz | 414,892,943 | 6,275 | ## Variable interest rate bonds quizlet
Start studying Fin 350 test 2. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Search. Variable interest rate bonds a. do not mature b. are an example of a discount bond Quizlet Live. Quizlet Learn. Diagrams. Flashcards. Mobile. Help. Sign up. Help Center. Honor Code. If interest rates rise after a bond is issued, 1. the bond may be called 2. the firm may repurchase the bond 3. the current yield exceeds the yield to maturity 4. the current yield is less than the yield to maturity Select one: a. 1 and 3 b. 1 and 4 c. 2 and 3 d. 2 and 4
A variable-rate demand bond is a type of municipal bond (muni) with floating coupon payments that are adjusted at specific intervals. The bond is payable to the bondholder upon demand following an interest rate change. Generally, the current money market rate is used to set the interest rate, Variable rate bonds, or loans made by issuers to bondholders, or lenders, may yield taxable or tax-free coupon interest. Coupon interest must be paid to lenders twice per year. According to the Federal Reserve Bank of San Francisco, low interest coupon bonds make variable rate bonds more appealing to investors. Variable Interest Rate: A variable interest rate is an interest rate on a loan or security that fluctuates over time, because it is based on an underlying benchmark interest rate or index that A floating-rate bond operates differently -- the bond issuer regularly adjusts the interest rate on a floater to match some well-known rate, such as LIBOR or the Fed Funds rate. Because floating-rate bonds pay a variable amount of interest equal to prevailing interest rates, Unlike traditional bonds that pay a fixed rate of interest, floating-rate bonds have a variable rate that resets periodically. Typically, the rates are based on either the federal funds rate or the London Interbank Offered Rate plus an added “spread.” Similar to the federal funds rate, LIBOR is a benchmark rate used by banks making short-term loans to other banks. A bond with a variable interest rate. These bonds typically have coupons renewable every three months and pay according to a set calculation. For example, a note may have an interest rate of "EURIBOR + 1%" and pay whatever the EURIBOR rate happens to be at the time plus 1%. When the LIBOR rate changed to 1.82%, the variable rate then changed to 6.82%. The 5% margin remains constant throughout; only the LIBOR index changes based on market conditions. Common Variable Rate Indices Used for Student Loans LIBOR: An interest rate at which banks can borrow funds from other banks.
## a variable rate of return on the book value of the investment. d. a smaller amount of interest income over the life of the bond issue than would result from use of the
Variable Interest Rate: A variable interest rate is an interest rate on a loan or security that fluctuates over time, because it is based on an underlying benchmark interest rate or index that A floating-rate bond operates differently -- the bond issuer regularly adjusts the interest rate on a floater to match some well-known rate, such as LIBOR or the Fed Funds rate. Because floating-rate bonds pay a variable amount of interest equal to prevailing interest rates, Unlike traditional bonds that pay a fixed rate of interest, floating-rate bonds have a variable rate that resets periodically. Typically, the rates are based on either the federal funds rate or the London Interbank Offered Rate plus an added “spread.” Similar to the federal funds rate, LIBOR is a benchmark rate used by banks making short-term loans to other banks. A bond with a variable interest rate. These bonds typically have coupons renewable every three months and pay according to a set calculation. For example, a note may have an interest rate of "EURIBOR + 1%" and pay whatever the EURIBOR rate happens to be at the time plus 1%. When the LIBOR rate changed to 1.82%, the variable rate then changed to 6.82%. The 5% margin remains constant throughout; only the LIBOR index changes based on market conditions. Common Variable Rate Indices Used for Student Loans LIBOR: An interest rate at which banks can borrow funds from other banks. A variable interest rate loan is a loan in which the interest rate charged on the outstanding balance varies as market interest rates change. As a result, your payments will vary as well (as long as your payments are blended with principal and interest).
### A variable rate mortgage is a type of home loan in which the interest rate is not fixed. Instead, interest payments will be adjusted at a level above a specific benchmark or reference rate (such as LIBOR + 2 points). Lenders can offer borrowers variable rate interest over the life of a mortgage loan.
some of these warnings about a drop in bond prices relate to the potential for a rise in interest rates. Interest rate risk is common to all bonds, particularly bonds Currency exchange rates. • Free trade up a system for buyers and sellers to rate each other. This became if the paint was not able to bond with the surface it. 1. short term rates exceed long term rates 2. long term rates exceed short term rates 3. the Federal Reserve is following a tight monetary policy 4. the Federal Reserve is following an easy monetary policy a. 1 and 3 b. 1 and 4 c. 2 and 3 d. 2 and 4 They are bonds that have a variable coupon interest rate, equal to a money market reference rate, like LIBOR (London Interbank Offered Rate) or federal funds rate, plus a quoted spread (also known as quoted margin). The spread is a rate that remains constant. 1. short-term rates exceed long-term rates 2. long-term rates exceed short-term rates 3. the Federal Reserve is following a tight monetary policy 4. the Federal Reserve is following an easy monetary policy a. 1 and 3 b. 1 and 4 c. 2 and 3 d. 2 and 4
### A variable rate bond allows investors to benefit from rising market interest rates over time. Corporate bonds that receive a ____ rating from credit rating agencies are normally placed at ____ yields.
They are bonds that have a variable coupon interest rate, equal to a money market reference rate, like LIBOR (London Interbank Offered Rate) or federal funds rate, plus a quoted spread (also known as quoted margin). The spread is a rate that remains constant.
## Given the tax benefits, the interest rate for municipal bonds is usually lower than on bond called a “variable rate demand obligation” that resets its interest rate
Variable Interest Rate: A variable interest rate is an interest rate on a loan or security that fluctuates over time, because it is based on an underlying benchmark interest rate or index that A floating-rate bond operates differently -- the bond issuer regularly adjusts the interest rate on a floater to match some well-known rate, such as LIBOR or the Fed Funds rate. Because floating-rate bonds pay a variable amount of interest equal to prevailing interest rates, Unlike traditional bonds that pay a fixed rate of interest, floating-rate bonds have a variable rate that resets periodically. Typically, the rates are based on either the federal funds rate or the London Interbank Offered Rate plus an added “spread.” Similar to the federal funds rate, LIBOR is a benchmark rate used by banks making short-term loans to other banks. A bond with a variable interest rate. These bonds typically have coupons renewable every three months and pay according to a set calculation. For example, a note may have an interest rate of "EURIBOR + 1%" and pay whatever the EURIBOR rate happens to be at the time plus 1%. When the LIBOR rate changed to 1.82%, the variable rate then changed to 6.82%. The 5% margin remains constant throughout; only the LIBOR index changes based on market conditions. Common Variable Rate Indices Used for Student Loans LIBOR: An interest rate at which banks can borrow funds from other banks. A variable interest rate loan is a loan in which the interest rate charged on the outstanding balance varies as market interest rates change. As a result, your payments will vary as well (as long as your payments are blended with principal and interest). Understanding Variable Rate Demand Note (VRDN) A variable rate demand note (VRDN) is a long-term municipal bond which is offered to investors through money market funds. The notes allow a municipal government to borrow money for long periods of time while paying short-term interest rates to investors.
a variable rate of return on the book value of the investment. d. a smaller amount of interest income over the life of the bond issue than would result from use of the Given the tax benefits, the interest rate for municipal bonds is usually lower than on bond called a “variable rate demand obligation” that resets its interest rate some of these warnings about a drop in bond prices relate to the potential for a rise in interest rates. Interest rate risk is common to all bonds, particularly bonds Currency exchange rates. • Free trade up a system for buyers and sellers to rate each other. This became if the paint was not able to bond with the surface it. | 1,927 | 9,154 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.625 | 3 | CC-MAIN-2022-05 | latest | en | 0.911197 |
https://thetopsites.net/article/52667597.shtml | 1,623,786,621,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487621519.32/warc/CC-MAIN-20210615180356-20210615210356-00042.warc.gz | 529,983,853 | 6,569 | ## How to extract just the IN count of a Tableau set
tableau count distinct by group
tableau count number of records in a group
tableau count number of records with same value
tableau number of records by dimension
how to count values in tableau
sum of count in tableau
tableau total count
tableau row count
How can I extract the IN count portion of a Tableau set? I can see the IN/OUT counts when I drop the set into Text but can't figure out how to get at the IN value by itself.
Ultimately, I want to create a Pie Chart of three sets with just the IN counts as the measures.
I am using Tableau Public if that is a factor.
You have to be a little careful about specifying what you wish to count.
One way to think of a set is as a Boolean function that gives a value to each data record denoting whether that record is associated with the set.
Another way to think of a set is as a mathematical set whose members are a subset of the values for some discrete field. (Or Tuple of fields)
The difference between the two views is really just a mindset, whether you consider the set as a Boolean function whose domain is a data row in the data source, or whose domain is the field on which the set definition is based.
Say you are looking at Tableau’s Superstore data set where each data record is a line item for a product attached to an order.
If your set is based on the field Region, say its called [My Favorite Regions] and currently contains {"East", "Central"} do you want your count to be 2 (i.e. the number of regions in the set) ? Or do you want your count to be in the tens of thousands (i.e the number of line items on orders from the regions in the set)? Or something in between, maybe the number of distinct orders (i.e. order ids) within the selected regions...
If you want to count data rows that are associated with the set, you can simply filter by the set and calculate SUM([Number of Records[). If you want to count the regions in the set even though the level of detail of the data is at the order line item level,then you’ll have to use either a COUNTD to count the distinct regions, or some approach to specify what it is you want Tableau to count.
For example, put your set on the filter shelf, and show COUNTD(Region) which could be slow for very large data sets. To get the same effect without an explicit filter, you can define a LOD calculation such as:
```{ COUNTD(if [My Favorite Regions] then [Region] end) }
```
Or you could use a table calc with the SIZE() function to do the calculation in the Tableau client instead of by the data source.
How to Show Top 10 Lists in Tableau Tooltips, 1. Re: Get the count from a set. Hi Pratik, If you drag the Set you created out onto your view, then drag Number of Records up to the Label section of the Marks card, you should be able to see how many are in and out of your set. This function is not available in the following cases: workbooks created before Tableau Desktop 8.2 that use Microsoft Excel or text file data sources, workbooks that use the legacy connection, and workbooks that use Microsoft Access data sources. Extract your data into an extract file to use this function. See Extract Your Data.
Not sure what your data looks like but you could set a certain condition when creating a set or split the IN/OUT into two different sets. Here's a link to sets in Tableau.
of Records measure onto the row or column shelf. You cannot refresh the extract. When connecting directly to an extract, Tableau treats that file as the true source, as opposed to a clone of underlying data. So, it's not possible to relate it back to your source data. The data model and relationships will be lost. The data model and relationships between the tables is stored in the .tds file and not in the .hyper file, so this information is lost when connecting directly to the .hyper file.
You can do this with an if statement
```IF [set] = TRUE THEN 1 ELSE 0 END
```
Then I suppose you could sum this calculated field
The most common usage is when you have a lot of categories and want to create an 'Other' category based on the categories that aren't in a set, if the set is a "Top N Set"
To do this:
```IF [set] = TRUE THEN [dimension] ELSE 'Others' END
```
How do you show only the top 10 values in tableau? Right click datasource --> extract --> Appen Data from file; Select the file to append the data from the extract. The file could be csv, excel, twb or tde extension. Therefore, it is possible to append an extract to the existing extract. Cons: Appending data to an extract is a manual effort and needs to be accomplished via Tableau desktop.
Below are some examples using the sample data set Superstore. CLICK TO EXPAND SOLUTION. Example 1: Using a Range of Values with Assuming you have the permission, you can download the extract from Tableau Server as a.tdsx file. You can then open an instance of Tableau Desktop and connect to the.tdsx as a data source. In Tableau Desktop, you would right-click on the data source and uncheck Use Extract.
Supports large data sets: You can create extracts that contain billions of rows of or supported by the original data, such as the ability to compute Count Distinct. a database view that contains just the data you need for your extract and then In Tableau Server or Tableau Online you can only aggregate the members of the set into In/Out categories. Show In/Out members in a set. In most cases, when you drag a set to the viz, Tableau displays the set using the In/Out mode. This mode separates the set into two categories: In - The members in the set. Out - The members that aren't part of
I'm just wondering, can anyone explain what's happening when tableau So if you have 1,000 rows and 20 columns it will count as 20,000 rows in My data set only has 1000 rows, currently waiting for the Extract to finish Create your chart at the grain you are counting, i.e. Products, Customers, etc. Category, Subcategory, Product. Now, we need to count the number of products within each subcategory. However, we cannot use the built-in COUNT () function because it counts at the grain of the data set, which is at the order line level. | 1,404 | 6,170 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.84375 | 3 | CC-MAIN-2021-25 | latest | en | 0.933753 |
https://wetweet.me/post/16922/how-to-read-schematics-5-steps-with-pictures-wikihow-how-to-read-electrical-diagrams.html | 1,555,830,220,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578530253.25/warc/CC-MAIN-20190421060341-20190421082341-00521.warc.gz | 589,025,985 | 13,189 | Home » Wiring Diagram » How To Read Schematics 5 Steps With Pictures Wikihow How To Read Electrical Diagrams #8620
# How To Read Schematics 5 Steps With Pictures Wikihow How To Read Electrical Diagrams #8620
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Undertaking electrical wiring by oneself can be tricky. This is certainly particularly so once you absence the expertise as well as the experience in electrical things. The matter is you can not do a trial and error process when working with electrical wiring. Mistakes could cost you a fortune as well as your life. Which is why ahead of beginning any do-it-yourself electrical repair, it's important to ask some electrical wiring concerns in order to make certain you understand what you are doing. One thing about electrical wiring is always that wires usually are color coded. Consequently, it can be actually a lot easier to be aware of which of them select which. Below tend to be the most typical electrical wiring thoughts whose solutions commonly contain colours to help you you determine each and every distinct wire. - Basics Of Electrical Wiring
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How do You Wire a Change?
Among quite possibly the most common electrical wiring issues is on how to wire a switch. While making use of switches in your house is fairly simple, wiring one particular might not be that easy for everybody. An ON-OFF switch is definitely quite simple to wire. There are actually several types of switches, but for this example, let us say you are installing a single-pole toggle switch, an incredibly frequent change (and also the simplest).
There are a few colours of wires in the standard single-pole toggle switch: black, white, and green. Splice the black wire in two and join them about the terminal screws - a single on best and the other around the bottom screw with the change. The white wire serves like a resource of uninterrupted electricity and is also commonly related to some light-weight colored terminal screw (e.g., silver). Link the environmentally friendly wire into the ground screw of your change.
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How can You Wire a Ceiling Fan?
For many rationale, how to wire a ceiling fan is likewise one of essentially the most widespread electrical wiring inquiries. To simplify this endeavor, you can use just one switch to get a single ceiling fan. To wire the lover, it is only a make a difference of connecting the black wire of the ceiling fan to the black wire from the change. When there is a lightweight, the blue wire needs to be linked into the black wire with the swap too.
How can You Replace a Breaker and exactly how Does one Incorporate a Sub Panel?
Although lots of endeavor to perform these tasks by themselves, a lot of people are encouraged to hire an electrician rather. It truly is much more difficult and thus perilous for most people to try to interchange a breaker or incorporate a panel. To provide you with an notion about such typical electrical wiring inquiries, you'll need to do the job over a incredibly hot electrical panel. For those who do not even determine what what this means is, you happen to be only not equipped to do the work your self. Even when you must expend much more by using the services of a professional electrician, it is really a great deal safer and more reasonable to accomplish this as an alternative. - How To Read Schematics 5 Steps With Pictures Wikihow How To Read Electrical Diagrams #8620
There are motives why these are generally by far the most commonly questioned electrical wiring queries. A person, quite a few believe it really is easy to do, and two, these are definitely the common electrical responsibilities in your own home. But then you definately shouldn't set your safety at risk as part of your purpose to save money. The stakes could even be a great deal increased when you try to cut costs and do an electrical wiring job with no adequate expertise or expertise.
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### Mechanical Electrical Workshop Jasa Wiring
Disclaimer: All of our content in the form of images we display because we believe the content was public domain. picpaper that displayed are from unknown origin, and we do not intend to infringe any legitimate intellectual, artistic rights or copyright. If you are the legitimate owner of the one of the content we display the picpaper, and do not want us to show, then please contact us and we will immediately take any action is needed either remove the picpaper or maybe you can give time to maturity it will limit our picpaper content view. All of the content we display the picpapers are free to download and therefore we do not acquire good financial gains at all or any of the content of each picpaper. | 1,469 | 6,483 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2019-18 | latest | en | 0.886582 |
https://physics.stackexchange.com/questions/303765/dynamics-of-a-rotating-coin | 1,726,628,194,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651835.68/warc/CC-MAIN-20240918000844-20240918030844-00664.warc.gz | 416,013,101 | 42,714 | # Dynamics of a rotating coin
Sometimes when I'm bored in a waiting area, I would take a coin out of my pocket and spin it on a table. I never really tried to figure out what was going on. But, recently I wondered about two things:
1. Can I determine the critical rotational speed that determines the instant when vertical displacement is involved? (Per Floris' clarification, 'vertical displacement' could be understood as 'tilting over'.)
2. Assuming that the initial rotational impulse is known, can I predict the exact location where the coin lands?
More precisely :
We assume that a coin of dimensions $R=\text{radius and } h=\text{height}$ where $R >> h$ is initially standing on a flat surface prior to receiving a rotational impluse in a plane parallel to the surface. Further, we assume that the coin has mass $M$, with uniform mass distribution and that air resistance is much more important than kinetic friction due to the surface on which the coin spins.
Empirically, I observed that there are two regimes:
1. Sliding contact with the flat surface, while the rotational speed $||\dot{\theta}||\geq c$ where $c$ is a constant which can be determined.
2. Rolling contact without slipping, when $||\dot{\theta}|| < c$
Here's what I've attempted so far:
1. Assuming small rotational speeds, which is reasonable, drag is proportional to the first power of rotational speed:
$$F_D = C_d \dot{\theta} \frac{4 \pi}{3 \pi} \tag{1}$$
where $C_d$ is the drag coefficient and $\frac{4 \pi}{3 \pi}$ is the distance of the centroid of the semicircular half of the coin from the coin's center of gravity. Now the work done by the $F_D$ is proportional to the distance travelled by the centroid on both halves of the coin, so the total energy dissipated at time $t$ is given by:
$$\Delta E(\theta, \dot{\theta},t) = 2 \int_{0}^{t} F_D \theta \frac{4 \pi}{3 \pi}= 2 C_d \big(\frac{4 \pi}{3 \pi}\big)^2 \int_{0}^{t} \dot{\theta} \theta dt= C_d \big(\frac{4 \pi}{3 \pi}\big)^2 {\theta (t)}^2\tag{2}$$
So the energy dissipated is just an explicit function of the angle $\theta$:
$$\Delta E(\theta) = C_d \big(\frac{4 \pi}{3 \pi}\big)^2 {\theta (t)}^2\tag{3}$$
So the Hamiltonian is given by:
$$H(\theta, \dot{\theta}) = \frac{1}{2} I \dot{\theta}^2+mg\frac{h}{2}-\Delta E(\theta) \tag{4}$$
The equations of motion are then given by:
$$\begin{cases} \dot{Q} = \frac{\partial H}{\partial \dot{\theta}} = I \dot{\theta} \\ \dot{P}=-\frac{\partial H}{\partial \theta} = 2 C_d(\frac{4R}{3 \pi})^2 \theta(t) \end{cases} \tag{5}$$
1. It's not clear to me how I should interpret the equations of motion but my hunch is that the first phase has ended when the kinetic energy vanishes. This happens when the dissipated energy equals the kinetic energy:
$$\frac{1}{2} I \dot{\theta}^2=C_d \big(\frac{4 \pi}{3 \pi}\big)^2 {\theta (t)}^2 \tag{6}$$
If we let $C_1 = \frac{I}{2}$ and $C_2 = C_d \big(\frac{4 \pi}{3 \pi}\big)^2$, the solutions I found are of the form:
$$\frac{\dot{\theta}}{\theta} = \sqrt{\frac{C_2}{C_1}} \tag{7}$$
But, this is problematic as the solution is meant to be a unique $\theta$. However, I assume that this difficulty can be resolved and I think it might be due to a problem that occurred earlier.
Now, it remains to explain why the coin enters a second phase and begins to roll without slipping instead of simply stopping completely. My argument is that in practice the surface on which the coin spins is never completely flat, and the initial rotational impulse is never completely planar.
1. In the second phase, assuming that there are no dissipative forces the total energy is given by:
$$E = MgR\sin(\alpha) + \frac{1}{2}I \Omega^2 \sin^2(\alpha) \tag{8}$$
where $\alpha$ is the angle of inclination with respect to the vertical and $\Omega$ is the precession rate. I can go further but the analysis becomes a lot more complicated due to the role of air resistance.
This leads me to two questions:
1. $\theta$ is monotonically increasing as a function of time so shouldn't we find a unique $\theta$ that determines the instant when vertical displacement is involved? (Note: the method I use is to equate kinetic energy and dissipated energy)
2. Beyond imperfect experimental conditions, can the second phase be explained by the minimum potential energy principle? (i.e. there's a theoretical reason why the coin doesn't simply stand still)
References :
3. http://puhep1.princeton.edu/~kirkmcd/examples/rollingdisk.pdf
4. http://www.eulersdisk.com/PRE56610.pdf
• I see that you do not include the drag offered by air. You might find this interesting: spinning ring versus spinning disc .<br> I haven't followed through to the links mentioned there but most probably you will find what you were looking for. Either way it will offer a fresh perspective. Cheers! Commented Jan 8, 2017 at 17:29
• There's a discrepancy in your assumptions: friction can't be so small as to be negligible compared to air drag, yet be large enough to bring the coin into a no slip condition. I believe it's actually the friction that will disrupt a perfectly vertical axis of rotation of a perfectly vertical coin, so neglecting it will prevent you from being able to solve when/how the coin starts tipping.
– Eph
Commented Oct 11, 2017 at 11:43
• I am trying to understand your question - is it "when and why does the coin tip over"? You say "vertical displacement is involved" which I think is just a complicated way of saying "tips over". Right? Commented Dec 22, 2017 at 14:35
• @Floris I didn't want to be misunderstood but I'd say your interpretation is correct.
– user29305
Commented Dec 23, 2017 at 4:15 | 1,520 | 5,632 | {"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": 8, "x-ck12": 0, "texerror": 0} | 3.75 | 4 | CC-MAIN-2024-38 | latest | en | 0.908637 |
https://epiphany-qatar.com/qa/what-is-9-digit-greatest-number.html | 1,653,186,133,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662543264.49/warc/CC-MAIN-20220522001016-20220522031016-00091.warc.gz | 294,134,446 | 37,281 | Asked By: Timothy Robinson Date: created: Feb 25 2021
## What is a nine digit number
Answered By: Brian Thomas Date: created: Feb 28 2021
The smallest 9-digit number is 1 followed by 8 zeros.
This number is called one hundred million.
The largest 9-digit number is 9 followed by another 8 nines.
This number is called nine hundred ninety-nine million nine hundred ninety-nine thousand nine hundred ninety-nine..
Asked By: Oliver Smith Date: created: Mar 28 2021
## What is the greatest 10 digit number
Answered By: Henry Brown Date: created: Mar 29 2021
This number is called one billion. The largest 10-digit number is 9 followed by another 9 nines. This number is called nine billion nine hundred ninety-nine million nine hundred ninety-nine thousand nine hundred ninety-nine. There are a total of nine billion different 10-digit numbers.
Asked By: Seth Cook Date: created: Jun 24 2021
## How many 8-digit numbers are there in all
Answered By: Francis Richardson Date: created: Jun 25 2021
Do you know how many 8-digit numbers are there in all? Answer: There are nine crore 8-digit numbers in all.
Asked By: Jordan Collins Date: created: Mar 24 2022
## Which is the smallest 9 digit number that has neither 0s nor 1s
Answered By: Jonathan Price Date: created: Mar 24 2022
Smallest 9 digit number is 100000000. the answer is 100,000,000 in international system. the answer is 10,00,00,000 in indian system.
Asked By: Zachary Nelson Date: created: Jan 15 2021
## What is the lowest number of 9 digit
Answered By: Neil Nelson Date: created: Jan 16 2021
What is the smallest number of 9 digits? The smallest 9-digit number is 10,00,00,000 and it is read as ten crores.
Asked By: Hayden Wilson Date: created: Mar 18 2022
## Where do 9 digit phone numbers come from
Answered By: Mason Russell Date: created: Mar 21 2022
If you mean 9 digits without including the country code, than there are a lot: Spain, Portugal, Netherlands and much more European countries which has 9 digit phone numbers.
Asked By: Harry Cook Date: created: Feb 26 2021
## What is a 10 digit number called
Answered By: Harold Lopez Date: created: Feb 26 2021
billionYes, a 10-digit number is read as a billion. For example, 2,000,000,000 is read as Two billion.
Asked By: Morgan Rodriguez Date: created: May 12 2022
## How much is a 9 digit number
Answered By: Elijah Foster Date: created: May 15 2022
Unsourced material may be challenged and removed. 100,000,000 (one hundred million) is the natural number following 99,999,999 and preceding 100,000,001.
Professional
### Question: What Is A 6 Digit Verification Code?
What is 6 digit OTP number? OTP is a six-digit numerical code sent in real time as SMS to your registered mobile number while performing the transaction.OTP is mandatory for authorizing the following transactions: Registration of beneficiary bank accounts of other banks.Bill payments.. What is verification code number? A verification code is a 4-digit PIN code that we send to your mobile phone via SMS. We use this code to verify your mobile phone number. This code can only be used once. What is the greatest number of 6 digit? Starting from the greatest 6 - digit number, write the previous five numbers in descending order.Hint: Descending order is arrangement of numbers from largest to smallest.Example 100, 45, 22, 18, 2 are in descending order.As you know the greatest 6 - digit number is 999999.More items... How do I get an OTP number? Step 2. Configure the OTP settingsGo to…
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### Question: What Is Epiphany Anglican?
How long does the epiphany last? Epiphany is celebrated 12 days after Christmas on 6th January (or January 19th for some Orthodox Church who have Christmas on 7th January) and is the time when Christians remember the Wise Men (also sometimes called the Three Kings) who visited Jesus.. What is the last day of Christmas called? Twelfth NightTwelfth Night (also known as Epiphany Eve) is a festival in some branches of Christianity that takes place on the last night of the Twelve Days of Christmas, marking the coming of the Epiphany. When should you take Xmas decorations down? Depending on what you're celebrating it's either January 5 or January 6 - and the last day you should keep festive decorations up. A day sooner or later is considered unlucky and if decorations are not removed on Twelfth Night then according to tradition they should stay up all year. Was there…
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### Question: Will Allah Forgive Me For Hurting Someone?
What makes Allah happy? “Verily, Allah is more pleased with the repentance of His slave than a person who has his camel in a waterless desert carrying his provision of food and drink and it is lost....He takes hold of its reins and then out of boundless joy blurts out: 'O Allah, You are my slave and I am Your Rubb'.. What is considered Zina? Zina encompasses any sexual intercourse except that between husband and wife or between a master and his slave woman. It includes both extramarital sex and premarital sex, and is often translated as "fornication" in English. What does Haram mean? forbidden by Islamic law: forbidden by Islamic law haram foods. Can you pray for Allah to punish someone? May be you could pray Allah to solve the matter and give hidayah to both you and other person. ... No, Punishment is only in Allah's Hands. If…
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### Question: Is It Better To Pray Isha Late?
Is it healthier to sleep naked? Sleeping Naked Is Healthier In addition to the metabolic effects of sleeping in the buff, removing your clothes improves blood circulation, which is good for your heart and muscles.The quality sleep you'll enjoy also increases the release of growth hormone and melatonin, both of which have anti-aging benefits.. How late can you offer Isha? midnight'Isha prayer must be performed before midnight, and it is not permissible to delay it until midnight, because the Prophet (peace and blessings of Allaah be upon him) said: “The time of 'Isha' is until midnight” (narrated by Muslim, al-Masaajid wa Mawaadi' al-Salaah, 964). Can I pray all 5 prayers at once? In Islamic tradition, Muslims perform five formal prayers at specified times each day. For people who miss a prayer for any reason, the tradition allows the prayer to be made up at a later time without it automatically…
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### Will Allah Forgive Me For Not Praying?
What happens if you don't pray in Islam? If you don't pray , it means you are only a muslim in name.You will be asked about it in the grave by the stern guards that will be responsible for you and you won't like the treatment the will give you.. What are the shirks in Islam? In Islam, shirk (Arabic: شرك širk) is the sin of idolatry or polytheism (i.e., the deification or worship of anyone or anything besides Allah). ... of mušrik مشرك) are those who practice shirk, which literally means "association" and refers to accepting other gods and divinities alongside God (as God's "associates"). Is it haram to listen to music? Some Muslims believe that only vocal music is permissible (halal) and that instruments are forbidden (haram). Hence there is a strong tradition of a cappella devotional singing. Yet some Muslims believe that any instrument is lawful as…
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### Question: Is Podbean An RSS Feed?
#### Brian Harris
Guest
How do I get WhatsApp verification code in my Gmail? No, there isn't a way you can get your WhatsApp verification code through Gmail.WhatsApp requires a phone number, and you can only get a code as an SMS to your mobile number.If you want to use WhatsApp without your actual phone number, you can try obtaining a virtual mobile number.. How do I reset my WhatsApp verification time? Open up Whatsapp and put your location manually and input your number as you regularly would, when it prompts you to confirm your number, turn off airplane mode and press OK. This should let it reset and you should receive another SMS which should verify. (This won't delete backed up messages). How can I activate WhatsApp with old number without SIM? Just follow the steps below to use WhatsApp without a mobile phone number or SIM card.Open WhatsApp on your phone, tablet…
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Professor
### Question: Was There A 4th Wise Man?
When was Jesus actually born? The date of birth of Jesus is not stated in the gospels or in any historical reference, but most theologians assume a year of birth between 6 and 4 BC.. When did the three kings visit Jesus? The Epiphany Holiday, known in Spanish speaking countries as Dia De Los Tres Reyes (Day of The Three Kings), falls annually on January 6th and marks the adoration of baby Jesus by the three Kings, also referred to as Wise Men or Magi. Who wrote the Fourth Wise Man? Henry van DykeThe Other Wise Man/Authors Who were the 3 wise men's names? Later tellings of the story identified the magi by name and identified their lands of origin: Melchior hailed from Persia, Gaspar (also called "Caspar" or "Jaspar") from India, and Balthazar from Arabia. Are the three kings mentioned in the Bible? The Three Kings, or Magi, are…
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### Quick Answer: Prayer Time Doha
Can I pray Fajr after I wake up? BACKGROUND: Muslims are required to wake up early to pray (Fajr) at dawn (approximately one and one-half hours before sunrise).Some Muslims wake up to pray Fajr and then sleep until it is time to work (split sleep), whereas others sleep continuously (consolidated sleep) until work time and pray Fajr upon awakening.. Is it OK to pray Fard only? The ruling is that there's no sin on the person who maintains only the fard (obligatory) prayers and skips nawafil (voluntary) ones. ... Whoever does not pray Witr is a bad man whose testimony should not be accepted. Can you pray after the prayer time? If a prayer is missed, it is common practice among Muslims to make it up as soon as it is remembered or as soon as they are able to do so. This is known as Qadaa. For example, if…
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### Quick Answer: Can I Login To WhatsApp Web Without Scanning The QR Code?
Where do I find the QR code on my phone? Open the Camera app from the Home screen, Control Center, or Lock screen.Select the rear facing camera.Hold your device so that the QR code appears in the viewfinder in the Camera app.Your device recognizes the QR code and shows a notification.. Can someone see my WhatsApp messages from another phone? Hackers can access your WhatsApp data by various means like via WhatsApp web or registering your number on another device. WhatsApp cannot work on two phones at the same time but hackers if register your number on another device, can easily get hold of all your chats including the personal ones. Can WhatsApp web be traced? “The origination of a WhatsApp message cannot be traced. To the best of my knowledge, a WhatsApp account is linked to a phone number and Internet, and not to a device. What is WhatsApp…
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### Epiphany Anglican
What Magi means? Modified Adjusted Gross IncomeMAGI stands for Modified Adjusted Gross Income.MAGI-based budgeting is used to calculate a person's household size and income, using federal income tax rules and a tax filer's family size to determine eligibility for Medicaid.. When should I take down my Christmas tree 2021? According to the Church of England, this day is Twelfth Night. The day of Epiphany – when the three wise men came – is the day after, on 6 January. Not everyone agrees however. Many other Christian groups count the 12 days of Christmas as starting the day after Christmas Day – making 6 January the Twelfth Night. What Zodiac is Jesus? With the story of the birth of Christ coinciding with this date, many Christian symbols for Christ use the astrological symbol for Pisces, the fishes. The figure Christ himself bears many of the temperaments and personality traits of a…
User | 2,758 | 11,870 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.046875 | 3 | CC-MAIN-2022-21 | latest | en | 0.893404 |
http://www.convertit.com/Go/ConvertIt/Measurement/Converter.ASP?From=verst&To=width | 1,519,474,710,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891815560.92/warc/CC-MAIN-20180224112708-20180224132708-00069.warc.gz | 428,567,944 | 3,868 | Partner with ConvertIt.com
New Online Book! Handbook of Mathematical Functions (AMS55)
Conversion & Calculation Home >> Measurement Conversion
Measurement Converter
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: ```Russian verst = 1066.8 length (length) ``` Related Measurements: Try converting from "verst" to Biblical cubit, bolt (of cloth), caliber (gun barrel caliber), cloth quarter, digitus (Roman digitus), fathom, gradus (Roman gradus), Greek fathom, inch, li (Chinese li), palm, parsec, point (typography point), Roman cubit, sazhen (Russian sazhen), skein, stadia (Greek stadia), stadium (Roman stadium), UK mile (British mile), yard, or any combination of units which equate to "length" and represent depth, fl head, height, length, wavelength, or width. Sample Conversions: verst = .02408717 arpentcan, 4,200,000 caliber (gun barrel caliber), 11.67 city block (informal), 9,333.33 cloth finger, 57,534.25 digitus (Roman digitus), 11.67 football field, 5.3 furlong (surveyors furlong), 576.29 Greek fathom, 10,500 hand, 503.6 ken (Japanese ken), 1.65 li (Chinese li), 1.13E-13 light yr (light year), .02528262 marathon, .66287879 mile, .19200864 nautical league, 14,000 palm, 212.12 rod (surveyors rod), 3,520.54 shaku (Japanese shaku), 4,666.67 span (cloth span), 1,166.67 yard.
Feedback, suggestions, or additional measurement definitions?
Please read our Help Page and FAQ Page then post a message or send e-mail. Thanks! | 486 | 1,710 | {"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-2018-09 | longest | en | 0.688843 |
http://footwww.academickids.com/encyclopedia/index.php/Law_of_universal_gravitation | 1,540,348,948,000,000,000 | text/html | crawl-data/CC-MAIN-2018-43/segments/1539583518753.75/warc/CC-MAIN-20181024021948-20181024043448-00043.warc.gz | 125,326,227 | 5,850 | Law of universal gravitation
The law of universal gravitation states that gravitational force between masses decreases with the distance between them, according to an inverse-square law. In addition, the theory notes that the greater an object's mass, the greater its gravitational force on another mass. Newton published his argument in Philosophiae Naturalis Principia Mathematica (1687). It is important to note that Newton was not "inventing" or "discovering" gravity; he was merely defining it mathematically. Newton would use universal gravitation, along with his laws of motion, to substantiate Kepler's laws of planetary motion. Newtonian gravitation can be derived from general relativity in the limit where the bodies are moving slowly with respect to the speed of light and the gravitational field is weak and unchanging with time. This would be a good example of the correspondence principle where the newer and more accurate or comprehensive theory breaks down to the previous theory in the domain where the previous theory is valid.
• Every object in the Universe attracts every other object with a force directed along the line of centers for the two objects that is proportional to the product of their masses and inversely proportional to the square of the separation between the two objects. (See also inverse-square law.)
• Two bodies attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Strictly speaking, this law applies only to point-like objects. If the objects have spatial extent, the true force has to be found by integrating the forces between the various points.
The law expressed as an equation:
[itex]F = G \frac{m_1 m_2}{r^2} [itex]
where:
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• Space and Astronomy | 388 | 1,918 | {"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-2018-43 | latest | en | 0.946103 |
https://it.mathworks.com/matlabcentral/profile/authors/6448448?s_tid=cody_local_to_profile | 1,603,574,341,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107884755.46/warc/CC-MAIN-20201024194049-20201024224049-00683.warc.gz | 387,061,261 | 20,822 | Community Profile
# Grzegorz Popek
66 total contributions since 2015
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Make a Palindrome Number
Some numbers like 323 are palindromes. Other numbers like 124 are not. But look what happens when we add that number to a revers...
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Given an unsigned integer x, find the largest y by rearranging the bits in x
Given an unsigned integer x, find the largest y by rearranging the bits in x. Example: Input x = 10 Output y is 12 ...
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Tell me the slope
Tell me the slope, given a vector with horizontal run first and vertical rise next. Example input: x = [10 2];
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Pattern matching
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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Solve the Sudoku Row
*Description* A simple yet tedious task occurs near the end of most Sudoku-solving algorithms, computerized or manual. The ta...
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Make one big string out of two smaller strings
If you have two small strings, like 'a' and 'b', return them put together like 'ab'. 'a' and 'b' => 'ab' For extra ...
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De-dupe
Remove all the redundant elements in a vector, but keep the first occurrence of each value in its original location. So if a =...
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Project Euler: Problem 2, Sum of even Fibonacci
Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 te...
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Project Euler: Problem 6, Natural numbers, squares and sums.
The sum of the squares of the first ten natural numbers is, 1^2 + 2^2 + ... + 10^2 = 385 The square of the sum of the first ...
oltre 5 anni ago
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Project Euler: Problem 1, Multiples of 3 and 5
If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23...
oltre 5 anni ago
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Replace NaNs with the number that appears to its left in the row.
Replace NaNs with the number that appears to its left in the row. If there are more than one consecutive NaNs, they should all ...
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Roll the Dice!
*Description* Return two random integers between 1 and 6, inclusive, to simulate rolling 2 dice. *Example* [x1,x2] =...
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Pangrams!
A pangram, or holoalphabetic sentence, is a sentence using every letter of the alphabet at least once. Example: Input s ...
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Bottles of beer
Given an input number representing the number of bottles of beer on the wall, output how many are left if you take one down and ...
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Remove all the consonants
Remove all the consonants in the given phrase. Example: Input s1 = 'Jack and Jill went up the hill'; Output s2 is 'a ...
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Remove the vowels
Remove all the vowels in the given phrase. Example: Input s1 = 'Jack and Jill went up the hill' Output s2 is 'Jck nd Jll wn...
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Which doors are open?
There are n doors in an alley. Initially they are all shut. You have been tasked to go down the alley n times, and open/shut the...
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Balanced number
Given a positive integer find whether it is a balanced number. For a balanced number the sum of first half of digits is equal to...
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The Hitchhiker's Guide to MATLAB
Output logical "true" if the input is the answer to life, the universe and everything. Otherwise, output logical "false".
oltre 5 anni ago
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Find the alphabetic word product
If the input string s is a word like 'hello', then the output word product p is a number based on the correspondence a=1, b=2, ....
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Pascal's Triangle
Given an integer n >= 0, generate the length n+1 row vector representing the n-th row of <http://en.wikipedia.org/wiki/Pascals_t...
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Binary numbers
Given a positive, scalar integer n, create a (2^n)-by-n double-precision matrix containing the binary numbers from 0 through 2^n...
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Reverse Run-Length Encoder
Given a "counting sequence" vector x, construct the original sequence y. A counting sequence is formed by "counting" the entrie...
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Find the longest sequence of 1's in a binary sequence.
Given a string such as s = '011110010000000100010111' find the length of the longest string of consecutive 1's. In this examp...
oltre 5 anni ago
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Cell joiner
You are given a cell array of strings and a string delimiter. You need to produce one string which is composed of each string fr...
oltre 5 anni ago
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Too mean-spirited
Find the mean of each consecutive pair of numbers in the input row vector. For example, x=[1 2 3] ----> y = [1.5 2.5] x=[1...
oltre 5 anni ago
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Create a row array using double colon operator
Create a row array from 9 to 1, using the double colon operator.
oltre 5 anni ago
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Nearest Numbers
Given a row vector of numbers, find the indices of the two nearest numbers. Examples: [index1 index2] = nearestNumbers([2 5 3...
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Circle area using pi
Given a circle's radius, compute the circle's area. Use the built-in mathematical constant pi.
oltre 5 anni ago
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Swap the input arguments
Write a two-input, two-output function that swaps its two input arguments. For example: [q,r] = swap(5,10) returns q = ...
oltre 5 anni ago | 1,483 | 5,532 | {"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-2020-45 | latest | en | 0.761904 |
https://ifc43-docs.standards.buildingsmart.org/IFC/RELEASE/IFC4x3/HTML/lexical/IfcArbitraryOpenProfileDef.htm | 1,708,564,307,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947473598.4/warc/CC-MAIN-20240221234056-20240222024056-00430.warc.gz | 315,556,337 | 5,551 | # 8.15.3.2 IfcArbitraryOpenProfileDef
## 8.15.3.2.1 Semantic definition
The open profile IfcArbitraryOpenProfileDef defines an arbitrary two-dimensional open profile for the use within the swept surface geometry. It is given by an open boundary from which the surface can be constructed.
Informal Propositions
1. The Curve has to be an open curve.
Figure 8.15.3.2.A illustrates the arbitrary open profile definition. The Curve is defined in the underlying coordinate system. The underlying coordinate system is defined by the swept surface that uses the profile definition. It is the xy plane of:
The Curve attribute defines a two dimensional open bounded curve.
## 8.15.3.2.5 Property sets
• Pset_ProfileMechanical
• MassPerLength
• CrossSectionArea
• Perimeter
• MinimumPlateThickness
• MaximumPlateThickness
• CentreOfGravityInX
• CentreOfGravityInY
• ShearCentreZ
• ShearCentreY
• MomentOfInertiaY
• MomentOfInertiaZ
• MomentOfInertiaYZ
• TorsionalConstantX
• WarpingConstant
• ShearDeformationAreaZ
• ShearDeformationAreaY
• MaximumSectionModulusY
• MinimumSectionModulusY
• MaximumSectionModulusZ
• MinimumSectionModulusZ
• TorsionalSectionModulus
• ShearAreaZ
• ShearAreaY
• PlasticShapeFactorY
• PlasticShapeFactorZ
## 8.15.3.2.7 Formal representation
ENTITY IfcArbitraryOpenProfileDef
SUPERTYPE OF (ONEOF
(IfcCenterLineProfileDef))
SUBTYPE OF (IfcProfileDef);
Curve : IfcBoundedCurve;
WHERE
WR11 : ('IFC4X3_DEV_d543ff3.IFCCENTERLINEPROFILEDEF' IN TYPEOF(SELF)) OR
(SELF\IfcProfileDef.ProfileType = IfcProfileTypeEnum.CURVE);
WR12 : Curve.Dim = 2;
END_ENTITY; | 449 | 1,577 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2024-10 | longest | en | 0.631035 |
http://us.metamath.org/mpeuni/rgen2a.html | 1,653,070,628,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662533972.17/warc/CC-MAIN-20220520160139-20220520190139-00152.warc.gz | 55,675,042 | 6,739 | Metamath Proof Explorer < Previous Next > Nearby theorems Mirrors > Home > MPE Home > Th. List > rgen2a Structured version Visualization version GIF version
Theorem rgen2a 3006
Description: Generalization rule for restricted quantification. Note that 𝑥 and 𝑦 are not required to be disjoint. This proof illustrates the use of dvelim 2368. (Contributed by NM, 23-Nov-1994.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof shortened by Wolf Lammen, 1-Jan-2020.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
rgen2a.1 ((𝑥𝐴𝑦𝐴) → 𝜑)
Assertion
Ref Expression
rgen2a 𝑥𝐴𝑦𝐴 𝜑
Distinct variable group: 𝑦,𝐴
Allowed substitution hints: 𝜑(𝑥,𝑦) 𝐴(𝑥)
Proof of Theorem rgen2a
Dummy variable 𝑧 is distinct from all other variables.
StepHypRef Expression
1 eleq1 2718 . . . . . 6 (𝑧 = 𝑥 → (𝑧𝐴𝑥𝐴))
21dvelimv 2369 . . . . 5 (¬ ∀𝑦 𝑦 = 𝑥 → (𝑥𝐴 → ∀𝑦 𝑥𝐴))
3 rgen2a.1 . . . . . . 7 ((𝑥𝐴𝑦𝐴) → 𝜑)
43ex 449 . . . . . 6 (𝑥𝐴 → (𝑦𝐴𝜑))
54alimi 1779 . . . . 5 (∀𝑦 𝑥𝐴 → ∀𝑦(𝑦𝐴𝜑))
62, 5syl6com 37 . . . 4 (𝑥𝐴 → (¬ ∀𝑦 𝑦 = 𝑥 → ∀𝑦(𝑦𝐴𝜑)))
7 eleq1 2718 . . . . . . 7 (𝑦 = 𝑥 → (𝑦𝐴𝑥𝐴))
87biimpd 219 . . . . . 6 (𝑦 = 𝑥 → (𝑦𝐴𝑥𝐴))
98, 4syli 39 . . . . 5 (𝑦 = 𝑥 → (𝑦𝐴𝜑))
109alimi 1779 . . . 4 (∀𝑦 𝑦 = 𝑥 → ∀𝑦(𝑦𝐴𝜑))
116, 10pm2.61d2 172 . . 3 (𝑥𝐴 → ∀𝑦(𝑦𝐴𝜑))
12 df-ral 2946 . . 3 (∀𝑦𝐴 𝜑 ↔ ∀𝑦(𝑦𝐴𝜑))
1311, 12sylibr 224 . 2 (𝑥𝐴 → ∀𝑦𝐴 𝜑)
1413rgen 2951 1 𝑥𝐴𝑦𝐴 𝜑
Colors of variables: wff setvar class Syntax hints: ¬ wn 3 → wi 4 ∧ wa 383 ∀wal 1521 ∈ wcel 2030 ∀wral 2941 This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1762 ax-4 1777 ax-5 1879 ax-6 1945 ax-7 1981 ax-9 2039 ax-10 2059 ax-11 2074 ax-12 2087 ax-13 2282 ax-ext 2631 This theorem depends on definitions: df-bi 197 df-or 384 df-an 385 df-tru 1526 df-ex 1745 df-nf 1750 df-cleq 2644 df-clel 2647 df-ral 2946 This theorem is referenced by: sosn 5222 isoid 6619 f1owe 6643 ordon 7024 fnwelem 7337 issmo 7490 oawordeulem 7679 ecopover 7894 unfilem2 8266 dffi2 8370 inficl 8372 fipwuni 8373 fisn 8374 dffi3 8378 cantnfvalf 8600 r111 8676 alephf1 8946 alephiso 8959 dfac5lem4 8987 kmlem9 9018 ackbij1lem17 9096 fin1a2lem2 9261 fin1a2lem4 9263 axcc2lem 9296 nqereu 9789 addpqf 9804 mulpqf 9806 genpdm 9862 axaddf 10004 axmulf 10005 subf 10321 mulnzcnopr 10711 negiso 11041 cnref1o 11865 xaddf 12093 xmulf 12140 ioof 12309 om2uzf1oi 12792 om2uzisoi 12793 wwlktovf1 13746 reeff1 14894 divalglem9 15171 bitsf1 15215 gcdf 15281 eucalgf 15343 qredeu 15419 1arith 15678 vdwapf 15723 catideu 16383 sscres 16530 fpwipodrs 17211 letsr 17274 mgmidmo 17306 frmdplusg 17438 nmznsg 17685 efgred 18207 isabli 18253 brric 18792 xrsmgm 19829 xrs1cmn 19834 xrge0subm 19835 xrsds 19837 cnsubmlem 19842 cnsubrglem 19844 nn0srg 19864 rge0srg 19865 fibas 20829 fctop 20856 cctop 20858 iccordt 21066 fsubbas 21718 zfbas 21747 ismeti 22177 dscmet 22424 qtopbaslem 22609 tgqioo 22650 xrsxmet 22659 xrsdsre 22660 retopconn 22679 iccconn 22680 iimulcn 22784 icopnfhmeo 22789 iccpnfhmeo 22791 xrhmeo 22792 iundisj2 23363 reefiso 24247 recosf1o 24326 rzgrp 24345 ercgrg 25457 2wspmdisj 27317 isabloi 27533 cncph 27802 hvsubf 28000 hhip 28162 hhph 28163 helch 28228 hsn0elch 28233 hhssabloilem 28246 hhshsslem2 28253 shscli 28304 shintcli 28316 pjmf1 28703 idunop 28965 idhmop 28969 0hmop 28970 adj0 28981 lnopunii 28999 lnophmi 29005 riesz4i 29050 cnlnadjlem9 29062 adjcoi 29087 bra11 29095 pjhmopi 29133 iundisj2f 29529 iundisj2fi 29684 xrstos 29807 xrge0omnd 29839 reofld 29968 xrge0slmod 29972 iistmd 30076 cnre2csqima 30085 mndpluscn 30100 raddcn 30103 xrge0iifiso 30109 xrge0iifmhm 30113 xrge0pluscn 30114 br2base 30459 sxbrsiga 30480 signswmnd 30762 indispconn 31342 ioosconn 31355 soseq 31879 f1omptsnlem 33313 isbasisrelowl 33336 poimirlem27 33566 exidu1 33785 rngoideu 33832 isomliN 34844 idlaut 35700 mzpclall 37607 kelac2lem 37951 clsk1indlem3 38658 icof 39725 prmdvdsfmtnof1 41824 sprsymrelf1 42071 uspgrsprf1 42080 plusfreseq 42097 nnsgrpmgm 42141 nnsgrp 42142 2zrngamgm 42264 2zrngmmgm 42271
Copyright terms: Public domain W3C validator | 2,504 | 4,330 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.40625 | 3 | CC-MAIN-2022-21 | latest | en | 0.221985 |
https://www.jiskha.com/questions/989745/the-jones-are-planning-a-vacation-the-total-cost-is-2500-they-are-able-to-save-1-5-of | 1,603,780,377,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107893402.83/warc/CC-MAIN-20201027052750-20201027082750-00343.warc.gz | 761,365,336 | 5,492 | the jones' are planning a vacation. the total cost is \$2500. they are able to save 1/5 of the cost each month. how much will they save in three months?
1. 👍 0
2. 👎 0
3. 👁 150
1. 1/5 * 2500 = 500
500 * 3 = ?
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👩🏫
Ms. Sue
2. oh... 1500 thanks so much!!!!!!!!!!!!!!
1. 👍 0
2. 👎 0
3. You're very welcome.
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Ms. Sue
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$\displaystyle \bar{x}=\frac{1}{n}(x_{1}+x_{2}+...+x_{n})$
$\displaystyle S{_{x}}^{2}=\frac{1}{n-1}((x_{1}-\bar{x})^2+(x_{2}-\bar{x})^2+...+(x_{n}-\bar{x})^2)$
Express the quadratic form $\displaystyle S{_{x}}^{2}$ in the matrix notation $\displaystyle x^{T}Ax$, where A is symmetric.
How do i do this? its getting ugly if i only try to expand $\displaystyle S{_{x}}^{2}$
so i tried it for n=2 to get some hint of what the matrix A would be. Well i got the matrix for n=2 but i can't figure out how it would be for an arbitary n.
this is what i got for n=2 : A = $\displaystyle \begin{bmatrix}\frac{1}{2}&-\frac{1}{2}\\-\frac{1}{2}&\frac{1}{2}\end{bmatrix}$
Thanks! | 270 | 717 | {"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} | 3.453125 | 3 | CC-MAIN-2018-22 | latest | en | 0.702801 |
https://www.webqc.org/balance.php?reaction=Pb%28OH%292+%2B+NaOH+%3D+Na2PbO2+%2B+H2O+ | 1,571,487,879,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986693979.65/warc/CC-MAIN-20191019114429-20191019141929-00269.warc.gz | 1,151,115,082 | 5,436 | #### Balance Chemical Equation - Online Balancer
Balanced equation:
Pb(OH)2 + 2 NaOH = Na2PbO2 + 2 H2O
Reaction type: double replacement
Reaction stoichiometry Limiting reagent
CompoundCoefficientMolar MassMolesWeight
Pb(OH)21241.21468
NaOH239.99710928
Na2PbO21285.17833856
H2O218.01528
Units: molar mass - g/mol, weight - g.
Direct link to this balanced equation:
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Example: Fe{3+} + I{-} = Fe{2+} + I2
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For instance equation C6H5C2H5 + O2 = C6H5OH + CO2 + H2O will not be balanced,
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chemical equations balanced today
Back to Online Chemical Tools Menu | 484 | 1,844 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.859375 | 3 | CC-MAIN-2019-43 | latest | en | 0.77433 |
https://bumpercarfilms.com/qa/quick-answer-is-vector-a-current.html | 1,621,149,059,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243989690.55/warc/CC-MAIN-20210516044552-20210516074552-00593.warc.gz | 176,629,919 | 9,056 | # Quick Answer: Is Vector A Current?
To be precise, current is not a vector quantity.
Although current has a specific direction and magnitude, it does not obey the law of vector addition.
The resultant current is less than that obtained in the previous situation..
## What is a vector diagram?
Vector diagrams are diagrams that depict the direction and relative magnitude of a vector quantity by a vector arrow. Vector diagrams can be used to describe the velocity of a moving object during its motion. … In a vector diagram, the magnitude of a vector quantity is represented by the size of the vector arrow.
## Is angular momentum a force?
Momentum is a vector, pointing in the same direction as the velocity. … Angular momentum is also a vector, pointing in the direction of the angular velocity. In the same way that linear momentum is always conserved when there is no net force acting, angular momentum is conserved when there is no net torque.
## Which is tensor quantity?
A tensor is a quantity, for example a stress or a strain, which has magnitude, direction, and a plane in which it acts. Stress and strain are both tensor quantities. … A tensor is a quantity, for example a stress or a strain, which has magnitude, direction, and a plane in which it acts.
## Is current a vector or scalar?
Electric current is a scalar quantity. Any physical quantity is termed as a vector quantity when the quantity has magnitude and direction.
## Is current a base quantity?
A fundamental quantity must be easy to measure therefore we use electric current as a fundamental quantity instead of charge. … But current is taken to be a fundamental unit, while charge is a derived unit. So current is a base ‘unit’ but not a base ‘quantity’.
## Is work a vector?
Work is a scalar because it is the “dot” product of 2 vectors, also called the scalar product. W can also be expressed in terms of the components of the force and displacement vectors. Work is a vector because you multiply a force (a vector) by distance (a vector).
## What type of vector is angular momentum?
First, the L vector represents the angular momentum—yes, it’s a vector. Second, the r vector is a distance vector from some point to the object and finally the p vector represents the momentum (product of mass and velocity).
## What tensor means?
In mathematics, a tensor is an algebraic object that describes a (multilinear) relationship between sets of algebraic objects related to a vector space. Objects that tensors may map between include vectors and scalars, and even other tensors.
## What is a vector in electricity?
What is a vector, and how can we use it in electrical design? According to the “IEEE Standard Dictionary of Electrical and Electronic Terms,” a vector quantity is “any physical quantity whose specification involves both magnitude and direction and that obeys the parallelogram law of addition.”
## Is impulse a vector?
Impulse is a vector, so a negative impulse means the net force is in the negative direction. Likewise, a positive impulse means the net force is in the positive direction. People mistake impulse with work. Both impulse and work depend on the external net force, but they are different quantities.
## Is distance a vector quantity?
Distance is a scalar quantity that refers to “how much ground an object has covered” during its motion. Displacement is a vector quantity that refers to “how far out of place an object is”; it is the object’s overall change in position.
## Is angular momentum conserved?
The conserved quantity we are investigating is called angular momentum. The symbol for angular momentum is the letter L. Just as linear momentum is conserved when there is no net external forces, angular momentum is constant or conserved when the net torque is zero.
## What is a tensor vector?
A tensor is a generalization of vectors and matrices and is easily understood as a multidimensional array. … A vector is a one-dimensional or first order tensor and a matrix is a two-dimensional or second order tensor.
## Is angular momentum scalar or vector?
Angular momentum is a vector quantity that represents the product of a body’s rotational inertia and rotational velocity about a particular axis. The angular momentum is the product of the moment of inertia and the angular velocity around an axis.
## Is current is a tensor quantity?
Current is I=∫A→J⋅d→A, where A is an area and d→A is a directed normal vector to a differential element of A. So, since it is the dot product of two vectors, current is a scalar. … Note, both scalars and vectors are tensors. Scalars are tensors of tank 0, and vectors are tensors of rank 1.
## What is the difference between phasor and vector?
Although the both the terms vectors and phasors are used to describe a rotating line that itself has both magnitude and direction, the main difference between the two is that a vectors magnitude is the “peak value” of the sinusoid while a phasors magnitude is the “rms value” of the sinusoid.
## Is heat a vector quantity?
Heat is a scalar. It may flow from place to place and that flow can be represented as a vector. … A scalar quantity only has magnitude, whereas a vector quantity has both magnitude and direction. Since specific heat does not have any direction, it is a scalar quantity.
## Can electric force negative?
Electric field is not negative. It is a vector and thus has negative and positive directions. An electron being negatively charged experiences a force against the direction of the field. For a positive charge, the force is along the field.
## Is Electric a vector charge?
1 Answer. Nothing is a vector until defined with a direction. Electric charge is a scalar quantity because charge never graduated into the level of vectors or tensors that need both magnitude and direction. | 1,191 | 5,838 | {"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-2021-21 | latest | en | 0.937273 |
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### Critical Speed Of A Tumbling Mill - greenrevolutionorgin
2012723- formula for calculating the critical speed of a ball mill, ball , critical speed equation in a tumbling mill –Grinding Mill China , Read more critical speed of a tumbling mill...
### ENERGY SAVINGS AND TECHNOLOGY COMPARISON ,
When calculating the recommended top size ball from Bond’s formula (1961) for regrind ball mill applications, the required size is less than 25 mm For the vertical stirred mill, no formula exists to precise which media size to use As mentionned by McIvor (1997) and Nesset et al (2006), the media...
### formula 39 s to calculate efficiency of ball mill
Apr 02, 2011· formula s to calculate efficiency of ball mill formula 39 s to calculate efficiency of ball mill formula s to calculate efficiency of ball millsmall The energy efficiency of ball milling in comminution Abstract Comminution efficiency is a technical term that relates some measure of the output from a comminution Service Online Ball Mills Get ....
### Electric Motor Torque Calculation Formula & Torque ,
AC 1 HP single-phase AC motor has an input voltage of 230V, the input current of 38 Amps and working at 2500 rpm, 08 pf, load Calculate the torque of the motor Apply our formula 1, T (Nm) = 230 x 38 x 08 x / (2 x 314 x 2500 / 60) = 266 Nm The torque produced by the motor is 266 Nm Hence 1 HP motor can produce 266 Nm...
### Formulas kiln - SlideShare
Jul 22, 2010· Rotary kiln Capacity Martin’s Formula : C = 2826 v X D^3 Vg C = Kiln Capacity Ton / Hr V = Gas Velocity in gas discharge end , m / sec Vg = specific gas volume , m^3 / kg clinker D = Kiln Diameter on Bricks, m 39...
### formula for maximum ball size in cement mill
- Ball top size (bond formula) calculation of the top size grinding media (balls or cylpebs) Modification of the Ball Charge This calculator analyses the granulometry of the material inside the mill and proposes a modification of the ball charge in order to improve the mill efficiency...
### Ball charges calculators - thecementgrindingoffice
- Ball top size (bond formula): calculation of the top size grinding media (balls or cylpebs):-Modification of the Ball Charge: This calculator analyses the granulometry of the material inside the mill and proposes a modification of the ball charge in order to improve the mill efficiency:...
### circulating load ball mill formulation
VRM and ball mill circulating load Page 1 of 1 Sep 07, 2011 Re: VRM and ball mill circulating load Mainly in USA,the term circulating load is more often used than the circulation factorCirculating load is percentage of coarse return in relation to fines & it can be calculated by : Coarse return TPH X 100 / Mill output TPHNormal range of cirulating load in a conventional close circuit ball ....
### Particle technology lab report - SlideShare
Feb 16, 2017· The formula used to calculate feed rate is shown below 𝑄 = 60𝜋𝐷𝐿𝑊𝜔𝜌 𝑏(ton/h) Calculation of double roll crusher efficiency The efficiency of the double roll crusher can be calculated by taking the ratio of surface energy crated to the energy absorb by the substance the formula is shown below: 𝜂 𝑐 ....
### Formula S To Calculate Efficiency Of Ball Mill-ball Mill
Formula Of Calculating Ball Mill Efficiency Formula amp 39 s to calculate efficiency of ball mill energy savings and technology comparison when calculating the recommended top size ball from bonds formula 1961 for regrind ball mill applications the required size is less than 25 mm for the vertical stirred mill no formula exists to power 50 amp ....
### crushing efficiency formula of a ball mill
formula amp 39 s to calculate efficiency of ball mill - Crushing Efficiency Formula Of A Ball Mill Ubc mine331 lecture notes - sagmilling nov 11, 2015 devices is (largely) reflective of the efficiency of the grinding device the ef4 formula requires both the rod mill and ball mill work index (rod mill wi is from a primary crusher product size, f80, to a ball mill cyclone overflow... | 2,511 | 11,236 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.765625 | 3 | CC-MAIN-2022-05 | longest | en | 0.846595 |
https://www.physicsforums.com/threads/is-c-bigger-than-r.282736/ | 1,531,698,108,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676589022.38/warc/CC-MAIN-20180715222830-20180716002830-00245.warc.gz | 1,000,583,313 | 14,098 | # Is C bigger than R?
1. Jan 4, 2009
### samkolb
Is it true that the set of complex number is bigger than the set of real numbers?
I know that card C = card (R x R) and I think that card (R x R) > card R. Is this true, and if so, why?
2. Jan 4, 2009
### marcus
I think card (RxR) = card R
I would show this by setting up a one-to-one map between RxR and R
I will just show you a one-to-one between the unit square [0,1]x[0,1] and the unit interval [0,1]
You just look at the two decimal expansions and merge
(0.abcdefg...., 0.mnopqrs....) -> 0.ambncodpeq.......
Last edited: Jan 4, 2009
3. Jan 4, 2009
### MathematicalPhysicist
C is with cardinality c, or aleph if you want, the same as R.
The simple bijection is a+ib |-> (a,b) into RxR.
If you want a bijection from C to R, then z=x+iy|->Im(z)/Re(z) it's a bijection to [-infinity,infinity] which is RU{infininity,-infinity} this cardinality is aleph+2=aleph.
QED
Last edited: Jan 4, 2009
4. Jan 4, 2009
### Big-T
How could that possibly be a bijection? Obviously, $$z_1=a+ib$$ is mapped to the same point as $$z_2=a z_1$$, so it is not an injection.
Marcus has already provided a valid bijection, his "decimal merging" is the classical example of this. Notice how it is also valid in $$\mathbb{R}^n$$.
5. Jan 4, 2009
### MathematicalPhysicist
Correct Big-T, but at least it's onto.
(-:
6. Jan 7, 2009
|C| = |R2| = |R|.
There's some discussion about that in this thread.
Minor point: marcus's function isn't even well-defined; consider decimal expansions with infinite trailing "9"s. (For example, 0.0999... = 0.1000..., but (0.0999..., 0.0000...) maps to 0.00909090..., and (0.1000..., 0.0000) maps to 0.10000000... .) However, the mapping from 0.abcdefgh... to (0.acef..., 0.bdfh...) is a well-defined surjection from [0, 1) to [0, 1)2, and that's all you need.
7. Jan 7, 2009
### Big-T
Marcus' function would be well defined if we agreed to use trailing nines wherever the decimal expansion is terminating, this should of course have been specified. | 664 | 2,034 | {"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} | 3.46875 | 3 | CC-MAIN-2018-30 | latest | en | 0.921119 |
https://testbook.com/question-answer/if-cos-sec-k-then-w--607f1143a75108b36b401f8b | 1,631,926,412,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780056120.36/warc/CC-MAIN-20210918002951-20210918032951-00218.warc.gz | 602,017,401 | 29,127 | # If cos θ + sec θ = k, then what is the value of sin2θ - tan2θ ?
This question was previously asked in
CDS Maths Previous Paper 10 (Held On: 8 Nov 2020) - 10
View all CDS Papers >
1. 4 - k
2. 4 - k2
3. k2 - 4
4. k2 + 2
Option 2 : 4 - k2
## Detailed Solution
Given:
cos θ + sec θ = k
Formula used:
sec θ = 1/cos θ
a2 + b2 = (a + b)2 - 2ab
Calculation:
cos θ + sec θ = k
⇒ cos θ + 1/cos θ = k
On squaring both sides, we get,
⇒ cos2θ + 1/cos2θ + 2 = k2
⇒ cos2θ + 1/cos2θ = k2 - 2
According to the question,
sin2θ - tan2θ = (1 - cos2θ) - (sec2θ - 1)
⇒ 2 - (cos2θ + 1/cos2θ)
⇒ 2 - (k2 - 2)
⇒ sin2θ - tan2θ = 4 - k2
∴ The value of sin2θ - tan2θ is 4 - k2. | 330 | 670 | {"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} | 4.28125 | 4 | CC-MAIN-2021-39 | latest | en | 0.444838 |
https://www.doubtnut.com/question-answer/if-two-intersecting-chords-of-a-circle-make-equal-angles-with-the-diameter-passing-through-their-poi-3837 | 1,680,121,683,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296949025.18/warc/CC-MAIN-20230329182643-20230329212643-00511.warc.gz | 818,108,075 | 24,301 | Question
If two intersecting chords of a circle make equal angles with the diameterpassing through their point of intersection, prove that the chords are equal
Khareedo DN Pro and dekho sari videos bina kisi ad ki rukaavat ke!
Updated On: 27-06-2022
Text Solution
Solution
Draw perpendicular to chords AB and CD
OLCDandONAB
MLOandMNO
OLM=ONM
LMO=NMO
OM=OM
MLOMNO
OL=ON
If two chods are equidistant from centre, Then two chods will be equal AB=CD. | 137 | 451 | {"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} | 3.03125 | 3 | CC-MAIN-2023-14 | latest | en | 0.754425 |
https://questions.llc/questions/1140919 | 1,716,226,998,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058293.53/warc/CC-MAIN-20240520173148-20240520203148-00034.warc.gz | 420,516,984 | 6,125 | # Suppose that represents the temperature of a cup of coffee set out in a room, where T is expressed in degrees Fahrenheit and t in minutes.
A physical principle known as Newton’s Law of Cooling tells us that
dT/dt = -1/15T+5
15T + 5.
a) Supposes that T(0) = 105. What does the differential equation give us for the
value of dT
dt |T=0? Explain in a complete sentence the meaning of these two
facts.
(b) Is T increasing or decreasing at t = 0?
(c) What is the approximate temperature at t = 1?
(d) On a graph, make a plot of dT/dt as a function of T.
(e)For which values of T does T increase?
(f) What do you think is the temperature of the room? Explain your thinking.
(g) Verify that T(t) = 75 + 30e^(-t/15) is the solution to the differential equation with initial value T(0) = 105. What happens to this solution after a long time?
## (a) To find the value of dT/dt when T = 0, we substitute T = 0 into the differential equation:
dT/dt = -1/15(0)+5 = 5.
This means that at T = 0, the rate of change of temperature with respect to time is 5 degrees Fahrenheit per minute.
(b) At t = 0, we need to evaluate the sign of dT/dt to determine whether T is increasing or decreasing. Since dT/dt is positive (5) at T = 0, this means that the temperature is increasing at t = 0.
(c) To find the approximate temperature at t = 1, we need to solve the differential equation numerically or use an approximation method. One way to do this is by using Euler's method:
- Use the equation dT/dt = -1/15T + 5 to find the rate of change at t = 0 and calculate T(1) approximately using the formula: T(1) = T(0) + (dT/dt)(∆t), where ∆t is the time step (in this case, 1 minute).
By substituting the values, we have:
T(1) = 105 + (5)(1) = 110.
So, the approximate temperature at t = 1 is 110 degrees Fahrenheit.
(d) To plot dT/dt as a function of T, we can choose different values for T and compute the corresponding values of dT/dt using the differential equation. We can create a table of values or use software like Excel or a graphing calculator. The resulting plot will show the relationship between T and dT/dt.
(e) To determine when T increases, we need to examine the sign of dT/dt. Since dT/dt = -1/15T + 5, we can see that T increases when dT/dt > 0. Simplifying the inequality, we have -1/15T + 5 > 0, which gives T < 75. Therefore, T increases when the temperature is less than 75 degrees Fahrenheit.
(f) The temperature of the room can be estimated by observing the behavior of T over time. As t approaches infinity, the term e^(-t/15) approaches zero, making T(t) approach the constant term in the equation, which is 75. This suggests that the temperature of the room is approximately 75 degrees Fahrenheit.
(g) To verify that T(t) = 75 + 30e^(-t/15) is the solution to the differential equation with initial value T(0) = 105, we substitute T(t) into the differential equation:
dT/dt = -1/15(75 + 30e^(-t/15)) + 5
= -5 + (2/5)e^(-t/15).
Taking the derivative of T(t) with respect to t, we have:
d/dt (75 + 30e^(-t/15)) = -30(1/15)e^(-t/15)
= -2e^(-t/15).
This derivative matches the expression -5 + (2/5)e^(-t/15), confirming that T(t) = 75 + 30e^(-t/15) is a solution to the differential equation.
As time (t) goes to infinity, e^(-t/15) goes to zero, making T approach 75. Thus, after a long time, the temperature of the cup of coffee will approach the temperature of the room, which is approximately 75 degrees Fahrenheit. | 989 | 3,435 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.5 | 4 | CC-MAIN-2024-22 | latest | en | 0.903211 |
https://brainmass.com/physics/velocity/differentiation-motion-launched-upwards-rocket-velocity-1381 | 1,685,782,569,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224649177.24/warc/CC-MAIN-20230603064842-20230603094842-00759.warc.gz | 178,872,098 | 75,453 | Explore BrainMass
# Differentiation: Describe the motion of an object launched up
Not what you're looking for? Search our solutions OR ask your own Custom question.
This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!
Questions are taken from the course book 'Physics with modern physics', Richard Wolfson & J. M. Pasachoff.
A model rocket is launched straight upward; its altitude as a function of time is given by y = bt-ct^2, where b=68 m/s, c=4.9 m/s, t is the time in seconds, and y is in meters.
(a) Use differentiation to find a general expression for the rocket's velocity as a function of time.
(b) When is the rockets velocity zero? | 167 | 705 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2023-23 | longest | en | 0.929103 |
https://www.numbersaplenty.com/1128990 | 1,653,372,505,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662564830.55/warc/CC-MAIN-20220524045003-20220524075003-00438.warc.gz | 798,885,363 | 3,387 | Search a number
1128990 = 23537633
BaseRepresentation
bin100010011101000011110
32010100200110
410103220132
5242111430
640110450
712411342
oct4235036
92110613
101128990
11701255
12465426
13306b55
14215622
151747b0
hex113a1e
1128990 has 16 divisors (see below), whose sum is σ = 2709648. Its totient is φ = 301056.
The previous prime is 1128979. The next prime is 1128997. The reversal of 1128990 is 998211.
It is a Harshad number since it is a multiple of its sum of digits (30), and also a Moran number because the ratio is a prime number: 37633 = 1128990 / (1 + 1 + 2 + 8 + 9 + 9 + 0).
It is a congruent number.
It is not an unprimeable number, because it can be changed into a prime (1128997) by changing a digit.
It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 18787 + ... + 18846.
It is an arithmetic number, because the mean of its divisors is an integer number (169353).
21128990 is an apocalyptic number.
1128990 is a gapful number since it is divisible by the number (10) formed by its first and last digit.
1128990 is an abundant number, since it is smaller than the sum of its proper divisors (1580658).
It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.
1128990 is a wasteful number, since it uses less digits than its factorization.
1128990 is an evil number, because the sum of its binary digits is even.
The sum of its prime factors is 37643.
The product of its (nonzero) digits is 1296, while the sum is 30.
The square root of 1128990 is about 1062.5394110338. The cubic root of 1128990 is about 104.1270021429.
The spelling of 1128990 in words is "one million, one hundred twenty-eight thousand, nine hundred ninety". | 519 | 1,743 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.359375 | 3 | CC-MAIN-2022-21 | latest | en | 0.87859 |
https://www.mapleprimes.com/users/patricks/questions | 1,726,145,158,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651457.35/warc/CC-MAIN-20240912110742-20240912140742-00272.warc.gz | 815,753,999 | 28,994 | ## 0 Reputation
6 years, 155 days
## How do I get Maple to show only one inst...
Maple 17
I've asked Maple to solve an equation, and the result is difficult to read because it is separating single variables into multiple multiplicative instances of that variable raised to different powers. Is there a way to tell Maple to combine all instances of a variable into one instance raised to the appropriate power?
For example:
pceq := (2/3)*Pi*G*rho^2*R^2:
pnonreleq := (1/5)*(3*Pi^2)^(2/3)*hbar^2*n^(5/3)/m:
rhocomposition := rho = m/((4/3)*Pi*R^3), n = Z*rho/(A*m_p):
obj := subs(rhocomposition, rhocomposition, pceq = pnonreleq):
req := R = simplify(solve(obj, R)[1]);
The above code produces
In the first place, I can't see why Maple would show what should be (Z/A)^(5/3) as z^3 / (A * [A*Z^2]^(2/3)), but I'd like to somehow tell it to not break up the variables like this.
Is this possible? Thanks for the help.
Page 1 of 1
| 292 | 938 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.859375 | 3 | CC-MAIN-2024-38 | latest | en | 0.910743 |
https://suyash67.github.io/homepage/project/2019/10/19/eff-proof-of-reserves.html | 1,719,006,274,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862157.88/warc/CC-MAIN-20240621191840-20240621221840-00022.warc.gz | 493,430,320 | 7,595 | Cryptocurrency exchanges (also called as crypto exchanges) provide a convenient way for customers to own and trade cryptocurrencies in exchange for fiat currencies. However, in cases of hacks and internal frauds in such exchanges result in huge loss of customer funds 1,2. Proof of solvency is one of the preventive measures which could help in early detection of such scams. As a part of my master’s thesis, I am working on designing a proof of reserves for crypto exchanges wherein the exchanges can prove that they own funds enough to recover their liabilities in unfortunate cases of hack or frauds.
To illustrate the idea, let’s say an exchange owns assets equal to $v_{a}$ and has lent out crypto assets worth $v_{l}$ to its customers in exchanage for fiat currency. Thus, the liabilities of en exchange towards its cutomers is $v_{l}$. An exchange is solvent if $v_{a} \ge v_{l}$. A proof of reserves is a proof that an exchange owns assets equal to some amount $v_a$. In case of crypto assets, an exchange can just reveal what addresses it owns to give a proof of its reserves. This is, however, undesirable from the point of view of privacy of the exchange’s customers. I am working on designing zero-knowledge proofs of reserves for different cryptocurrencies.
To do this without revealing the addresses and amounts, an exchange can generate two Pedersen commitments $C_a$ and $C_l$ to $v_a$ and $v_l$ respectively. To prove $v_a \ge v_l$, exchange gives a range proof that $C_a \cdot C_l^{-1}$ is a commitment to a non-negative amount.
I am working on designing zero-knowledge proofs of reserves for different cryptocurrencies. I designed Revelio+, an efficient proof of reserves for MimbleWimble based cryptocurrencies. MimbleWimble has outputs instead of addresses to store coins. Using our protocol, an exchange proves in zero-knowledge that it owns particular outputs from the set of unspent outputs on the blockchain preserving privacy of outputs owned by an exchange. Further, it also helps detect collusion between exchanges when they try to share an output in their respective proofs of reserves.
A typical Revelio+ proof would be of the form $\Pi_{\text{Rev+}} = \{ t, I_1, I_2, \dots, I_m, \Pi_{+} \}$
where $t$ is the block height which denotes the blockchain state. All the unspent outputs $(C_1, C_2, \dots, C_n)$ on the blockchain till those included in $t$-th block form the anonymity set. The exchange owns outputs $(C_{i_1}, C_{i_2}, \dots, C_{i_m})$. Additionally, it defines key-images $(I_1, I_2, \dots, I_{m})$ for each output it owns. The key-images help detect collusion between exchanges, i.e. if two exchanges generate their proofs of reserves at block height $t$ and if any of their key-images match, we declare collusion. $\Pi_{+}$ is a zero-knowledge argument of knowledge which proves that the exchange actually owns the forementioned outputs. It is logarithmic in the size of set of all the unspent outputs.
Revelio, the existing protocol had a proof size linear in the size of anonymity set. Also, collusion between the exchanges could be detected only if the anonymity sets in the two proofs are the same. We alleviate both of these issues by giving a log-sized protocol and linking the proof generation with the blockchain state, we cryptographically enforce exchanges to generate proofs at the same time and thus give a foolproof way to detect collusion. Further, log-sized proof also allows us to have the anonymity set as the entire set of unspent outputs corresposing to a particular blockchain state. This enhances the privacy of exchange-owned outputs.
The downside of our protocol, however, is the time needed to generate the proof and verify the same. It is linear in the size of anonymity set size. The following graph shows the performance of our protocol in comparison to Revelio.
The linear proof generation times motivate the need for specialized hardware for cryptographic operations like elliptic curve point addition. The links for the preprint and presentation would be added soon. | 891 | 4,050 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 19, "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-2024-26 | latest | en | 0.943787 |
https://www.cemc.uwaterloo.ca/events/mathcircle_presentations_gr78.html | 1,695,368,408,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233506339.10/warc/CC-MAIN-20230922070214-20230922100214-00012.warc.gz | 800,324,458 | 12,191 | # Math Circle Presentations
Math Circles is a weekly enrichment activity for grade 6 to 12 students organized by the Faculty of Mathematics of the University of Waterloo.
Information about the audience, dates and location.
Listed below are summaries of previous weekly presentations and related student exercises for the Grade 7/8 classes. These resources are provided for both students and teachers. Please use them!
Fall 2022 Winter 2023 Recursive Sequences [pdf, prob set, solns] Mathematical Logic [pdf, prob set, solns] Radians [pdf, prob set, solns] Gauss Prep [pdf, prob set & solns] Induction [pdf, prob set, solns] Modular Arithmetic [pdf, prob set, solns] Complex Numbers [pdf, prob set, solns] Jeopardy [pdf] Circle Geometry [pdf, prob set, solns] Prime Factorization [pdf, probs set, solns] Musical Scales [pdf, prob set, solns] BCC/Gauss Prep [pdf, prob set, solns] Recursion and Stack ADTs [pdf, prob set, solns] Trigonometry [pdf, prob set, solns] Vectors [pdf, prob set, solns]
Fall 2021 Winter 2022 Probability [pdf, prob set, solns] Systems of Equations [pdf, prob set, solns] Sequences [pdf, prob set, solns] Polygonal Numbers [pdf, prob set, solns] Counting Systems [pdf, prob set, solns] Game Theory [pdf, prob set, solns] Ancient Mathematics [pdf, prob set, solns] Boolean Algebra [pdf, prob set, solns] Graph Theory [pdf, prob set, solns, extension] Inequalities and Absolute Values [pdf, prob set, solns, extension]
Fall 2020 Winter 2021 BCC Prep - Problem Set [pdf, prob set, solns] BCC Graph Theory Proofs [pdf, prob set, solns] Propositions and Control Flow [pdf, prob set, solns] Algorithms [pdf, prob set, solns] Intro to Vectors [pdf, prob set, solns] Interest [pdf, prob set, solns] Random Sampling [pdf, prob set, solns] Confidence Intervals [pdf, prob set, solns] Significance Testing [pdf, prob set, solns] Squares & Radicals [pdf, prob set, solns] Triangles [pdf, prob set, solns] Turing Machines [pdf, prob set, solns]
Fall 2019 Winter 2020 Triangles [pdf, solns] Circles [pdf, solns] Physics [pdf, solns] Probability [pdf, solns] Group Theory [pdf, solns] Modular Arithmetic [pdf, solns] Introduction to Computer Science [pdf, solns] Jeopardy [pdf, solns] Earth Circumference [pdf, solns] Fractals [pdf, solns] Infinite Series [pdf, solns] Unsolved Problems [pdf, solns] Applications [pdf, solns] Infinity [pdf, solns] General Relativity & Black Holes [pdf, solns]
Fall 2018 Winter 2019 Angles & Light [pdf, solns] Matrices [pdf, solns] Qualitative Graph Analysis [pdf, solns] Boolean Logic [pdf, solns Coordinate Systems [pdf, solns] Introduction to Special Relativity [pdf, solns] Symmetry and Music [pdf, solns] Jeopardy [pdf, solns] Ruler Compass [pdf, solns] Complex Numbers [pdf, solns] Exponentiation [pdf, solns] Pythagorean Theorem [pdf, solns] Inequalities [pdf, solns] Cryptography [pdf, solns] Gauss Prep [pdf, prob set, solns] Math Jeopardy [pdf, solns]
Fall 2017 Winter 2018 Series & Polygonal Numbers [pdf, solns] Angles & Circles [pdf, solns] Probability [pdf, solns] Graph Theory [pdf, solns] Scientific Equations [pdf, solns] Estimations [pdf, solns] The Scale of Numbers [pdf, solns] Math Jeopardy [pdf, solns] Mental Math [pdf, solns] Circuits [pdf, solns] Geometry [pdf, solns] Mathematicial Magic [pdf] Math of Voting [pdf, solns] Types of Numbers [pdf, solns] Word Problems [pdf, solns] Jeopardy [pdf, solns]
Fall 2016 Winter 2017 Mathematical Puzzles [pdf, solns, video] Continued Fractions [pdf, solns, video] Sequences [pdf, solns, video] Visual Group Theory [pdf, solns, video] The Matrix [pdf, solns, video] Combinatorial Counting [pdf, solns] Areas of Triangles [pdf, solns, video] Math Jeopardy [pdf, solns, video] Number Theory [pdf, solns] Game Theory [pdf, solns] Sets [pdf, solns] Fractals [pdf, solns] Spatial Visualization and Origami [pdf, solns] Geometric Arithmetic [pdf, solns] Math Olympics [pdf, solns] Gauss Prep [pdf, solns]
Fall 2015 Winter 2016 Greek Constructions [pdf, solns, video] Graph Theory [pdf, solns, video] Computer Science Algorithms [pdf, solns, video] Combinatorial Games [pdf, solns, video] Escher Tessellations [pdf, solns, video] Logic [pdf, solns, video] Knot Theory [pdf, solns, video] Review [pdf, solns] Logic Puzzles [pdf, solns, video] Modular Arithmetic [pdf, solns, video] Create Your Own Business [pdf, video] Number Theory [pdf, solns, video] Word Problems [pdf, solns, video] Physics [pdf, solns, video] Mathematical Thinking [pdf, solns, video] Review [pdf, solns]
Fall 2014 Winter 2015 Exponents and Roots [pdf, solns, video] Angles [pdf, solns, video] Sequence [pdf, solns, video] Series [pdf, solns, video] Pythagorean Theorem [pdf, solns, video] How We Make Money [pdf, solns, video] Game Theory [pdf, solns, video] Gauss Prep [pdf, solns] Arithmetic Aerobics [pdf, solns, video] Pi [pdf, solns, video] Circle Geometry [pdf, solns, video] Kinematics [pdf, solns, video] Types of Numbers [pdf, solns, video] Number Theory [pdf, solns, video] Cryptography [pdf, solns, video] Math Jeopardy [pdf, solns]
Fall 2013 Winter 2014 Algebra [pdf, solns, video] History of Numbers [ pdf, solns, video] Finance [pdf, solns, video] Logic Puzzles [pdf, solns, video] Similarity & Congruence [pdf, solns, video] Mathematical Gems [pdf, solns, video] Mathematical Games [pdf, solns, video] Origami Math Trivia [pdf, solns, video] Operations with Sets [pdf, solns, video] Counting I [pdf, solns, video] Counting II [pdf, solns, video] Probability [pdf, solns, video] Graph Theory I [pdf, solns, video] Graph Theory II [pdf, solns, video] Gauss Prep [pdf, solns, video] Modular Arithmetic [pdf, solns, video]
Fall 2012 Winter 2013 Sequences and Series [pdf, solns] Sets and Venn Diagrams [pdf, solns] Counting [pdf, solns] Geometric Arithmetic [pdf, solns] Cryptography [pdf, solns] Factors and Primes [pdf, solns] Probability [pdf, solns] Gauss Math Contest [pdf, solns] Fibonacci Series [pdf, solns] Pascals Triangle [pdf, solns] 2D Geometry [pdf, solns] 3D Geometry [pdf, solns] Graph Theory [pdf, solns] Circles, Circles, Circles [pdf, solns] Gauss Preparation [pdf, solns] Review Challenge [pdf, problem set, solns]
Fall 2011 Winter 2012 Mental Division [pdf, solns] Modular Arithmetic [pdf, solns] Prime Numbers [pdf, solns] Fractals [pdf, solns] Dimensional Analysis [pdf, solns] Logic Puzzles [pdf, solns] Polygonal Numbers [pdf, solns] Jeopardy [pdf, solns] Speedy, Speedy Arithmetic [pdf, solns] Ancient Geometric Constructions [pdf, solns] Algebraic Approaches [pdf, solns] Spatial Visualization and Origami [pdf, solns] Introduction to Graph Theory [pdf, solns] Circuits [pdf, solns] Gauss Contest Preparation [pdf, solns] Math Olympics [pdf, solns]
Fall 2010 Winter 2011 Graphs and Transformations [pdf, solns] Percents and Ratios [pdf, solns] Statistics I [pdf, solns] Statistics II [pdf, solns] Pascal's Triangle [pdf, solns] Number Theory [pdf] Logic [pdf] Game Theory [pdf, solns] Cryptography and Binary Numbers [pdf, solns] Commission, Taxes & Discounts [pdf, solns] Markup & Markdown [pdf, solns] Probability I [pdf, solns] Probability II [pdf, solns] Gauss Contest Preparation [pdf, solns] Jeopardy [pdf, solns] | 2,122 | 7,159 | {"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-2023-40 | latest | en | 0.678724 |
https://testbook.com/question-answer/by-considering-the-net-area-as-an-ultimate-stress--6290a255996d463e3c1f264e | 1,675,409,815,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764500044.16/warc/CC-MAIN-20230203055519-20230203085519-00134.warc.gz | 574,057,315 | 73,700 | # By considering the net area as An, ultimate stress as fu and the partial safety factor as γml, the IS code formula for the preliminary design of a tension member for design strength due to rupture (Tdn) of the critical section is
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1. $$T_{dn} = {\alpha A_n f_u\over2\gamma_{ml}}$$
2. $$T_{dn} = {A_n f_u\over\alpha\gamma_{ml}}$$
3. $$T_{dn} = {\gamma_{ml}A_n f_u\over\alpha}$$
4. $$T_{dn}={\alpha A_nf_u\over\gamma_{ml}}$$
Option 4 : $$T_{dn}={\alpha A_nf_u\over\gamma_{ml}}$$
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## Detailed Solution
Explanation
As per code IS 800:2007
As per Clause 6.3 Design Strength Due to Rupture of Critical Section of IS 800: 2007, design strength is given for different members separately as follows.
$$T_{dn}={\alpha A_nf_u\over\gamma_{ml}}$$
Where γml- partial safety factor for failure at ultimate stress = 1.25 (refer to Table 5 of IS 800: 2007)
fu - ultimate stress of the material
An - the net effective area of the member
Net section rupture
• When a tension member is connected using bolts, the cross-section reduces because of the holes present and this is referred to as net area. Holes in the members cause stress concentration at service loads. From the theory of elasticity, the tensile stress adjacent to a hole will be about two to three times the average stress on the net area.
• The ratio of maximum elastic stress to the average stress (fmax/favg) is called the stress concentration factor.
• Stress concentration is an important factor when a member is subjected to dynamic load where there is a possibility of brittle fracture or when the repeated application of load may lead to fatigue failure.
• In static loading of a tension member with a hole, the point adjacent to the hole reaches the field stress (fy) first. With further loading, the stress at that point remains constant at yield stress and each fiber away from the hole progressively reaches the yield stress.
• Deformations continue with increasing load until rupture/tension failure of the member occurs when the entire net cross-section of the member reaches the ultimate stress (fu). | 573 | 2,255 | {"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} | 3.34375 | 3 | CC-MAIN-2023-06 | latest | en | 0.893917 |
https://www.lmfdb.org/EllipticCurve/Q/36414/l/1 | 1,624,450,782,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488538041.86/warc/CC-MAIN-20210623103524-20210623133524-00630.warc.gz | 792,626,974 | 26,327 | # Properties
Label 36414.l1 Conductor $36414$ Discriminant $1.099\times 10^{17}$ j-invariant $$\frac{14489843500598257}{6246072}$$ CM no Rank $1$ Torsion structure $$\Z/{2}\Z$$
# Related objects
Show commands: Magma / Pari/GP / SageMath
## Minimal Weierstrass equation
sage: E = EllipticCurve([1, -1, 0, -13210533, -18477825219])
gp: E = ellinit([1, -1, 0, -13210533, -18477825219])
magma: E := EllipticCurve([1, -1, 0, -13210533, -18477825219]);
$$y^2+xy=x^3-x^2-13210533x-18477825219$$
## Mordell-Weil group structure
$$\Z\times \Z/{2}\Z$$
### Infinite order Mordell-Weil generator and height
sage: E.gens()
magma: Generators(E);
$$P$$ = $$\left(\frac{145989}{25}, \frac{39846303}{125}\right)$$ $$\hat{h}(P)$$ ≈ $8.9024258968101037762820120519$
## Torsion generators
sage: E.torsion_subgroup().gens()
gp: elltors(E)
magma: TorsionSubgroup(E);
$$\left(-\frac{8397}{4}, \frac{8397}{8}\right)$$
## Integral points
sage: E.integral_points()
magma: IntegralPoints(E);
## Invariants
sage: E.conductor().factor() gp: ellglobalred(E)[1] magma: Conductor(E); Conductor: $$36414$$ = $$2 \cdot 3^{2} \cdot 7 \cdot 17^{2}$$ sage: E.discriminant().factor() gp: E.disc magma: Discriminant(E); Discriminant: $$109907680537767672$$ = $$2^{3} \cdot 3^{14} \cdot 7 \cdot 17^{7}$$ sage: E.j_invariant().factor() gp: E.j magma: jInvariant(E); j-invariant: $$\frac{14489843500598257}{6246072}$$ = $$2^{-3} \cdot 3^{-8} \cdot 7^{-1} \cdot 11^{3} \cdot 17^{-1} \cdot 37^{3} \cdot 599^{3}$$ Endomorphism ring: $$\Z$$ Geometric endomorphism ring: $$\Z$$ (no potential complex multiplication) Sato-Tate group: $\mathrm{SU}(2)$ Faltings height: $$2.6124626868348249493494620881\dots$$ Stable Faltings height: $$0.64654987047266206352707216070\dots$$
## BSD invariants
sage: E.rank() magma: Rank(E); Analytic rank: $$1$$ sage: E.regulator() magma: Regulator(E); Regulator: $$8.9024258968101037762820120519\dots$$ sage: E.period_lattice().omega() gp: E.omega[1] magma: RealPeriod(E); Real period: $$0.079189842518279784688287246603\dots$$ sage: E.tamagawa_numbers() gp: gr=ellglobalred(E); [[gr[4][i,1],gr[5][i][4]] | i<-[1..#gr[4][,1]]] magma: TamagawaNumbers(E); Tamagawa product: $$16$$ = $$1\cdot2^{2}\cdot1\cdot2^{2}$$ sage: E.torsion_order() gp: elltors(E)[1] magma: Order(TorsionSubgroup(E)); Torsion order: $$2$$ sage: E.sha().an_numerical() magma: MordellWeilShaInformation(E); Analytic order of Ш: $$1$$ (exact)
## Modular invariants
Modular form 36414.2.a.l
sage: E.q_eigenform(20)
gp: xy = elltaniyama(E);
gp: x*deriv(xy[1])/(2*xy[2]+E.a1*xy[1]+E.a3)
magma: ModularForm(E);
$$q - q^{2} + q^{4} - 2q^{5} + q^{7} - q^{8} + 2q^{10} - 6q^{13} - q^{14} + q^{16} + O(q^{20})$$
sage: E.modular_degree() magma: ModularDegree(E); Modular degree: 1769472 $$\Gamma_0(N)$$-optimal: no Manin constant: 1
#### Special L-value
sage: r = E.rank();
sage: E.lseries().dokchitser().derivative(1,r)/r.factorial()
gp: ar = ellanalyticrank(E);
gp: ar[2]/factorial(ar[1])
magma: Lr1 where r,Lr1 := AnalyticRank(E: Precision:=12);
$$L'(E,1)$$ ≈ $$2.8199268191961911961981958584904110447$$
## Local data
This elliptic curve is not semistable. There are 4 primes of bad reduction:
sage: E.local_data()
gp: ellglobalred(E)[5]
magma: [LocalInformation(E,p) : p in BadPrimes(E)];
prime Tamagawa number Kodaira symbol Reduction type Root number ord($$N$$) ord($$\Delta$$) ord$$(j)_{-}$$
$$2$$ $$1$$ $$I_{3}$$ Non-split multiplicative 1 1 3 3
$$3$$ $$4$$ $$I_8^{*}$$ Additive -1 2 14 8
$$7$$ $$1$$ $$I_{1}$$ Split multiplicative -1 1 1 1
$$17$$ $$4$$ $$I_1^{*}$$ Additive 1 2 7 1
## Galois representations
The image of the 2-adic representation attached to this elliptic curve is the subgroup of $\GL(2,\Z_2)$ with Rouse label X34.
This subgroup is the pull-back of the subgroup of $\GL(2,\Z_2/2^3\Z_2)$ generated by $\left(\begin{array}{rr} 5 & 0 \\ 4 & 3 \end{array}\right),\left(\begin{array}{rr} 7 & 7 \\ 4 & 3 \end{array}\right),\left(\begin{array}{rr} 3 & 0 \\ 0 & 3 \end{array}\right),\left(\begin{array}{rr} 7 & 0 \\ 4 & 3 \end{array}\right)$ and has index 12.
sage: rho = E.galois_representation();
sage: [rho.image_type(p) for p in rho.non_surjective()]
magma: [GaloisRepresentation(E,p): p in PrimesUpTo(20)];
The mod $$p$$ Galois representation has maximal image $$\GL(2,\F_p)$$ for all primes $$p$$ except those listed.
prime Image of Galois representation
$$2$$ B
## $p$-adic data
### $p$-adic regulators
sage: [E.padic_regulator(p) for p in primes(5,20) if E.conductor().valuation(p)<2]
$$p$$-adic regulators are not yet computed for curves that are not $$\Gamma_0$$-optimal.
## Iwasawa invariants
$p$ Reduction type $\lambda$-invariant(s) $\mu$-invariant(s) 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 nonsplit add ordinary split ss ordinary add ss ordinary ordinary ordinary ordinary ordinary ordinary ss 10 - 3 2 1,1 1 - 1,1 1 1 1 1 1 1 1,1 1 - 0 0 0,0 0 - 0,0 0 0 0 0 0 0 0,0
An entry - indicates that the invariants are not computed because the reduction is additive.
## Isogenies
This curve has non-trivial cyclic isogenies of degree $$d$$ for $$d=$$ 2 and 4.
Its isogeny class 36414.l consists of 3 curves linked by isogenies of degrees dividing 4.
## Growth of torsion in number fields
The number fields $K$ of degree less than 24 such that $E(K)_{\rm tors}$ is strictly larger than $E(\Q)_{\rm tors}$ $\cong \Z/{2}\Z$ are as follows:
$[K:\Q]$ $E(K)_{\rm tors}$ Base change curve $K$ $2$ $$\Q(\sqrt{238})$$ $$\Z/2\Z \times \Z/2\Z$$ Not in database $2$ $$\Q(\sqrt{-21})$$ $$\Z/4\Z$$ Not in database $2$ $$\Q(\sqrt{-102})$$ $$\Z/4\Z$$ Not in database $4$ $$\Q(\sqrt{-21}, \sqrt{-102})$$ $$\Z/2\Z \times \Z/4\Z$$ Not in database $8$ Deg 8 $$\Z/2\Z \times \Z/4\Z$$ Not in database $8$ Deg 8 $$\Z/8\Z$$ Not in database $8$ Deg 8 $$\Z/8\Z$$ Not in database $8$ Deg 8 $$\Z/6\Z$$ Not in database $16$ Deg 16 $$\Z/4\Z \times \Z/4\Z$$ Not in database $16$ Deg 16 $$\Z/2\Z \times \Z/8\Z$$ Not in database $16$ Deg 16 $$\Z/2\Z \times \Z/8\Z$$ Not in database $16$ Deg 16 $$\Z/2\Z \times \Z/6\Z$$ Not in database $16$ Deg 16 $$\Z/12\Z$$ Not in database $16$ Deg 16 $$\Z/12\Z$$ Not in database
We only show fields where the torsion growth is primitive. For fields not in the database, click on the degree shown to reveal the defining polynomial. | 2,405 | 6,299 | {"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} | 3.28125 | 3 | CC-MAIN-2021-25 | latest | en | 0.226575 |
http://www.listserv.uga.edu/cgi-bin/wa?A2=ind0302a&L=sas-l&D=1&F=P&O=D&P=21014&F= | 1,371,533,618,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368706933615/warc/CC-MAIN-20130516122213-00036-ip-10-60-113-184.ec2.internal.warc.gz | 560,463,783 | 3,521 | ```Date: Tue, 4 Feb 2003 13:39:42 -0800 Reply-To: Mark Terjeson Sender: "SAS(r) Discussion" From: Mark Terjeson Subject: Re: Problem Comments: To: Jishnu In-Reply-To: <80d9e10e.0302041252.4af46d9a@posting.google.com> Content-Type: text/plain; charset="us-ascii" Hi, Here is one possibility. I threw in an extra in one year just in case that needed to be covered. data Table1; input uid \$ year; cards; x 1999 x 2000 x 2000 y 2001 x 2001 y 2002 x 2002 ; run; proc sql; create table Table2 as select uid, count(uid) as count, year from Table1 group by year,uid order by uid,year ; quit; proc transpose data=Table2 out=Table3(drop=_name_); by uid; id year; var count; run; Hope this is helpful, Mark Terjeson Northwest Crime and Social Research, Inc. A SAS Alliance Partner 215 Legion Way SW Olympia, WA 98501 360.870.2581 - voice,cell 360.570.7533 - fax mailto:mark.terjeson@nwcsr.com www.nwcsr.com "Nothing is particularly hard if you divide it into small jobs." - Henry Ford, Industrialist -----Original Message----- From: SAS(r) Discussion [mailto:SAS-L@LISTSERV.UGA.EDU] On Behalf Of Jishnu Sent: Tuesday, February 04, 2003 12:52 PM To: SAS-L@LISTSERV.UGA.EDU Subject: Problem Hi does any body how to solve this isssue: Original Dataset uid year x 1999 x 2000 y 2001 x 2001 y 2002 x 2002 I would like to transform it into 99 00 01 02 1 1 1 1 1 1 Since x originated on 1999 that is why 99 gets 1 and stays on till the year is available Since y is originated in 2001 it gets a 1 at 2001. Thank you ```
Back to: Top of message | Previous page | Main SAS-L page | 501 | 1,560 | {"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-2013-20 | latest | en | 0.759195 |
https://www.88tuition.com/library/transfer-of-heat | 1,723,283,302,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640805409.58/warc/CC-MAIN-20240810093040-20240810123040-00499.warc.gz | 479,290,932 | 16,390 | ×
Heat can be transferred across different bodies in the following ways:
Conduction: Conduction is the transfer of heat energy between molecules of a substance due to collisions between its molecules. A hot body has molecules that are rapidly vibrating about their position. These vibrating molecules impart their energy to nearby molecules, which start to vibrate. This process continues till heat energy is transferred across the whole conductor. Note that the molecules only vibrate about their mean positions but do not travel across the conductor. Generally, solids make the best conductors.
Transfer of heat
Convection: Convection involves heat transfer via the actual movement of hot molecules of a substance. Liquids and gasses undergo this process since their molecules can move from place to place. The hotter molecules rise towards the top while the colder ones tend to sit down, causing heat transfer.
Radiation: Radiation involves heat transfer without any medium. It occurs via the emission and absorption of electromagnetic waves, which are emitted from hot bodies. Generally, hot bodies emit EM waves in the infrared region but very hot bodies can emit in the visible or even ultraviolet region.
Solved examples
1. Determine the amount of heat energy dissipated if 50 kg of water is cooled down from 800 ℃ to 500 ℃. The specific heat of water is
We are given that,. The relation between heat and specific heat capacity is given by Q=mcT. In this example, the change in temperature, ΔT=(800℃-500℃)= -300 ℃, where the negative sign signifies heat loss. Hence,
2. How much heat energy is required to raise the temperature of 1 kg of iron from 150 to 500 . The specific heat of iron is
Proceeding just as in the last example, we have:
Summary
In this article, we developed an understanding of the concept of heat, its units, and conversion across units. Further, we analyzed how to solve numerical related to heat transfer using a few solved examples.
1. What are the uses of heat energy?
Heat is an inseparable part of our lives and we list a few applications below:
1. Thermal power plants utilize heat energy to generate electricity.
2. Heat therapy is used to aid in pain relief.
3. Automobiles make use of heat energy generated by burning petrol and diesel.
4. We cook our food using heat.
2. How are heat and temperature related to each other?
Temperature and heat are closely related. Temperature measures the average kinetic energy of molecules. And heat is the form of energy that gives rise to the vibration of molecules.
3. What is a calorimeter?
A calorimeter is used to measure how much energy is involved in a chemical reaction. It is based on the principle of conservation of energy.
4. What is the law of conservation of energy?
The law of conservation of energy states that energy in this universe can never appear or disappear out of nowhere. It can only be transferred across its different forms. It is also possible to create energy from the mass using Einstein’s mass-energy equivalence.
5. What is specific heat?
Specific heat of a substance refers to the amount of heat energy required to raise the temperature of one unit mass of that substance by one unit. | 654 | 3,218 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.40625 | 3 | CC-MAIN-2024-33 | latest | en | 0.928141 |
https://whatisconvert.com/345-tablespoons-in-teaspoons | 1,597,384,025,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439739177.25/warc/CC-MAIN-20200814040920-20200814070920-00247.warc.gz | 536,010,380 | 7,253 | # What is 345 Tablespoons in Teaspoons?
## Convert 345 Tablespoons to Teaspoons
To calculate 345 Tablespoons to the corresponding value in Teaspoons, multiply the quantity in Tablespoons by 3.0000000000122 (conversion factor). In this case we should multiply 345 Tablespoons by 3.0000000000122 to get the equivalent result in Teaspoons:
345 Tablespoons x 3.0000000000122 = 1035.0000000042 Teaspoons
345 Tablespoons is equivalent to 1035.0000000042 Teaspoons.
## How to convert from Tablespoons to Teaspoons
The conversion factor from Tablespoons to Teaspoons is 3.0000000000122. To find out how many Tablespoons in Teaspoons, multiply by the conversion factor or use the Volume converter above. Three hundred forty-five Tablespoons is equivalent to one thousand thirty-five Teaspoons.
## Definition of Tablespoon
In the United States a tablespoon (abbreviation tbsp) is approximately 14.8 ml (0.50 US fl oz). A tablespoon is a large spoon used for serving or eating. In many English-speaking regions, the term now refers to a large spoon used for serving, however, in some regions, including parts of Canada, it is the largest type of spoon used for eating. By extension, the term is used as a measure of volume in cooking.
## Definition of Teaspoon
A teaspoon (occasionally "teaspoonful") is a unit of volume, especially widely used in cooking recipes and pharmaceutic prescriptions. It is abbreviated as tsp. or, less often, as t., ts., or tspn. In the United States one teaspoon as a unit of culinary measure is 1⁄3 tablespoon, that is, 4.92892159375 ml; it is exactly 1 1⁄3 US fluid drams, 1⁄6 US fl oz, 1⁄48 US cup, and 1⁄768 US liquid gallon and 77⁄256 or 0.30078125 cubic inches. For nutritional labeling on food packages in the US, the teaspoon is defined as precisely 5 ml.
### Using the Tablespoons to Teaspoons converter you can get answers to questions like the following:
• How many Teaspoons are in 345 Tablespoons?
• 345 Tablespoons is equal to how many Teaspoons?
• How to convert 345 Tablespoons to Teaspoons?
• How many is 345 Tablespoons in Teaspoons?
• What is 345 Tablespoons in Teaspoons?
• How much is 345 Tablespoons in Teaspoons?
• How many tsp are in 345 tbsp?
• 345 tbsp is equal to how many tsp?
• How to convert 345 tbsp to tsp?
• How many is 345 tbsp in tsp?
• What is 345 tbsp in tsp?
• How much is 345 tbsp in tsp? | 649 | 2,364 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2020-34 | latest | en | 0.891191 |
http://oeis.org/A100864 | 1,597,028,573,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439738603.37/warc/CC-MAIN-20200810012015-20200810042015-00494.warc.gz | 79,282,301 | 3,849 | The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A100864 Continued fraction expansion of the square of the constant (A100338) which has the continued fraction equal to A006519 (highest power of 2 dividing n). 4
1, 1, 4, 1, 74, 1, 8457, 1, 186282390, 1, 1, 1, 2, 1, 430917181166219, 11, 37, 1, 4, 2, 41151315877490090952542206046, 11, 5, 3, 12, 2, 34, 2, 9, 8, 1, 1, 2, 7, 13991468824374967392702752173757116934238293984253807017, 3, 4, 1, 3, 100, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,3 COMMENTS Decimal expansion is 1.832967032396... (see A100863). Records are doubly exponential and form A100865. LINKS Dzmitry Badziahin, Jeffrey Shallit, An Unusual Continued Fraction, arXiv:1505.00667 [math.NT], 2015. PROG (PARI) {CFM=contfracpnqn(vector(650, n, 2^valuation(n, 2))); contfrac((CFM[1, 1]/CFM[2, 1])^2, 71)} CROSSREFS Cf. A006519, A100338, A100863, A100865. Sequence in context: A173008 A298828 A114917 * A295178 A255192 A299582 Adjacent sequences: A100861 A100862 A100863 * A100865 A100866 A100867 KEYWORD cofr,nonn AUTHOR Paul D. Hanna, Nov 21 2004 STATUS approved
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Last modified August 9 22:52 EDT 2020. Contains 336335 sequences. (Running on oeis4.) | 555 | 1,572 | {"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} | 2.734375 | 3 | CC-MAIN-2020-34 | latest | en | 0.674241 |
http://theweightofmoney.com/ebooks/statistics-a-guide-to-the-use-of-statistical-methods | 1,596,644,974,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439735963.64/warc/CC-MAIN-20200805153603-20200805183603-00470.warc.gz | 102,267,114 | 9,632 | # Download Statistics: a guide to the use of statistical methods by R. J. Barlow PDF
By R. J. Barlow
An creation to the strategies of utilized statistics. presents heritage info on every one approach coated, targeting the idea of measurements and blunders and the matter of estimation.
Read or Download Statistics: a guide to the use of statistical methods PDF
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Additional resources for Statistics: a guide to the use of statistical methods
Example text
T P>|t| [95% Conf. 4990 y Asthma Normal _cons Coef. 25 Std. Err. 633 P>|t| [95% Conf. 48547 22 Statistics at square two model because these refer to the overall model which differs from the earlier one only in the formulation of the parameters. 25, which is not significant. Thus the only significant difference is between asthmatics and normals. This method of analysis is also known as one-way analysis of variance. 1 One could ask what is the difference between this and simply carrying out two t-tests: asthmatics vs normals and bronchitics vs normals.
Sometimes a term can be added that gives a significant P-value, but only a marginal improvement in R2 adjusted, and for the sake of simplicity may not be included as the best model. 4 Two independent variables: both continuous Here we were interested in whether height or age or both were important in the prediction of deadspace. 6. 045 ϫ Age. 2. Note a peculiar feature of this output. 291, respectively)! This occurs because age and height are strongly correlated, and highlights the importance of looking at the overall fit of a model.
04362 Std. Err. 5091 z P>|z| [95% Conf. 07466 Logistic regression 45 of subjects with and without hypertension and who are in the old or young age group before fitting a parameter corresponding to the interaction between the two to assess whether age and hypertension were associated. By contrast, in logistic regression, the presence or absence of hypertension is unequivocally the dependent variable and age an independent variable. 7 Case–control studies One of the main uses of logistic regression is in the analysis of case–control studies.
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Rated 4.26 of 5 – based on 35 votes | 863 | 3,932 | {"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-2020-34 | latest | en | 0.714775 |
http://opencollege.com/simsim/php/ResourceManager.php?cmd=get_view&catID=1435&resID=63&outcat=1 | 1,521,871,109,000,000,000 | text/html | crawl-data/CC-MAIN-2018-13/segments/1521257649931.17/warc/CC-MAIN-20180324054204-20180324074204-00455.warc.gz | 220,221,149 | 4,868 | Newton`s Rings
If a convex surface of a lens is in contact with a plane glass plate, a thin film of air forms between the two surfaces. Under monochromatic light, you will observe circular interference fringes called Newton's rings. The radii rm of Newton's rings depend on the incident light?s wavelength λ. The center of the pattern is always dark. T. Young explained this phenomenon using the wave concept. Newton's rings are the result of interference between the waves reflected by the surface of the lens and the plane surface of the plate. A path difference exists between these two waves. It is twice as thick as the air layer involved in the wave generation (if the rays of the incident light are normal to the surface). If this path difference equals an integral multiple of the wavelength, both waves reinforce each other and reach their maximal amplitude. If the path difference equals a half of the integral multiple of the wavelengths, both waves cancel each other out and their amplitude is at a minimum. A change in the phase of the wave by π during the reflection at the interface between the air layer and the glass plate -- which corresponds to a λ/2 increase in the path difference -- produces the minimal amplitude (dark spot) in the center of the pattern, where the thickness of the air film is significantly less than the wavelength λ. Radius rm of the m'th dark ring is equal to rm = (mλR) 1/2, where R is the radius of curvature of the convex surface of the lens. By measuring the dark ring's radii, one can determine the radius of the curvature of the lens? surface given the wavelength λ of the light. | 339 | 1,630 | {"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} | 3.21875 | 3 | CC-MAIN-2018-13 | latest | en | 0.908894 |
https://www.enotes.com/homework-help/an-object-acted-by-either-horizontal-vertical-534078 | 1,481,007,392,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698541883.3/warc/CC-MAIN-20161202170901-00239-ip-10-31-129-80.ec2.internal.warc.gz | 871,954,916 | 11,048 | Is an object acted on by either horizontal or vertical forces?
Asked on by enotes
1 Answer |Add Yours
gsenviro | College Teacher | (Level 1) Educator Emeritus
Posted on
An object can be acted upon by either horizontal or vertical forces or both forces at the same time. Even at a state of rest, any object on planet earth feels a downward force. This vertically downwards force is due to the gravitational pull of the Earth on the object. And this is the very reason why everything falls downwards (when no other force is acting on it; conversely we will need another force to prevent objects from falling down).
Horizontal force can be applied by someone or something on an object, be it wind gust or machine push (or pull). If one is pushing a book along a table, horizontal force is being exerted on the book. One can throw a ball at some angle and the ball will feel both a horizontal component of the force as well as a vertical component of the force at the same time.
Hope this helps.
We’ve answered 318,928 questions. We can answer yours, too. | 231 | 1,059 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2016-50 | longest | en | 0.932027 |
https://www.physicsforums.com/threads/do-moving-masses-slow-down-due-to-gravitational-waves.972995/ | 1,726,255,818,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651535.66/warc/CC-MAIN-20240913165920-20240913195920-00266.warc.gz | 884,326,881 | 20,589 | # Do Moving Masses Slow Down Due to Gravitational Waves?
• A
• Cato
In summary, gravitational waves are produced by accelerating masses, but they are so weak that their effect is probably something like a rounding error in the 15th decimal place. Objects in free fall don't produce gravitational waves, but objects that merge will speed up.
Cato
TL;DR Summary
Gravitational waves are produced by accelerating masses. Since all space is curved -- more curved near large masses stars, less curved in intergalactic space -- all moving masses are being accelerated to some degree. Do all moving masses therefore produce gravitational waves? If they do, will all moving masses lose energy and slow down?
Gravitational waves are produced by accelerating masses. Since all space is curved -- more curved near large masses stars, less curved in intergalactic space -- all moving masses are being accelerated to some degree. Do all moving masses therefore produce gravitational waves? If they do, will all moving masses lose energy and slow down?
Technically, yes, gravity waves are produced but they are so weak in the kind of situation that you describe that their effect is probably something like a rounding error in the 15th decimal place.
Last edited:
Objects in free fall aren't accelerating in any meaningful sense. The source of gravitational radiation is stress-energy with a changing quadropole moment.
That does mean that any pair of objects ought to emit gravitational radiation unless they are at rest with respect to one another (I think - there might be exceptions). And that does mean that they'll slow down with respect to one another, but that may or may not mean slow down with respect to whatever coordinate system you are using.
Back-of-the-envelope, the kinetic energy of Earth in its orbit is 1031J. The power output from gravitational radiation is around 100W, if memory serves. So I think that this effect is rather weaker even than @phinds says - even for a system as massive as our planet.
Finally, extending this argument to "every object" is risky. We strongly suspect that GR is not an accurate description of gravity when quantum effects are important for its source. So gravitational radiation may or may not be emitted by very small objects.
Last edited:
phinds
Ibix said:
That does mean that any pair of objects ought to emit gravitational radiation unless they are at rest with respect to one another (I think - there might be exceptions). And that does mean that they'll slow down with respect to one another, but that may or may not mean slow down with respect to whatever coordinate system you are using.
Looking at the the merger of two compact objects I think they speed up independent of the chosen coordinate system. Or do you think of non-inertial frames here?
Last edited:
timmdeeg said:
speed up independent of the chosen coordinate system.
Can “speed up” ever have a coordinate-independent meaning? “Experiences proper acceleration” has a coordinate-independent meaning and in an inertial frame does imply what most people would mean by “speed up”... but we’re talking gravitational effects here, so are considering regions of spacetime that aren’t properly described by any inertial frame.
I don't know this kind of physics enough to discuss the details. "Finally, extending this argument to "every object" is risky. We strongly suspect that GR is not an accurate description of gravity when quantum effects are important for its source. So gravitational radiation may or may not be emitted by very small objects." So perhaps objects where quantum effects are important don't produce gravitational waves. Thanks for all your answers.
## 1. How do gravitational waves affect moving masses?
Gravitational waves are ripples in the fabric of spacetime that are created when massive objects accelerate. As these waves pass through a region of space, they cause the space itself to stretch and compress. This stretching and compressing can affect the motion of objects, including moving masses.
## 2. Do gravitational waves cause moving masses to slow down?
Yes, gravitational waves can cause moving masses to slow down. This is because the waves transfer energy to the objects they pass through, which can result in a loss of kinetic energy and a decrease in speed.
## 3. How significant is the effect of gravitational waves on moving masses?
The effect of gravitational waves on moving masses is very small. For most everyday objects and motions, the impact of gravitational waves is negligible and cannot be detected. However, for extremely massive objects such as black holes or neutron stars, the effect can be significant.
## 4. Can gravitational waves completely stop a moving mass?
No, gravitational waves cannot completely stop a moving mass. While they can cause a decrease in speed, they cannot bring an object to a complete halt. The effect of gravitational waves is limited and cannot overcome the inertia of the object.
## 5. How do scientists study the impact of gravitational waves on moving masses?
Scientists study the impact of gravitational waves on moving masses through various experiments and observations. This includes using highly sensitive instruments such as interferometers to detect the stretching and compressing of spacetime caused by gravitational waves. They also use computer simulations and mathematical models to understand the effects of gravitational waves on different types of moving masses.
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1K | 1,161 | 5,681 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2024-38 | latest | en | 0.956411 |
https://geoana.simpeg.xyz/api/generated/geoana.em.fdem.MagneticDipoleWholeSpace.magnetic_field.html | 1,702,013,853,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100724.48/warc/CC-MAIN-20231208045320-20231208075320-00038.warc.gz | 329,033,997 | 11,341 | # geoana.em.fdem.MagneticDipoleWholeSpace.magnetic_field#
MagneticDipoleWholeSpace.magnetic_field(xyz)#
Magnetic field for the harmonic magnetic dipole at a set of gridded locations.
For a harmonic magnetic dipole oriented in the $$\hat{u}$$ direction with moment amplitude $$m$$ and harmonic frequency $$f$$, this method computes the magnetic field at the set of gridded xyz locations provided.
The analytic solution is adapted from Ward and Hohmann (1988). For a harmonic magnetic dipole oriented in the $$\hat{x}$$ direction, the solution at vector distance $$\mathbf{r}$$ from the dipole is:
$\begin{split}\mathbf{H}(\mathbf{r}) = \frac{m}{4\pi r^3} e^{-ikr} \Bigg [ \Bigg ( \frac{x^2}{r^2}\hat{x} + \frac{xy}{r^2}\hat{y} + \frac{xz}{r^2}\hat{z} \Bigg ) ... \\ \big ( -k^2r^2 + 3ikr + 3 \big ) \big ( k^2 r^2 - ikr - 1 \big ) \hat{x} \Bigg ]\end{split}$
where
$k = \sqrt{\omega^2 \mu \varepsilon - i \omega \mu \sigma}$
Parameters:
xyz(n, 3) numpy.ndarray
Gridded xyz locations
Returns:
(n_freq, n_loc, 3) numpy.array of complex
Magnetic field at all frequencies for the gridded locations provided. Output array is squeezed when n_freq and/or n_loc = 1.
Examples
Here, we define an z-oriented magnetic dipole and plot the magnetic field on the xz-plane that intercepts y=0.
>>> from geoana.em.fdem import MagneticDipoleWholeSpace
>>> from geoana.utils import ndgrid
>>> from geoana.plotting_utils import plot2Ddata
>>> import numpy as np
>>> import matplotlib.pyplot as plt
Let us begin by defining the electric current dipole.
>>> frequency = np.logspace(1, 3, 3)
>>> location = np.r_[0., 0., 0.]
>>> orientation = np.r_[0., 0., 1.]
>>> moment = 1.
>>> sigma = 1.0
>>> simulation = MagneticDipoleWholeSpace(
>>> frequency, location=location, orientation=orientation,
>>> moment=moment, sigma=sigma
>>> )
Now we create a set of gridded locations and compute the magnetic field.
>>> xyz = ndgrid(np.linspace(-1, 1, 20), np.array([0]), np.linspace(-1, 1, 20))
>>> H = simulation.magnetic_field(xyz)
Finally, we plot the real and imaginary components of the magnetic field.
>>> f_ind = 2
>>> fig = plt.figure(figsize=(6, 3))
>>> ax1 = fig.add_axes([0.15, 0.15, 0.40, 0.75])
>>> plot2Ddata(
>>> xyz[:, 0::2], np.real(H[f_ind, :, 0::2]), vec=True, ax=ax1, scale='log', ncontour=25
>>> )
>>> ax1.set_xlabel('X')
>>> ax1.set_ylabel('Z')
>>> ax1.autoscale(tight=True)
>>> ax1.set_title('Real component {} Hz'.format(frequency[f_ind]))
>>> ax2 = fig.add_axes([0.6, 0.15, 0.40, 0.75])
>>> plot2Ddata(
>>> xyz[:, 0::2], np.imag(H[f_ind, :, 0::2]), vec=True, ax=ax2, scale='log', ncontour=25
>>> )
>>> ax2.set_xlabel('X')
>>> ax2.set_yticks([])
>>> ax2.autoscale(tight=True)
>>> ax2.set_title('Imag component {} Hz'.format(frequency[f_ind])) | 884 | 2,771 | {"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-2023-50 | latest | en | 0.647584 |
http://www.trafficimagine.com/www.shahvani.com | 1,369,556,838,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368706762669/warc/CC-MAIN-20130516121922-00087-ip-10-60-113-184.ec2.internal.warc.gz | 760,876,127 | 3,991 | # Shahvani.com - Can you imagine their visitors ?
## Shahvani.com has 51,850 daily visitors. Can you imagine how big the country was if these 51,850 visitors would have been the population of a country?
Shahvani.com would be on of the bigger countries of the world. We've created a table below, so you can see it in the pick-order. You'll find the number of humans living in that country and also find the percentage of the world population living in that country. As you can see Shahvani.com would be bigger then the country Faroe Islands!
Rank Country Population % of world population 204 Saint Kitts and Nevis 52,000 0.001% 205 www.shahvani.com 51,850 - 206 Faroe Islands 48,917 0.001% 207 Turks and Caicos Islands 40,357 0.0006% 208 Sint Maarten 37,429 0.0005% 209 Liechtenstein 35,904 0.0005%
## How many of these cars would be needed to seat the Shahvani.com visitors?
The car below consists of 17 people! Yes you won't believe it but it's true! That means that if those 51,850 have to be seated in cars like this, you would need at least 3,050 cars. If there would be a big traffic jam with those 3,050 cars, it would be 12,200 meters long (12 kilometers).
## Their website visitors compared to the daily internet users.
From all people of the world, there are around 1,400,000,000 (1,4 billion) people surfing daily on the internet. If you compare this to the 51,850 visitors of Shahvani.com, you'll see that 1 of the 27,001 people is visiting their site on a daily basis.
If there would be a list of top websites in the world. The site Shahvani.com would be on place #12787. Off course this is an estimated value. There are about 200 million websites around the world.
## How many kilometers will those people reach hand in hand?
The average person in the world is about 1.7 meters (5 ft 7 in). That means that if 51,850 people (the Shahvani.com visitors) would connect their hands and form a big line, it would be 88,145 meters long. A kilometer consists of 1000 meters, so it would be 88 kilometers long.
Below you will see an image of 4 humans connected by their hands.
## How many electricity would this site use?
As we estimated the total number of visitors to 51,850 earlier, this mean they have around 103,700 pageviews per day. This correspondents to 29 per second and 1,740 requests per minute. We think their are using 1 servers to host this website. A regular server uses about 2,200 kWh of power on a yearly basis. The commercial pricing average of one kWh is \$0.107. Factoring in the cooling load at 1X (2.0 PUE) puts the annual energy cost per server at ~\$800. for Shahvani.com this means that their total server costs per year are about \$800. Off course, this are rough estimates. We've not even included the "Managing the server and network" time and costs. | 722 | 2,799 | {"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-2013-20 | longest | en | 0.944701 |
https://www.koofers.com/files/exam-d13cpbpwcy/ | 1,606,350,805,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141185851.16/warc/CC-MAIN-20201126001926-20201126031926-00069.warc.gz | 731,183,209 | 14,003 | # Past Exam for MTH 1001 - Calculus 1 with Jones at Florida Tech (FIT)
## Exam Information
Material Type: Final Professor: Jones Class: MTH 1001 - Calculus 1 Subject: Mathematics University: Florida Institute of Technology Term: Spring 2008 Keywords: ApproachingApproximationsAcceleration
## Sample Document Text
Name ____ ~K~e~J6~---------------------- MTH 1001 GSA Name Grade: PRACTICE FINAL EXAM Evaluate the following indefinite integrals: 1. f(200X 9 +6x 3 +30W}ix::: \ )00 X'1 + b X 3 + 30 o. -' X 'O + r 5/ 3 10 ~ X X + 2. I :2 X + )\ I 3 S t' n (5 x=C l:zox (5 3. f[120xcos 3 (Sx 2 )sin(sx 2 )}ix::: 4. U= CDS du Sill (50 Jx, (5x d,h ~ ~ ')0 I: _/ ~ -, dr -- U I U -, Expand the following sigma notation and find the sum: I + ~5 +- I ?:> { X 5 do U~+ -- + 5. Setup and evaluate the Riemann Sum using right-endpoint approximations to find the area under the curve j(x) = 4x + 1 from x = 1 to x = 3 \\',l>oD \ 1M ( \\~" cO [ L ( I~ , (I ."'c() Il'rtl ( + ) )0 fI 00 n n n n Hint: ~) = nand L:k = n(~+l) and L:e = n(n+l~2n+l) k=l k"'l k=l b 6X == 6. The areas of the various regions are indicated in the picture to the right. Evaluate the following integrals based on the ... | 433 | 1,185 | {"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-2020-50 | latest | en | 0.652191 |
http://fermatslibrary.com/s/combinatorial-proof-of-fermats-little-theorem | 1,505,853,500,000,000,000 | text/html | crawl-data/CC-MAIN-2017-39/segments/1505818686034.31/warc/CC-MAIN-20170919202211-20170919222211-00370.warc.gz | 118,798,159 | 276,848 | Instructions: To add a question/comment to a specific line, equation, table or graph simply click on it.
Click on the annotations on the left side of the paper to read and reply to the questions and comments.
Pierre de Fermat first stated what would become his ”Little" Theore...
For simplicity, let's assume we only have 2 colors {R,G} ($n=2$) an...
Note that the number of cyclic permutations of a string of size $p$...
Would a learner appreciate double factorials?
Hi Tony, there aren't any double factorials in the proof. Note that the number of cyclic permutations of a string of size $p$ that result in the same necklace is only equal to $p$ if $p$ is prime. If the size of the string is not a prime it might be possible to divide the string into other sub-strings of smaller size and so we need to take into account other permutations between the sub-strings. For instance, for p=4 the string RGRG has only one cyclic permutation that results in the same necklace (RGRG $\equiv$ GRGR). Would a learner appreciate double factorials? From a purely beginner approach to the Pigeon-Hole Problem Pierre de Fermat first stated what would become his ”Little" Theorem in a letter dated October 18, 1640, to his friend [Frénicle de Bessy](https://en.wikipedia.org/wiki/Bernard_Fr%C3%A9nicle_de_Bessy). Fermat did not include a proof for fear the proof would be too long. The first proof of this theorem was published more than fifty years later by Leonhard Euler, in 1736. In this paper S.W.Golomb proves Fermat's "Little" Theorem using only some basic combinatorial machinery. Add cases. Counting Principle of place value (order, distinguishable) The Pigeon-Hole Problem is dependent on the modular congruence, right? Not one nest left unfilled. Thanks, could one tell me how to remove the comment? For simplicity, let's assume we only have 2 colors {R,G} ($n=2$) and the necklaces have 3 beads ($p=3$). In that case, there are $2^{3}=8$ possible strings of beads. RRR, GRR, RGR, RRG, RGG, GRG, GGR, GGG Now we bring the ends of each string together to create necklaces. We consider two strings as the same necklace if we can rotate one string to obtain the second string. We can observe that for each non-constant string there are precisely p=3 strings (3 cyclic permutations of the beads) that determine the same necklace. For instance, GRR $\equiv$ RGR $\equiv$ RRG , which is the same necklace. As a consequence, the number of distinguishable necklaces is the total number of strings $2^3$ minus the strings made of the same bead (RRR,GGG) divided by the number of permutations that result in equivalent necklaces : $\frac{2^{3}-2}{3}=2$. Generalizing the result for an arbitrary positive integer $n$ and prime $p$ we get $\frac{n^{p}-n}{p}=k$. Since $k$ is just the number of distinguishable necklaces it must therefore be an integer. | 710 | 2,838 | {"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} | 3.359375 | 3 | CC-MAIN-2017-39 | longest | en | 0.911114 |
https://www.shaalaa.com/question-bank-solutions/a-bag-contains-3-red-balls-5-black-balls-4-white-balls-ball-drawn-random-bag-what-probability-that-ball-drawn-is-not-red-chance-probability-chance_61652 | 1,619,036,695,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618039550330.88/warc/CC-MAIN-20210421191857-20210421221857-00029.warc.gz | 1,117,031,828 | 9,165 | # A Bag Contains 3 Red Balls, 5 Black Balls and 4 White Balls. a Ball is Drawn at Random from the Bag. What is the Probability that the Ball Drawn Is: Not Red? - Mathematics
A bag contains 3 red balls, 5 black balls and 4 white balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is:
not red?
#### Solution
$\text{ Number of red balls } = 3$
$\text{ Number of black balls } = 5$
$\text{ Number of white balls } = 4$
$\text{ Total number of balls }= 3 + 5 + 4 = 12$
$\text{ Therefore, the total number of cases is 12 } .$
$P\left( \text{ not a red ball } \right) = 1 - P\left( \text{ a red ball }\right) = 1 - \frac{1}{4} = \frac{3}{4}$
Is there an error in this question or solution?
#### APPEARS IN
RD Sharma Class 8 Maths
Chapter 26 Data Handling-IV (Probability)
Exercise 26.1 | Q 7.4 | Page 15 | 266 | 844 | {"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} | 4.5 | 4 | CC-MAIN-2021-17 | latest | en | 0.800296 |
https://www.answers.com/Q/What_is_iodine_relative_molecular_mass | 1,611,137,673,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703519984.9/warc/CC-MAIN-20210120085204-20210120115204-00511.warc.gz | 654,931,792 | 34,116 | Molecular Mass
# What is iodine relative molecular mass?
## Related Questions
the relative molecular mass or molecular weight of a compound is the mass of a molecule of the compound relative to the mass of a carbon atom taken as exactly 12.
Relative molecular mass is obtained.It is about 17
The atomic mass of I is 127. The atomic mass of F is 19. Therefore the molecular mass of the compound is 127+5x19=214u.
The molecular mass of a compound is the sum of the chemical elements weights contained in the molecule.
You need to know the Relative Molecular Mass of the compound, then you find the ratio of that compared to the R.M.M. of I2O5 and then multiply the ratio by I2O5. That should be it.
I = 126.9 ~ 127 Molecular Formula of Iodine = I2 therfore 1 mole of iodine = 127 x 2 = 254
The iodine pentafluoride (IF5) is a molecular compound.
As they are isobars, they have the same relative molecular mass.
It is the mass of a given molecule in relation to 1/12th the mass of a C-12 atom.
Moles = Mass/ Relative Molecular Mass Aluminum forms Al2 compounds, so the relative molecular mass is 2 * 13 = 26. 856/26 = 32.9 (3sf)
The RMM of sulfate ion is 96u. In sulfuric acid, two protons are attached to a sulfate ion. Hence its relative molecular mass is 96+2=98.
The atomic mass of calcium is 40. The molecular mass of the nitrate ion is 62. Therefor the RMM of calcium nitrate is 40+62x2=164.
Relative molecular mass is obtained by summing up the atomic masses of atoms in the formula. The gram molecular mass denotes the mass of a mole of the substance in grams. Both of them are same in number.
The relative mass of sodium carbonate is 106. The term decahydrate refers to 10 water molecules attached which has relative mass of 180. Therefore the relative mass of compound is 286.
Mr is the symbol for the relative molecular mass.
The atomic mass of Mg is 24. The atomic mass of fluorine is 19. Therefore the relative mass of the substance is 62.
Formula of water = H2O Relative atomic mass of hydrogen = 1 Relative atomic mass of oxygen = 16 Relative molecular mass of H2O = 1 + 1 + 16 = 18 Moles = mass of substance/relative molecular mass Moles = 100/18 Moles of water in 100g = 5 and 4/9 moles or approximately 5.56 moles
Relatve Molecular Mass is the average mass of one molecule of a substance when compared with 1/12 of the mass of one atom of carbon -12 Find the Atomic mass of the atoms together and add them together to get heir relative molecular mass. Example: NH3 Find the atomic mass of 1 Nitrogen and also 3 Hydrogen 14 + 3(1) = 17 Therefore it is 17g
They are values that are calculated in relation (hence are relative) to the mass of C-12 atoms, and therefore the mass (g) units cancel out in the equation, leaving no units.
The molecular geometry of iodine trifluoride IF3 is T-shaped.
###### Molecular MassChemistryElements and CompoundsAtomic MassAcids and BasesSchool Subjects
Copyright © 2021 Multiply Media, LLC. All Rights Reserved. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply. | 791 | 3,134 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2021-04 | latest | en | 0.895192 |
https://scribesoftimbuktu.com/factor-16t3-4t2y-2ty2/ | 1,675,663,344,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764500304.90/warc/CC-MAIN-20230206051215-20230206081215-00452.warc.gz | 512,042,756 | 14,694 | # Factor 16t^3-4t^2y-2ty^2
16t3-4t2y-2ty2
Factor 2t out of 16t3-4t2y-2ty2.
Factor 2t out of 16t3.
2t(8t2)-4t2y-2ty2
Factor 2t out of -4t2y.
2t(8t2)+2t(-2ty)-2ty2
Factor 2t out of -2ty2.
2t(8t2)+2t(-2ty)+2t(-1y2)
Factor 2t out of 2t(8t2)+2t(-2ty).
2t(8t2-2ty)+2t(-1y2)
Factor 2t out of 2t(8t2-2ty)+2t(-1y2).
2t(8t2-2ty-1y2)
2t(8t2-2ty-1y2)
Factor.
Factor by grouping.
For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=8⋅-1=-8 and whose sum is b=-2.
Reorder terms.
2t(8t2-1y2-2ty)
Reorder -1y2 and -2ty.
2t(8t2-2ty-1y2)
Factor -2 out of -2ty.
2t(8t2-2(ty)-1y2)
Rewrite -2 as 2 plus -4
2t(8t2+(2-4)(ty)-1y2)
Apply the distributive property.
2t(8t2+2(ty)-4(ty)-1y2)
Remove unnecessary parentheses.
2t(8t2+2ty-4(ty)-1y2)
Remove unnecessary parentheses.
2t(8t2+2ty-4ty-1y2)
2t(8t2+2ty-4ty-1y2)
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
2t((8t2+2ty)-4ty-1y2)
Factor out the greatest common factor (GCF) from each group.
2t(2t(4t+y)-y(4t+y))
2t(2t(4t+y)-y(4t+y))
Factor the polynomial by factoring out the greatest common factor, 4t+y.
2t((4t+y)(2t-y))
2t((4t+y)(2t-y))
Remove unnecessary parentheses.
2t(4t+y)(2t-y)
2t(4t+y)(2t-y)
Factor 16t^3-4t^2y-2ty^2
### Solving MATH problems
We can solve all math problems. Get help on the web or with our math app
Scroll to top | 659 | 1,384 | {"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} | 3.65625 | 4 | CC-MAIN-2023-06 | latest | en | 0.783878 |
http://www.enotes.com/homework-help/party-one-childrem-invited-given-2-books-gift-338549 | 1,398,307,181,000,000,000 | text/html | crawl-data/CC-MAIN-2014-15/segments/1398223204388.12/warc/CC-MAIN-20140423032004-00391-ip-10-147-4-33.ec2.internal.warc.gz | 566,006,772 | 6,377 | Homework Help
# At a party one of the childrem invited is given 2 books as a gift. If there were 15...
math30fail | Student, Undergraduate | Honors
Posted May 16, 2012 at 7:17 PM via web
dislike 2 like
At a party one of the childrem invited is given 2 books as a gift. If there were 15 different books to choose from, how many different gifts were possible?
Tagged with math
Matthew Fonda | eNotes Employee
Posted May 16, 2012 at 8:12 PM (Answer #1)
dislike 1 like
We are interested in the number of ways to choose 2 items from a set of 15 items. We use combinations for this:
15C2 = `((15),(2)) = (15!) / (2!*13!) = (15*14) / 2 = 105`
Therefore there are 105 total gifts possible.
### Join to answer this question
Join a community of thousands of dedicated teachers and students. | 227 | 794 | {"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-2014-15 | latest | en | 0.951141 |
http://www.columbia.edu/itc/sipa/math/slope_linear.html | 1,719,341,991,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198866218.13/warc/CC-MAIN-20240625171218-20240625201218-00333.warc.gz | 33,586,786 | 2,744 | # Slope of Linear Functions
The concept of slope is important in economics because it is used to measure the rate at which changes are taking place. Economists often look at how things change and about how one item changes in response to a change in another item.
It may show for example how demand changes when price changes or how consumption changes when income changes or how quickly sales are growing.
Slope measures the rate of change in the dependent variable as the independent variable changes. The greater the slope the steeper the line.
Consider the linear function:
y = a + bx
b is the slope of the line. Slope means that a unit change in x, the independent variable will result in a change in y by the amount of b.
slope = change in y/change in x = rise/run
Slope shows both steepness and direction. With positive slope the line moves upward when going from left to right. With negative slope the line moves down when going from left to right.
If two linear functions have the same slope they are parallel.
Slopes of linear functions
The slope of a linear function is the same no matter where on the line it is measured. (This is not true for non-linear functions.)
An example of the use of slope in economics
Demand might be represented by a linear demand function such as
Q(d) = a - bP
Q(d) represents the demand for a good
P represents the price of that good.
Economists might consider how sensitive demand is to a change in price.
This is a typical downward sloping demand curve which says that demand declines as price rises.
This is a special case of a horizontal demand curve which says at any price above P* demand drops to zero. An example might be a competitor's product which is considered just as good.
This is a special case of a vertical demand curve which says that regardless of the price quantity demanded is the same. An example might be medicine as long as the price does not exceed what the consumer can afford.
Supply might be represented by a linear supply function such as
Q(s) = a + bP
Q(s) represents the supply for a good
P represents the price of that good.
Economists might consider how sensitive supply is to a change in price.
This is a typical upward sloping supply curve which says that supply rises as price rises.
An example of the use of slope in economics
The demand for a breakfast cereal can be represented by the following equation where p is the price per box in dollars:
d = 12,000 - 1,500 p
This means that for every increase of \$1 in the price per box, demand decreases by 1,500 boxes.
Calculating the slope of a linear function
Slope measures the rate of change in the dependent variable as the independent variable changes. Mathematicians and economists often use the Greek capital letter D or D as the symbol for change. Slope shows the change in y or the change on the vertical axis versus the change in x or the change on the horizontal axis. It can be measured as the ratio of any two values of y versus any two values of x.
Example 1
Find the slope of the line segment connecting the following points:
(1,1) and (2,4)
x1 = 1 y1 = 1
x2 = 2 y2 = 4
Example 2
Find the slope of the line segment connecting the following points:
(-1,-2) and (1,6)
x1 = -1 y1 = -2
x2 = 1 y2 = 6
Example 3
Find the slope of the line segment connecting the following points:
(-1,3) and (8,0)
x1 = -1 y1 = 3
x2 = 8 y2 = 0
[Index] | 813 | 3,499 | {"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} | 4.03125 | 4 | CC-MAIN-2024-26 | latest | en | 0.944841 |
http://www.roseindia.net/answers/viewqa/Java-Beginners/14953-quick-sort.html | 1,490,445,508,000,000,000 | text/html | crawl-data/CC-MAIN-2017-13/segments/1490218188924.7/warc/CC-MAIN-20170322212948-00421-ip-10-233-31-227.ec2.internal.warc.gz | 694,484,129 | 19,641 | moni sharma
quick sort
1 Answer(s) 6 years and 3 months ago
Posted in : Java Beginners
sir, i try to modify this one as u sugess me in previous answer "array based problem" for run time input.but i am facing some problem.plz solve this one also.
import java.util.*; public class QuickSort1 { public static void quick_srt(int array[],int low, int n){ int lo = low; int hi = n; if (lo >= n) { return; } int mid = array[(lo + hi) / 2]; while (lo < hi) { while (lo mid) { hi--; } if (lo < hi) { int T = array[lo]; array[lo] = array[hi]; array[hi] = T; } } if (hi < lo) { int T = hi; hi = lo; lo = T; } quick_srt(array, low, lo); quick_srt(array, lo == low ? lo+1 : lo, n); }
public static void main(String a[]){ Scanner input=new Scanner(System.in); int array[]=new int[10]; int i;
``` System.out.println(" Quick Sort\n\n");
System.out.println("Values Before the sort:\n");
for(i = 0; i < array.length; i++){
array[i]=input.nextInt();
}
for(i = 0; i < array.length; i++){
System.out.println(array[i]);
}
quick_srt(array,0,array.length-1);
System.out.print("Values after the sort:\n");
for(i = 0; i <array.length; i++)
System.out.print(array[i]+" ");
System.out.println();
System.out.println("PAUSE");
```
}
}
January 5, 2011 at 10:13 AM
Hi Friend,
Here is required code:
```import java.util.*;
public class QuickSort1 {
public static void main(String a[]){
int i;
int array[] = new int[5];
Scanner input=new Scanner(System.in);
System.out.println(" Quick Sort\n\n");
System.out.println("Values Before the sort:\n");
for(i = 0; i < array.length; i++){
array[i]=input.nextInt();
}
quick_srt(array,0,array.length-1);
System.out.print("Values after the sort:\n");
for(i = 0; i <array.length; i++)
System.out.print(array[i]+" ");
System.out.println();
System.out.println("PAUSE");
}
public static void quick_srt(int array[],int low, int n){
int lo = low;
int hi = n;
if (lo >= n) {
return;
}
int mid = array[(lo + hi) / 2];
while (lo < hi) {
while (lo<hi && array[lo] < mid) {
lo++;
}
while (lo<hi && array[hi] > mid) {
hi--;
}
if (lo < hi) {
int T = array[lo];
array[lo] = array[hi];
array[hi] = T;
}
}
if (hi < lo) {
int T = hi;
hi = lo;
lo = T;
}
quick_srt(array, low, lo);
quick_srt(array, lo == low ? lo+1 : lo, n);
}
}
```
Thanks
quick sort
; System.out.println(" Quick Sort\n\n"); System.out.println("Values Before...quick sort sir, i try to modify this one as u sugess me in previous... static void quick_srt(int array[],int low, int n){ int lo = low; int hi
quick sort
; System.out.println(" Quick Sort\n\n"); System.out.println("Values Before...quick sort sir, i try to modify this one as u sugess me in previous... static void quick_srt(int array[],int low, int n){ int lo = low; int hi
quick sort
; System.out.println(" Quick Sort\n\n"); System.out.println("Values Before...quick sort sir, i try to modify this one as u sugess me in previous... static void quick_srt(int array[],int low, int n){ int lo = low; int hi
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Sort program to sort a list of numbers in decendimg order Hi Friend, Try the following code: import java.util.*; class SortListInDescendingOrder{ public static void main(String[] args
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Waiting for ur quick response Hi, I have two different java programs like sun and moon. In both of these two programs i have used same class name like A. For example, File name:sun.java Then the code is here: Class
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Insertion Sort In Java
. There are more efficient algorithms such as quick sort, heap sort, or merge sort... Insertion Sort In Java ... In this example we are going to sort integer values of an array using insertion sort
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Tutorials | 1,758 | 6,710 | {"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} | 3.03125 | 3 | CC-MAIN-2017-13 | longest | en | 0.293004 |
https://www.tutorialspoint.com/the-connection-between-bmi-numbers-and-obesity-levels | 1,701,625,554,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100508.42/warc/CC-MAIN-20231203161435-20231203191435-00477.warc.gz | 1,185,326,322 | 24,064 | # The Connection Between BMI Numbers and Obesity Levels
An individual's weight and height are used to compute their body mass index (BMI). The BMI is summed by dividing the squared value of the person's height by the body weight. It is represented in kilograms per square meter (kg/m2). The BMI can be totalled by operating through a table or diagram that plots BMI as a ratio of size and mass utilizing shades to separate various BMI classes and may utilize different measurement units.
With rising obesity rates in affluent Western nations, there has been research on such a scale that quantifies body fat. BMI was categorically deemed by Keys to be acceptable for population research but unfit for the assessment phase. Yet, it is often utilized for first diagnosis because it is easy to use. Waist measurement is one additional statistic that may be helpful.
As weight = kilograms and height = meters, the BMI is given in kilograms per square meter (kg/m2). If pounds and inches are utilized, a conversion factor = 703 (kg/m2) or (lb/in2) is employed. The units are often left out when the word "BMI" is used casually.
## How to Calculate BMI?
BMI = Mass (in kg)/ Height 2 (in metres) = (Mass (in lb) x 703) / Height 2 (in inches)
Nowadays, there are online BMI calculators that find your BMI easily if you put in the correct details about your body. However, consider that children between 2 – 19 years of age have different BMI calculators and adults, i.e., individuals 20 years or above, have adult BMI Calculators.
## Need of BMI index
The BMI is indeed a helpful tool for gauging overweight and obesity in a demographic. Every adult, regardless of age or gender, uses it in the same way. To determine how well BMI can predict adiposity, researchers have looked at the link between BMI and the percentage of body fat (BF%) in various ethnic groups. With a sample of South Asian individuals with a different physical structure than currently researched ethnic groups, scientists investigated the link between BMI and BF%. They found them quite different from Europeans and East Asians. To determine if this connection is linear or curved, researchers looked at the effects of age and gender.
Nonetheless, BMI is not infallible. Today's experts advise against using BMI as a diagnosis; they advise using it as a diagnostic method to determine if you are overweight or obese. BMI should be considered as one aspect among several variables your doctor considers when determining your amount of body fat and general health rather than as the only one.
## Classifications and Groups
According to the WHO, an adult with less than 18.5 BMI is considered underweight and may be a sign of malnourishment, chronic eating disorders, or other medical conditions. In contrast, a BMI of 25 or more is considered overweight, while a BMI of 30 or more is considered obese. Four different cut-off values for at-risk Asians (23, 27.5, 32.5, and 37.5) were found in addition to the standard global WHO BMI split points (16, 17, 18.5, 25, 30, 35, and 40). These BMI value limits are only reliable as statistical categories.
CATEGORY BMI (in kg/m2) Underweight (Class III) < 16.0 Underweight (Class II) 16.0 - 16.9 Underweight (Class I) 17.0 - 18.4 Normal 18.5 - 24.9 Overweight 25.0 - 29.9 Obesity (Class I) 30.0 - 34.9 Obesity (Class II) 35.0 - 39.9 Severe Obesity (Class III) >= 40
If you find these figurines too confusing to understand here is a simple format for you −
• BMI under 18.5 indicates being underweight.
• BMI of 18.5 to 24.9 equals a healthy weight.
• BMI of 25.0 to 29.9 indicates obesity.
• Obesity if BMI is 30.0 or greater.
• Morbidly obese at a BMI of 40 or above.
The BMI is applied differently to adolescents and children. Similar to adults, it is computed, and the results are then contrasted with those of similar-aged children or youth to determine normal values. The BMI is evaluated to percentiles of children of the same age and gender rather than predetermined standards for being underweight and overweight.
## Does a high BMI only Indicate Obesity?
Simply put, no. The most straightforward approach to determine if an individual is overweight or obese is likely to be their BMI, but it's not the only method available. Other reliable measures of obesity include the waist-to-hip ratio and waist measurement. Each of these puts a lot of attention on visceral fat, which is hazardous abdominal fat.
Obesity is described by the World Health Organization (WHO) as a waist-to-hip ratio that is more than 0.85 for women and 0.9 for males. The formula for determining this is to divide the waist circumference by the pelvic measurements taken at the broadest portion of the buttocks.
## Drawbacks
The fact that BMI is affordable and straightforward is one of its main benefits. It is a measurement that can be determined for all trustworthy, non-invasive, and consistent populations. Nevertheless, using BMI alone to determine healthy weight measures does have some limitations, and its precision has recently come under scrutiny. BMI is not an optimum choice, and doctors advise against using it exclusively because it only provides a partial view of one's fitness. It doesn't consider a person's gender, ethnicity, age, muscle mass, body fat distribution, or kind of body fat.
There is no method to discern between muscle and body fat when using BMI alone to determine obesity, which is one of the main problems. When they are in excellent health, athletes and persons with a significant muscle mass could be considered obese, even if they do not have the same health concerns as people with a high-fat mass.
## Fun Facts
• With the same BMI, women frequently have greater body fat than males do.
• With the same BMI, older individuals often have fewer muscles than younger individuals and more concentration of body fat.
• Athletes, both professional and amateur, might have a higher BMI due to increased muscle mass rather than excess body fat.
• Asians have a higher body fat percentage than non-Asians.
## Alternate ways to Diagnose Obesity
• Using callipers, measure the thickness of a skinfold.
• Weighing when underwater.
• Bioelectric impedance test.
• Dual-energy X-ray Absorption measurement (DXA).
## Conclusion
The BMI shouldn't be used to estimate body fat mass any longer. However, the classifications and standards should be updated to reflect the current variety in BMIs worldwide if BMI is to be used indefinitely.
It would be nice to have a technique for measuring body fat percentage and its link with various illnesses and deaths more precisely than the BMI.
The BMI was not initially created as a measure of fatness for use in population-based investigations. It has, however, been appropriated for this use since it is simple to acquire measure. It is essential to realize that the BMI may include significant limitations when measuring the percentage of body fat mass. It could be deceptive in this sense, especially for guys. Furthermore, biassed language is now being employed. In Western, developed countries, it is considered the norm for at least half of adults to be overweight (preobese) or obese.
Updated on: 02-Mar-2023
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Engineering
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# Try this! - Oscillations and Waves - JEE Main-5
A body executing SHM has maximum acceleration and max velocity . The amplitude of SHM
• Option 1)
64/9
• Option 2)
1024/9
• Option 3)
3/32
• Option 4)
32/3
Views
S Safeer
Answered 2 months, 1 week ago
Equation of S.H.M. -
$a=-\frac{d^{2}x}{dt^{2}}= -w^{2}x$
$w= \sqrt{\frac{k}{m}}$
- wherein
$x= A\sin \left ( wt+\delta \right )$
x=Xsin(wt)
v = dx/dt=Xwcos(wt)
a=d2x/dt=-Xw2sin(wt)
given V max=Xw =16
and a max =Xw2 =24
solving
x=32/3
Option 1)
64/9
Option 2)
1024/9
Option 3)
3/32
Option 4)
32/3
## JEE Main Articles
Test Series JEE Main April Maths
Exams
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# MULTI-WAVELENGTH ASTRONOMY - PowerPoint PPT Presentation
## MULTI-WAVELENGTH ASTRONOMY
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##### Presentation Transcript
1. MULTI-WAVELENGTHASTRONOMY (or “Oh Say, What Can You See by Different Kinds of Light ?”)
2. How Fast is Light ? • Speed of light designated by the letter “c” • Nothing can go faster • c = 186,000 miles per second (in a vacuum) • How many miles does light travel in one year? 6 trillion (= 6 million million) miles • How do we get this answer?
3. What Kinds of Light Are There? • Electromagnetic radiation includes a lot more than just the light we use to see with. • Look at the diagram on the next slide.
4. LOW ENERGYHIGH ENERGY
5. Energy, Frequency, and Wavelength – Basic Stuff • The diagram shows different kinds of Electromagnetic Radiation. • Right side of the diagram = highest energy = very high frequency = very short wavelength. • Left side of the diagram = lowest energy = very low frequency = very long wavelength.
6. Energy, Frequency, and Wavelength – Gamma Rays • Gamma Rays (right side of the diagram) have the highest energy of all – even more powerful than X-Rays. • Gamma Rays have very high frequency and very short wavelength. They will fry you fast.
7. Energy, Frequency, and Wavelength – Visible Light • Visible Light is in the middle of the Electromagnetic Spectrum, so it’s intermediate in energy. Visible Light has intermediate frequency and intermediate wavelength. • Human eyes use Visible Light to see (duh – that’s why we call it Visible Light).
8. Energy, Frequency, and Wavelength – Visible Light (cont’d) • Remember the colors of Visible Light – red, orange, yellow, green, blue, indigo, violet (ROYGBIV). • Red light = lower energy/longer wavelength. • Violet light = higher energy/shorter wavelength.
9. Energy, Frequency, and Wavelength – Infrared & Ultraviolet • “Infrared” means “below the red,” so Infrared has lower energy/longer wavelength than visible red light. Infrared = heat radiation. • “Ultraviolet” means “beyond the violet,” so Ultraviolet has higher energy/shorter wavelength than visible violet light. • BTW, bees can see in Ultraviolet – flowers look different to them than what we humans see (but “A rose by any other name would smell as sweet”).
10. Energy, Frequency, and Wavelength – Radio Waves • Radio Waves (left side of the diagram) have the lowest energy of all. • Radio Waves have very low frequency and very long wavelength. Everyday examples include microwaves (ovens and cell phones), FM radio, TV, and AM radio. • The Big Bang (creation of the Universe) left microwaves that are more than 13 billion years old. Who knew ?!
11. Gamma Rays • Temperature = more than 108 (100 million) degrees Kelvin (K) = highest energy of all (oKelvin = oC + 273) • Objects that give off Gamma Rays • Interstellar clouds where cosmic rays collide with hydrogen nuclei • Accretion disks around black holes • Pulsars or neutron stars
12. X-Rays • Temperature = 106 to108 K (1 million to 100 million degrees) • Objects that give off X-Rays • Regions of hot, shocked gas • Hot intergalactic gas in clusters of galaxies • Neutron stars • Supernova remnants • Stellar coronas
13. Ultraviolet • Temperature = 104 to106 K (10 thousand to 1 million degrees) • Objects that give off Ultraviolet • Supernova remnants • Very hot stars • Quasars
14. Visible Light • Temperature = 103 to104 K (1 thousand to 10 thousand degrees) • Objects that give off Visible Light • Planets • Stars • Galaxies • Reflection nebulae • Emission nebulae
15. Infrared (Heat Radiation) • Temperature = 10 to103 K (10 to 1 thousand degrees) • Objects that give off Infrared • Cool stars • Star-forming regions • Interstellar dust warmed by starlight • Planets • Comets • Asteroids
16. Radio Waves (including Microwaves) • Temperature = less than 10 K = lowest energy of all • Objects that give off Radio Waves • Cosmic Background Radiation from The Big Bang • Inter-stellar plasmas • Cold interstellar medium • Regions near neutron stars • Regions near white dwarfs • Supernova remnants • Dense regions near centers of galaxies • Cold dense regions in spiral arms of galaxies
17. Family Photo Album • Let’s take a look at some of the members of the astronomical fam seen in different kinds of light (different radiation wavelengths). • A planet – Saturn • A star – our Sun • A nebula formed by an exploding star • A couple of galaxies • The Universe (really !!)
18. Saturn – Different Wavelengths
19. Saturn – Different Wavelengths Ultraviolet Visible Infrared Radio
20. Sun – Different Wavelengths
21. Sun – Different Wavelengths X-Ray Ultraviolet Visible Infrared Radio
22. Supernova Remnant (Crab Nebula)
24. Whirlpool Galaxy M 51
25. Whirlpool Galaxy M 51 X-Ray Visible Infrared Radio
26. Our Galaxy – The Milky Way
27. Where are the Telescopes ? • For Gamma Rays, X-Rays, Ultraviolet and Infrared, the telescopes have to be above the Earth’s atmosphere. Why ? • For Visible Light and Radio Waves, the telescopes can be on the Earth’s surface or above the atmosphere. Why ? • Following are some famous telescopes.
28. Thanks to Tim Compernolle
29. Swift Gamma Ray Telescope
30. Chandra X-Ray Observatory
31. Hubble Space Telescope(Ultraviolet, Visible, Infrared)
32. Spitzer Space Telescope (Infrared)
33. Keck Telescope – Hawaii(Visible)
34. Keck Telescope – Hawaii(Visible)
35. Keck Telescope – Hawaii(Visible)
36. Arecibo Radio Telescope –Puerto Rico
37. Arecibo Radio Telescope –Puerto Rico
40. Radio Telescope – Very LongBaseline Array
41. Wilkinson MicrowaveAnisotropy Probe (WMAP)
42. Light is Weird – Part 1 – Photons • Light sometimes behaves like a wave, like we have been talking about. • But light also can behave like a particle (called a photon). • Einstein proposed that light travels as waves with the energy enclosed in photons. • Shorter wavelength = higher energy photon. • Longer wavelength = lower energy photon. • So what kind of light has the highest energy photons? Look at the Electromagnetic Radiation diagram. • What kind of light has the lowest energy photons? Look at the diagram.
43. LOW ENERGYHIGH ENERGY
44. Light is Weird – Part 2 –Doppler Shift • Light wavelength is changed by motion of the light source – just like sound waves are. • This means light changes color according to how the light source is moving. • Light source (like a star) moves away from you = light looks more red to you = Doppler Redshift. • Light source (like a star) moves toward you = light looks more blue to you = Doppler Blueshift. • Look at the following diagrams.
45. Doppler Shift for Sound
46. Doppler Shift for Light – Moving Star
47. More Doppler – What if YOU are Moving?
48. Light and Telescopes – What Do You Think? (Ch. 3, p. 62) • What is light? • Which type of electromagnetic radiation is most dangerous to life? • What is the main purpose of a telescope? • Why do stars twinkle? • What types of electromagnetic radiation can telescopes currently detect? | 1,729 | 7,115 | {"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-2020-05 | latest | en | 0.858553 |
http://inflateyourmind.com/microeconomics/unit-9-microeconomics/section-5-progressive-regressive-and-proportional-taxes/ | 1,719,247,133,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198865401.1/warc/CC-MAIN-20240624151022-20240624181022-00502.warc.gz | 16,241,861 | 15,301 | The Difference Between Average and Marginal Tax Rates
The United States individual income tax system is a progressive tax system. This means that households with higher incomes pay a higher percentage in tax. Because of the recently passed tax reform, the tax brackets for individuals and married couples have changed (see tables below).
For persons filing “single”, the marginal tax rates are as follows:
2023 Rate Income Bracket Old (2017) Rate Old Income Bracket 10% Up to \$11,000 10% Up to \$9,525 12% \$11,000-\$44,725 15% \$9,525-\$38,700 22% \$44,725 -\$95,375 25% \$38,700-\$93,700 24% \$95,375– \$182,100 28% \$93,700-\$195,450 32% \$182,100-\$231,250 33% \$195,450-\$424,950 35% \$231,250 -\$578,125 35% \$424,950-\$426,700 37% \$578,125+ 39.6% \$426,700+
In the new system, an individual who earns, for example, \$100,000 is in the 24% marginal tax bracket. This means that for every additional dollar earned over \$100,000 (and up to \$182,100), this person pays 24 cents in federal income tax. Note that this person still only pays 10% over the first \$11,000 earned; 12% of the amount in the next bracket, 22% of the amount in the next bracket, etc. Therefore the average tax paid for this person will be less than 24% (see video at the bottom of this page for a sample calculation).
For married couples filing jointly, the marginal tax rates are as follows:
2023 Rate Income Bracket Old (2017) Rate Old Income Bracket 10% Up to \$22,000 10% Up to \$19,050 12% \$22,000-\$89,450 15% \$19,050-\$77,400 22% \$89,450-\$190,750 25% \$77,400-\$156,150 24% \$190,750-\$364,200 28% \$156,150-\$237,950 32% \$364,200-\$462,500 33% \$237,950-\$424,950 35% \$462,500-\$693,750 35% \$424,950-\$480,050 37% \$693,750 + 39.6% \$480,050+
Source: Internal Revenue Service (www.irs.gov)
For most tax payers the marginal tax rate is lower in the new tax system. In addition, there is a higher standard deduction (\$13,850 for single filers and double that for joint filers). However, there are fewer deductions for persons who itemize. For example, the limit on deducting state and local taxes is \$10,000 (these include state and local income, sales, real estate, or property taxes). Mortgage interest deductions are limited to the interest on the first \$750,000 of mortgage debt. In addition, interest on home equity loans will not be deductible (even those taken out before December 31, 2017). The marginal tax rate on long-term capital gains (earnings from selling stocks, bonds and other financial assets) continues to range from 0% to 20% (0, 15, or 20%, depending on your income). High-income tax payers pay an additional 3.8% net investment tax. Short-term (one year or shorter) capital gains are taxed at regular individual income tax rates. For a summary of all of the 2018 tax reform changes, see https://turbotax.intuit.com/tax-tips/irs-tax-return/tax-reform-changes-that-impact-your-2017-taxes/L9kree6l2.
Tax Calculations
Let’s say that an individual who files as a single person earns \$100,000. This person is in the 24% marginal tax bracket. However, this person still only pays 10% over the first \$11,000 earned; 12% over the amount in the next bracket, etc.
To illustrate the total amount of tax paid and the difference between average and marginal tax rates, consider the following three individuals filing as a single person:
Individual 1
This person has taxable income of \$6,000. Her marginal tax rate is 10%, and the total amount of tax paid equals \$6,000 times 10%, or \$600. The average tax is the total amount of tax paid divided by the total income. This equals \$600 divided by \$6,000, or .10, or 10%. This person’s average and marginal tax rates are the same.
Individual 2
This person has a taxable income of \$25,000. His marginal tax rate is 12%. However, he pays only 10% over the first \$11,000. Then he pays 12% over the remaining \$14,000. The total tax equals:
(.10 x \$11,000) + (.12 x \$14,000) = \$1,100 + \$1,680 = \$2,780. So his average tax rate is \$2,780 divided by \$25,000, or .1112, or 11.12%. Thus, his average tax rate (11.12%) is lower than his marginal tax rate (12%).
Individual 3
Let’s say that this person has a taxable income of \$100,000. Their marginal tax rate is 24%. They pay 10% over the first \$11,000. Then they pay 12% over the amount in the next bracket (\$33,725), 22% over the amount in the following bracket (50,650), plus 24% over the remaining amount in their last tax bracket (\$4,625). This person’s total tax equals:
(.10 x \$11,000) + (.12 x \$33,725) + (.22 x \$50,650) + (.24 x \$4,625) = \$1,100 + \$4,047 + \$11,143 + \$1,110 = \$17,400. So their average tax rate is \$17,400 divided by \$100,000, which equals .174, or 17.4%. Thus, their average tax rate (17.4%) is lower than their marginal tax rate (24%).
In general, for every person in the 12% or higher marginal tax bracket, the average tax rate is lower than the marginal tax rate in the above progressive tax system.
Tax Deductions
Our current federal, state and local income tax systems allow households to deduct a variety of expenses from their gross income. Gross income minus tax deductions equals taxable income. For example, the mortgage interest a person pays each year on her/his house is deductible (up to a \$750,000 mortgage). Other deductions include (up to a \$10,000 limit) state and local taxes, real estate taxes and loan points, certain retirement contributions, capital gains losses, health care expenses, dependent care expenses, self-employment expenses, and charitable expenses. If the person’s income is \$100,000, and has \$40,000 in deductible expenses, then her/his taxable income (adjusted gross income, or AGI) is \$60,000. Because of deductions, this person will only have to pay taxes on \$60,000, instead of on \$100,000.
Tax Systems
The Federal individual income tax system described above is an example of a progressive tax. Taxes can also be proportional or regressive. These systems are explained below.
1. Progressive tax.
In a progressive tax system, higher income earners pay a higher marginal tax rate than lower income earners. In the table at the top of this page, federal marginal tax rates range from 10% to 37%. For example, a single individual who earns \$20,000 in taxable income is in the 12% tax bracket. This means that each additional dollar earned by this person (until she reaches the next higher bracket) is subject to a 12% federal tax.
2. Proportional tax.
In a proportional tax system, high- and low-income earners pay the same tax rate. Most United States state and local individual income tax systems are proportional. For example, a person who earns \$10,000 pays 5% in state income taxes, and a person who earns \$500,000 also pays 5%. Some economists support a proportional, or flat tax for our federal income tax system. Most flat tax proposals do not allow many deductions, except for an exemption to pay any tax for lower income households. Therefore, it is very simple.
In the United States, everyone pays the same percentage of Social Security tax up to a certain threshold level (\$160,200 in 2023). Up to this threshold, the Social Security tax is proportional. After the threshold, it becomes regressive, because an income earner pays 0% in Social Security tax on income of more than \$160,200. The Social Security tax is 6.2% of your income and is matched by your employer (so the government receives 12.4%). The Medicare tax applies to all income and is 1.45% and matched by your employer (so the government receives 2.9%).
3. Regressive tax
In a regressive tax system, low-income earners pay a higher rate than higher-income earners. For example, a person who earns \$10,000 pays 20% in tax, and a person who earns \$100,000 pays 10%. Most state sales tax systems are regressive. Lower income households usually spend their entire income on consumer products. Therefore, if all products are subject to a sales tax of 5%, then they pay 5% of their income on sales tax. Higher income households usually spend only a portion of their income on consumer products. Therefore, as a percentage of their income, they pay less than 5%. Some states try to avoid the regressive nature of the sales tax by exempting essential consumer products such as food and clothing.
The Alternative Minimum Tax
If people apply a large number of deductions, so that the total amount of taxes falls below a certain level, then they may be subject to the alternative minimum tax. The alternative minimum tax was passed in the United States to ensure that everyone pays at least some minimum amount of tax.
Other Common Taxes
In addition to the various taxes mentioned in the examples above, there are numerous other taxes. Earlier we discussed the FICA (Social Security and Medicare) tax. Corporations pay federal income taxes (maximum rate of 21%) and state income taxes (varies from 2.5% in North Carolina to 12% in Iowa) . Most local governments collect property taxes and income taxes. Most states collect sales taxes and individual income taxes. There are also various other federal taxes, including excise taxes, capital gains taxes, and estate taxes. An excise tax is similar to a sales tax, but it is usually levied by the federal government on products such as tobacco, cigarettes, spray cans, and gasoline. A capital gains tax is a tax paid over an asset, which has gained value. For example, if someone purchases stock worth \$10,000 on January 1, and then sells the same stock for \$14,000 two years later, the \$4,000 in gained income is subject to a capital gains tax. Estate taxes are paid when someone dies and leaves a valuable estate. The heirs will have to pay an estate tax if the value of the estate exceeds a certain amount. | 2,454 | 9,760 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2024-26 | longest | en | 0.895044 |
https://ephy.in/defects-of-vision-and-correction-of-eye-defects-using-lens/ | 1,558,835,966,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232258620.81/warc/CC-MAIN-20190526004917-20190526030917-00258.warc.gz | 449,715,593 | 14,139 | : +91 124 4007927
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# DEFECTS OF VISION AND CORRECTION OF EYE DEFECTS USING LENS
Home » Ray optics and optical instruments » DEFECTS OF VISION AND CORRECTION OF EYE DEFECTS USING LENS
### DEFECTS OF VISION AND CORRECTION OF EYE DEFECTS USING LENS
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The ciliary muscles control the curvature of the lens in the eye and hence can alter the effective focal length of the system.
When the muscles are fully relaxed, the focal length is maximum.
When the muscles are strained, the curvature of the lens increases and focal length decreases.
For a clear vision, the image must be formed on the retina. The image distance is, therefore, fixed for clear vision and it equals the distance of the retina from the eye lens i.e 2.5 cm for a grown – up person.
Here v is fixed, hence by changing ‘f ’, the eye can be focussed on objects placed at different values of u.Thus, if f increases, u increases and vice – versa.
The maximum distance we can see is
maximum focal length possible for the eye lens.
For a normal eye,
= distance v i.e from lens to retina.
Thus
A person can theoretically have clear vision of objects situated at any large distance from the eye.
For closer objects, u is smaller and hence f should be smaller. The smaller distance at which a person can clearly see, is the minimum possible focal length f, for which ciliary muscles are most strained.
The closest distance for clear vision:
For an average grown – up person, should be around 25 cm or less. Thus, for a normal eye, distance of the near point should be around 25 cm or less and the far should be at infinity.
(1) Myopia or Near sightedness:
A person suffering from this defect cannot see distance objects clearly because is less than the distance from the lens to the retina. The parallel beam coming from the distance object focus short of the retina.
Cause: The lens is too thick or the diameter of the eyeball is larger than usual.
Remedy: The rays should be made a bit divergent before entering the eye so that they focus a little later.
Power of lens needed: Suppose, a person can see an object at a maximum distance x. Thus with fully relaxed muscles, rays coming from the distance x converge on the retina. If the eye is to see a distance object clearly, the diverging lens should form the virtual image of the distant object at a distance x.
Put
(2) Hyper metropia or far sightedness:
A person suffering from this defect cannot clearly see objects close to the eye.
Cause: The eye – lens is too thin at the center and/ or the eyeball is shorter than normal, So that they focussed the incoming light at a point behind the retina.
Remedy: A convergent lens is needed to compensate the defect.
Power of a lens needed: Let the eye can clearly see an object at a minimum distance Y. If the eye see clearly an object at 25 cm, the converging lens should form an image of this object at a distance Y.
Here,
(3) Astigmatism:
This occurs when the cornea is not spherical in shape e.g the cornea could have a larger curvature in vertical plane than in horizontal plane or vice – versa. Such a person cannot see all the directions equally well. A particular direction in a plane perpendicular to the line of sight is most visible while direction perpendicular to this is least visible.
Remedy: Glasses with different curvatures in different planes are used to compensate for the deshaping of the eye lens. Optician call them cylindrical glasses.
This defect can occur along with myopia or hypermetropia.
Note: In old age, a person may develop myopia and hypermetropia then he need a converging glass for reading purpose and a diverging glass for seeing at a distance. Such person either keep two sets of spectacles or a spectacle with upper portion divergent and lower portion convergent (bifocal). | 860 | 3,834 | {"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-2019-22 | latest | en | 0.876286 |
http://mathhelpforum.com/calculus/74156-integrating-problem.html | 1,526,876,797,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794863923.6/warc/CC-MAIN-20180521023747-20180521043747-00033.warc.gz | 186,048,232 | 9,221 | 1. ## integrating problem
The problem is
integral of sin(x)/(1+x^2) from -1 to 1
I have tried integration by parts and substitution but it never seems to get any simpler. Any help would be appreciated.
Thanks
2. note that $\displaystyle \frac{\sin{x}}{1+x^2}$ is an odd function.
so ... $\displaystyle \int_{-1}^1 \frac{\sin{x}}{1+x^2} \, dx = \, ?$
3. the integral of an odd function from -a to a is 0 | 126 | 407 | {"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} | 3.015625 | 3 | CC-MAIN-2018-22 | latest | en | 0.896923 |
https://functions.wolfram.com/EllipticFunctions/EllipticTheta1/18/ShowAll.html | 1,701,233,543,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100056.38/warc/CC-MAIN-20231129041834-20231129071834-00308.warc.gz | 325,184,235 | 9,552 | html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }
EllipticTheta
Identities involving the group of functions
Basic Algebraic Identities
Relations involving squares
Relations involving quartic powers
For theta1(z,q)
For theta2(z,q)
For theta3(z,q)
For theta4(z,q)
For mixed pairs
Relation between the four theta functions with zero argument
Double angle formulas
For theta1(z,q)
For theta2(z,q)
For theta3(z,q)
For theta4(z,q)
The 16 fundamental algebraic identities (from Enneper)
Four linear combinations of the fundamental identities
Alternative version of fundamental identities (from Tannery and Molk)
Automatically generated triple addition formulas (using 16 fundamental relations)
Automatically generated addition formulas with two variables
Automatically generated double angle formulas
Identities involving transformation of nome q
Equations for z->2z, q->q4
Equations for z->2z, q->q2
General argument
Argument equal to zero
Equations for q->q1/2
General argument
Argument equal to zero
Equations involving integer powers of q | 375 | 1,462 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2023-50 | latest | en | 0.62698 |
https://www.quizover.com/course/section/nyquist-shannon-sampling-theorem-by-openstax | 1,527,398,772,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794868003.97/warc/CC-MAIN-20180527044401-20180527064401-00135.warc.gz | 819,826,983 | 21,591 | # 10.1 Sampling theorem
Page 1 / 2
This module builds on the intuition developed in the sampling module to discuss the Nyquist-Shannon sampling theorem, including a full statement and a proof.
## Introduction
With the introduction of the concept of signal sampling, which produces a discrete time signal by selecting the values of the continuous time signal at evenly spaced points in time, it is now possible to discuss one of the most important results in signal processing, the Nyquist-Shannon sampling theorem. Often simply called the sampling theorem, this theorem concerns signals, known as bandlimited signals, with spectra that are zero for all frequencies with absolute value greater than or equal to a certain level. The theorem implies that there is a sufficiently high sampling rate at which a bandlimited signal can be recovered exactly from its samples, which is an important step in the processing of continuous time signals using the tools of discrete time signal processing.
## Statement of the sampling theorem
The Nyquist-Shannon sampling theorem concerns signals with continuous time Fourier transforms that are only nonzero on the interval $\left(-B,B\right)$ for some constant $B$ . Such a function is said to be bandlimited to $\left(-B,B\right)$ . Essentially, the sampling theorem has already been implicitly introduced in the previous module concerning sampling. Given a continuous time signals $x$ with continuous time Fourier transform $X$ , recall that the spectrum ${X}_{s}$ of sampled signal ${x}_{s}$ with sampling period ${T}_{s}$ is given by
${X}_{s}\left(\omega \right)=\frac{1}{{T}_{s}}\sum _{k=-\infty }^{\infty }X\left(\frac{\omega -2\pi k}{{T}_{s}}\right).$
It had previously been noted that if $x$ is bandlimited to $\left(-\pi /{T}_{s},\pi /{T}_{s}\right)$ , the period of ${X}_{s}$ centered about the origin has the same form as $X$ scaled in frequency since no aliasing occurs. This is illustrated in [link] . Hence, if any two $\left(-\pi /{T}_{s},\pi /{T}_{s}\right)$ bandlimited continuous time signals sampled to the same signal, they would have the same continuous time Fourier transform and thus be identical. Thus, for each discrete time signal there is a unique $\left(-\pi /{T}_{s},\pi /{T}_{s}\right)$ bandlimited continuous time signal that samples to the discrete time signal with sampling period ${T}_{s}$ . Therefore, this $\left(-\pi /{T}_{s},\pi /{T}_{s}\right)$ bandlimited signal can be found from the samples by inverting this bijection.
This is the essence of the sampling theorem. More formally, the sampling theorem states the following. If a signal $x$ is bandlimited to $\left(-B,B\right)$ , it is completely determined by its samples with sampling rate ${\omega }_{s}=2B$ . That is to say, $x$ can be reconstructed exactly from its samples ${x}_{s}$ with sampling rate ${\omega }_{s}=2B$ . The angular frequency $2B$ is often called the angular Nyquist rate. Equivalently, this can be stated in terms of the sampling period ${T}_{s}=2\pi /{\omega }_{s}$ . If a signal $x$ is bandlimited to $\left(-B,B\right)$ , it is completely determined by its samples with sampling period ${T}_{s}=\pi /B$ . That is to say, $x$ can be reconstructed exactly from its samples ${x}_{s}$ with sampling period ${T}_{s}$ .
can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
is it 3×y ?
J, combine like terms 7x-4y
im not good at math so would this help me
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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# Math in the News: Issue 54
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In this issue of Math in the News we look at the recent earthquake near Indonesia and compare it to the devastating earthquake of 2004.
Published in: Education, Technology
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### Math in the News: Issue 54
1. 1. The Indonesian Earthquake This map shows the location of the earthquake, which is near Indonesia. (Source for all map graphics: http://www.usgs.gov.)
2. 2. The Indonesian Earthquake This map shows the location of the epicenter relative to population density.
3. 3. The Indonesian Earthquake This map shows the epicenter of the 2004 earthquake.
4. 4. The Indonesian Earthquake A side-by-side comparison of the two epicenters shows that the 2004 earthquake was closer to land. Because it was a much stronger earthquake, its proximity also meant the potential for more damage. Note that both earthquakes occurred under water, which is what causes tsunamis.
5. 5. The Indonesian Earthquake This graph compares the magnitude of the two earthquakes. The close numerical values of the two magnitudes (8.6 vs. 9.1) suggests comparably strong earthquakes. But magnitude uses a logarithmic scale. 0 1 2 3 4 5 6 7 8 9 10 2012 2004 Magnitude Comparison of Two Indonesian Earthquakes
6. 6. The Indonesian Earthquake This graph compares the intensity of each of earthquake. Here you can see the dramatic difference in intensity. 0.00E+00 2.00E+08 4.00E+08 6.00E+08 8.00E+08 1.00E+09 1.20E+09 1.40E+09 2012 2004 Intensity Comparison of Two Indonesian Earthquakes
7. 7. The Indonesian Earthquake The intensity of an earthquake is proportional to an exponential expression of base 10 whose exponent is the size of the earthquake magnitude. For simplicity, let’s assume this proportion is an equation.
8. 8. The Indonesian Earthquake We can express the intensity of each earthquake using these expressions.
9. 9. The Indonesian Earthquake To see how much more intense the 2004 earthquake was calculate the ratio of the two terms. You can see that the 2004 earthquake was three times more intense. | 613 | 2,354 | {"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} | 3.28125 | 3 | CC-MAIN-2017-39 | latest | en | 0.878006 |
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#1
A laboratory determination of the specific latent heat of vaporisation of water uses a
120 W heater to keep water boiling at its boiling point. Water is turned into steam at the
rate of 0.050 g / s. Calculate the value of the specific latent heat of vaporisation obtained from this
How would you do this?
0
2 years ago
#2
I would - use the power given to tell me how much energy in Joules is supplied to the water every second.
Then I'd use the latent heat equation, with this energy, and the mass of water turned to vapour in 1second, to calculate the latent heat. Somewhere in that second step I'd probably change the g to kg but it doesn't really matter if you don't do that - it just means your latent heat will be in J/g instead of J/Kg.
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https://ch.mathworks.com/matlabcentral/cody/problems/44901-rearrange-the-given-matrix-to-have-all-its-zeros-climb-up-to-the-top-of-each-column-using-for-loop/solutions/1834128 | 1,581,966,148,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875143079.30/warc/CC-MAIN-20200217175826-20200217205826-00049.warc.gz | 330,048,722 | 16,296 | Cody
# Problem 44901. Rearrange the given matrix to have all its zeros climb up to the top of each column - using for loops.
Solution 1834128
Submitted on 1 Jun 2019 by Shlomi Shomonov
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
x = [0 0 1 1 0 1 -1 -1 2 1 -1 2 2 2 0 0 -1 0 2 1 0 1 0 1]; y_correct = [0 0 0 0 0 0 0 1 0 1 1 -1 2 1 -1 2 2 2 -1 1 -1 1 2 1]; assert(isequal(zerosFirst(x),y_correct))
m = 6 n = 4 b = 0 b = 0 0 b = 0 0 0 b = 0 b = 0 0 b = 0 b = 0 0 b = 0 0 0 0 0 0 0 0 1 0 1 1 -1 2 1 -1 2 2 2 -1 1 -1 1 2 1
2 Pass
x = [12 56 0 0 65 122 0 37]' y_correct = [0 0 0 12 56 65 122 37]' assert(isequal(zerosFirst(x),y_correct))
x = 12 56 0 0 65 122 0 37 y_correct = 0 0 0 12 56 65 122 37 m = 8 n = 1 b = 0 b = 0 0 b = 0 0 0 0 0 0 12 56 65 122 37
3 Pass
filetext = fileread('zerosFirst.m'); assert(isempty(strfind(filetext, 'regexp')),'regexp hacks are forbidden')
4 Pass
filetext = fileread('zerosFirst.m'); assert(~isempty(strfind(filetext, 'for')),'must use a for loop in solving this problem')
5 Pass
filetext = fileread('zerosFirst.m'); assert(isempty(strfind(filetext, '!echo')),'!echo hacks are forbidden') | 544 | 1,257 | {"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-2020-10 | latest | en | 0.558286 |
https://www.officialdata.org/1931-CAD-in-2018 | 1,527,184,314,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794866733.77/warc/CC-MAIN-20180524170605-20180524190605-00572.warc.gz | 792,476,660 | 6,544 | # CA\$100 in 1931 → CA\$1,656.96 in 2018
CA\$
### Canadian Inflation Rate, 1931-2018 (CA\$100)
According to Statistics Canada consumer price index, the dollar experienced an average inflation rate of 3.28% per year. Prices in 2018 are 1557.0% higher than prices in 1931.
In other words, CA\$100 in the year 1931 is equivalent in purchasing power to CA\$1,656.96 in 2018, a difference of CA\$1,556.96 over 87 years.
Compared to last year's annual rate, the inflation rate in 2018 is now 0.38%1. If this number holds, CA\$100 today would be equivalent to CA\$100.38 next year.
Cumulative price change 1556.96% Average inflation rate 3.28% Price difference (CA\$100 base) CA\$1,556.96 CPI in 1931 7.9 CPI in 2018 130.9
### How to calculate the inflation rate for CA\$100 since 1931
This inflation calculator uses the following inflation rate formula:
CPI in 2018 / CPI in 1931 * 1931 CAD value = 2018 CAD value
Then plug in historical CPI values. The Canadian CPI was 7.9 in the year 1931 and 130.9 in 2018:
130.9 / 7.9 * CA\$100 = CA\$1,656.96
CA\$100 in 1931 has the same "purchasing power" as CA\$1,656.96 in 2018.
Politics and news often influence economic performance. Here's what was happening at the time:
• The Empire State Building opens in New York.
• A railway explosion is faked by the Japanese in order to create a pretext for their Manchuria invasion.
• Proclamation of the Chinese People's Republic by Mao Zedong.
### Inflation Data Source
Raw data for these calculations comes from the government of Canada's annual Consumer Price Index (CPI), established in 1914 and computed by Statistics Canada (StatCan).
You may use the following MLA citation for this page: “1931 dollars in 2018 | Canada Inflation Calculator.” U.S. Official Inflation Data, Alioth Finance, 24 May. 2018, https://www.officialdata.org/1931-CAD-in-2018. | 529 | 1,854 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2018-22 | latest | en | 0.893525 |
http://www.chegg.com/homework-help/questions-and-answers/finance-community-college-education-joanna-takes-stafford-loan-4500-year-joanna-decides-pa-q1527353 | 1,369,221,208,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368701614932/warc/CC-MAIN-20130516105334-00032-ip-10-60-113-184.ec2.internal.warc.gz | 390,717,622 | 7,778 | ## To finance her community college education, Joanna takes out a Stafford loan for $4500. After one year, Joanna decides to pay off the interest, which is 8% of$4500. How much will she pay?
To finance her community college education, Joanna takes out a Stafford loan for $4500. After one year, Joanna decides to pay off the interest, which is 8% of$4500. How much will she pay?
• 8% of 4500 =
0.08 * 4500 =
8/100 * 4500 =
8 * (4500/100) =
8 * 45 =
8 * (40 + 5) =
(8 * 40) + (8 * 5) =
320 + 40 =
360
Answer: $360 • It's simply$4500 * 0.08 which would equal.....??
Get homework help | 188 | 592 | {"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} | 3.953125 | 4 | CC-MAIN-2013-20 | latest | en | 0.94759 |
https://www.algebra-class.com/direct-variation-and-slope-intercept-form.html | 1,721,698,416,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763517931.85/warc/CC-MAIN-20240723011453-20240723041453-00640.warc.gz | 552,885,599 | 7,648 | # Direct variation and slope intercept form
by Cindy
(Ocoee, Florida, US)
What are some examples of slope intercept form representing direct variation?
____________________________________________________
Hi Cindy,
Thank you for contributing to Algebra-class.com. Direct variation is when two variable quantities have a constant ratio. The formula for direct variation is:
y = kx where k is the constant of variation.
You asked for an example in slope intercept form. As you can see, direct variation is set up in slope intercept form.
y = kx is very similar to y = mx. With direct variation, the y-intercept is 0, so you won't have the "+b" portion of slope intercept form. The constant of variation (k) is very similar to the slope in slope intercept form.
Some examples of equations that represent direct variation are:
y = 5x
y = 1/2x
y = .3x
As you can see, these are all set up in slope intercept form (with a y-intercept of 0).
These equations are called "direct variation" because y varies directly with x. If x increases, then y increases as well. If x decreases, then y decreases.
I hope this helps.
Karin
Need More Help With Your Algebra Studies? | 264 | 1,173 | {"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-2024-30 | latest | en | 0.932353 |
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# MGT 6203 Self-Assessment 5 – Week 9 Content. Complete With Answers. Georgia Institute Of Technology
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## [Solved] MGT 6203 Self-Assessment 5 – Week 9 Content. Complete With Answers. Georgia Institute Of Technology
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MGT 6203 Self-Assessment 5 – Week 9 Content. Complete With Answers. Georgia Institute Of Technology.1. In 1999, product placement of Etch-A-Sketch in the movie sequel Toy Story 2 helped boost the sales of the drawing toy by? a. 25% b. 20% c. 30% d. 35% Answer: B 2. According to the paper, wh...
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http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch23/problems/ex23_8s.html | 1,516,637,516,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084891485.97/warc/CC-MAIN-20180122153557-20180122173557-00412.warc.gz | 72,294,902 | 1,257 | Practice Problem 8
How long would it take for a sample of 222Rn that weighs 0.750 g to decay to 0.100 g? Assume a half-life for 222Rn of 3.823 days.
Solution
We can start by calculating the rate constant for this decay from the half-life:
We then turn to the integrated form of the first-order rate law:
The ratio of the number of atoms that remain in the sample to the number of atoms present initailly is the same as the ratio of grams at the end of the time period to the number of grams present initially:
Solving for t, we find that is takes 11.1 days for 0.750 g of 222Rn to decay to 0.100 g of this nuclide. | 168 | 622 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.34375 | 3 | CC-MAIN-2018-05 | latest | en | 0.918021 |
https://journalofinequalitiesandapplications.springeropen.com/articles/10.1155/2009/104043 | 1,660,877,177,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882573540.20/warc/CC-MAIN-20220819005802-20220819035802-00057.warc.gz | 313,458,396 | 51,862 | # Bargmann-Type Inequality for Half-Linear Differential Operators
## Abstract
We consider the perturbed half-linear Euler differential equation , , , with the subcritical coefficient . We establish a Bargmann-type necessary condition for the existence of a nontrivial solution of this equation with at least zero points in .
## 1. Introduction
The classical Bargmann inequality [1] originates from the nonrelativistic quantum mechanics and gives an upper bound for the number of bound states produced by a radially symmetric potential in the two-body system. In the subsequent papers, various proofs and reformulations of this inequality have been presented, we refer to [2, Chapter XIII], and to [35] for some details.
In the language of singular differential operators, Bargmann's inequality concerns the one-dimensional Schrödinger operator
(11)
It states that if the Friedrichs realization of has at least negative eigenvalues below the essential spectrum (what is equivalent to the existence of a nontrivial solution of the equation having at least zeros in ), then
(12)
where .
This inequality can be seen as follows. The Euler differential equation
(13)
with the subcritical coefficient is disconjugate in , that is, any nontrivial solution of (1.3) has at most one zero in this interval. Hence, if the equation , with given by (1.1), has a solution with at least positive zeros, the perturbation function must be "sufficiently positive" in view of the Sturmian comparison theorem. Inequality (1.2) specifies exactly what "sufficient positiveness" means.
In this paper, we treat a similar problem in the scope of the theory of half-linear differential equations:
(14)
In physical sciences, there are known phenomena which can be described by differential equations with the so-called -Laplacian , see, for example, [6]. If the potential in such an equation is radially symmetric, this equation can be reduced to a half-linear equation of the form (1.4).
There are many results of the linear oscillation theory, which concern the Sturm-Liouville differential equation:
(15)
which has been extended to (1.4). In particular, the linear Sturmian theory holds almost verbatim for (1.4), see, for example, [7, 8]. We will recall elements of the half-linear oscillation theory in the next section. Our main result concerns the perturbed half-linear Euler differential equation
(16)
where is a continuous function, and shows that if is the so-called subcritical coefficient, that is, , and there exists a solution of (1.6) with at least zeros in , then the integral satisfies an inequality which reduces to (1.2) in the linear case .
## 2. Preliminaries
In this short section, we present some elements of the half-linear oscillation theory which we need in the proof of our main result. As we have mentioned in the previous section, the linear and half-linear oscillation theories are in many aspects very similar, so (1.4) can be classified as oscillatory or nonoscillatory as in the linear case.
If is a solution of (1.4) such that is some interval , then is a solution of the Riccati-type differential equation
(21)
If (1.4) is nonoscillatory, that is, (2.1) possesses a solution which exists on some interval , among all such solutions of (2.1), there exists the minimal one , minimal in the sense that any other solution of (2.1) which exists on some interval satisfies in this interval, see [9, 10] for details.
In our treatment, the so-called half-linear Euler differential equation
(22)
appears. If we look for a solution of this equation in the form , then is a root of the algebraic equation
(23)
By a simple calculation (see, e.g., [8, Section 1.3]), one finds that (2.3) has a real root if and only if is less than or equal to the so-called critical constant , and hence (2.2) is nonoscillatory if and only if . In this case, the associated Riccati equation is of the form
(24)
and its minimal solution is , where is the smaller of (the two real) roots of (2.3). If , then is a solution of the equation
(25)
and is the minimal solution of this equation. A detailed study of half-linear Euler equation and of its perturbations can be found in [11].
## 3. Bargmann's Type Inequality
In this section, we present our main results, the half-linear version of Bargmann's inequality. We are motivated by the work in [4] where a short proof of this inequality based on the Riccati technique is presented. Here we show that this method, properly modified, can also be applied to (1.6).
Theorem 3.1.
Suppose that (1.6) with has a nontrivial solution with at least zeros in Then
(31)
where is the absolute value of the difference of the real roots of
(32)
and is the conjugate number to Moreover, the constant is strict in the sense that for every , there exists a continuous function such that (1.6) possesses a solution with zeros in and
(33)
Proof.
Let be a solution of (1.6) with zeros in denote these zeros by , and let Then by a direct computation we see that is a solution of the Riccati-type differential equation
(34)
(35)
Let be the roots of (3.2). Such pair of roots exists and it is unique since the function is convex, , , and According to (3.5), there exist such that , , and for , which means that for Then, we have
(36)
Now we prove that the constant is exact. Let be arbitrary and be sequences of positive real numbers constructed in the following way. Let be arbitrary and consider the differential equation
(37)
Denote by its nontrivial solution satisfying , (such solution exists and it is unique, see, e.g., [8, Section 1.1]) and let Since , see [8, page 39], there exists such that .
Now, let
(38)
and define for the function
(39)
Consider the solution of the equation
(310)
given by the initial conditions . Then for
(311)
Hence,
(312)
Now consider again (3.7) and the associated Riccati-type differential equation
(313)
(which is related to (3.7) by the substitution ). This equation has a constant solution and this solution is the minimal one (see the end of Section 2). This means that any solution of (3.13) which starts with the initial condition blows down to at a finite time , which is a zero point of the associated solution of (3.7). Now, let
(314)
In summary, we have constructed a solution of the equation
(315)
for which and
(316)
The construction of and is now analogical. As a result we obtain the function defined as for and , and for , for which
(317)
and the equation
(318)
has a solution with zeros at
Finally, we change the discontinuous function to a continuous one such that Such a modification is an easy technical construction which can be described explicitly, but for us is only important its existence. According to the Sturmian comparison theorem, the equation possesses a nontrivial solution with at least zeros and
(319)
which we needed to prove.
Remark 3.2.
If , then and the roots of (3.2) are
(320)
Hence, and (3.1) reduces to (1.2).
## References
1. Bargmann V: On the number of bound states in a central field of force. Proceedings of the National Academy of Sciences of the United States of America 1952, 38: 961–966. 10.1073/pnas.38.11.961
2. Reed M, Simon B: Methods of Modern Mathematical Physics, Vol. IV. Analysis of Operators. Academic Press, Boston, Mass, USA; 1978.
3. Blanchard Ph, Stubbe J: Bound states for Schrödinger Hamiltonians: phase space methods and applications. Reviews in Mathematical Physics 1996,8(4):503–547. 10.1142/S0129055X96000172
4. Schmidt KM: A short proof for Bargmann-type inequalities. The Royal Society of London 2002,458(2027):2829–2832. 10.1098/rspa.2002.1021
5. Setô N: Bargmann's inequalities in spaces of arbitrary dimension. Publications of the Research Institute for Mathematical Sciences. Kyoto University 1974, 9: 429–461.
6. Díaz JI: Nonlinear Partial Differential Equations and Free Boundaries. Vol. I: Elliptic Equations, Research Notes in Mathematics. Volume 106. Pitman, Boston, Mass, USA; 1985:vii+323.
7. Agarwal RP, Grace SR, O'Regan D: Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations. Kluwer Academic Publishers, Dordrecht, The Netherlands; 2002:xiv+672.
8. Došlý O, Řehák P: Half-Linear Differential Equations, North-Holland Mathematics Studies. Volume 202. Elsevier, Amsterdam, The Netherlands; 2005:xiv+517.
9. Elbert Á, Kusano T: Principal solutions of non-oscillatory half-linear differential equations. Advances in Mathematical Sciences and Applications 1998, 18: 745–759.
10. Mirzov JD: Principal and nonprincipal solutions of a nonlinear system. Tbilisskiĭ Gosudarstvennyĭ Universitet. Institut Prikladnoĭ Matematiki. Trudy 1988, 31: 100–117.
11. Elbert Á, Schneider A: Perturbations of the half-linear Euler differential equation. Results in Mathematics 2000,37(1–2):56–83.
## Acknowledgment
The authors thank the referees for their valuable remarks and suggestions which contributed substantially to the present version of the paper. The first author is supported by the Grant OTKA CK80228 and the second author is supported by the Research Project MSM0021622409 of the Ministry of Education of the Czech Republic and the Grant 201/08/0469 of the Grant Agency of the Czech Republic.
## Author information
Authors
### Corresponding author
Correspondence to Ondřej Došlý.
## Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Bognár, G., Došlý, O. Bargmann-Type Inequality for Half-Linear Differential Operators. J Inequal Appl 2009, 104043 (2009). https://doi.org/10.1155/2009/104043
• Revised:
• Accepted:
• Published:
• DOI: https://doi.org/10.1155/2009/104043
### Keywords
• Nontrivial Solution
• Real Root
• Essential Spectrum
• Minimal Solution
• Nonrelativistic Quantum | 2,457 | 10,047 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2022-33 | latest | en | 0.914628 |
https://www.answers.com/Q/The_weight_and_height_of_an_object_give_an_object_what_type_of_potential_energy | 1,606,582,828,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141195687.51/warc/CC-MAIN-20201128155305-20201128185305-00670.warc.gz | 563,497,937 | 35,444 | Energy
# The weight and height of an object give an object what type of potential energy?
345
Top Answer
###### 2012-02-25 11:22:04
That is called gravitational potential energy.
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## Related Questions
Gravitational potential energy depends on the weight of the object and the height that the object is located at. Gravitational potential energy is the product of an objects weight and height.
The formula for potential energy is: G.P.E. (gravitational potential energy) = Weight x Height
Gravitational potential energy. The formula for gravitational potential energy is weight x height, which is equal to mgh (mass x gravity x height). A+:)
Gravitational potential energy = (weight of the object) x (height) or Potential energy = (mass) x (acceleration of gravity) x (height)
The gravitational potential energy is equal to: GPE = mass x gravity x height Or equivalently: GPE = weight x height
Weight and height. The potential energy of an object is its weight times its height. The potential energy is turned into kinetic energy as the object is dropped. Potential energy is weight times height, kinetic energy is one half mass times velocity-squared. Mgh = ½ M V^2 To reach a speed of 10 m/s this equation can be solved to show that the object must be dropped through a height of 5.1 metres.
When an object is lifted to a certain height, the mechanical energy of the person or system lifting the object gets transferred into the potential energy of the object. Thus if an object of mass/weight 'm' is lifted to a height 'h', then the potential energy possed by the object at height 'h' is given as: Potential Energy (P.E)= m*g*h, where g is acceleration due to gravity and whose value is 9.8 m/s2.
You calculate the potential energy as: weight x height. This is equal to mass x gravity x height.
Gravitational potential energy is the product of weight and height. It is often calculated as mgh = mass x gravity x height. (Mass x gravity, by itself, is the weight.)
If you are talking about Gravitational Potential Energy then this is the formula: ~GPE = wh ~Gravitational Potential Energy = weight of an object multiplied by the height of an object. ~ w = weight ~ h = height ~The SI unit for GPE, or any other energy related problem, is joules or a capital J.
Potential Energy is calculated by the product of the mass of the object ( not weight! ), the gravitational acceleration ( 9.81 m/s/s ) and the height of the object above a datum. mass x 9.81 x height
The two factors that influence the gravitational potential energy of an object include its weight and height. The joule is the SI unit used for measuring work and energy.
potential energy dependent upon an objects weight and height
Potential energy that is dependent on height is called gravitational potential energy. Potential energy is energy of position. ex: A book on a shelf has gravitational potential energy. Formula: G.P.E.=Weight x Height
PEgravitational = mass * gravity * height. Mass * gravity = weight Therefore the two factors are weight and height.
Weight and height. PE = mgh (mass x gravity x height); you might also say weight x height, since the weight = mass x gravity.
Gravitational potential energy=mgh Where: -m=mass (not weight) of the object -g=gravity (or the rate at which an object will accelerate in free-fall) -h=height (usually in meters, but depends on what height units are in your "g" value)
Dropping a weight from a height. It loses potential energy and gains kinetic energy
On earth, mass and height. PE = mgh Weight and height. (note that m*g, as above, equals weight). This therefore applies not just on Earth.
Increase in potential energy = weight x increase in height
There is less gravity on the Moon. Gravitational potential energy can be calculated by multiplying weight x height, or the equivalent mass x gravity x height.
###### ScienceEnergyMath and ArithmeticMechanical EngineeringPhysicsElectrical WiringAstronomy
Copyright ยฉ 2020 Multiply Media, LLC. All Rights Reserved. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply. | 955 | 4,198 | {"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} | 4.03125 | 4 | CC-MAIN-2020-50 | latest | en | 0.930798 |
https://johnsinclairradio.com/basic-algebra-worksheets-year-7/ | 1,643,089,134,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320304760.30/warc/CC-MAIN-20220125035839-20220125065839-00665.warc.gz | 370,924,395 | 8,315 | Staggering Basic Algebra Worksheets Year 7
Worksheet. December 24th , 2020.
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Feb 03, 2021 | Audrey Party | 1,400 | 6,571 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.1875 | 3 | CC-MAIN-2022-05 | latest | en | 0.905031 |
https://rjallain.medium.com/principal-axes-of-inertia-sometimes-things-rotate-in-weird-ways-3ab0db2505ac?source=user_profile---------9---------------------------- | 1,695,299,778,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233506027.39/warc/CC-MAIN-20230921105806-20230921135806-00596.warc.gz | 553,953,915 | 35,632 | # Principal Axes of Inertia. Sometimes Things Rotate in Weird Ways.
If you take a block and toss it in the air, it might do something weird — it could tumble such that the angular velocity vector is not constant. Here’s an example.
Notice that once the eraser leaves my hand, it doesn’t rotate just one way. Instead, it flips over. If you think about this, it’s pretty weird.
# Ball and Spring Model
One way to model the rotation of a rigid object is to not have a rigid object. I know that seems crazy, but it’s going to work. Trust me. Imagine that I have three masses in space and each masses is connected to the other masses with a stiff spring. Something like this.
Each mass (I’m going to call them A, B, C) have two forces acting on them from the two springs. I can calculate the vector values of these spring forces. In general, the vector spring force can be calculated as:
In this expression, k is the spring constant and L is a vector from one side to the other side of the spring (and L_0 is the unstretched length). If you use this method (along with the unit vector L-hat) you get a VECTOR value for the spring force. It’s kind of a big deal since it allows us to model the motion of these mass in 3D.
I’m not going to go into ALL the details of this build (because I want to focus on the results) but here is a video going over some of the important stuff.
Here’s part of the code (full code here). | 331 | 1,421 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2023-40 | longest | en | 0.937883 |
https://www.yaclass.in/p/english-language-cbse/class-8/supplementary-2960/the-comet-i-5143/re-8973103f-bc2e-469d-8c09-0ba12d42b7e3 | 1,632,244,981,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780057225.57/warc/CC-MAIN-20210921161350-20210921191350-00214.warc.gz | 1,083,949,175 | 8,916 | ### Theory:
Duttada was optimistic... he knew that the professionals with their pre-assigned programmes would be looking at faint stars and nebulous galaxies. They might miss such an insignificant thing as a comet which they were not expecting to see anyway! Indeed amateurs had often discovered new comets which the professionals had missed.
And, it looked to Duttada that tonight was going to be the big night. For against the background of the same old stars Duttada had detected a faint stranger. He re-examined the charts with him, checked his Dibya for any smudges on the optics, did some calculations on his pocket calculator in torchlight — for, though absent-minded about daily chores, he was meticulous in his observations.
Yes, there can be no mistake. What he was looking at had not been there earlier and it did look like a new comet.
Explanation:
In paragraph $$10$$, the author responds to the query about how an amateur astronomer like Duttada can compete with expert astronomers. The response to the question is as follows. Though there were some experienced scientists and astronomers in the astronomy field, they would be preoccupied with their own tasks and spend time observing and learning about vague, undefined galaxies. As a result, they don't bother to devote time to detecting such comets, and they place a lower priority on it. Indeed, amateur astronomers have repeatedly discovered new comets that professional astronomers have missed in the past. Duttada's positive outlook may be seen in this thought.
Duttada's intuition assured him that it would be a big night. There was something that his telescope pointed at, true to his intuition. He discovered something odd among the twinkling stars that night. He went through the charts again. The term 'chart' here refers to a 'star chart' or 'star map,' which is a night sky map. Astronomical objects like as stars, constellations, and galaxies are identified and located using them. Also, he double-checked everything with his telescope, Dibya. To arrive at the exact conclusion, he utilised his pocket calculator in torchlight once more.
Though Duttada failed at leading a practical life, being oblivious to everyday daily events, he was meticulous in his calculations, paying attention to even the smallest details. As a result, there was no blunder. The faint stranger he saw through his telescope was nothing but a "comet" that has been demanding his time for the last few days, during which he had sleepless nights. Finally, Duttada discovered a comet.
Meaning of difficult words:
S.No Words Meanings 1. Optimistic Looking hopefully on things in a way that only good thing will happen 2. Nebulous Things which are not clear
Reference:
National Council of Educational Research and Training (2008). The Comet I - Jayant Narlikar (pp. 73-80). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi. | 624 | 2,973 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.9375 | 3 | CC-MAIN-2021-39 | latest | en | 0.986138 |
https://developer.numscale.com/bsimd/documentation/v1.17.6.0/group__group-ieee_ga8693e6a2ac3a7116b5b0fe379153b72b.html | 1,544,575,201,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376823710.44/warc/CC-MAIN-20181212000955-20181212022455-00476.warc.gz | 590,325,441 | 17,322 | ## ◆ minmag()
Value boost::simd::minmag ( Value const & x, Value const & y )
This function object returns the input value which have the least absolute value.
Example:
#include <boost/simd/ieee.hpp>
#include <boost/simd/pack.hpp>
#include <boost/simd/constant/nan.hpp>
#include <iostream>
namespace bs = boost::simd;
using pack_ft = bs::pack <float, 4>;
int main()
{
pack_ft pf = { 3.0f, -2.0f, -0.0f, 0.0f };
pack_ft qf = { 4.0f, -1.0f, 0.0f, bs::Nan<float>() };
std::cout
<< "---- simd" << '\n'
<< " <- pf = " << pf << '\n'
<< " <- qf = " << qf << '\n'
<< " -> bs::minmag(pf, qf) = " << bs::minmag(pf, qf) << '\n';
float xf = 3.0f, yf = 4.0f;
std::cout
<< "---- scalar" << '\n'
<< " xf = " << xf << '\n'
<< " yf = " << yf << '\n'
<< " -> bs::minmag(xf, yf) = " << bs::minmag(xf, yf) << '\n';
return 0;
}
Possible output:
---- simd
<- pf = (3, -2, -0, 0)
<- qf = (4, -1, 0, -nan)
-> bs::minmag(pf, qf) = (3, -1, -0, 0)
---- scalar
xf = 3
yf = 4
-> bs::minmag(xf, yf) = 3 | 403 | 975 | {"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-2018-51 | latest | en | 0.379434 |
https://it.scribd.com/document/173591439/Guia-Ingenieria-Parte-2 | 1,685,889,076,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224649986.95/warc/CC-MAIN-20230604125132-20230604155132-00459.warc.gz | 348,040,865 | 117,154 | Sei sulla pagina 1di 92
1. A) 2.
## Metro, Kilogramo, Segundo (m,k,s)
Como 1 min = 60 s y 1rev = 2 rad rad rev 1 min 2 rad v = 60 = 6.283 s min 60 s 1 rev
3.
## Como 1 Km = 1000 m y 1 h = 3600 s Km 1000 m 1 h m v = 120 = 33.3 h 1Km 3600 s s
4.
(7.50 x 10 4 ) (3.20 x 10 7 ) 4 x 10
4
= 6 x 10 4 x 10 4 x 10 7 = 6 x 10 7
5. (6.28 x 10 9 ) ( 4.35 x 10 8 ) 1.44 x 10 = = 0.36 x 10 8 4 x 10 9 4 x 10 9 6. 7. 8. 9. B) A) (r, ) La magnitud del vector y el ngulo que forma ste con el eje positivo x.
r = x2 + y2
r=
(2)2 + (5)2
= 29 = 5.38
= tan 1
5 = 68.2 2
## Es decir, el punto (2, 5) tiene las coordenadas polares ( 5.38, 68.2 )
FGC-SUBEV-38
75
10. Como Fx = Fcos = 100N cos120 = 100N (-0.5) = 50N Fy = Fsen = 100N sen120 = 100N(0.87) = 87N 11. DATOS: F1 = 30 N F2 = 40N FR = ? Frmula Sustitucin
2 2
FR = F1 + F2
FR = (30N) 2 + ( 40N) 2
FR = 900N2 + 1600N2
## FR = 2500N2 FR = 50N 12. Como FR = F1 +F2 +F3 FR =
( F ) + ( F )
2 x y
Fy = tan 1 F x
Fx = F cos Fy = F sen Se descompone cada una de las fuerzas en sus componentes rectangulares y tenemos: F1x = F1 cos 35 = 25N (0.8191) = 20.48 N F1y = F1 sen 35 = 25N (0.5736) = 14.34 N F2x = F2 cos 50 = 35N (0.6428) = 22.5 N F2y = F2 sen 50 = 35N (0.7660) = 26.81 N F3x = F3 cos 115 = 50N (-0.4226) = -21.13 N F3y = F3 sen 115 = 50N (0.9063) = 45.31 N Se obtiene la suma de las componentes
## Fy = 14.34 N + 26.81N + 45.31N = 86.46 N
FR = (21.85N) 2 + (86.46N) 2
FGC-SUBEV-38
76
## FR= 89.18N MECNICA 13.
v(m/s) 40 30 20 10
= 76.13
t(s) 0 1 2 3 4 5 6 7 8 9 10 11 12
## 14. El rea total, es la suma de las reas I, II, y III
v(m/s) 40 30 20 I 10 t(s) 0 1 2 3 4 5 6 7 8 9 10 11 12 II III
Al =
b1 h1 (3s )(30m/s ) = = 45m 2 2 AII = b2h2 = (2s)(30m/s) = 60m b h (6s)(30m/s ) = 180 = 90m AIII = 3 3 = 2 2 2 AT = AI + AII + AIII = 45m + 60m + 90m = 195 m
FGC-SUBEV-38
77
15.
m m + 30 v + vf s = 15 m v1 = i = s 2 2 s m m 30 + 30 vi + vf s s = 30 m = v2 = 2 2 s m m 30 + 0 vi + vf s s = 15 m v3 = = 2 2 s 0
16.
m d1 = v 1 t 1 = 15 (3 s ) = 45 m s m d 2 = v 2 t 2 = 30 (2 s ) = 60 m s m d3 = v 3 t 3 = 15 (6 s ) = 90 m s
## 17. d = d1 + d2 + d3 = (45 +60 + 90) m = 195 m 18. Datos d1 = 3m, = 0 d2 = 4m, = 90
dR = d1 +d2
dR = d1 + d2 = ( 4m) 2 + (3m) 2
2 2
## = 16m 2 + 9m 2 = 25m 2 =5m
FGC-SUBEV-38
78
19. A) Velocidades medias, ya que se trata de aceleraciones constantes en cada una de las partes, tenemos: I.
## v0 + v 0 + 3 = = 1.5m/s 2 2 3+3 = 3 m/s 2 3+0 = 1.5m/s 2
II.
III. B)
Aceleraciones: I.
a=
vv t
30 = 2m/s 2 1.5
II.
a=
33 = 0m/s 2 2
III.
03 = 6 m/s 2 El signo menos indica que el cambio de velocidad 0.5 y la aceleracin tienen signo contrario, por lo que se pierde velocidad a razn de 6 m/s durante cada segundo. a=
C)
Velocidad media en todo el recorrido. Como el desplazamiento es el rea bajo la curva, tenemos: I. II. III.
d=
## base x altura 1.5 x 3 = = 2.25 m 2 2
d = base x altura = 2 x 3 = 6 m
d=
## 0.5 x 3 = 0.75 m 2 desplazamiento total 9m = = 2.25 m/s v media = tiempo total 4s
FGC-SUBEV-38
79
20.
x
C) Aceleracin constante
1)
0 x
2)
0 x
3)
B) V = 0
21. En el intervalo t [3, 5] la velocidad es constante 22. En el intervalo t [3, 5] y para t = 0s y t = 11s
## 23. Los resultados son iguales
FGC-SUBEV-38
80
24. Datos d = 160m m v 1 = 10 s m v 2 = 7. 5 s t1 = t2 d1 = ? d2 = ? Frmula d = d1 +d2 d v1 = 1 t1 d v2 = 2 t2 como t1 = t2 d1 d 2 = v1 v 2 v d2 = 2 d1 v1 m 7 .5 s d d2 = m 1 10 s d2 = 0.75d1 ; d1 = d d2 d2 = 0.75(d d2) d2 + 0.75 d2 = 0.75 d 1.75 d2 = 0.75(160m) 0.75(160m) d2 = 1.75 d1 = 160m 68.5m d2 = 68.5m, = 91.5m
25. Para el primer autobs, el tiempo que ocupa en recorrer los 220 km es:
t=
## A la hora en que se encuentran es las 2 hrs. 56 min.
Para el segundo automvil, el tiempo que utiliz para recorrer 220 km. es de 2 hrs. 26 min. y su rapidez supuesta constante es:
v=
FGC-SUBEV-38
81
## 27. En el intervalo t (5, 11] la velocidad disminuye
28. En el intervalo t (0, 3) el cuerpo acelera 29. En el intervalo t (5, 11) el cuerpo desacelera 30. Datos cm a=2 2 s t = 30s vi = 0 Frmula vf = vi + at cm cm v f = 0 + 2 2 (30s) = 60 s s
31. Datos vi = 0 d = 1500m Km v f = 25 h a=? t=? Como: vf2 = vi2 +2ax Conversiones m Km 1000m 1 h v = 25 = 6.94 s 1 Km 3600s s
FGC-SUBEV-38
82
## 32. Considerando el diagrama de cuerpo libre siguiente:
Movimiento, V=10 m/s
f=40 N
m
N W=mg
F=60 N
Donde f es la fuerza de rozamiento y N la fuerza de reaccin sobre el piso. La ecuacin de fuerzas es la siguiente: Suma de fuerzas verticales: Fv = N W = ma Como no hay movimiento vertical, la aceleracin en este caso, es cero y por lo tanto: FV = N W = 0 Es decir, que la reaccin sobre el piso es igual al peso de la masa. Suma de fuerzas horizontales: Fn = 60 40 = ma Ahora la aceleracin no es cero, ya que si hay movimiento en sentido horizontal: ma 20 N 20 N = ma a= = = 10 m seg 2 m 2 kg Como se pide la velocidad a los 6 segundos de haberse aplicado la fuerza, debemos considerar como velocidad inicial 10 m/s y ya que la aceleracin se v v0 define como a = , podemos resolver para la velocidad final v: t
## m m m 10 m (6seg) = 10 + 60 = 70 v = v 0 + at = 10 m seg + 2 seg seg seg seg
Es decir, que su velocidad despus de 6 segundos de haber aplicado la fuerza es de 70 m/seg
FGC-SUBEV-38
83
m
d
sen37 =
15 d
15 m 37O
d=
15 = 24.9m sen37
## Trazamos el diagrama de cuerpo libre:
y N=fuerza normal
W sen37o=Wx
O Wy=W cos 37o 37
37O x W=mg
Luego descomponemos el vector peso en dos componentes, una en direccin paralela al plano inclinado y la otra perpendicular al mismo. Del diagrama de cuerpo libre obtenemos la componente en direccin de x (Wx) y la componente en la direccin de y (Wy): Wx = Wsen37 = mgsen37 Wy = Wcos37 = mgcos37 haciendo la suma de fuerzas tenemos: Fx = mg sen 37 = ma dividiendo entre m: gsen 37 = a a = (9.8m/s2) sen37 = 5.9 m/s2 Es decir, el cuerpo tiene una aceleracin de 5.9 m/s2
FGC-SUBEV-38
84
## 1 d = v 0 t + at 2 , sustituyendo 2 1 d = (0)t + 5.9 m 2 t 2 = 2.94t 2 = 24.9m s 2
= 24.9m = 2.9seg 2.94 m 2 s
34. Datos
m s hmx = ? tT = ? v 0 = 15
## Frmulas vf = v0 gt 1 h = v 0 t gt 2 2 tT = 2t 1 m m 2 h = 15 (1.52s ) 9.81 2 (1.52g) = 11.47 m 2 s s vf = v0 gt | m 15 v s = 1.52 s t= 0 = m g 9.81 2 s tT = 2t = 2(1.52s) = 3.045
35. B)
Permanece constante
## 36. Datos m g = 9.81 2 s v0x = 52 m/s = 22 Frmulas V0x = V0 cos 2 v 0 sen2 x= g
v 0x cos m m 52 s = s v0 = cos 22 0.9271 m = 56 s 52
= v0;
FGC-SUBEV-38
85
## m 56 sen 44 s x= = 2 9.81 2 s x = 222 m
m2 3136 s2
(0.6946 ) m 9.81 2 s
37. El permetro de las ruedas es: Permetro =D Permetro =(0.5) Permetro =1.57m Que se recorren en: v =
d t
10m / s =
t=0.157
1.57m t
Este es el tiempo en que una rueda gira una vuelta completa, es decir:
## 1rev 0.157s w=6.369 rps w=6.369(60)rev/min w=382.16 rpm
w=
38. Todo cuerpo permanece en su estado de reposo, o de movimiento uniforme en lnea recta, a menos que se vea forzado el cambio debido a las fuerzas que se le apliquen.
39. A)
La masa
40. B)
FGC-SUBEV-38
86
## m 1Kg 2 F 1N s a= = = m 1Kg 1Kg m a =1 2 s
43.
a(m/s2)
7 6 5 4 3 2 1 0 1 2 3 4 5 6 7
F(N)
44. A)
mayor
45. A)
## Una regla de proporcionalidad directa
46. B)
Aumenta al triple
## 47. Nos da la inversa de la masa del cuerpo
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48.
a(m/s2) 2
m(kg)
49. B)
Menor
50. B)
Inversa
51. En el sistema MKS la fuerza se mide en Newtons, [F] = N En el sistema CGS la fuerza se mide en dinas [F] = dina 1N = 105 dinas
## 52. Datos m g = 9.81 2 s m = 10g W=?
Conversiones 1 Kg = 1000gr 10g = ? 1Kg m = 10g x = 0.01Kg 1000 g W = mg m = (0.01Kg) 9.81 2 = 0.098 N s
53. Del problema, se sabe que m = 1000 kg y F = 800 N, sustituyendo estos datos en F 800N la ecuacin a = , se obtiene: a = = 0.8 m/s2 m 1000Kg
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54. De acuerdo al enunciado del problema, se conocen la aceleracin de la lancha (0.50 m/s2) y la fuerza aplicada (150 N), debido a que lo que se quiere conocer es F la masa de la lancha, se despeja de la ecuacin a = la masa (m) y se m sustituyen los datos conocidos: F 150 N = = 300 Kg. m= a 0.50 m/s 2
55.
(a) Fuerza de la tierra sobre la manzana (peso) (b) Fuerza del libro sobre la manzana
(a) (b)
(a)
(b)
(c)
(a) Fuerza de la manzana sobre el libro (b) Fuerza de la mesa sobre el libro (c) Fuerza de la tierra sobre el libro
(a)
(b)
## (a) Fuerza del libro y manzana sobre la mesa
(b) Fuerza de la tierra sobre la mesa (c) Fuerzas del suelo sobre la mesa (c)
(c)
S Ma Me L
(S) Fuerzas de la mesa sobre la tierra (Ma) Fuerza de la manzana sobre la tierra (Me) Fuerza de la mesa sobre la tierra (L) Fuerza del libro sobre la tierra
56. B)
## Tercera ley de Newton
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57. Datos h = 2m s2 m = 0.3 Kg g = 9.81 m A) Frmulas Ep = mgh 1 E c = mv 2 2 EM = Ep +Ec = const m E p = (0.3Kg) 9.81 2 (2m) = 5.9 J s
B)
mgh =
1 mv 2 2
v = 2gh
## 58. Al trmino del primer segundo m m m v f = v 0 + at = 0 + 2 2 (1s ) = 2 s s s
1 1 m E c = mv 2 = (2000Kg) 2 = 4000J 2 2 s
Para el siguiente segundo m m m v f = v 0 + at = 0 + 2 2 (2s) = 4 s s s
1 1 m E c = mv 2 = (2000Kg) 4 = 16000J 2 2 s
E = E cf E ci = 16000 J 4000 J = 12000 J
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## 59. B) p2 , donde p es la cantidad de movimiento p = mv 2m (mv ) 2 Ec = 2m m 2 v 2 mv 2 = Ec = 2m 2 Ec =
60.
F=86 N 30o
Recordemos que la nica fuerza que realiza trabajo es aquella que acta en la MISMA direccin del movimiento, sea en el mismo sentido o en sentido contrario. Tenemos que la fuerza de 86N se puede descomponer en dos componentes, una de sus componentes apuntar en direccin perpendicular al movimiento, sta no realiza trabajo alguno; y la otra componente, apuntar en la misma direccin y sentido que el movimiento y ser esta fuerza precisamente la que realizar todo el trabajo.
Fy
N 86
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61. A)
Escalares
## P1 + P2 = 0; es decir: (P1 - P1) + (P2 + P2) = 0
En funcin de la masa se puede escribir como: (m1v1 - m1v1) + (m2v2-m2v2)=0 o de otra forma: m1v1 + m2v2 = m1v1 + m2v2 En el problema tenemos que: m1 = 0.1 kg, v1 = 400 m/s, la masa de bloque m2, y la velocidad inicial del bloque v2=0. Despus de la interaccin tenemos que: v1 = v2 = 6.5 m/s. Sustituyendo la informacin anterior: (0.1kg)(40 0m/s) + m 2 (0) = (0.1kg)(6.5m/s) + m 2 (6.5m/s) kgm kgm = 0.65 + m 2 (6.5 m/s) s s kgm kgm kgm 0.65 = 39.35 m 2 (6.5m/s) = 40 s s seg kgm 39.35 s = 6.05kg m2 = m 6.5 s 40 La masa del bloque es de 6.05kg.
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## 1 1 1 1 1 11 = + = + = Ceq C1 C 2 5pF 6pF 30
de la cual C = B)
30 pF = 2.73pF 11
En este tipo de combinacin, cada capacitor porta la misma carga, entonces: q1 = q2 = q = Ceq V = (2.73x10-12 F)(1000V)= 2.73 nc
C)
Para la diferencia de potencial en: C1: V1 = q1 2.73 x10 9 C = = 546 V C1 5 x10 12 F q 2.73 x10 9 C = 455 V C2: V2 = 2 = C2 6 x10 12 F Para la energa en cada capacitor: C1: EnergaC1 =
D)
1 1 q1V1 = (2.73 x10 9 C)(546 V ) = 7.45 x10 7 J 2 2 1 1 C2: EnergaC 2 = q 2 V2 = (2.73 x10 9 C)( 455 V ) = 6.21x10 7 J 2 2
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64. La fuerza elctrica entre dos partculas cargadas se puede hallar por medio de la ley de Coulomb: Fe = k q1xq2 r2
N x m2 C2
## q1 y q2 = carga de las partculas r = distancia entre partculas
2 2 1.6 x 10 19 C 9 Nxm = 8.2 x 10 8 N Fe = 9 x 10 2 2 11 C 5.3 x 10 m
( (
) )
## La fuerza de accin gravitacional entre dos masas se encuentra por:
Fg = G
M1 x M2 r2
N x m2 kg 2
donde G = 6.67x10 11
## La fuerza gravitacional entre ellas ser: mp = 1.67 x 1027 kg me = 9.11 x 1031 kg
N x m 2 1.67 x 10 27 kg 9.11 x 10 31kg Fg = 6.67 x 10 11 2 2 kg 5.3 x 10 11 m
)(
) = 36.13 x 10
48
## Haciendo la comparacin tenemos que: Fe Fg
36 x 10 gravitacional
8.2 x 10 8 N
48
## = 2.27 x 10 39 veces mayor la fuerza elctrica que la fuerza
Es decir, que en los casos prcticos la fuerza gravitacional se puede despreciar en los problemas donde se involucren fuerzas elctricas.
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65. La fuerza entre las cargas separadas una distancia r, est dada por: F1 = K q1 x q2 r2
## Pero si la distancia se reduce a la mitad, la fuerza ser: F2 = K q1 x q 2
2
r2 r r 4 2 comparando: q xq 4K 1 2 2 F2 r = =4 q x q2 F1 1 K r2 Es decir, que la fuerza aumenta 4 veces su valor cuando la separacin se reduce a la mitad.
=K
q1 x q 2
2
= 4K
q1 x q 2
66. Datos del problema: VB VA = 6 V d = 3.0 mm A) El campo elctrico se puede calcular de la expresin de la definicin de potencial: VB VA = E d
E=
B)
VB VA 6V = = 2 x 10 3 V m -3 d 3 x 10 m
## La fuerza se calcula de la definicin de campo elctrico:
E=
F q
F = q E = (1.6 x 10 19 C) (2 x 103 V/m) = 3.2 x 1016 N
Unidades: J V C N m = C m C m = m = [N]
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67. El trabajo se puede calcular por medio de la ecuacin: T = q (VB VA) donde: T = Trabajo q = Carga (C) VBVA = Diferencia de potencial del punto A al punto B De los datos del problema tenemos que: q = 1.6 x 1019 C VBVA = 50 V
## Haciendo la comprobacin de las unidades: J [C][V]=[C] =[J] C
68. En este caso apoyndonos en el teorema del trabajo y la energa, se tiene que: T = EC Donde EC = mvf2 mv02 T = q ( VB VA ) = 8 x 1018J V0 = Velocidad inicial Vf = Velocidad final de los datos del problema: mp = 1.67 x 1027 kg VB VA = 50 V V0 = 0 sustituyendo: 8 x 1018 J = (1.67 x 1027 kg) Vf2 (1.67 x 1027 kg) (0) 8 x 1018 J = (1.67 x 1027 kg) Vf2 0 Vf =
2 x 8 x 10 18 J 1.67 x 10
27
kg
## = 9.78 x 104 m/s
Unidades: m2 m m [ J ] = [ N x m ] ; N = kg x 2 , J = kg x 2 x m = kg x 2 s s s
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J = kg
kg x
m2 s2 kg
2 = m =m s s2
## 69. El potencial elctrico se calcula por medio de la expresin: q V =k r
N x m2 donde k = 9 x 109 2 C
q = Carga elctrica [ C ] r = Distancia entre la carga y el punto
2 6 9 N xm 4 x 10 C V = 9 x 10 C 2 0.75 m
V = 48000
## Nxm J = 48 x 103 = 48 x 103 Voltios C C
70. La expresin que nos define la resistencia elctrica es: R = donde: L = Longitud (m) A = Area transversal (m2) = Resistividad ( m) teniendo en cuenta que: AL=2.828 x 108 m L=4my dimetro = 3 mm A=
L A
## 1 2 d2 = 3 x 10 3 m = 7.07 x 10 6 m 2 4 4 4m R = 2.828 x 10 8 m = 16 x 10 3 2 6 7.07 x 10 m
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71. Usando la ley de Ohm: V=RI Donde: V = Cada de voltaje (V) R = Resistencia elctrica () I = Intensidad de corriente elctrica (A) En el problema: I=5A R = 100 V = (100 ) (5 A) = 500 V 72. La resistencia del primer alambre se calcula por: L R1 = 1 A1 Al calcular la resistencia del segundo alambre se debe tomar en cuenta que la resistividad (), es la misma porque es del mismo material, por lo tanto, la resistencia del segundo alambre ser: L R2 = 2 A2 Del problema sabemos que: L2 = 2L1 d2 = 4d1; A1 = d12 A2 = d22; Sustituyendo los datos que conocemos:
= = 1 1 1 2 2 2 d2 (4 d1 ) 16 d1 4 4 4 2 2 5 R1 = 20 = = 16 16 2 A2 R2 = L2 = 2 L1 2 L1 2 L1 2 2 L1 = 16 1 2 d1 4 =
73. La frmula para calcular la potencia es P = I V; pero segn la ley de Ohm V , la cual se sustituye en la expresin de la potencia: I= R V2 V P= V = R R
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De acuerdo a los datos del problema: V = 110 V P = 500 w Al despejar R de la expresin obtenida y despus de sustituir los datos, se obtiene: V 2 (110V) 2 R= = = 24.2 500W P 74. Analizando el circuito y teniendo en cuenta que la cada de voltaje de la fuente debe ser igual a la suma de las cadas de voltaje en los elementos, se tiene:
Ri=0.01
+ Vf -
I=3.5 A 12 V
La cada de voltaje en Ri es: Vi = Ri I = (0.01)(3.5) = 35 x 103 V 12 V = cada de voltaje en Ri + Vf 12 V = 35 x 103 V + Vf Vf = 12 V 35 x 103 = 11.97 V Es decir, que el voltaje que se mide en las terminales de la batera es 11.97 V
75. A)
En serie:
8
=
4
Re=8 + 4 = 12
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B)
En paralelo:
8 4
Re=
(8)(4) 8+4
= 2.667
76. La corriente elctrica se define como la cantidad de carga que pasa por un punto entre el tiempo que le toma hacerlo:
I=
q 40 C C = = 10 t 4s s
C = 1 Amperio s I = 10 A 1
## 77. Despejando de la expresin que define la corriente elctrica:
q t q = I t Datos: I = 10 A,
I=
t = 2 s
Sustituyendo valores numricos: q =( 10 A ) ( 2 s ) = 20 C Unidades: C 1A = 1 s Y como cada electrn tiene una carga de 1.6 x 1019 C, podemos calcular el nmero de electrones dividiendo la carga total: No. de electrones = 20 C = 125 x 1018 electrones 1.6 x 10 -19 C
Por lo tanto, pasan por el alambre 125 x 1018 electrones en dos segundos.
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78. En este caso: q = 1.8 C y t = 2 s q 1.8 C = = 0.9 A I= t 2s 79. Para calcular la carga que pasa en un intervalo dado, se utiliza la definicin de corriente elctrica: I = 3 x 10-2 A t = 20 min q I= t Despejando q: q = I t Sustituyendo los datos: 60s q = ( 3 x 10-2 A ) ( 20 min) 1min q = 36 C El nmero de electrones se calcula dividiendo la carga total entre la carga de un electrn (1.6 x 1019 C).
## q 36 C = = 225 x 1018 electrones q 1.6 x 10 19 C
80. A)
La potencia en las dos bobinas es la misma para ambas: P = I1V1 y P = I2V2 Despejando I1 y sustituyendo los valores de P = 40 w y V1 = 120 v: P 40w I1 = = = 0.33 A V1 120v
B)
El nmero de vueltas es directamente proporcional al voltaje. Es decir: N1 V = 1 N2 V2 Sustituyendo datos: 1000 120v = 15000 V2 Despejando V2: 120x15000 V2 = = 1800v 1000
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C)
La corriente es inversamente proporcional al nmero de vueltas N1 I1 = N2 I 2 Sustituyendo datos: I2 1000 = 15000 0.33A Despejando I2: 0.33 x 1000 I2 = = 0.022 A = 22 mA 15000
81. Sabemos que: N1 V1 = N2 V2 En este caso: V1 = 100 v V2 = 10 v N2 = 1000 vueltas Sustituyendo: N1 1000 = 1000 10 Despejando N1: 100 N1 = x1000 = 10000 vueltas 10 La primaria debe tener 10000 vueltas.
## 82. La potencia consumida por el motor se determina por:
Potencia = P = VI = (120 V)(6A)=720W = 0.720 KW Para el consumo de energa: Energa = Pt = (720 W)(10800s) = 7.8x106J Energa = Pt = (0.720 KW) (3h) = 2.16 KW.h
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## F) 6.75 cc G) 4.921 ft/s H) 0.25 l I) 3850 mm
2. A) SE B) SI C) SE D) SI E) SE 3. 4. 5. 6. 7. 8. A) 4.74 x 103 B) 1.01 x 103 C) 9.16 x 105 D) 2.74 x 104 E) 2.244 x 10-12 F) 3.63 x 10-5 G) 2.2 x 10-14 H) 7 x 10-5 2005.6505 g A) 4.12 x 105 D) 4.12 x 105 A) Kilo D) Centi F) SE G) SI H) SI I) SE J) SE K) SI L) SE M) SI N) SI O) SE P) SE Q) SI R) SI S) SE T) SI
MATERIA Y ENERGA
9.
Los estados fsicos de la materia: slido, lquido, gaseoso y coloide. Ejemplos: Slido = Hielo Lquido = Agua Gaseoso = Vapor de agua Coloide = Gelatina
## 10. A) Elemento B) Solucin C) Mezcla D) Materia E) Compuesto F) Sustancia pura
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11. A)
La materia homognea. Es uniforme en su composicin y en sus propiedades, no varia en ninguna de sus partes. La materia heterognea. No es uniforme ni en composicin, ni en propiedades, consiste en dos o mas porciones o fases distintas fsicamente.
B)
El tomo, es la partcula estable ms pequea de un elemento que define sus propiedades elementales. La molcula, es la partcula estable ms pequea de un compuesto que determina sus propiedades, tanto fsicas y qumicas. Las propiedades fsicas, son todas las que se pueden observar sin cambiar la naturaleza de la sustancia, en cambio las propiedades qumicas, son las que pueden observarse solo cuando la sustancia sufre un cambio en su naturaleza interna.
C)
12. A) Punto de Fusin. Temperatura a la cual una sustancia cambia de estado slido a lquido, a presin constante. Punto de Ebullicin. Temperatura a la cual una sustancia pasa del estado lquido al estado gaseoso a presin constante. Punto de condensacin. Temperatura a la cual una sustancia cambia de vapor al lquido, a presin constante. Punto de sublimacin. Temperatura a la cual un slido cambia al estado a gaseoso sin pasar por el estado lquido, a presin constante. Punto de licuefaccin. Presin a la cual un gas se convierte en lquido a temperatura constante.
B)
C)
D)
E)
13. S =
Por lo tanto: =
## m 3.17gr = = 8.954 gr/ml v 0.354ml
D) Fsico E) Qumico F) Qumico
## 14. A) Fsico B) Qumico C) Fsico
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15. Escala Fahrenheit F Escala Celsius C Escala Kelvin 16. A) 77 F B) 31.7 C, 241.3 K C) 274.8 K F = 9/5 C + 32 C = (F 32) /1.8 K = C + 273
17. Propiedades fsicas: Brillo metlico notable (Plata) Elevada conductividad trmica y elctrica (Cobre) Maleabilidad (Estao) Ductibilidad (Oro) Densidad elevada (Plomo) Punto de fusin elevado (Hierro) Propiedades qumicas: No se combinan fcilmente unos con otros. Se combinan con los NO metales (ejemplo, xido de fierro) 18. Se combinan con los metales. Tambin, se pueden combinar unos con otros, ejemplo: dixido de carbono, tetracloruro de carbono, dixido de silicio (arena) 19. A) B) Calor.- Cantidad de energa que contiene un cuerpo. Temperatura.- Manifestacin de la energa que transmite un cuerpo a su entorno.
20. A) Mezcla B) Elemento C) Mezcla D) Mezcla 21. A) H B) Ca C) N D) C E) Pb F) U G) O H) Na I) Fe J) Ag K) P L) Sn M) Hg N) Cl O) Cu P) K E) Elemento F) Compuesto G) Elemento H) Compuesto
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TABLA PERIODICA
22. Todos aquellos terminan su configuracin en p1. Esta es una caracterstica de las familias qumicas, donde cada una de ellas tiene una configuracin igual entre s, a sto se debe muchas de las propiedades de la familia como lo es la valencia. 23. 16 Familias. Se conocen 7 familias del grupo A y 8 de la familia B, agregndose la familia 8A conocida como familia cero o de los gases nobles. 24. Oxgeno. El poder de atraer electrones (electronegatividad) se encuentra en la esquina superior derecha de la tabla peridica, siendo los principales el Flor, Oxgeno y Nitrgeno, de acuerdo a la escala de Pauling, En cambio, los elementos ms electropositivos estn en la parte inferior y del lado izquierdo, siendo su principal representante el Francio. 25. El Astatino En la tabla peridica, el tamao del radio atmico aumenta de arriba hacia abajo y de izquierda a derecha (verifica la tabla peridica y obsrvalo en otras familias. 26. Germanio. Revisa en tu texto los bloques de elemento que agrupan los orbitales s,p,d y f y su relacin con los niveles y observa como en el cuarto rengln se encuentran el Potasio, Calcio en S2 y Galio y Germanio en p2 (estos son los electrones del nivel de valencia)
27. K, Na, Al, B, C Este concepto esta ligado al poder de electronegatividad, la cual disminuye hacia la izquierda y hacia abajo, volviendo ms electropositivos. Ubica estos elementos y determina la razn de la respuesta. 28. Nmero Atmico En el siglo XIX, Mendeleev, clasific a los elementos de acuerdo a sus propiedades, aos mas tarde, Werner separ los elementos en subgrupos A y B. Actualmente, la tabla peridica de Moseley, indica que las propiedades de los elementos son funcin peridica de sus nmeros atmicos. Moseley demostr experimentalmente, que en el tomo existe una cantidad fundamental que vara en forma escalonada de un elemento a otro y que fue llamada nmero atmico. 29. 1s2 2s2 2p6 3s2 3p6 4s2 3d6 Desarrolla la configuracin de varios elementos y observa como, si la configuracin y la posicin del elemento en la tabla estn en funcin del nmero atmico, determina como se correlacionan.
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30. n Recuerda los valores de los nmeros cunticos. n = nivel de energa l = subnivel m = campo magntico s = giro o spin
31. Gases nobles o inertes o familia cero. Se denominan as, por que en la antigedad se les consideraba de la nobleza real, al no unirse con algn elemento, ya que contienen 8 electrones en su ltimo nivel, por lo que no ganan ni pierden electrones (familia cero).
32. Radio atmico.- Varan peridicamente en funcin del nmero atmico, indicando el tamao aproximado de los tomos. Radio inico.- Los radios de los iones negativos son mayores que los radios de los tomos neutros, debido a que el ion negativo se produce ganando electrones en el nivel energtico exterior lo que lo hace ms grande, en cambio los radios inicos de iones positivos al perder electrones son ms pequeos. Energa de ionizacin o potencial de ionizacin.- Disminuye en un mismo grupo hacia abajo y en un mismo perodo hacia la izquierda y representa la energa necesaria para arrancar un electrn a un tomo neutro. Electronegatividad.- Capacidad de un tomo para atraer y retener electrones de enlace. Es un nmero positivo que se asigna a cada elemento, aumentan de izquierda a derecha en la tabla peridica. Afinidad electrnica.- Tendencia de los tomos a ganar electrones.
ESTRUCTURA ATMICA
33. D) A) B) C) E)
## La relacin de carga-masa del electrn.
Millikan, fue el que midi la carga del electrn con el experimento de la gota de aceite. No es relevante la medicin de la temperatura de los electrones, stos tendrn la misma temperatura que los tomos. El nmero atmico, nos indica el nmero de protones y stos fueron descubiertos por Rutherford en 1919. Se determin la masa del electrn como consecuencia de conocer la relacin carga-masa y la carga del electrn.
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34. D) A) B) C) E)
Ernest Rutherford
John Dalton, contribuy con su teora atmica. Henry Moseley, determin la estructura cristalina de los tomos a travs de Rayos X. Robert Millikan, determin la carga del electrn. J. J. Thomson, mostr en 1890 que los tomos de cualquier elemento pueden emitir pequeas partculas negativas.
35. A) B) C) D)
Protn.
El neutrn tiene una masa de aproximadamente 1.0072 uma y no tiene carga. El electrn tiene carga negativa y una masa de 0.000549 uma. El neutrino.
36.
B) Consultando la tabla peridica, encontramos que ste elemento tiene el nmero atmico 37, por lo tanto tendr 37 protones en su ncleo.
37. B) A) C) D) E)
## El mismo nmero de protones.
No pueden tener la misma masa atmica, puesto que el nmero de neutrones es variable. El nmero de neutrones en los istopos es variable. Si tienen el mismo nmero de protones y neutrones, ser el mismo istopo. Si tienen la misma masa molecular, corresponder al mismo tipo de tomos.
38. B) A) C) E)
112 48
In contiene 49 protones.
## Este istopo del Cd contiene 48 protones y D) contienen 47 protones contiene 48 protones
39. D)
27 protones y 29 neutrones
A), B), E) Si se refiere al ncleo de Cobalto, el ncleo no contiene electrones. C) No puede contener 29 protones, porque sera el cobre, el cobalto tiene nmero atmico 27 y, por lo tanto, tiene en el ncleo 27 protones.
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40.
A) La masa atmica es la suma de protones y neutrones, del ncleo del tomo, y el nmero atmico nos indica la cantidad de protones y/o electrones, por lo tanto si el Fierro tiene una masa atmica de 56 y su nmero atmico es de 26, restamos: 56 26 = 30 neutrones, 26 protones y 26 electrones.
41. A) El azufre tiene nmero atmico 16, por lo que contiene 16 protones, al ionizarse como S2 gana dos electrones, que sumados a los 16, hacen un total de 18 electrones. B) C) D) El nmero atmico del Ar es 18 (18 protones, 18 electrones), al ionizarse como Ar2 adquiere 2 electrones, lo que da un total de 20 electrones. El Cloro tiene nmero atmico 17 (17 p+, 17 e), al ionizarse como Cl adquiere un electrn ms, 17+1=18 electrones. El Potasio neutro contiene 19 protones y 19 electrones, al ionizarse como K+ pierde 1 electrn, quedndole solo 18 electrones.
42.
B) Toda la materia contiene electrones. Al sustituir los electrodos con elementos diferentes, se continan produciendo los rayos catdicos que son un flujo de electrones.
A) C) D)
Esto fue descubierto a travs del experimento de Rutherford de la hoja de oro. En un tubo de rayos catdicos no se producen rayos positivos Las partculas alfa s son ms pesadas que los protones, pero no se descubri esto en un experimento con rayos catdicos.
43. B)
El selenio tiene nmero atmico 34 (34 p+ y 34e) al ionizarse como Se2 adquiere 2 electrones que sumados a los 34 dan un total de 36 electrones, que son los mismos que contiene el Kr (NA = 36)
Electrn, con una masa de 9.11 x 1028 g
44. C) A) B)
El protn tiene una masa de 1.672 x 1024 g. El neutrn tiene una masa de 1.675 x 1024 g.
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45.
C) El calcio al perder dos electrones queda con dos protones de ms, por lo que el calcio adquiere una carga 2+., lo cul se conoce como in.
A) B) D) E)
Es una partcula fundamental del tomo con carga positiva. Es aquel elemento donde la suma de sus cargas elctricas es igual a cero. El tomo de Argn tiene 18 protones, 18 electrones y 22 neutrones en su ncleo. El istopo es aquel elemento que cuenta con un exceso de neutrones y difiere con los dems elementos en su masa.
El mismo nmero de neutrones, el 60Co tiene 27 protones, por lo que si al nmero de masa 60 (que es la suma de protones y neutrones) se le restan 27, que son los protones, da como resultado 33 neutrones. Para el 59Fe ser 59 26 = 33 neutrones. Para el 62Cu ser 62 29 = 33 neutrones
46.
D)
A) y E) El nmero de masa es diferente. 60 para el Co, 59 para el Fe y 62 para el Cu. B) La carga nuclear tambin es diferente, para el Co es de 27 protones, para el Fe 26 protones y 29 protones para el cobre. C) Los electrones no son iguales; 27 electrones del Cobalto, 26 electrones para el Fe y 29 electrones para el cobre. 47.
C) 2 electrones en el orbital s y 6 electrones en tres orbitales p, dos en cada orbital. s de giro o spin, puede tener dos valores +1/2 y 1/2.
48. D) A) B) C) E) 49. E)
La letra p designa al subnivel que tiene tres orbitales. l es el nmero cuntico, el cual describe la forma del orbital. m es el nmero cuntico magntico. n es el nmero cuntico principal. Siete. Cuando el valor del nmero cuntico l=3, los valores del nmero cuntico m son 3, 2, 1, 0, 1, 2, 3, los cuales nos representan 7 orbitales.
50.
A) Despus de llenar el primer nivel de energa con 2 electrones en el orbital s, se inicia el segundo nivel con el 2s y no con 2p.
## (B, C y D) Son correctas.
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51.
B) El Manganeso tiene nmero atmico 25; se llena el orbital 4s primero y despus se empieza a llenar el 3d. Esta configuracin es del elemento magnesio, de nmero atmico 20. Incorrecta, primero se llena el 4s antes que el 3d. Incorrecta, hay que llenar primero el 3s antes que el 3p.
A) C) D) 52. B)
1 1
H ; el cual iguala tanto los nmeros de masa como los nmeros atmicos. 14 4 17 1 7 N+ 2 He 8 O + 1 H
14
## NOMENCLATURA DE COMPUESTOS INORGANICOS
53. A) Enlace covalente.- Se forma cuando 2 tomos que se unen comparten un par de electrones para formar el enlace, aportando un electrn cada uno de los tomos involucrados. Enlace covalente coordinado.- Se forma cuando dos tomos que se unen comparten un par de electrones para formar el enlace, en este caso el par de electrones compartido lo proporciona uno de los tomos. Fuerzas de Van der Waals.- Se forma cuando existe una atraccin electrosttica provocada por la influencia del campo elctrico de los tomos vecinos. Enlaces puente de hidrgeno.- Se forma cuando los tomos de hidrgeno son atrados por la fuerza electrosttica generada entre el hidrgeno y otro elemento electronegativo. Se forma cuando un tomo transfiere completamente electrones a otro tomo que los recibe, generndose una fuerza de atraccin electrovalente entre los iones formados.
B)
C)
D)
E)
54. Enlace inico > enlace covalente > puente de hidrgeno> fuerzas de Van der Waals
55. A) B) C)
xido metlico + H2O Base o hidrxido anhdrido u xido no metlico + H2O cido Base + cido sal + H2O
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56. A) B) C) D) E) F) G) H) I) J) 57. A) Oxido de berilio B) Ioduro de magnesio C) Sulfuro de sodio D) Oxido de aluminio 58. B) D) E) E) Cloruro de hidrgeno (gaseoso), cido clorhdrico (acuoso) F) Fluoruro de litio G) Sulfuro de plata H) Hidruro de calcio Na2O + H2O 2NaOH (hidrxido de sodio) CaO + H2O Ca(OH)2 (hidrxido de calcio) Al2O3 + H2O 2Al(OH)3 (hidrxido de aluminio) K2O + H2O 2KOH (hidrxido de potasio) ZnO + H2O Zn(OH)2 (hidrxido de zinc) H2CO3 (cido carbnico) CO2 + H2O SO2 + H2O H2SO3 (cido sulfuroso) SO3 + H2O H2SO4 (cido sulfrico) H2 + S2 2H2S (cido sulfhdrico) NO2 + H2O HNO3 (cido ntrico)
debe ser Hidruro de Aluminio. debe ser hidrxido de Hierro (II), no (III) deber ser Cloruro de Cobalto (III), no (II)
59. A) Bromuro de hierro (II) B) Sulfuro de cobalto (II) C) Sulfuro de cobalto (III) D) Oxido de estao (IV) E) Cloruro de mercurio (I) F) Cloruro de mercurio (II)
60. A) Bromuro cobltico B) Ioduro plmbico C) Oxido frrico 61. A) Hexafluoruro de Xenn B) Difluoruro de oxgeno C) Triyoduro de arsnico D) Tetraxido de dinitrgeno E) Monxido de dicloro F) Hexafluoruro de azufre D) Sulfuro ferroso E) Cloruro estnico F) Oxido estanoso
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62. A) B)
C) D) E) F) G) H) I) J) K)
Oxido de aluminio (inico) Trixido de diboro (molculas), aunque el bario se encuentra en el grupo IIIA, se comporta comnmente como no metal, formando compuestos no inicos. El punto de fusin es solo de 45 C, el cual es muy inferior a los valores del punto de fusin tpicos de los verdaderos compuestos inicos. Tetraxido de dinitrgeno (molecular) Pentxido de dinitrgeno (molecular) Sulfuro de aluminio (inico) Sulfuro de hierro (III) (inico), sulfuro frrico Cloruro de oro (III), o cloruro urico (inico) Trihidruro de arsnico (molecular) Monofluoruro de cloro (molecular) Oxido de potasio (inico) Dixido de carbono (molecular)
63.
A) NO3 B) NO2 A) CO32 B) HCO3 A) Fosfato dicido de litio B) Cianuro de cobre (II) C) Nitrato de plomo (II)
C) NH4+ D) CN C) CH3COO C2H3O2 D) CN D) Fosfato cido sodio E) Clorito de sodio F) Sulfato de cobalto (III) E) cido sulfuroso F) cido cianhdrico G) cido sulfhdrico H) cido fosfrico
64.
65.
66. A) cido perclrico B) cido idico C) cido bromoso D) cido hipocloroso 67. A) CaCl2 B) Ag2O C) Al2S3 D) BeBr2 68. A) SO2 B) N2O C) XeF4 D) P4O10 E) PCl5 F) SF6 G) NO2 E) H2S F) KH G) MgI2 H) CsF
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69. A) AgClO4 B) Co(OH)3 C) NaClO D) K2Cr2O7 70. A) HCN B) HNO3 C) H2SO4 D) H3PO4 71. A) K2O B) MgO C) FeO D) Fe2O3 E) ZnO F) PbO G) Al2O3 E) HClO F) HF G) HBrO2 H) HBr E) NH4NO2 F) Fe(OH)3 G) NH4HCO3 H) KBrO4
ESTEQUIOMETRA.
72. A) B) C) Masa molecular.- Es la suma de las masa de los tomos que cnforman una molcula de una sustancia, expresada en gramos. Mol.- Es la cantidad de sustancia que contiene tantas partculas como 12 tomos hay en 12 gramos de C . Nmero de Avogadro.- Es el nmero de tomos de un elemento que resulta lo suficientemente grande como para pesarse y cuyo peso en gramos es exactamente igual al peso atmico del elemento su valor es 6.023 x 1023. 2C2H2 + 5O2 4CO2 + 2H2O
73. A)
Para determinar si es correcto el balance, realizamos el siguiente cuadro, y si entra lo mismo que sale, entonces es correcto el balance. Entra 4 4 10 Sale 4 4 10
C H O
Puedes utilizar el procedimiento del TANTEO, experimentando varios valores, hasta encontrar el correcto o puedes utilizar el ms exacto que es el mtodo
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algebraico, para lo cual estableces una ecuacin para cada elemento y le asignas una letra a cada reactante y producto. C2H2 + O2 CO2 + H2O A B C D Elemento C H O Ecuacin 2A = C 2A = 2D 2B = 2C + D
Resuelve el sistema de ecuaciones por cualquier mtodo algebraico. Para este caso, le asigno un valor arbitrario a una sola letra y de ah obtengo los dems. Si yo digo que A vale 5 y 2A=C tengo que C=2(5)=10, Si A=5 y 2A=2D, Substituyo el valor de A y obtengo: 2(5) = 2D 10 = 2D despejando D: 10/2 = D D=5 y si 2B = 2C + D y substituyo los valores de C y D tengo que: 2B = 2(10) + 5 2B = 20 + 5 2B = 25 B= 25/2 Si todos los nmeros obtenidos los multiplico por 2 y divido por 5 tengo: A=2 C=4 D=2 B=5 A) B) C) D) E) 74. A) 2 B) 3 C) 54 g D) 159.6 2C2H2 + 5O2 4CO2 + 2H2O 4AsO + 3O2 2As2O5 4NH3 + 5O2 4NO + 6H2O 2CS + 5Cl2 2CCl4 + S2Cl2 PCl3 + 3H2O H3PO3 + 3HCl
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76. A)
Se dice que:
## Resolviendo esta regla de tres tenemos: x = 100 x 1 /44 = 2.2727
B) C)
1.136 0.02727
77. 15 % de alcohol es igual a 15 ml de alcohol en 100 ml de vino. Haciendo una regla de tres: 15 ml de alcohol ---- 100 ml de vino X ---- 1000 ml de vino X = 150 ml de alcohol 78. El 45 % en peso de un litro son 450 ml considerando para el agua una densidad de 1 es decir, 1 ml (volumen) = 1 g (peso). Por lo tanto para preparar una solucin al 45 % en peso de cloruro de sodio en un litro de solucin se requieren 450g de sal. 79. El peso de la solucin final ser la suma de los pesos del azcar + cido ctrico + Cloruro de sodio + agua, es decir: 57.2 g (azcar) + 25.2 g (ac. Ctrico) + 2.5 g (NaCl) + 500 g (H2O) = 584.9 g (100%) Considerando que la densidad del agua es 1, o sea 1 g (peso) = 1 ml (volumen) As el peso total de la solucin es 584.9 g que equivale al 100%. Haciendo una regla de tres: A) Para el azcar: 584.9 g ------ 100 % 57.2 g ------ X X = 9.78 % B) Para el cido ctrico: 584.9 g ------ 100 % 25.2 g ------ X X = 4.31 %
## C) Para el cloruro de sodio: 584.9 g ------ 100 % 2.5 g ------ X
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X = 0.43 %
80. El volumen total de la solucin final ser: 50 ml (alcohol) + 100 ml (refresco de cola) + 150 ml (agua mineral) + 5 ml (jugo de limn) = 305 ml, que equivale al 100 %. Por lo tanto: A) para el alcohol: 305 ml ----- 100 % 50 ml ----- X X = 16.59 % 305 ml ----- 100 % 100 ml ----- X X = 32.79 % 305 ml ----- 100 % 150 ml ----- X X = 49.18 % 305 ml ----- 100 % 5 ml ----- X X = 1.64 %
## D) Para el jugo de limn:
81. Una solucin normal (N) es la que contiene disuelto en un litro de solucin ( 1000 ml), el peso normal o equivalente del soluto.
a VE Donde: N = Normalidad de la solucin = g equivalentes / l a = gramos de soluto V = Volumen de la solucin = l E = Peso equivalente = g/g equivalente Se obtiene el peso molecular del Na OH: N=
Elemento Na = O = H = Peso atmico 23 x 16 x 1 x No. De tomos 1 = 1 = 1 = P.M. = Total 23 16 1 40 g
Se despeja a que corresponde a los gramos de soluto que nos preguntan: a = NVE a = 0.5 g equivalente/ l x 1 l x 40 g/ g equivalente = 20 g de NaOH
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## a ; obtenemos el P.M. del H2SO4: VE
No. De tomos 2 = 1 = 4 = P.M. = Total 2 32 64 98 g
Peso atmico 1 x 32 x 16 x
E H2SO 4 =
PM 98 g = = 49 2 2 g equivalene
N=
49 g g 1l 49 g equiv.
= 1N
83. A) La concentracin porcentual (peso/volumen): 500 ml ---- 100 % 17.2 g ------ X X = 3.44 % de H3PO4 B) Concentracin Normal: Se obtiene el Peso molecular del H3PO4 Elemento H = P = O = Peso atmico 1 x 31 x 16 x No. De tomos 3 = 1 = 4 = P.M. = Total 3 31 64 98 g
Nmero de equivalentes = 3
E H3PO 4 = PM 98 g = = 32.67 3 3 g equivalene
N=
## 17.2 g g 0.5 l 32.67 g equiv.
= 1.05 N
C)
Solucin molar.- La solucin molar (M), se expresa como un mol de soluto disuelto en un litro de solucin y su frmula es:
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M=
## Moles de soluto n = 1litro de solucin V
El peso molecular del H3PO4 = 98 g/mol, pero nos estan dando los gramos que se utilizan = 17.2 g, por lo que requerimos el nmero de moles de sta cantidad:
n= m 17.2 g = = 0.1755 moles P.M. 98 g / mol
Sustituyendo en la frmula: M =
## 0.1755 = 0.35 M 0.5 l
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MATEMTICAS I, ARITMTICA Y ALGEBRA Samuel Fuenlabrada De la Vega Trucios Editorial Mc Graw Hill, 1994 ALGEBRA Max A. Sobel / Norvert Lerner Editorial Prentice Hall, 1996. Cuarta Edicin MATEMTICAS II, GEOMETRA Y TRIGONOMETRA Samuel Fuenlabrada De la Vega Trucios Editorial Mc Graw Hill, 1994 ALGEBRA Y TRIGONOMETRA Barnett Editorial Mc Graw Hill LGEBRA Y TRIGONOMETRA CON GEOMETRA ANALTICA A. Goodman / L. Hirsch Editorial Prentice Hall, 1996 FUNDAMENTOS DE GEOMETRA H. S. M. Coexeter Editorial Limusa GEOMETRA PLANA CON COORDENADAS Barnett Rich Serie Schaums, Mc Graw Hill GEOMETRA ANALTICA PARA BACHILLERATO Gerra Tejeda / Figueroa Campos Editorial Mc Graw Hill, 1992 CLCULO Y GEOMETRA ANALTICA, VOLUMEN I Y II Shermas K. Stein / Anthony Barcellos Editorial Mc Graw Hill, 1995 CLCULO Y GEOMETRA ANALTICA,VOLUMEN I Y II Larson / Hostetler / Edwards Editorial Mc Graw Hill, 1995 CLCULO DIFERENCIAL E INTEGRAL Frank Ayres Jr. / Elliot Mendelson Serie Schaums, Mc Graw Hill. Tercera edicin CLCULO DIFERENCIAL E INTEGRAL Edwin Purcell / Dale Var Berg Editorial Prentice Hall. Sexta edicin CLCULO DIFERENCIAL E INTEGRAL Granville / Smith / Longley Editorial Uthea
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FSICA GENERAL Alvarenga, B. / Mximo, A. Editorial Harla, 1983 INTRODUCCIN A LAS CIENCIAS FSICAS Daz, J. Ediciones y Distribuciones Cdice, S.A., 1988 FUNDAMENTOS DE FSICA Semat, H. / P. Baumel Editorial Interamericana, 1974 ELECTRICIDAD Y MAGNETISMO Serway, R. A. Editorial Mc Graw Hill , 1997
FSICA FUNDAMENTAL Valero, M. Editorial Norma. 1986 FSICA RECREATIVA Walker, J. Editorial Limusa, 1988 MECNICA T. Therington /J. G. Rimmer. Editorial Centro Regional de Ayuda Tcnica, 1973 FSICA I PARA BACHILLERATOS TECNOLGICOS Reynoso Ureoles, Sergio. Editorial SEP-SEIT-DGETA, 1. Ed.
FSICA CREATIVA Y RECREATIVA
Brown, Elipcer / Flores Asdribal. Editorial. Trillas, 1993 FUNDAMENTOS DE FSICA Bueche, F. Editorial Mc Graw Hill, 1988 FSICA FUNDAMENTAL Orear, J. Editorial Limusa-Willey, 1972 FSICA I Serway, R. A. Editorial Mc Graw Hill , 1996
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FSICA. FUNDAMENTOS Y FRONTERAS Stollberg R. / F.F. Hill Editorial Publicaciones Cultural S.A., 1967 FSICA I Vargas, C. A. / P. Carmona G. Editorial Secretaria de Educacin y Cultura, 1997 FSICA MODERNA VOL. 1 While Harvey E. Editorial Uteha, 1992 FSICA 1. PARTE Resnick Robert / Halliday David Editorial CECSA, 1990 FSICA GENERAL Cisneros Montes de Oca, Esparza. Editorial Valdez Estrada, 1993 FSICA, CONCEPTOS Y APLICACIONES Tippens, Paul E. Editorial Mc graw-hill, 2. Ed. QUMICA. Gregory R. Choppin. Editorial Publicaciones cultural S.A. 1974 QUMICA. T. Flores del & C. Garca de D.I. Editorial Publicaciones Cultural S.A. 1990 PROBLEM EXERCISES FOR GENERAL CHEMISTRY. G. Gilbert Long & Forrest C.Hents. Editorial Wiley, 1986 QUMICA LA CIENCIA CENTRAL. Brown. Editorial Interamericana. 1990. QUMICA. William S. Seense/G. William Daub. Editorial Hispanoamericana, 1989.
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## 8. RECOMENDACIONES PARA PRESENTAR LA PRUEBA
A continuacin, se te presenta una lista de tiles indicaciones que debers tomar en cuenta:
1.
Presntate el da del examen treinta minutos antes de la hora sealada, con el objeto de localizar el lugar donde sta se efectuar.
2.
Debes ser puntual, ya que no se permitir la entrada a ningn aspirante que llegue cuando ya haya comenzado el examen y por ningn motivo se le aplicar ste posteriormente.
3.
Lleva al examen lpices del nmero 2, goma suave, sacapuntas, calculadora, etc., ya que no se permitir el prstamo de ninguno de estos objetos.
4.
En caso de que algn reactivo te genere dificultades o no ests seguro de la respuesta, no te detengas, pasa al siguiente, evita invertir tiempo que te puede ser til para resolver otros reactivos.
Al contestar el examen administra el tiempo que tienes establecido para contestarlo, sin descuidar ninguna de las tres secciones. (matemticas, fsica y qumica).
En la seccin siguiente, se te presenta un examen de prctica, el cual es semejante a el examen de ingreso que presentars. Familiarzate con el en cuanto a su estructura y datos que se te piden y cuando te sientas preparado para ello. Se sugiere que utilices en promedio un minuto y medio para cada reactivo. Es importante que una vez terminado el examen de prctica, compares tus respuestas con las claves que se presentan al final.
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9. PRUEBA PRCTICA
PRESENTACIN
El material de este examen de prctica consta de 2 secciones, la primera es el cuadernillo de preguntas semejante al examen que presentars. La segunda seccin est conformada por la hoja de respuestas y la clave de respuestas correspondiente.
## Al contestar el examen respeta el tiempo y autoevala tus resultados.
Lo anterior, es con la finalidad de que te familiarices con los aspectos que incluye el examen de conocimientos, as como para que te ejercites en la forma de contestarlo.
Cabe mencionar, que adems de resolver los reactivos que aqu se te presentan, te ser de mucha utilidad que realices otros ejercicios parecidos a los de este examen de prctica. Si encuentras dificultades al resolver los problemas que se te plantean, no dudes en pedir apoyo a tus profesores y no te des por satisfecho hasta estar seguro de haber comprendido.
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## I. INSTRUCCIONES PARA EL LLENADO DE LA HOJA DE RESPUESTAS
DATOS DE IDENTIFICACIN
Antes de empezar a contestar estos exmenes, lee las siguientes indicaciones: 1. 2. 3. 4. NO MALTRATES LA HOJA DE RESPUESTAS El material consta de un cuadernillo de preguntas y la hoja de respuestas Utiliza lpiz del nmero 2 para contestar la prueba. Anota en la parte superior de la hoja de respuestas tu nombre completo: apellido paterno, apellido materno y nombre (s). Ubcate en la parte superior izquierda de tu hoja de respuestas, correspondiente a DATOS ADICIONALES, y procede a realizar el llenado de la siguiente forma: 5.1. En las dos primeras columnas, anota la clave y rellena los valos correspondientes a tu escuela de procedencia de acuerdo a la siguiente relacin:
Plantel Clave
5.
Colegio de bachilleres Preparatorias estatales Preparatorias particulares Centro de Bachillerato Tecnolgico Industrial y de Servicios (CBTIS) Centro de Estudios Tecnolgicos, Industrial y de Servicios (CETIS) Centro de Estudios Tecnolgicos del Mar (CETMAR) Centro de Estudios Tecnolgicos de Aguas Continentales (CETAC) Centro de Bachillerato Tecnolgico Agropecuario (CBTA) Centro de Bachillerato Tecnolgico Forestal (CBTF) Colegio de Ciencias y Humanidades Escuela Nacional Preparatoria Colegio de Estudios Cientficos y Tecnolgicos Estatales (CECyTE) Centro de Estudios Cientficos y Tecnolgicos (IPN) Centro de Enseanza Tcnica Industrial (CETI) de Guadalajara Colegio Nacional de Educacin Profesional Tcnica (CONALEP) Otros
01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16
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Ejemplo: supongamos que tu escuela de procedencia es de un Centro de Bachillerato Tecnolgico Industrial y de Servicios, t anotars la clave 04 en los recuadros y rellenars los valos 0 y 4 respectivamente, como se muestra a continuacin.
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9
0
0 1 2 3 4 5 6 7 8 9
5.2. En las siguientes dos columnas correspondientes a datos adicionales, anotars la clave de la entidad federativa donde concluiste tus estudios de bachillerato, de acuerdo a la relacin siguiente y proceders a realizar el procedimiento similar al citado en el punto anterior.
Aguascalientes Baja California Baja California Sur Campeche Coahuila Colima Chiapas Chihuahua Distrito Federal Durango Edo. de Mxico Guanajuato Guerrero Hidalgo Jalisco Michoacn Morelos
01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17
Nayarit Nuevo Len Oaxaca Puebla Quertaro Quintana Roo San Luis Potos Sinaloa Sonora Tabasco Tamaulipas Tlaxcala Veracruz Yucatn Zacatecas Extranjero
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
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5.3. En la siguiente columna, anotars la clave del ao en que concluiste tu bachillerato, de acuerdo a la siguiente relacin:
## Ao 2000 2001 2002
Clave 1 2 3
Ao 2003 2004
Clave 4 5
Ao 2005 Otro
Clave 6 7
5.4. En las siguientes dos columnas, anotars la clave de la carrera a la que deseas ingresar y rellenars los valos de acuerdo a la relacin citada a continuacin:
CARRERAS Lic. en Administracin. Lic. en Contadura. Ing. en Agronoma. Ing. en Pesqueras. Ing. Naval. Ing. Bioqumica. Ing. en Sistemas Computacionales. Lic. en Informtica. Ing. Mecnica. Ing. Elctrica. Ing. Electromecnica. Ing. Electrnica. Ing. en Geociencias. Ing. en Materiales. Ing. Qumica. Ing. Industrial. Arquitectura. Ing. Civil. Lic. en Biologa. Lic. Tcnica en Administracin General. Ing. Forestal. Ing. en Alimentos. Ing. en Industrias Alimenticias. Ing. Industrial en Instrumentacin y Control de Procesos Ing. Electrnica en Computacin Ing. Industrial en Mecnica Ing. Tcnica en Sistemas Computacionales. Ing. Tcnica en Electrnica. Ing. Tcnica Industrial. Ing. Tcnica Civil. Tcnico Superior en Buceo Industrial. Tcnico Superior en Buceo Deportivo. Ing. Ambiental. Ing. en Desarrollo Comunitario. Ing. en Mecatrnica. Ing. Tcnico Minero. Otra CLAVE 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
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5.5. En la siguiente columna, anotars la clave de tu sexo y rellenars los valos correspondientes de acuerdo a la relacin siguiente:
Sexo Clave 1 2
Masculino Femenino
## Con esto se concluye el llenado de Datos Adicionales y proceders con lo siguiente:
6.
Anotars tu nmero de folio o ficha en los recuadros y rellenars los valos correspondientes. RECUERDA QUE ESTE NUMERO DE FOLIO, DEBER SER EL MISMO QUE INDIQUES EN TU HOJA DE RESPUESTAS DE LA PRUEBA DE HABILIDADES VERBAL Y MATEMTICA, YA QUE DE NO SEGUIR ESTAS INDICACIONES SE PERDERN LOS RESULTADOS DE TU EXAMEN
7.
Enseguida, rellenars el valo que corresponda al tipo de plantel en el que ests realizando tu examen.
8.
Deja en blanco el rea correspondiente a nmero de plantel y procede a anotar tu edad (en aos cumplidos) y rellena los valos correspondientes. Inmediatamente, procede a anotar el promedio que obtuviste en el bachillerato (en nmeros enteros, redondea de .5 hacia el entero mayor, por ejemplo, 7.5 a 8 y de 7.4 a 7).
9.
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## II. INSTRUCCIONES PARA CONTESTAR EL EXAMEN
Antes de empezar a contestar este examen, lee con cuidado las siguientes indicaciones: 1. Este cuadernillo te servir nicamente para leer las preguntas correspondientes al Examen de Conocimientos del rea de Ingeniera, que contempla las disciplinas de matemticas, fsica y qumica, por lo que se te solicita que no hagas anotaciones ni marcas en l. Las preguntas contienen cinco posibles respuestas, indicadas con las letras A, B, C, D y E, siendo NICAMENTE UNA DE ELLAS LA RESPUESTA CORRECTA. Tu respuesta la debers registrar en la HOJA DE RESPUESTAS que contiene una serie progresiva de nmeros. Cada nmero corresponde al nmero de cada pregunta del cuadernillo. Asegrate de que el nmero de pregunta y de respuesta coincidan. Para contestar debers leer cuidadosamente cada pregunta y elegir la respuesta que consideres correcta. Al contestar cada pregunta, debers rellenar SOLAMENTE UNO DE LOS VALOS, ya que el no marcar o marcar ms de uno invalida tu respuesta. No marques hasta que ests seguro de tu respuesta.
2.
3.
4.
5.
6.
NO CONTESTES LAS PREGUNTAS AL AZAR, ya que las respuestas incorrectas afectarn tu puntuacin. Si no sabes cul es la respuesta correcta a alguna pregunta, es preferible que no la marques en la hoja de respuestas.
7.
Si deseas cambiar de respuesta, puedes hacerlo pero asegurndote de borrar completamente la marca que deseas cancelar. Sin maltratar la hoja de respuestas. Al final del examen de qumica, se anexa una informacin adicional y una tabla peridica de los elementos, que puede ser de utilidad para resolver algunos de los reactivos correspondientes a esta disciplina.
8.
9.
No se podr consultar ninguna informacin para resolver el examen, nicamente se permite el uso de calculadora.
10. El tiempo lmite para la resolucin del examen es de 2 horas con 30 min.
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EJEMPLO
## 24. Un enegono es un polgono formado por:
A) B) C) D) E)
En este caso, la opcin correcta es la A); por lo tanto, DEBERS LOCALIZAR en la HOJA DE RESPUESTAS EL NUMERO QUE CORRESPONDA a la pregunta que leste y, con t lpiz, DEBERS RELLENAR COMPLETAMENTE el valo correspondiente a la letra de la opcin que hayas elegido como correcta.
## 23. A 24. A 25. A
B B B
C C C
D D D
E E E
PUEDES COMENZAR!
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EXAMEN DE MATEMTICAS
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1.
Al obtener el producto de (a + 3) (a2 + 9) (a 3) resulta ser: A) B) C) D) E) (a 3)4 (a + 3)2 (a + 9)2 a4 81 (a 3)2 (a + 9)2 a4 + 81
2.
3.
## 1 x 1 ; su mnima expresin es: Al simplificar el cociente 1 1+ 2 x 1 1+ A) B) C) D) E)
x x +1 x+1 x +1 x 2 x x x 1
4.
Un hacendado compr 4 vacas y 7 caballos por \$514 y mas tarde, a los mismos precios, compr 8 vacas y 9 caballos por \$818. Hallar el costo de una vaca y de un caballo. A) B) C) D) E) v = 45, c = 52 v = 52, c = 45 v = 42, c = 55 v = 55, c = 42 v = 52, c = 45
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5.
## Al completar cuadros en la ecuacin cuadrtica 4x 2 - 6x + A) B) C) D) E) (x - 3/2)2 =0 (x + 3/2)2 =0 (x + 2/3)2 =0 (x - 4/3)2 =0 (x - 3/4)2 =0
9 = 0 se reduce a: 4
6.
3 es: 2
A)
B)
-3
-3
C)
D)
-3
-3
## E) Ninguna de las anteriores
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7.
Tomando como referencia las identidades trigonomtricas csc2x cot2x = 1. El valor de la expresin: 3sec2x + 5csc2x 3tan2x 5cot2x , es: 2 2 0 8 -8
sec2x tan2x = 1 y
A) B) C) D) E)
8.
## En la siguiente figura, cul de las rectas es tangente al crculo?
Y F
A) B) C) D) E)
OK JK
OF WV XY
W
O V
9.
Tomando como referencia la identidad trigonomtrica, figura del tringulo rectngulo; el valor del sen2 es: A) B) C) D) E)
## sen2 = 2 sen cos y la
12 25 24 25 25 24 25 12 12 24
135
10 8
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10. Con base en la siguiente figura, la ley de los cosenos afirma que: a2 = b2 + c2 2bc cos a = b + c 2bc cos
2 2 2
A) B) C) D) E)
c a
## a2 = b2 + c2 2bc cos a2 = b2 + c2 2ab cos a2 = b2 + c2 2ac cos
b
11. En la figura formada por las rectas AD, BE y CF , calcular la suma de los ngulos y considerando que = 25 y = 30. + = 115
A
A) B) C) D) E)
B C
## 12. Calcule la longitud del lado a y los ngulos y del tringulo:
A c = 25 40 b = 15 C a B
A) B) C) D) E)
37.70, 14.80, 125.19 25.57, 23.6, 116.40 16.60, 35.50, 104.50 14.32, 20.10, 119.90 12.43, 27.90, 112.10 136
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13. En cuanto excede el rea sombreada de la figura A del rea sombreada de la figura B?
A) B) C) D) E)
3 2 2 3 2 4 2 4 1
Figura A
Figura B
4x
6x + 15
A) B) C) D) E)
## 250 m 230 m 210 m 190 m 170 m
15. Dados los puntos A(2, 1) y B(5, 1), cules son las coordenadas de un punto C, de modo que se forme un tringulo equiltero en el primer cuadrante? A) B) C) D) E) (-3.5, 3.6) (-3.5, 3.6) (3.6, 3.5) (3.6, -3.5) (3.5, 3.6)
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16. Cul ser la ecuacin de la recta, cuya abcisa al origen es 3 y la ordenada al origen es igual a 5 ? A) B) C) D) E) 8x 5y 15 = 0 3x + 8y + 8 = 0 5x + 3y 15 = 0 5x 3y + 15 = 0 3x 5y 15 = 0
17. Las coordenadas del centro de la circunferencia (x 3) 2 +(y+7) 2 25=0; son: A) B) C) D) E) (7, 3) (7, 3) (3, 7) (3, 7) (3, 7)
18. Cuando la parbola con vrtice en el origen se abre hacia el lado positivo de las x, las coordenadas del foco son: A) B) C) D) E) (0, p) (p, 0) (0,0) (p, 0) (0, p)
19. Dada la elipse cuyos focos son los puntos (3, 0), (-3,0) y sabiendo que la longitud de uno cualquiera de sus lados rectos es igual a 9. Hallar la ecuacin de la elipse. A) B) C) D) E) x2 y2 + 36 25 x2 y2 + 36 27 x2 y2 27 36 x2 y2 + 27 36 x2 y2 36 25 =1 =1 =1 =1 =1
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20. Hallar la ecuacin de la hiprbola cuyos vrtices son lo puntos V(2, 0) y V(-2, 0) y los focos son los puntos F(3, 0), F(-3, 0). A) B) C) D) E) x2 4 x2 5 x2 5 x2 4 y2 4 y2 5 y2 + 4 y2 4 y2 5 x2 5 + =1 =1 =1 =1 =1
21. Determinar la solucin de la siguiente desigualdad: x2 3x x2 +6x 2. A) B) C) D) E) (-, 2/9] [2/9, ) (2/9, ) (-, -2/9) [-2/9, )
22. Encontrar el conjunto solucin de 10 x 3 : A) B) C) D) E) (-, 7), (7, ) (-, -7), [7, ) [-3, -7), (7, , [-3, 3], [7, ] (-, -3], [7, )
23. La ecuacin de la circunferencia con centro en el origen y radio 6 es: A) B) C) D) E) x2 + y2 = 6 x2 +y2 + 36 = 0 (x2 + y2) = 6 x2 + y2 36 = 0 x2 + y2 + 6 = 0
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24. Cul es la relacin considerada como implcita? A) B) C) D) E) f(x) = sen 6x cos x + 7 x2 y2 + 2xy 8x 4y 9 = 0 ex 22x 33 = y x y = log 2x2 + x 5 2 y = arc tan x3 5x2 + 1
25. Dadas las funciones f(x) = 3x 2 +3 y g(x)=x+1; la evaluacin de f [ g(x) ] es: A) B) C) D) E) f [ g(x) ] = 6x2 + 3x 6 f [ g(x) ] = 3x2 + 6x + 6 f [ g(x) ] = 3x2 6x +6 f [ g(x) ] = 6x2 3x 6 f [ g(x) ] = 3x2 + 6x 6 (1 + x)2 1 , es: x
## 26. El resultado de Lim
x 0
A) B) C) D) E)
2 0 1 2
27. Determinar los intervalos donde la funcin f(x) = x3 +6x2 15x +8 es continua. A) B) C) D) E) (-, 1), (1, 5) (5, ) (-, -1), (-1, 5) (5, ) (-, -5), (-5, 1) (1, ) (-, -5), (-5, -1) (-1, ) (-, -5), (-5, 5) (5, )
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## 29. La derivada de y = Ln(x2 + 3) es: A) B) C) D) E) x x +3 2x 2 x +3 x2 x2 + 3 2x 2 x +3 x 2 x +3
2
30. La segunda derivada de y = exsenx es: A) B) C) D) E) -2excosx 2excosx 2e-xcosx 2excosx -2e-xcosx
31. Encontrar la ecuacin de la recta tangente a la curva y = 5x2 +12x 3 y que pasa por el punto (-1, 3) A) B) C) D) E) y = 2x +5 y = 5 2x y=x-5 y = 2x - 5 y=5-x
32. La abcisa del punto mnimo de la funcin f(x) = x2 + 6x; es: A) B) C) D) E) x=6 x=3 x=0 x = 3 x = 6
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## 33. El resultado de la integral 2 (8 + x ) 2 +C 3
1
8 + x dx es:
A) B) C) D) E)
3 (8 + x ) 2 +C 2
1
3 (8 + x ) 2 +C 2
3
2 (8 + x )3 +C 3
2
2 (8 + x ) 2 +C 3
3
## 34. El resultado de la integral definida A) B) C) D) E) 0 2 3 4 16
x3 dx ; es:
FINAL DE MATEMTICAS !
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EXAMEN DE FSICA
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35. Es una unidad comn tanto en el Sistema Internacional como en el Sistema Ingles A) B) C) D) E) La unidad de longitud La unidad de peso La unidad de masa La unidad de tiempo La unidad de velocidad
36. Cuntos kgf son 2000 N? A) B) C) D) E) 0.0049 0.49 20.4 204 19600
37. Las figuras A y B, representan grficamente la posicin del punto P. Cul de las opciones corresponde al nombre que se le da a las coordenadas?
N N
O r p S
p S A
A) B) C) D) E)
A: Cartesianas, B: Vectoriales A: Vectoriales, B: Polares A: Cartesianas, B: Cartesianas A: Cartesianas, B: Polares A: Polares, B: Cartesianas
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38. Sobre un piso sin rozamiento, un hombre jala un paquete con una fuerza de 60 N, que forma un ngulo de 30 con la horizontal. Cul es la fuerza que el hombre ejerce sobre el paquete, si ste se acelera 3 m/s2? A) B) C) D) E) 60 / cos 30 N 6.66 cos 30 N 60 / sen 30 N 6.66 sen 30 N 60 cos 30 N
v ((m/s)
d (m)
d2(m2)
t (s)
t (s)
t (s)
A)
B)
C)
a
2
v (m/s)
t (s)
t2(s2)
D)
E)
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## 40. Apoyndote en la siguiente grfica, calcula la aceleracin en el instante t=4s.
v (cm/s)
A) B) C) D) E)
8.0 cm/s2 2.0 cm/s2 4.0 cm/s2 6.0 cm/s2 0.0 cm/s2
1 2 3 4 5 6 7 5 4 3 2 1 t (s)
41. A partir de cierto instante un perro que corre a una velocidad constante de 10m/s persigue a una liebre que corre a una velocidad de 5 m/s, tambin constante. Si la liebre a ventaja al perro en 1m, cunto debe correr este ltimo para alcanzar a la liebre? A) B) C) D) E) 1m 2m 3m 4m 5m
42. Un automvil deportivo alcanza una velocidad de 0 a 100 km/h en 4s.Cul es su aceleracin? A) B) C) D) E) 3.27m/s2 6.94m/s2 7.18m/s2 9.42m/s2 10.15m/s2
43. Con qu velocidad llega al agua un clavadista que se lanza desde la plataforma de 10 m cuando parte del reposo? A) B) C) D) E) 10m/s 11m/s 12m/s 13m/s 14m/s
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44. Desde un helicptero que se encuentra esttico en el aire se lanza hacia abajo un proyectil con una velocidad de 1m/s. Si este tarda en llegar al suelo 3s. A qu altura se encuentra el helicptero? A) B) C) D) E) 32.177m 47.145m 51.271m 55.926m 57.062m
45. Cul es la componente vertical de la velocidad de un proyectil que viaja a 10m/s y un ngulo de 30 con la horizontal? A) B) C) D) E) 5m/s 6m/s 7m/s 8m/s 9m/s
46. Desde lo alto de un acantilado cuya altura es de 70 m, se dispara horizontalmente un proyectil con una velocidad de 50 m/s. A qu distancia x, horizontal, llegar el proyectil? A) B) C) D) E) 120m 189m 490m 686m 3500m
47. Cul es la velocidad lineal de una partcula que se encuentra en una centrfuga que gira a 2000 rpm y que tiene un radio de giro de 10cm? A) B) C) D) E) 15.123m/s 18.365m/s 19.642m/s 20.944m/s 22.643m/s
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48. Supn que se da un empujn a un paquete que se encuentra colocado sobre el piso. Sin considerar la friccin, cul de las siguientes afirmaciones sobre el paquete es cierta? A) B) C) D) E) Volver al reposo paulatinamente Contina movindose indefinidamente Experimenta una fuerza de accin y una de reaccin Experimenta una fuerza de reaccin Contina movindose por un lapso de tiempo
49. Un cuerpo permanece en reposo o en movimiento rectilneo uniforme, a menos que sobre el acte una fuerza externa que cambie su estado de movimiento. Este enunciado corresponde a? A) B) C) D) E) 1a Ley de Newton 2a Ley de Newton 1 Ley de la termodinmica La conservacin de la energa La conservacin del movimiento
50. Calcula la aceleracin de un auto de 1 Ton, si se aplica una fuerza de 8000N. A) B) C) D) E) 0.125 m/s2 8 m/s2 80 m/s2 8000 m/s2 8000000 m/s2
51. Un cuerpo de masa m, se desliza sin friccin horizontalmente, si se aplica una fuerza de 15Newton se acelera a razn de 1.5 m/s2. Si aumentamos la masa al triple aplicando la misma fuerza, cul es su aceleracin? A) B) C) D) E) 0.05 m/s2 0.5 m/s2 5.0 m/s2 50 m/s2 500 m/s2
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52. Suponiendo que el tamao de la flecha es proporcional a la fuerza que representa, cul es el diagrama de fuerzas correcto segn la tercera ley de Newton?
A)
B)
C)
D)
E)
53. Desde un helicptero que vuela a velocidad v y altura h se suelta un paquete de vveres de peso w, como se muestra en la figura, si se desprecia el rozamiento, la velocidad con la que viaja el paquete al llegar a la aldea est dado por:
A) B) C) D) E)
## 2gh 2ghcos 2gh cos 2ghw cos h/v
54. Desde una altura de 80m se lanza hacia abajo un objeto con una velocidad de 3m/s. Qu velocidad tendr el objeto cuando llegue a la altura de 30m? A) B) C) D) E) 5.11 m/s 16.67 m/s 31.46m/s 78.48m/s 150.25m/s
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55. Si comparamos la energa cintica con la energa potencial entre los puntos A y B de la rueda de carreta que se muestra en la figura, cul de las siguientes opciones es correcta?
A
A) B) C) D) E)
ECA > ECB ECA = EPB EPA > EPB EPA < EPB ECA < ECB
B
56. Un hombre empuja una pulidora de pisos con una fuerza de 5 kgf, si el mango de la pulidora forma un ngulo de 50 con el piso, cul es el trabajo efectuado despus de mover el aparato 10 m? A) B) C) D) E) 5 cos 50 J 50 sen 50 J 50 J 50 cos 50 J 10 sen 50 J
57. Qu potencia se requiere para efectuar un trabajo de 300 J en 3s? A) B) C) D) E) 50 W 100 W 150 W 200 W 250 W
58. Una gra eleva una masa de 500kg a 50m en 5 minutos, cul es la potencia de su motor? A) B) C) D) E) 1 hp 2 hp 3 hp 4 hp 5 hp
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59. Desde un globo aerosttico que se encuentra esttico se lanza un proyectil de 10kg a una velocidad de 10m/s hacia arriba. Si el globo tiene una masa de 90kg. Cul es la velocidad final de este ltimo? A) B) C) D) E) 0.57m/s hacia abajo 1.11m/s hacia abajo 2.03m/s hacia abajo 2.56m/s hacia abajo 3.15m/s hacia abajo
60. Para un condensador de placas paralelas de rea A y separadas una distancia d, la capacitancia es: A) B) C) D) E) inversamente proporcional a d directamente proporcional a d inversamente proporcional a d2 directamente proporcional a d2 no depende del parmetro d
61. Un condensador de placas paralelas tiene una capacitancia 3mf, si la separacin de placas es de 1mm. Cul es el rea de las placas? A) B) C) D) E) 3.39 x 10-5m2 3.39 x 10-4m2 3.39 x 10-3m2 3.39 x 10-2m2 3.39 x 10-1m2
62. El campo elctrico en funcin de la carga Q y la distancia r, E(Q,r), cumple qu es: A) B) C) D) E) directamente proporcional a r inversamente proporcional a r directamente proporcional a r2 inversamente proporcional a r2 no depende del parmetro r
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63. Para una carga Q=7 x 10-6 coul y a una distancia de 15cm, el campo elctrico es: A) B) C) D) E) 2.8 x 10-6 N/C 2.8 x 10-3 N/C 2.8 x 100 N/C 2.8 x 103 N/C 2.8 x 106 N/C
64. Si en cierto lugar el campo elctrico es cero, entonces en ese lugar el potencial es: A) B) C) D) E) cero variable positivo negativo constante
65. A la distancia de 30cm de una carga Q, el campo elctrico es de 2 v/m, a la distancia de 70cm. Qu valor tiene el campo elctrico? A) B) C) D) E) 0.86 v/m 1.25 v/m 2.53 v/m 3.67 v/m 4.67 v/m
## 66. La corriente elctrica que circula por el siguiente circuito es: A) B) C) D) E)
R1 + R 2 V V V I= + R1 R 2 R I= 1 V R2 V I= R1 + R 2 R I= 2 V R1 I=
i + V -
R1 R2
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67. Por un conductor circula una corriente de 2 Amperes por segundo. Cuntos electrones cruzan por segundo, cierta rea transversal del conductor? A) B) C) D) E) 5.12 x 1010 6.31 x 1013 2.31 x 1015 3.12 x 1018 1.25 x 1019
68. En un conductor circulan 3 x 1010 electrones por segundo, qu corriente conduce el conductor ? A) B) C) D) E) 1.5 x 10 6 A 4.8 x 10-9 A 3.2 x 10-10 A 5.1 x 10-12 A 6.6 x 10-15 A
FINAL DE FSICA !
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EXAMEN DE QUMICA
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69. El volumen de un mm de agua equivale a: A) B) C) D) E) 100 mm. 2.54 in3. 1 cm3 0.01 m 0.1 cm3
70. Una gota de agua contiene 165,000,000,000 molculas de agua. Cul de las siguientes expresiones equivale al dato anterior? A) B) C) D) E) 0.165 x 1011 16.5 x 109 1.65 x 1011 165 x 1010 1.65x1010
71. El punto de congelacin del agua es 0O C. A cunto equivale esta temperatura en O F? A) 0.1 F B) 1.8 F C) 32 F D) 212 F E) 32 F 72. Clase de materia en la que todos sus tomos presentes tienen cargas cuantitativamente idnticas en sus ncleos e igual configuracin elctrica, que no puede descomponerse en substancias ms sencillas por medio de mtodos qumicos ordinarios. A) B) C) D) E) Sustancia Elemento Mezcla Solucin Compuesto
73. En cul de las siguientes sustancias el agua se presenta con la menor densidad? A) B) C) D) E) Agua desmineralizada Agua de mar Vapor de agua Hielo Agua de lluvia
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74. Cul es la densidad del metal con el que se fabric una moneda si 10 de ellas pesan 31.7 g, considerando que cada moneda ocupa un volumen de 0.35 ml? A) B) C) D) E) 9.06 g/ml 8.95 g/ml 5.28 g/ml 1.11 g/ml 0.11 g/ml
75. Cul de las siguientes sustancias es un compuesto qumico? A) B) C) D) E) Diamante Grafito Bronce Vinagre Cobre
76. Cul de las siguientes sustancias es un elemento? A) B) C) D) E) Aire Agua Madera Hierro Sal
## 77. Es la cantidad de energa contenida en un cuerpo. A) B) C) D) E) Temperatura Calor C F K
78. Dentro de la tabla peridica, cul ser el elemento que se encuentra en el 4to. periodo y en el grupo de los gases nobles? A) B) C) D) E) Se (selenio) Kr (kriptn) I (iodo) Ar (argn) K (potasio)
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79. La configuracin electrnica para el tomo de vanadio es: A) B) C) D) E) [Ar] 4s2, 4d3 [Ar ] 4s2, 4p3 [Ar ] 4s2, 3d3 [Ar ] 3d5 [Ar ] 3d6
80. Cules valencias son las ms comunes en la familia (grupo) IVA de la tabla peridica? A) B) C) D) E) +2, 4 2, 4 +2, +4 +1, +4 +3, +4
81. De los siguientes tomos, cul es el que tiene el mayor radio atmico? A) B) C) D) E) Be Mg Ca Ba Sr
82. Un elemento X tiene en su nivel de valencia la configuracin 3s2,3p1. A qu familia y a qu periodo pertenece? A) B) C) D) E) IA, periodo 3 IIIA, periodo 3 IIA, periodo 4 IIIB, periodo 4 IVA, periodo 3
83. Partcula subatmica que participa en la formacin de los enlaces qumicos. A) B) C) D) E) Mesn Neutrn Protn Fotn Electrn
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84. A cuntas umas corresponde el peso (masa) atmica del cloro? A) B) C) D) E) 17 14 34 35.5 1
## 85. Qu nmero cuntico determina el campo magntico? A) B) C) D) E) s m n l p
86. Cules seran los valores que tomara el nmero cuntico secundario para el Nen, que tiene el nmero atmico de 10? A) B) C) D) E) 0, 1 1, 2 2, 3 3, 4 4, 5
87. Se forma cuando dos tomos que se unen comparten un par de electrones para formar el enlace, en este caso el par de electrones compartido lo proporciona uno de los tomos. A) B) C) D) E) Fuerzas de Van der Waals Puentes de hidrgeno Covalente coordinado Covalente Inico
88. Si el elemento radio se desintegra perdiendo 2 protones, qu elemento nuevo se formar? A) B) C) D) E) Plomo Francio Radn Actinio Astatino 158
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89. Cul es el nombre de los siguientes compuestos qumicos cuyas frmulas son: SiF4, CO2, NH3? A) B) C) D) E) Tetrafluoruro de silicio, carbonato, amoniaco Fluoruro de silicio, dixido de carbono, amoniaco Tetrafluoruro de sodio, dixido de crbono, hidruro de nitrgeno Tetrafluoruro de silicio, dixido de carbono, amoniaco Ninguno de los anteriores
90. Cul es la frmula del compuesto inico sulfuro de cobalto (III)? A) B) C) D) E) Co2HS Co2S3 Co2(SO4)3 CoH2SO4 Ninguno de los anteriores
91. Cul de los siguientes compuestos est formado por un enlace inico? A) B) C) D) E) HF NH3 CH4 NaCl H2O
92. Selecciona el nombre del siguiente compuesto: Na2CO3 A) B) C) D) E) Carbonato cido de sodio Carbonito de sodio Carburo de sodio Bicarbonato de sodio Carbonato de sodio
93. En la siguiente reaccin, identifica el (los) cidos existentes. HClO4 + NH3 A) B) C) D) E) NH3 HClO4 HClO4, NH3 HClO4, NH4ClO4 NH4ClO4 NH4ClO4
FGC-SUBEV-38
159
94. Identifica los nombres de los siguientes compuestos qumicos: NH4OH, Ba(OH)2, Zn(OH)2 A) B) C) D) E) Hidrxido de amonio, hidrxido de bario, oxido de zinc Nitruro de amonio, hidrxido de bario, hidrxido de zinc Hidrxido de amonio, xido de bario, hidrxido de zinc Hidrxido de amonio, hidrxido de bario, hidrxido de zinc Hidrxido de amonio, xido de bario, xido de zinc , los
95. Al Balancear la siguiente reaccin: ___KClO3 ___KCl + __O2 coeficientes del reactivo y productos son respectivamente: A) B) C) D) E) 2, 1, 3 2, 2, 1 2, 2, 3 1, 1, 2 2, 1, 1
96. Cul es la masa molecular del compuesto cuya frmula es Na2CO3? A) B) C) D) E) 79 80 113 139 106
## 97. A cuntos gramos equivalen 2 moles de Na2CO3? A) B) C) D) E) 106 g 53 g 212 g 71 g 66 g
98. Cul es la molaridad de una solucin que contiene 20 g de NaOH en un litro de solucin? A) B) C) D) E) 1M 0.75 M 0.5 M 0.25 0.1 M
## FINAL DEL EXAMEN !
FGC-SUBEV-38
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INFORMACIN ADICIONAL QUE TE PUEDE SER DE UTILIDAD, PARA RESOLVER ALGUNOS REACTIVOS DE QUMICA
## Equivalencias necesarias para resolver los problemas
1 galn = 3.785 L 1 pulgada = 2.54 cm 1 cm = 10 mm 1 km = 1000 m 1 m = 100 cm 1 milla=1609 m 1 mol=6.022x10-23 partculas 1 calora=4.184 joules 1 pm (picmetro) = 10-12 m 1 1b = 454 g C (o F 32) = 100 180
o
n=
g PM
## C = K - 273 1nm (nanmetro) = 10-9 m Velocidad de la luz (C) = 3x108m/s
masa volumen
FGC-SUBEV-38
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TABLA PERIDICA
IA 1 H 1.00794 IIA 3 Li 6.941 4 Be 9.01218 IIIA 5 B 10.81 IVA 6 C 12.011 VA 7 N 14.0067 VIA 8 O 15.9994 VIIIA 9 F 18.998403 10 Ne 20.179 O 2 He 4.00260
11 Na 22.9897 7
VIIIB IB IIB
13 Al 26.9815 4
14 Si 28.0855
15 P 30.9737 6
16 S 32.06
17 Cl 35.453
18 Ar 39.948
19 K 39.0983
20 Ca 40.08
21 Sc 44.9559
22 Ti 47.88
23 V 50.9415
24 Cr 51.996
25 Mn 54.9380
26 Fe 55.847
27 Co 58.9332
28 Ni 58.69
29 Cu 63.546
30 Zn 65.38
31 Ga 69.72
32 Ge 72.59
33 As 74.9216
34 Se 78.96
35 Br 79.904
36 Kr 83.80
37 Rb 85.4678
38 Sr 87.62
39 Y 88.9059
40 Zr 91.22
41 Nb 92.9064
42 Mo 95.94
43 Tc (98)
44 Ru 101.07
45 Rh 102.905 5
46 Pd 106.42
47 Ag 107.868 2
48 Cd 112.41
49 In 114.82
50 Sn 118.69
51 Sb 121.75
52 Te 127.60
53 I 126.9045
54 Xe 131.29
55 Cs 132.905 4
56 Ba 137.33
57 *La 138.905 5
72 Hf 178.49
73 Ta 180.947 9
74 W 183.85
75 Re 186.207
76 Os 190.2
77 Ir 192.22
78 Pt 195.08
79 Au 196.966 5
80 Hg 200.59
81 Tl 204.383
82 Pb 207.2
83 Bi 208.980 4
84 Po (209)
85 At (210)
86 Rn (222)
87 Fr (223)
88 Ra 226.025 4
89 Ac 227.027 8
58 Ce 140.12
59 Pr 140.907 7
60 Nd 144.24
61 Pm (145)
62 Sm 150.36
63 Eu 151.96
64 Gd 157.25
65 Tb 158.925 4
66 Dy 162.50
67 Ho 164.930 4
68 Er 167.26
69 Tm 168.934 2
70 Yb 173.04
71 Lu 174.967
90 Th 232.038 1
91 Pa 231.035 9
92 U 238.028 9
93 Np 237.048 2
94 Pu (244)
95 Am (243)
96 Cm (247)
97 Bk (247)
98 Cf (251)
99 Es (252)
100 Fm (257)
101 Md (258)
102 No (259)
103 Lr (260)
## 10 CLAVE DE RESPUESTAS DE LA PRUEBA PRCTICA RESPUESTAS DE MATEMTICAS
REACTIVO RESPUESTA REACTIVO RESPUESTA REACTIVO RESPUESTA
1 2 3 4 5 6 7 8 9 10 11 12
C C C D E B D E B C C C
13 14 15 16 17 18 19 20 21 22 23 24
C A E C E D B D A B D B
25 26 27 28 29 30 31 32 33 34
B D C B D D A D E D
RESPUESTAS DE FSICA
REACTIVO RESPUESTA REACTIVO RESPUESTA REACTIVO RESPUESTA
35 36 37 38 39 40 41 42 43 44 45 46
D D D E A E B B E B A B
47 48 49 50 51 52 53 54 55 56 57 58
D B A B B B A C C D B A
59 60 61 62 63 64 65 66 67 69
B A E D E A A D E B
RESPUESTAS DE QUMICA
REACTIVO RESPUESTA REACTIVO RESPUESTA REACTIVO RESPUESTA
69 70 71 72 73 74 75 76 77 78
C C C B C A D D B B
79 80 81 82 83 84 85 86 87 88
C C D B E D B A C C
89 90 91 92 93 94 95 96 97 98
D B D E B D C E C C
FGC-SUBEV-38
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## SECRETARIA DE EDUCACIN PBLICA SUBSECRETARIA DE EDUCACIN E INVESTIGACIN TECNOLGICAS
NOMBRE DEL ASPIRANTE APELLIDO PATERNO APELLIDO MATERNO NOMBRE(S)
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9
No. DE FOLIO
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9
TIPO DE PLANTEL NIVEL SUPERIOR ITA ITF IT ITMAR ITS OTROS ESPECIFIQUE 1 2 3 4 5 6
No. DE PLANTEL
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
PROM. BACH.
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9
EXAMEN DE CONOCIMIENTOS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 A A A A A A A A A A A A A A A A A A A A A A A A A B B B B B B B B B B B B B B B B B B B B B B B B B C C C C C C C C C C C C C C C C C C C C C C C C C D D D D D D D D D D D D D D D D D D D D D D D D D E E E E E E E E E E E E E E E E E E E E E E E E E 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 A A A A A A A A A A A A A A A A A A A A A A A A A B B B B B B B B B B B B B B B B B B B B B B B B B C C C C C C C C C C C C C C C C C C C C C C C C C D D D D D D D D D D D D D D D D D D D D D D D D D E E E E E E E E E E E E E E E E E E E E E E E E E 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 A A A A A A A A A A A A A A A A A A A A A A A A A B B B B B B B B B B B B B B B B B B B B B B B B B C C C C C C C C C C C C C C C C C C C C C C C C C D D D D D D D D D D D D D D D D D D D D D D D D D E E E E E E E E E E E E E E E E E E E E E E E E E 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 A A A A A A A A A A A A A A A A A A A A A A A A A B B B B B B B B B B B B B B B B B B B B B B B B B C C C C C C C C C C C C C C C C C C C C C C C C C D D D D D D D D D D D D D D D D D D D D D D D D D E E E E E E E E E E E E E E E E E E E E E E E E E
## PERSONAL QUE PARTICIP EN LA ELABORACIN DE LA PRESENTE GUA
COORDINACIN
ACT. GOTARDO VILLALOBOS SNCHEZ CONSEJO DEL SISTEMA NACIONAL DE EDUCACIN TECNOLGICA
ELABORACIN DE EJERCICIOS
Q.F.B. REN BARRIOS VARGAS M.C. MA. MAGDALENA CAZARES QUINTERO ING. JESS ERNESTO GURROLA PEA M.C. JORGE REFUGIO REYNA DE LA ROSA INSTITUTO TECNOLGICO DEL MAR DE MAZATLN
## ING. GINO ROBERTO LONGONI LANZARINI INSTITUTO TECNOLGICO DE PACHUCA
ARQ. PORFIRIO PALMEROS ALARCN M.C. ALEJANDRO REBOLLEDO VLEZ INSTITUTO TECNOLGICO AGROPECUARIO No. 18 DE VILLA RSULO GALVN
FGC-SUBEV-38
## PERSONAL QUE PARTICIP EN LA REVISIN DE LA GUA
ING. IGNACIO JUREZ RUELAS INSTITUTO TECNOLGICO DE CULIACN ING. NICOLAS ORTEGA MIRANDA INSTITUTO TECNOLGICO SUPERIOR DE IRAPUATO FS. MOISS HERNNDEZ OLVERA INSTITUTO TECNOLGICO SUPERIOR DE LIBRES ING. JORGE ALBERTO PARRA MAYORQUN INSTITUTO TECNOLGICO DE TEPIC M. en C. HORTENSIA MARTNEZ RODRGUEZ CENTRO DE ESTUDIOS TECNOLGICOS INDUSTRIALES Y DE SERVICIOS No. 9
DR. MIGUEL ANGEL FRANCO NAVA INSTITUTO TECNOLGICO DEL MAR DE MAZATLN
FGC-SUBEV-38 | 30,013 | 74,700 | {"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} | 4.09375 | 4 | CC-MAIN-2023-23 | latest | en | 0.223453 |
https://www.sawaal.com/series-questions-and-answers/find-the-wrong-number-in-the-series--7-28-63-124-215-342-511_7320 | 1,537,682,773,000,000,000 | text/html | crawl-data/CC-MAIN-2018-39/segments/1537267159160.59/warc/CC-MAIN-20180923055928-20180923080328-00195.warc.gz | 857,144,046 | 14,901 | 41
Q:
# Find the wrong number in the series7, 28, 63, 124, 215, 342, 511
A) 28 B) 124 C) 215 D) 342
Explanation:
Here the number follows the given rule
But 28 has been given in problem series.
so 28 is wrong number.
Q:
The missing number in the series 9 81 ? 6561 59049
A) 729 B) 3561 C) 4213 D) None of the above
Explanation:
The given series is 9 81 ? 6561 59049
It follows a pattern that
9
81 = 9 x 9
729 = 9 x 9 x 9
6561 = 9 x 9 x 9 x 9
59049 = 9 x 9 x 9 x 9 x 9
Hence, the missing number in the series is 729.
1 59
Q:
Find the next number in the given number series?
6, 6, 12, 36, 144, 720, ?
A) 4320 B) 3547 C) 2154 D) 1765
Explanation:
The given series is 6, 6, 12, 36, 144, 720, ?
6
6 x 1 = 6
6 x 2 = 12
12 x 3 = 36
36 x 4 = 144
144 x 5 = 720
720 x 6 = 4320
Hence, the next number in the given number series is 4320.
2 98
Q:
Find the next number in the given number sequence?
4, 15, 37, 81, ?
A) 196 B) 169 C) 144 D) 121
Explanation:
The given number series follows a pattern that, 4, 15, 37, 81, ?
4
4 + 11 = 15
15 + 22 = 37
37 + 44 = 81
81 + 88 = 169
Hence, the next number in the sequence is 169.
3 257
Q:
Find the next number in the series
404, 415, 402, 413, 400, ?
A) 411 B) 421 C) 417 D) 414
Explanation:
The given series 404, 415, 402, 413, 400, ? follows a pattern that,
404
404 + 11 = 415
415 - 13 = 402
402 + 11 = 413
413 - 13 = 400
400 + 11 = 411
Hence the next number in the given number series is 411.
2 239
Q:
Find the next number in the given number sequence?
101, 98, 93, 86, 75, ?
A) 62 B) 68 C) 71 D) 73
Explanation:
The given number sequence is 101, 98, 93, 86, 75, ?
101
101 - 3 = 98
98 - 5 = 93
93 - 7 = 86
86 - 11 = 75
75 - 13 = 62
Here the series follows a pattern that consecutive subtraction of prime numbers.
Hence, the next number in the sequence is 62.
0 174
Q:
Find the next number in the given sequence?
11, 17, 39, 85, ?
A) 133 B) 143 C) 153 D) 163
Explanation:
Her the given number series is 11, 17, 39, 85, ?
Hence, the next number in the given sequence is 163.
4 370
Q:
Next number in the given series is
9 7 10 6 11 ?
A) 5 B) 4 C) 13 D) 15
Explanation:
The given number series is 9 7 10 6 11 ?
Here in this we have two number sequences, they are
9, 10, 11, ... and 7, 6, 5, ...
Hence, the next number in the given number series is 6 - 1 = 5.
1 254
Q:
Find the missing number in the given number series?
1 8 36 ? 1100 7701
A) 97 B) 129 C) 164 D) 183
Explanation:
The given number series is 1 8 36 ? 1100 7701
It follows a pattern that,
1
1 x 3 + 5 = 8
8 x 4 + 4 = 36
36 x 5 + 3 = 183
183 x 6 + 2 = 1100
1100 x 7 + 1 = 7701
Hence, the missing number in the given series is 183. | 1,077 | 2,729 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.5 | 4 | CC-MAIN-2018-39 | latest | en | 0.652077 |
https://training.incf.org/search?f%5B0%5D=topics%3A22&f%5B1%5D=topics%3A25&f%5B2%5D=topics%3A50&f%5B3%5D=topics%3A70&f%5B4%5D=topics%3A77&%3Bf%5B1%5D=topics%3A70 | 1,568,791,897,000,000,000 | text/html | crawl-data/CC-MAIN-2019-39/segments/1568514573258.74/warc/CC-MAIN-20190918065330-20190918091330-00471.warc.gz | 719,475,456 | 14,768 | ## Difficulty level
Lesson title:
The probability of a hypothesis, given data.
Difficulty level: Beginner
Duration: 7:57
Speaker: : Barton Poulson
Lesson title:
Why math is useful in data science.
Difficulty level: Beginner
Duration: 1:35
Speaker: : Barton Poulson
Lesson title:
Why statistics are useful for data science.
Difficulty level: Beginner
Duration: 4:01
Speaker: : Barton Poulson
Lesson title:
Statistics is exploring data.
Difficulty level: Beginner
Duration: 2:23
Speaker: : Barton Poulson
Lesson title:
Graphical data exploration
Difficulty level: Beginner
Duration: 8:01
Speaker: : Barton Poulson
Lesson title:
Numerical data exploration
Difficulty level: Beginner
Duration: 5:05
Speaker: : Barton Poulson
Lesson title:
Simple description of statistical data.
Difficulty level: Beginner
Duration: 10:16
Speaker: : Barton Poulson
Lesson title:
Basics of hypothesis testing.
Difficulty level: Beginner
Duration: 06:04
Speaker: : Barton Poulson
In this lecture, the speaker demonstrates Neurokernel's module interfacing feature by using it to integrate independently developed models of olfactory and vision LPUs based upon experimentally obtained connectivity information.
Difficulty level: Intermediate
Duration: 29:56
Speaker: : Aurel A. Lazar
Lesson title:
This lecture will highlight our current understanding and recent developments in the field of neurodegenerative disease research, as well as the future of diagnostics and treatment of neurodegenerative diseases.
Difficulty level: Beginner
Duration: 39:05
Speaker: : Nir Giladi
Lesson title:
2nd part of the lecture. This lecture will highlight our current understanding and recent developments in the field of neurodegenerative disease research, as well as the future of diagnostics and treatment of neurodegenerative diseases.
Difficulty level: Beginner
Duration: 45:27
Speaker: : Nir Giladi
Lesson title:
This lecture will discuss how understanding and applying simple neuroanatomical rules, one can localize the damage along the neuroaxis, the first crucial step toward making the correct clinical diagnosis and initiating treatment.
Difficulty level: Beginner
Duration: 44:52
Speaker: : Eitan Auriel
Lesson title:
2nd part of the lecture. This lecture will discuss how understanding and applying simple neuroanatomical rules, one can localize the damage along the neuroaxis, the first crucial step toward making the correct clinical diagnosis and initiating treatment.
Difficulty level: Beginner
Duration: 42:35
Speaker: : Eitan Auriel
Lesson title:
This lecture focuses on how the immune system can target and attack the nervous system to produce autoimmune responses that may result in diseases such as multiple sclerosis, neuromyelitis and lupus cerebritis manifested by motor, sensory, and cognitive impairments. Despite the fact that the brain is an immune-privileged site, autoreactive lymphocytes producing proinflammatory cytokines can cause active brain inflammation, leading to myelin and axonal loss.
Difficulty level: Beginner
Duration: 37:36
Speaker: : Anat Achiron
Most psychiatric disorders (most notably dependence syndromes, depression, psychosis, and autism) are characterized by impaired social interaction, with many patients preferring a drug of abuse. This lecture focuses on the latest research on the neural basis of normal and impaired social interaction.
Difficulty level: Beginner
Duration: 41:56
Speaker: : Gerald Zernig
Lesson title:
This lecture will provide an overview of neuroimaging techniques and their clinical applications.
Difficulty level: Beginner
Duration: 45:29
Speaker: : Dafna Ben Bashat
Lesson title:
This lecture will provide an overview of neuroimaging techniques and their clinical applications
Difficulty level: Beginner
Duration: 41:00
Speaker: : Dafna Ben Bashat
This lecture will highlight our current understanding and recent developments in the field of neurodegenerative disease research, as well as the future of diagnostics and treatment of neurodegenerative diseases
Difficulty level: Beginner
Duration: 1:02:29
Speaker: : Nir Giladi
This lecture provides an overview of depression (epidemiology and course of the disorder), clinical presentation, somatic co-morbidity, and treatment options.
Difficulty level: Beginner
Duration: 37:51
How genetics can contribute to our understanding of psychiatric phenotypes.
Difficulty level: Beginner
Duration: 55:15
Speaker: : Sven Cichon | 957 | 4,453 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.796875 | 3 | CC-MAIN-2019-39 | latest | en | 0.790328 |
http://ng-outsourcing.com/loan-to-value-ratio.html | 1,679,686,922,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296945288.47/warc/CC-MAIN-20230324180032-20230324210032-00664.warc.gz | 34,079,927 | 20,104 | # Loan to Value Ratio (LTV)
## What is Loan-to-Value (LTV)?
Definition: The loan to value ratio (LTV) is a risk assessment measurement that calculates the loan amount as a percentage of the appraised value of the collateral. In other words, it’s a tool used to compare the purposed loan amount with the value of the property being purchased in order to evaluate the risk of the loan becoming underwater or upside-down.
Although this formula can be applied to any type of loan, it’s most commonly used in the mortgage industry. Banks, underwriters, and other financial institutions use this calculation during the mortgage application process to determine what amount of down payment is required for the purchase of a home. In essence, they are calculating the collateral needed to secure a loan.
Every lender has slightly different requirements that must be approved before they will issue a mortgage. Some lenders will not issue mortgages to individuals who can’t meet a maximum LTV, while other lenders alter their loan terms to accommodate the added risk by increasing the interest rate or requiring the borrower to purchase mortgage insurance. This private mortgage insurance policy, commonly abbreviated PMI, helps protect the lender from the borrower’s possible default. If the borrower can’t make his or her payments and goes bankrupt, the insurance company will pay the lender according to the terms of the policy. This is a great alternative for individuals who don’t have enough money for a proper down payment because it allows them to qualify for a loan by making a small monthly insurance payment with their mortgage payment.
Now that we know what loan to value is, let’s see how to calculate the LTV ratio.
## Formula
The loan to value ratio formula is calculated by dividing the mortgage amount by the appraised value of the home being purchased.
The appraised value in the denominator of the equation is almost always equal to the selling price of the home, but most mortgage companies will require the borrower to hire a professional appraiser to value the property.
This is understandable because the agreed upon sales price doesn’t necessarily reflect the true market value of the property. The bank wants to ensure the loan is properly collateralized. For instance, they don’t want to issue a \$200,000 mortgage for a house that is only worth \$125,000. Just because the purchaser is willing to buy the house for more than it’s worth, doesn’t mean the bank will make a poor investment decision.
## Analysis
Each mortgage company typically sets their own acceptable loan to value limits, but the average rate in the United States is 80 percent. This means the issued mortgage cannot be more than 80 percent of the appraised value of the home.
In order to get approved for a mortgage that is more than 80 percent of the home’s value, the borrower would have to have a specific credit score in addition to pay a higher interest rate and PMI.
This is only one tool that banks use to evaluate the risk involved in lending mortgages. Just like any other investment, the return must increase as the risk increases. If the collateral decreases, the loan becomes inherently more risky and the bank must be compensated for this increased risk. Banks look to make a return off their mortgage portfolios just like traditional investors in the stock market, so they structure their mortgages accordingly.
Let’s take a look at an example.
## Example
Ted just graduated college and got his first big job. Now he is looking to purchase a home near his new company valued at \$250,000. Ted’s bank requires an 80 percent loan to value ratio. The bank would use loan to value calculator to calculate Ted’s minimum required down payment like this.
As you can see, the maximum mortgage that the bank will issue Ted for this house purchase is \$200,000. In other words, Ted has to pay a down payment of \$50,000 in order to get approved for the loan.
[i]
[i] | 791 | 3,974 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.765625 | 3 | CC-MAIN-2023-14 | latest | en | 0.951685 |
https://www.pranavisions.pl/plant/6786/difference-between-ncv-gcv-uhv.html | 1,653,138,573,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662539101.40/warc/CC-MAIN-20220521112022-20220521142022-00451.warc.gz | 1,076,559,487 | 6,724 | difference between ncv gcv uhv
#### gcv arb coal indicator
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#### MODIFICATION ARISING OUT OF MIGRATION FROM UHV ,
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#### How do you calculate UHV to GCV in coal
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#### difference between ncv and gcv for coal and gas
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difference between ncv and gcv for coal and gas , difference ncv gcv uhv sand washing machine Default GCV Natural Gas Questionnaire Overview GCV The GCV/NCV difference is gross calorific value What is difference between gcv NCV and GCV of coal More...
#### What is the difference between gross and net calorific ,
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Net Calorific Value NCV also known as lower heating value LHV or lower calorific value LCV is determined by the subtracting the heat of vaporization of the water vapour from the higher heating valueThis treats any H20 formed as a vapor Natural gas prices are decided on the basis of GCV and NCV...
#### gcv and ncv of indian coal
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CALORIFIC VALUE-DEFINE Energy content of the Indian Coal is expressed in Useful Heating Value Net Calorific Value = GCV - 1002M UHV, GCV, NCV More Info Calorific Value of Coal - bioreference , What is the difference between GCV and NCV - What is the difference between GCV and NCV? GCV of coal has 17 grades and prices are linked to ....
#### What is the difference between GCV and NCV?
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Difference in GCV and UHV of coal? GCV, gross calorific value, is the quantity of heat produced bycombustion UHV, useful heat value, is the gradation of non-cokingcoal...
#### Difference in GCV and UHV of coal
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GCV, gross calorific value, is the quantity of heat produced bycombustion UHV, useful heat value, is the gradation of non-cokingcoal...
#### difference between gar nar gcv coal
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What is the difference between GCV and NCV - Answers , Difference in GCV and UHV of coal? GCV, gross calorific value, is the quantity of heat produced bycombustion Get a Price difference between gcv and ncv of coal - hochglanz-fronteneu...
#### difference between gar nar gcv coal
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difference between gcv and ncv of coal - gurusrestaurantin difference between gcv and ncv of coal - , difference between gar nar gcv coal - rafmareu gcv to nar coal conversion - Gold Ore Crusher NON COKING STEAM COAL COKING , difference between gar and gcv - Grinding Mill China...
#### indian coal gcv and ncv
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NCV/LHV/UHV GCV/HHV The CV of a , correlation exists between GCV and UHV of Indian Coal in order to firm up a valid , 2012-8-16Read More , The chemical GCV of lignite on as received basis , gcv ncv difference of coal in relation of , Read More GCV INDIAN POWER SECTOR...
#### defination of ncv coal grades
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What is the difference between GCV and NCV - , What is the difference between GCV and NCV? , of coal deducted ash and moisture content from standard formula and in this coal is categorised into 7 ,...
#### formula to convert gcv to ncv
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formula convert gcv ncv sitopin gcv adb conversion formula of gcv to ncv formula for converting coal gcv to ncv crusher south formula to convert gar to gcv in , to convert gar to gcv in coal difference between ncv gcv uhv formula for gcv and uhv of coal Check price Basic Decimal System Prefixes ieaorg Depending on the product, we may ....
#### How Calculate Gcv Of Coal Charcoal
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The difference between GCV and NCV is the amount of The calorific value of coal varies considerably Get Price And Support Online how to conversion gcv to ncv in coal - -CUSTOMER...
#### THERMAL POWER PLANTS CALORIFIC VALUE
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It is usually expressed in Gross Calorific Value GCV or Higher Heating Value HHV and Net Calorific Value NCV or Lower Calorific Value LHV The difference being the latent heat of condensation of the water vapour produced during the combustion process...
#### Calorific Value of Coalpdf Coal Combustion
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Calorific Value of Coal Fig 3 7/1 Difference GCV vs Unit Cost of electricity2 it is concluded that UHV system is dated and out of Table 10 Effect of Moisture on CV of Coal1 and 11...
#### Coal Grades Ministry of Coal, Government of India
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Coal Grades The gradation of non-coking coal is based on Useful Heat Value UHV , the gradation of coking coal is based on ash content and for semi coking / weakly coking coal it is based on ash plus moisture content , as in vogue as per notification...
#### Difference Between Arb Ncv
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ncv to arb conversion iffdc what is the difference between gcv on arb and adb basis gcv arb adb ncv conversion formula, gcv arb adb ncv conversion formula What is the difference between GCV and UHV? qaanswers...
#### Who created GCV
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What is the difference between GCV and UHV? Useful heat value UHV pricing mechanism of coal deducted ash and moisture content from standard formula and in this coal is categorised into 7 grad , GCV to NCV conversion - Using the following IPCC formulae determine the NCV of those fortnightly samples - NCV = GCV - 0212H - 00245M - 00008O ....
#### Calorific Value of Coalpdf Coal Combustion
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The major difference between GCV/HHV and UHV/LHV/NCV is the water vapour or latent heat 4 crucible and place inside a Bomb Calorimeter filled with 30 bar of oxygen 4...
#### what is the difference betweem gar and nar coal
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Reckoner for all Coal Conversions - Knowledge is , The difference between net and gross as received NAR v/s GAR specific energy values is the latent heat of the water vapour which lowers the effective calorific value in the boiler...
#### What is the difference between GCV and UHV?
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Another difference is in band of grading ie GoI divides UHV band in 6 interval while GCV band was divided in 17 bands so in later case the interval range is narrow about 300kcal/kg so, there is least variation in price paid and quality of coal received against a particular grade, and so again beneficial for consumer as well as supplier...
#### Net calorific value Editorial coordination R D Aliapur ,
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For gaseous fuels, the NCV is a value around 90 of the GCV It is expressed in megaJoule per kilo MJkg -1 , multiplied by the specific heat of the water multiplied by the difference between the initial temperature and the maximum temperature attained during the experiment, all divided by the...
#### difference between gar and gcv
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what is difference between ncv gcv - Stone Crusher and Grinding Mill For Quarry units of measurement in water treatment - notions of heat, The difference between the NCV and the GCV is the latent water vaporisation heat The NCV, alone used for plant , Free Quote...
#### gcv dmmf vs gcv adb
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#### conversion uhv on unit coal basis to gcv
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arb to ncv coal conversion convert arb to gar coal calorific value about coal calculator to convert gcv arb gcv adb coal conversion dried basis what is the difference between arb and gar in coal gcv arb adb ncv arb to ncv coal conversion,arb to ncv coal conversion sand washing machinegcv، ncv uhv تعریف ssi group biz how to conversion...
#### What is the exact difference between GCV NCV?
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What is the exact difference between GCV NCV? Update Cancel ad by Grammarly Take your writing to the next level Grammarly s free writing app makes sure everything you type is easy to read, effective, and mistake-free , What is the exact difference between sense and perspective? What is the difference between different and difference?...
#### What is the difference between GCV and UHV?
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What is the difference between GCV and NCV? The calorific value is the measurement of heat or energy produced, and is measured either as gross calorific value or net calorific value , I do not think that there can be a way to calculate GCV from the UHV... | 2,191 | 9,175 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2022-21 | latest | en | 0.90628 |
https://la.mathworks.com/matlabcentral/cody/problems/1702-maximum-value-in-a-matrix/solutions/1832752 | 1,607,116,707,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141743438.76/warc/CC-MAIN-20201204193220-20201204223220-00448.warc.gz | 374,990,820 | 16,936 | Cody
# Problem 1702. Maximum value in a matrix
Solution 1832752
Submitted on 31 May 2019 by rolf harkes
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
x = [1 2 3; 4 5 6; 7 8 9]; y_correct = 9; assert(isequal(your_fcn_name(x),y_correct))
2 Pass
x = -10:0; y_correct = 0; assert(isequal(your_fcn_name(x),y_correct))
3 Pass
x = 17; y_correct = 17; assert(isequal(your_fcn_name(x),y_correct))
4 Pass
x = magic(6); y_correct = 36; assert(isequal(your_fcn_name(x),y_correct))
5 Pass
x = [5 23 6 2 9 0 -1]'; y_correct = 23; assert(isequal(your_fcn_name(x),y_correct))
### Community Treasure Hunt
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Start Hunting! | 273 | 824 | {"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-2020-50 | latest | en | 0.660096 |
https://oeis.org/A308479 | 1,716,511,027,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058675.22/warc/CC-MAIN-20240523235012-20240524025012-00463.warc.gz | 376,001,875 | 4,387 | The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
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A308479 Least k such that k*n and (k+1)*n fail to have a common nonzero digit, or 0 if this property never occurs. 3
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 4, 1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 4, 3, 1, 1, 1, 1, 2, 1, 1, 4, 1, 1, 2, 3, 1, 1, 1, 1, 1, 8, 1, 1, 2, 1, 1, 3, 1, 11, 1, 21, 1, 1, 1, 2, 5, 3, 5, 0, 1, 1, 2, 1, 1, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,12 COMMENTS a(n) = 0 for the members of A308466. LINKS David Radcliffe, Table of n, a(n) for n = 1..10000 David Radcliffe, Python script for A308479 FORMULA If a(n) = k, then a(10*n) = k. EXAMPLE a(3) = 1 since 1*3 and 2*3 have no digit in common; a(12) = 2 since 1*12 and 2*12 have the digit 2 in common, but 2*12 and 3*12 have no nonzero digit in common, thus a(12) = 2; a(25) = 3 since 1*25 and 2*25 have the digit 5 in common, 2*25 and 3*25 have the digit 5 in common, but 3*25 and 4*25 have no nonzero digit in common; etc. MATHEMATICA a = Compile[{{n, _Integer}}, Module[{k = 1, id1 = DeleteCases[ IntegerDigits[ n], 0], id2 = DeleteCases[ IntegerDigits[ 2n], 0]}, While[k < 1001 && Intersection[id1, id2] != {}, id1 = id2; k++; id2 = DeleteCases[ Union[ IntegerDigits[(k + 1) n]], 0]]; If[k == 1001, 0, k]]]; Array[a, 198] CROSSREFS Cf. A308466. Sequence in context: A330751 A327407 A290104 * A031280 A134870 A031286 Adjacent sequences: A308476 A308477 A308478 * A308480 A308481 A308482 KEYWORD nonn,base AUTHOR David Radcliffe, Daniel Griller, and Robert G. Wilson v, May 29 2019 STATUS approved
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Last modified May 23 20:34 EDT 2024. Contains 372765 sequences. (Running on oeis4.) | 928 | 2,244 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.640625 | 4 | CC-MAIN-2024-22 | latest | en | 0.620472 |
https://mytutorsource.com/blog/math-in-everyday-life/ | 1,718,901,444,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861957.99/warc/CC-MAIN-20240620141245-20240620171245-00852.warc.gz | 356,802,968 | 41,479 | # Math in Everyday Life: Unexpected Applications You Never Knew Existed
Let’s face it: Math is a tricky subject, and over 37% of teens find it harder than other courses they take. We have all been there, having a bittersweet relationship with Math, sometimes being joyous after solving a tricky problem and crying over some integration concepts the next moment.
Some of us study math only to get through high school, but there are other students who enjoy practicing Math problems.
Whatever the case may be, Math remains a polarized subject with some mind-blowing daily life applications.
Have you ever thought that, in one way or another, you practically use and will require some basic knowledge of maths in daily life?
We bet you have not thought about these examples. Let’s study some interesting facts about Math one by one:
## 1. Weather Prediction
There are multiple notable examples of math in daily life that you probably have not heard of before, one of which is weather forecasting.
Now, weather prediction remains one of the most difficult tasks for scientists because weather contains numerous tiny complex molecules that interact with each other. Even with the usage of many supercomputers and weather station satellites, scientists cannot accurately predict it for more than a few weeks.
But how do they do so?
It involves the usage of mathematical models and concepts. In the atmosphere, the fluid follows a set of rules called Navier Stokes equations. The atmosphere is then divided into millions of one cubic kilometer blocks, then numerical simulations are used to calculate high-resolution forecasts.
## 2. MRI & Tomography
If you study it deeply, you will understand why math is important in our day-to-day life. It is not only in technical fields, but it has applications in science as well. For instance, it is used in MRI and tomography techniques.
MRI machines take lots of pictures of the body from different angles to make 3D images or snapshots. Putting all these pictures together to create a 3D model is called tomography. Math, like Radon Transforms, plays a significant role in making this possible. So, math is really important in helping doctors save lives.
Tips From an Educationist: How Can You Learn Without Forgetting?
## 3. Wireless Connections
The Internet and phone networks are huge systems that let people share data, such as websites or calls. All users are linked by connections, each with its own capacity. When you make a call or visit a website, operators have to figure out how to connect you and the other person without overloading any link.
Mathematics, especially queuing theory, is important for ensuring a dependable service. Using mathematical models based on things like Poisson processes, operators can make sure you'll hear a dial tone when you call someone.
Routing internet connections is trickier because requests come in at different rates and durations. So, they came up with packet-switching, breaking data into small bits called "packets" that can travel independently. This makes the network stronger and faster, but sometimes routers get overwhelmed with too many packets, which causes the connection to drop.
Some people think that using Fractals could lead to an even better internet in the future, making it more reliable.
## 4. Epidemic Analysis
We all remember the time of COVID-19 when we were confined to our homes due to the fatality of the disease. But, without math, we cannot predict any imminent epidemic.
When a new epidemic begins, it might seem like it will never end because new cases keep popping up. But math tells us otherwise.
The critical thing to look at is the reproductive ratio, called R0. This number explains how many people, on average, are affected by the disease. If R0 is less than 1, the epidemic will fizzle out. But if R0 is greater than 1, the epidemic will keep spreading.
Knowing the value of R0 helps us plan how to control the epidemic. Especially when resources are limited, like not having enough vaccines for everyone, the goal is to use those resources to bring R0 down below 1.
## 5. Mapping The Earth
Mapping our round Earth onto a flat map is a challenging task. Some parts need to be changed to fit them onto a flat surface, which can stretch or squish them. But math comes to the rescue here as well.
Cartography, the science of making maps, tackles this challenge. There are various map projections designed to handle this problem of turning our 3D Earth into a 2D map, including spherical and hyperbolic geometry.
Upskill Yourself: How to Develop and Sharpen Your Math Skills?
## 6. Coding CDs and DVDs
A lot of us used to use CDs and DVDs a decade ago when they were popular, but you might have not heard of this application of math before.
CDs and DVDs store data using tiny bumps and dents on their surface (hills and valleys), each smaller than a human hair. If these get scratched or dusty, they can mess up the data and make the disc not work properly.
But this application of maths in real life saves the day! Reed-Solomon codes are used to encode the data on discs. These codes are cleverly designed so that even if some of the data is wrong or missing, computers can still figure out what it should be and fix it.
This only works if some of the data is still okay, though. So, if a CD is too scratched up, it won't work.
## 7. Glacier Melting
Climate change is a major challenge for us all, and one big concern is the melting of the polar ice caps, which affects global sea levels and the temperature of the Earth.
Satellite images can only tell us so much about the ice caps and how they're melting. But by using probability and statistics, scientists can analyze environmental data, like ice thickness and composition.
On top of that, scientists use complex math models involving concepts like differential equations and thermodynamics to understand how wind, ocean currents, and heat transfer interact with the ice. These concepts help them understand the details of climate change, and then they can find ways to tackle these issues.
## 8. Cosmology
Cosmology is the study of the origin of our universe and its evolution over time. Math helps us model this journey from the Big Bang to now and even predict what might happen in the future.
The universe is expanding fast, and we can understand this using equations like the Friedmann Equations, which come from Einstein's theory of gravity. What happens to the universe depends on how much matter and energy it contains. Astronomers think there's stuff we can't see directly, called dark matter and dark energy.
Mathematicians also use supercomputers to simulate what happened right after the Big Bang, giving us insights into the early universe.
## 9. Carbon Dating
Carbon dating is a method used to determine the age of once-living organisms by measuring the amount of a radioactive form of carbon, carbon-14, remaining in their fossils. Living organisms accumulate carbon, including a small amount of carbon-14 and when they die, it starts to decay at a steady rate.
By measuring the remaining carbon-14 and knowing the original proportion and decay rate, scientists can use math to figure out how long it's been decaying. This helps determine when the organism died.
Math is also useful in other parts of archaeology. For example, the size of bones can be used to calculate the weight they support, giving insights into the size of the animals or humans they belong to.
## 10. Search Engines
The internet is a massive resource, and search engines like Google make it simple to find what you need quickly.
To rank websites and show the most helpful ones at the top, Google uses a huge matrix that represents all the pages on the internet. This matrix considers how sites are linked together. Math concepts like linear algebra, probability, and graph theory help identify the most popular sites.
But Google doesn't stop there. Math is behind many other features, like giving directions in Maps, filtering out spam in Gmail, recognizing voices on Android, scanning books for text, compressing videos on YouTube, spotting faces in images, and translating text.
## 11. Finance and Budgeting
In finance, traders deal with buying and selling stocks, commodities like oil and gold, and derivatives, which are basically virtual goods whose prices are based on other things. For example, you might buy options, giving you the right to buy or sell a stock at a set price in the future if you choose to.
Financial analysts use a variety of math tools to make smarter decisions. They analyze past economic data using statistical models, and they use probability and stochastic calculus to forecast how financial markets might behave.
One well-known tool is the Black-Scholes equation, a type of partial differential equation used to figure out the right value of derivatives.
## Using 3 Common Math Concepts in Real Life
### 1. Fractions
Daily, we use numerous examples of fractions in real life but we don’t ponder over it.
Have you ever hit the snooze button of your alarm before getting up, and calculated the number of minutes you still have left to sleep?
It involves fractions.
You might think you don’t understand fractions, but you use them daily. Another example is dividing the sum of money between different accounts, sharing 5 cookies among 7 people, and making a study timetable while breaking your day into hours and quarters.
When cooking twice or thrice a day, it is very likely that you use the concept of fractions at least once. Like, when a recipe calls for ¾ of a cup of sugar, and all you have is ¼ cup measuring cup, what will be your next step?
### 2. Trigonometry
Although it might not be used daily, there are numerous real-life applications of trigonometry.
In healthcare systems, sine and cosine functions of trigonometry are used to detect diseases in human body. Tisses in our body emit electromagnetic waves in presence of magnetic or electric fields which are then detected by MRI or CT scans as represented by sin and cosine functions.
Trigonometry has its functions in navigation as well. It is used to find the distance and horizon after placing the compass in the right direction. Moreover, trigonometry is used in finding angles, the distance between two points, and the heights of objects.
### 3. Pythagoras Theorem
We all remember Pythagoras theorem from high school and wonder,
When will I ever apply this topic in real life?
Well, it’s used by hikers and mountaineers to find the steepness and slope of a hill or a mountain. In construction, laborers use it to calculate the steepness of the staircase required according to the space. Painters also use it to paint high buildings or walls by determining how far a ladder should be kept so they don’t tip over.
One cool application of the Pythagoras theorem is in artificial intelligence. It is used in face recognition features of security cameras by calculating the distance between the person and the camera. Then, the scene's dimensions are used to calculate the number of pixels representing the culprit’s face.
## 10 Uses of Math in Our Daily Life
Now, let’s talk about some specifics. You may ask this question yourself multiple times a day (if you hate math):
Why is Math important?
Well, maths in real life is used in various ways and contexts that you might overlook unknowingly. For instance, on a very usual and mundane day, you may have used Math multiple times.
• Cooking — measuring ingredients and distributing food items.
• Shopping — budgeting, finding the best deals, and calculating discounts.
• Driving — calculating speed, fuel consumption, time, and distance.
• Home decoration and remodeling — buying design and construction stuff and placing it properly using perimeter and area calculations.
• Sports — understanding the direction and angle of the ball and making a run around the track.
• Music and dancing — recognizing musical patterns, understanding rhythms, and creating a melody based on consonance among tones.
• Exercising— calculating repetitions, time, measuring weights, and designing diet plans based on calories
• Technology — computer and phone algorithms use linear algebra and calculus to complete commands.
## Wrap Up!
We have discussed some unexpected and fascinating maths facts you probably had not heard of before. With all its complications, it remains the most advanced field of study. So, if you want to pursue a career which requires basic math skills, hire an online math tutor to help you, or practice your word problems daily.
### Find Top Tutors in Your Area
With over 3 years of experience in teaching, Chloe is very deeply connected with the topics that talk about the educational and general aspects of a student's life. Her writing has been very helpful for students to gain a better understanding of their academics and personal well-being. I’m also open to any suggestions that you might have! Please reach out to me at chloedaniel402 [at] gmail.com | 2,670 | 13,052 | {"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} | 3.640625 | 4 | CC-MAIN-2024-26 | latest | en | 0.942366 |
http://wiki.gp2x.org/articles/c/p/u/Talk:CPU_Frequency.html | 1,516,115,713,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084886437.0/warc/CC-MAIN-20180116144951-20180116164951-00488.warc.gz | 376,886,972 | 4,864 | # Talk:CPU Frequency
Could someone explain this?
I didn't find any explanation in the docs (MMSP2 Databook v1.0). Did anybody measure the resulting frequency?
The question restated using C code (mm points to 0xc0000000):
unsigned cpuHz920() {
``` /* Crystal input p.31 */
const unsigned XTI=7372800;
uint16_t *mm16=(unsigned short *)mm;
/* p.108 FCLK PLL Value Setting Register
PLL = phase-locked loop?
http://en.wikipedia.org/wiki/PLL
*/
uint16_t FPLLVSETREG=mm16[0x912>>1];
/* p.109
[15:8] mdiv of pll */
uint8_t FMDIVR= (FPLLVSETREG & 0xff00) >> 8;
DEBUG(FMDIVR);
/* [7:2] pdiv of pll */
uint8_t FPDIVR = (FPLLVSETREG & 0xfc) >> 2;
DEBUG(FPDIVR);
/* [1:0] sdiv of pll */
uint8_t FSDIVR = FPLLVSETREG & 3;
DEBUG(FSDIVR);
```
``` /* p. 88, 109
System clock set register
*/
uint16_t SYSCSETREG=mm16[0x91c>>1];
```
``` /* [8:6] DCLK Clock Generation F-PLL Divide Set Value (N-1)
DCLK means Double Clock, it is used for the memory controller
so, BCLK is DCLK*1/2 */
uint8_t DCLKDIV = (SYSCSETREG & 0x1c0) >> 6;
DEBUG(DCLKDIV);
/* [5:3] A940T FCLK Clock Generation F-PLL Divide Set Value (N-1) */
uint8_t A940TFDIV = (SYSCSETREG & 0x38) >> 3;
DEBUG(A940TFDIV);
/* [2:0] A920T FCLK Clock Generation F-PLL Divide Set Value (N-1) */
uint8_t A920TFDIV = SYSCSETREG & 7;
DEBUG(A920TFDIV);
```
``` /* why? perhaps p.85? */
unsigned FCLKin = (XTI * (((unsigned)FMDIVR) + 8))
/((((unsigned)FPDIVR) + 2) << FSDIVR);
return FCLKin / (((unsigned)A920TFDIV)+1);
```
}
The FCLKin line is the one I couldn't verify in the docs. | 559 | 1,517 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.796875 | 3 | CC-MAIN-2018-05 | latest | en | 0.652272 |
https://www.teachoo.com/2124/578/Ex-2.3--5---Find-range-f(x)-=-2---3x--f(x)-=-x2---2--f(x)-=-x/category/Ex-2.3/ | 1,529,500,672,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267863519.49/warc/CC-MAIN-20180620124346-20180620144346-00365.warc.gz | 937,912,522 | 13,738 | 1. Chapter 2 Class 11 Relations and Functions
2. Serial order wise
Transcript
Ex2.3, 5 (Method 1) Find the range of each of the following functions. f(x) = 2 – 3x, x ∈ R, x > 0. Given f(x) = 2 – 3x where x ∈ R, x > 0 We find various values of f(x) for x ∈ R , x > 0 We note that value of f(x) is less than 2 (not including 2) Hence, Range = ( – ∞ , 2) Ex2.3, 5 (Method 2) Find the range of each of the following functions. f(x) = 2 – 3x, x ∈ R, x > 0. We know that x > 0, Multiplying 3 both sides 3x > 0 × 3 3x > 0 Multiplying -1 both sides – 1 × 3x < – 1 × 0 – 3x < 0 Adding 2 both sides 2 – 3x < 2 + 0 2 – 3x < 2 f(x) < 2 We note that value of f(x) is less than 2 (not including 2) Hence, Range = ( – ∞ , 2) Ex2.3, 5(Method 1) Find the range of each of the following functions. (ii) f(x) = x2 + 2, x, is a real number. Here we are given x is real We find values of f(x) by putting different values of x We note that f(x) has a minimum value of 2 and the value can increase upto infinity. So, range of f = [2, ∞ ) Ex2.3, 5(Method 2) Find the range of each of the following functions. (ii) f(x) = x2 + 2, x, is a real number. Given that x is a real number Square of a number will always be positive or 0 So we can say that x2 ≥ 0 Adding 2 both sides ⇒ x2 + 2 ≥ 0 + 2 ⇒ x2 + 2 ≥ 2 ⇒ f(x) ≥ 2 ∴ Range of f = [2, ∞ ) Ex2.3, 5 Find the range of each of the following functions. (iii) f(x) = x, x is a real number Here we are given x is real We find values of f(x) by putting different values of x We can see that f(x) can be all real numbers as x is all real number ∴ Range of f(x) = R | 579 | 1,583 | {"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} | 4.78125 | 5 | CC-MAIN-2018-26 | longest | en | 0.860143 |
https://brilliant.org/problems/large-power-sum-2/ | 1,579,698,353,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579250606975.49/warc/CC-MAIN-20200122101729-20200122130729-00338.warc.gz | 371,661,969 | 10,580 | # Power Sums: Coefficient Sum
Calculus Level 5
All power sums have a closed polynomial forms for integral powers. For example,
$1^2+2^2+3^2+\cdots+n^2=\displaystyle \sum_{k=1}^n k^2=\frac{n^3}{3}+\frac{n^2}{2}+\frac{n}{6}$
More generally
$1^m+2^m+3^m+\cdots+n^m=\displaystyle \sum_{k=1}^n k^m=\displaystyle \sum_{i=1}^{m+1} a_i n^i$
In the case of $m=2$, $a_1=\frac{1}{6}$, $a_2=\frac{1}{2}$, and $a_3=\frac{1}{3}$.
When $m=864$, if $\displaystyle \sum_{i=1}^{864} a_i$ can be written as $\dfrac{p}{q}$ for coprime positive integers $p,q$, find $p+q$.
Like this problem? Try these too.
× | 251 | 596 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 11, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.875 | 4 | CC-MAIN-2020-05 | latest | en | 0.535824 |
http://euler.ltran.co/problems/p9 | 1,582,268,441,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875145443.63/warc/CC-MAIN-20200221045555-20200221075555-00110.warc.gz | 53,634,741 | 2,736 | # Project Euler
### A Taste of Number Theory
#### Problem 9: Special Pythagorean Triplet
A Pythagorean triplet is a set of three natural numbers, a < b < c, for which, a2 + b2 = c2. For example, 32 + 42 = 9 + 16 = 25 = 52. There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc.
#### The Catch
How to generate Pythagorean triplets.
#### The Light
Utilize the Euclid's Formula to create Pythagorean triplets: given an arbitrary pair of positive integers m and n with m > n, the formula states that:
• a = m2 - n2
• b = 2 * m * n
• c = m2 + n2
Check when their sum equals 1,000 and find their product.
#### The Code
```public class Problem9
{
public static void main(String[] args)
{
for(int m = 2;; m++)
{
for(int n = 1; n < m; n++)
{
int a = m * m - n * n;
int b = 2 * m * n;
int c = m * m + n * n;
int sum = a + b + c;
if( sum == 1000 )
{
System.out.println("a = " + a);
System.out.println("b = " + b);
System.out.println("c = " + c);
System.out.println(a * b * c );
return;
}
}
}
}
}
``` | 336 | 1,040 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.609375 | 4 | CC-MAIN-2020-10 | latest | en | 0.606472 |
https://oeis.org/A127762 | 1,695,626,354,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233506686.80/warc/CC-MAIN-20230925051501-20230925081501-00457.warc.gz | 483,028,939 | 3,586 | The OEIS is supported by the many generous donors to the OEIS Foundation.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A127762 Integer part of Gauss's Arithmetic-Geometric Mean M(2,n^2). 4
1, 2, 4, 7, 10, 13, 16, 20, 25, 29, 34, 39, 45, 51, 57, 64, 71, 78, 86, 93, 102, 110, 119, 128, 137, 147, 157, 167, 177, 188, 199, 210, 222, 234, 246, 258, 271, 284, 297, 311, 325, 339, 353, 368, 382, 398, 413, 429, 444, 461, 477, 494, 511, 528, 545, 563, 581 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,2 LINKS Table of n, a(n) for n=1..57. FORMULA a(n) ~ Pi*n^2/(4*log(n) + 2*log(2)). - Vaclav Kotesovec, May 09 2016 MATHEMATICA Table[Floor[ArithmeticGeometricMean[2, n^2]], {n, 1, 100}] CROSSREFS Cf. A127758, A127759, A127760, A127761, A127763, A127764, A127765, A127766. Sequence in context: A295513 A194228 A194236 * A137281 A287420 A003067 Adjacent sequences: A127759 A127760 A127761 * A127763 A127764 A127765 KEYWORD nonn AUTHOR Artur Jasinski, Jan 28 2007 STATUS approved
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Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
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Last modified September 25 02:38 EDT 2023. Contains 365582 sequences. (Running on oeis4.) | 519 | 1,360 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2023-40 | latest | en | 0.584157 |
https://www.thejuliagroup.com/blog/statistics-save-the-world/ | 1,558,509,502,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232256764.75/warc/CC-MAIN-20190522063112-20190522085112-00464.warc.gz | 962,198,040 | 43,608 | # Statistics save the world
I will be the first to admit that I’m not the warm fuzzy type. Maybe you’re like me, you’d like to do good for your community but you just can’t see yourself as a physician.
Maybe your bedside manner is to snap at someone to quit being a whiner.
Or maybe you really are a sweet kind person but you are not very extroverted. You just can’t see yourself looking someone in the eye and asking them to tell you about their problems at home. Perhaps you really genuinely care about children in your community and really would like to help them succeed in school but the thought of speaking in front of the 30 people makes you break out into a cold sweat – even if the 30 people are all under 13 years old.
Maybe, like me, you really like math. To be specific, maybe you really like analyzing data, looking for correlations, inspecting distributions. Maybe, you really like programming. Or that’s what we called it in my day – now all the cool kids call it coding.
Does that mean that we are condemned to be a bunch of Silicon Valley dwelling, Soylent swigging, soulless drones with nothing to keep us warm at night but our stock options? In fact, quite the opposite! These last few years I have been having a lot of fun working with statistics in two very different ways.
First of all, I’ve been working with our team at 7 Generation Games to make adventure games that teach statistical concepts.
Let me give you an example. Some items are more valuable than others. Why? Try to figure it out by looking at this distribution.
Players can click on this interactive graph for help reading it. They have a sentence written with blanks to fill in to model academic language.
Once a student answers one or two questions in the game correctly, the reward is being able to play a related game – in this case, collecting items in the jungle. As you might guess, the more common items are worth less in the game.
Here is a second example. Below, we have a section of our 3D game where the player is building a pyramid.
To build your pyramid fast enough that the Emperor doesn’t decide to chop off your head, you want to get stronger than average workers. What is an easy way to determine if you have stronger than average workers? Find the median!
Players can also click a button to switch the page to an explanation in Spanish.
Just because we were all out last night at the Latino Tech meet-up to celebrate Hispanic Heritage Month, don’t assume everything we make it is focused on Latinos.
Here is yet another example of teaching statistics in a game, this one re-tracing the Ojibwe migration.
In this case, the player computes an average to figure how many miles need to be walked per day to get to the end of the trail in eight days.
Get this question right and you can play the next level, where you canoe down the river to meet up with your old uncle who will – surprise – pose another statistics problem before you can move on to the next level.
So, there you have it! You can apply your knowledge of statistics to create adventure video games that teach students. As you can see, you also can apply knowledge of programming to meet the special needs of students whether it is to have a page read to them (did you notice the read it to me button in the page above?) Or to have it translated into a second language.
I’ll bet that you thought I was going to talk about using statistics to evaluate whether the games worked. That, is a post for another day.
_______
You can buy Forgotten Trail now. Only \$4.99 . Yep, under five bucks. Runs on Mac, Windows or Chromebook.
local_offerevent_note October 14, 2016
account_box
## One thought on “Statistics save the world”
This site uses Akismet to reduce spam. Learn how your comment data is processed. | 817 | 3,792 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.796875 | 3 | CC-MAIN-2019-22 | longest | en | 0.970172 |
https://fr.mathworks.com/help/aerotbx/ug/angle2dcm.html | 1,696,100,257,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510707.90/warc/CC-MAIN-20230930181852-20230930211852-00491.warc.gz | 288,600,601 | 20,842 | # angle2dcm
Convert rotation angles to direction cosine matrix
## Syntax
``dcm = angle2dcm(rotationAng1,rotationAng2,rotationAng3)``
``dcm = angle2dcm(___,rotationSequence)``
## Description
example
````dcm = angle2dcm(rotationAng1,rotationAng2,rotationAng3)` calculates the direction cosine matrix `dcm` given three sets of rotation angles, `rotationAng1`, `rotationAng2`, and `rotationAng3`, specifying yaw, pitch, and roll. The rotation angles represent a passive transformation from frame A to frame B. The resulting direction cosine matrix represents a series of right-hand intrinsic passive rotations from frame A to frame B.`dcm = angle2dcm(___,rotationSequence)` calculates the direction cosine matrix given the rotation sequence, `rotationSequence`.```
## Examples
collapse all
Calculate the direction cosine matrix from three rotation angles.
```yaw = 0.7854; pitch = 0.1; roll = 0; dcm = angle2dcm( yaw, pitch, roll )```
```dcm = 3×3 0.7036 0.7036 -0.0998 -0.7071 0.7071 0 0.0706 0.0706 0.9950 ```
Calculate the direction cosine matrix from rotation angles and a rotation sequence.
```yaw = [0.7854 0.5]; pitch = [0.1 0.3]; roll = [0 0.1]; dcm = angle2dcm( pitch, roll, yaw, 'YXZ' )```
```dcm = dcm(:,:,1) = 0.7036 0.7071 -0.0706 -0.7036 0.7071 0.0706 0.0998 0 0.9950 dcm(:,:,2) = 0.8525 0.4770 -0.2136 -0.4321 0.8732 0.2254 0.2940 -0.0998 0.9506 ```
## Input Arguments
collapse all
First rotation angles, specified as an m-by-1 array, in radians.
Data Types: `double` | `single`
Second rotation angles, specified as an m-by-1 array, in radians.
Data Types: `double` | `single`
Third rotation angles, specified as an m-by-1 array, in radians.
Data Types: `double` | `single`
Rotation sequence, specified as a scalar.
Data Types: `char` | `string`
## Output Arguments
collapse all
Direction cosine matrices, returned as a 3-by-3-by-m matrix, where `m` is the number of direction cosine matrices.
## Version History
Introduced in R2006b | 609 | 1,971 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.125 | 3 | CC-MAIN-2023-40 | longest | en | 0.655427 |
https://www.softmath.com/algebra-software/point-slope/prime-factorization-worksheets.html | 1,701,899,192,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100603.33/warc/CC-MAIN-20231206194439-20231206224439-00509.warc.gz | 1,107,300,122 | 9,388 | prime factorization worksheets
Related topics:
inequality equation games | math exercise | how to solve for absolute value on ti-83 calculator | polynomials,2 | solving rational expressions free tools | algebra teachers edition online answers free | ti 83 + solve for variables | how do you type fractions into you eqation with the texas instruments ti83 | simplify exponential sum | solving radical expressions | How Do You Determine If A Polynomial Is The Difference Of Two Squares | how to solve large simultaneous equations mathematica | equations involving rational algebraic expressions
Author Message
Dinetron Ame
Registered: 14.04.2005
Posted: Monday 28th of Aug 11:14 Can anybody help me? I have a math test coming up next week and I am totally confused. I need help particularly with some problems in prime factorization worksheets that are very complex . I don’t wish to go to any tutorial and I would really appreciate any help in this area. Thanks!
IlbendF
Registered: 11.03.2004
From: Netherlands
Posted: Tuesday 29th of Aug 18:36 I have no clue why God made algebra, but you will be happy to know that a group of people also came up with Algebrator! Yes, Algebrator is a program that can help you solve math problems which you never thought you would be able to. Not only does it provide a solution the problem, but it also gives a detailed description of how it got to that solution. All the Best!
alhatec16
Registered: 10.03.2002
From: Notts, UK.
Posted: Thursday 31st of Aug 08:41 I allow my son to use that program Algebrator because I believe it can significantly help him in his algebra problems. It’s been a long time since they first used that program and it did not only help him short-term but I noticed it helped in improving his solving capabilities. The software helped him how to solve rather than helped them just to answer. It’s great !
Milre
Registered: 25.11.2002
From: Riihimäki, Finland
Posted: Thursday 31st of Aug 12:54 Wow! Do these types of software exist? That would really help me in solving my homework. Is (programName) available for free or do I need to buy it? If yes, where can I buy it from?
Noddzj99
Registered: 03.08.2001
From: the 11th dimension
Posted: Saturday 02nd of Sep 08:42 I would suggest trying out Algebrator. It not only helps you with your math problems, but also gives all the required steps in detail so that you can enhance the understanding of the subject. | 583 | 2,438 | {"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-2023-50 | latest | en | 0.947415 |
https://rdrr.io/github/MaleneJuul/ncdDetectTools/src/R/ncdDetect.R | 1,555,693,576,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578527865.32/warc/CC-MAIN-20190419161226-20190419183226-00514.warc.gz | 538,066,014 | 13,493 | # R/ncdDetect.R In MaleneJuul/ncdDetectTools: Functions to perform convolution
#### Documented in ncdDetect
```#' Add discrete stochastic random variables of same dimension
#'
#' @param predictions A matrix in which each row corresponds to a discrete random variable and each column corresponds to a discrete outcome. The matrix contains the probabilities of each outcome, and each row must sum to one.
#' @param scores A matrix in which each row corresponds to a discrete random variable and each column corresponds to a discrete outcome. The matrix contains the values for each outcome for each random variable.
#' @param observations A matrix (optional) in which each row corresponds to a discrete random variable and each column corresponds to a discrete outcome. The matrix contains the observed outcome for each variable. Each row must contain exactly one 1, while the rest of the entries must be 0.
#' @param thres An optional number to set a threshold. If set, the probabilities of all possible outcomes of the sum of the random variables are only caluclated below this value.
#' @return score_dist The convoluted distribution of the sum of the discrete random variables defined by input matrices predictions and scores.
#' @return obs_score The observed score. Only returned if matrix observations is provided as input.
#' @return p_value The p-value resulting from evaluating the observed score in the convoluted distribution. Only returned if matrix observations is provided as input.
#' @examples
#' ncdDetect(predictions = matrix(rep(1/6, 12), nrow = 2), scores = matrix(rep(1:6, 2), nrow = 2, byrow = TRUE),
#' observations = matrix(c(0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0), nrow = 2, byrow = TRUE))
#' ncdDetect(predictions = matrix(rep(1/6, 12), nrow = 2), scores = matrix(rep(1:6, 2), nrow = 2, byrow = TRUE), thres = 6)
#' ncdDetect(predictions = matrix(rep(1/6, 12), nrow = 2), scores = matrix(rep(1:6, 2), nrow = 2, byrow = TRUE))
#' @useDynLib ncdDetectTools
#' @import data.table
#' @export
ncdDetect <- function(predictions, scores, observations = NA, thres = NA) {
# Make initial checks on input --------------------------------------------
observation_available <- F
if (sum(as.numeric(is.na(observations))) == 0) {
observation_available <- T
}
# - data dimenstions
if (!identical(nrow(predictions), nrow(scores))) {
stop("the row numbers of predictions, scores and observations must be identical")
}
if (observation_available) {
if (!identical(nrow(predictions), nrow(observations))) {
stop("the row numbers of predictions, scores and observations must be identical")
}
}
# - negative scores (cannot be handled)
if (any(scores < 0)) {
stop("ncdDetect can currently not handle negative scores")
}
# row sums of predictions matrix
if (unique(round(rowSums(predictions),10)) != 1) {
stop("the row sums of the prediction matrix must sum to one")
}
# row sums of observations must sum to one (must contain only one 1; the rest must be zero)
if (observation_available) {
if (unique(round(rowSums(observations), 10)) != 1) {
stop("each row in the observation matrix must contain one 1, with the rest being zeros")
}
}
# Convert data into data.tables -------------------------------------------
predictions <- as.data.table(predictions)
scores <- data.table(scores)
if (observation_available) {
observations <- data.table(observations)
}
# Add x-values to data ----------------------------------------------------
# (needed in the convolution step in order to know which positions go together)
predictions[, x := 1:.N]
scores[, x := 1:.N]
if (observation_available) {
observations[, x := 1:.N]
}
# Get data in long format -------------------------------------------------
predictions_long <- melt(predictions, id.vars = c("x"), measure.vars = setdiff(names(predictions), "x"),
variable.name = "mutation_type", value.name = "probability", variable.factor = F)
scores_long <- melt(scores, id.vars = c("x"), measure.vars = setdiff(names(scores), "x"),
variable.name = "mutation_type", value.name = "y", variable.factor = F)
if (observation_available) {
observations_long <- melt(observations, id.vars = c("x"), measure.vars = setdiff(names(observations), "x"),
variable.name = "mutation_type", value.name = "observation", variable.factor = F)
}
# Combine predictions, scores and observations ----------------------------
# - set key columns for merging
setkeyv(predictions_long, c("x", "mutation_type"))
setkeyv(scores_long, c("x", "mutation_type"))
# - merge predictions and scores; set key columns
dat <- predictions_long[scores_long]
setkeyv(dat, c("x", "mutation_type"))
# - finally, merge observations onto the data
if (observation_available) {
setkeyv(observations_long, c("x", "mutation_type"))
dat <- dat[observations_long]
}
# Perform convolution -----------------------------------------------------
score_dist <- convolution(dat, threshold = thres)
# Get observed score and p-value ------------------------------------------
if (observation_available) {
obs_score <- dat[observation == 1, sum(y)]
p_value <- score_dist[y >= obs_score, sum(probability)]
}
# Return results ----------------------------------------------------------
if (observation_available) {
return(list("score_dist" = score_dist, "obs_score" = obs_score, "p_value" = p_value))
} else {
return(list("score_dist" = score_dist))
}
}
```
MaleneJuul/ncdDetectTools documentation built on Aug. 25, 2018, 2:16 p.m. | 1,278 | 5,434 | {"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} | 2.75 | 3 | CC-MAIN-2019-18 | latest | en | 0.700897 |
https://forums.space.com/threads/the-speed-of-light.9262/ | 1,675,816,165,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764500664.85/warc/CC-MAIN-20230207233330-20230208023330-00598.warc.gz | 275,531,106 | 27,895 | # The speed of light
Status
Not open for further replies.
B
#### BoJangles
##### Guest
<p style="margin-top:0cm;margin-left:0cm;margin-right:0cm" class="MsoNormal"><font face="Calibri" size="3">Everyone knows we are moving, our continents are drifting, our earth is spinning, the earth is orbiting the sun, the sun is orbiting the Milky Way, the Milky Way is moving in our local galactic cluster, and our galactic cluster is moving compared to the cosmic background radiation. </font></p><p style="margin-top:0cm;margin-left:0cm;margin-right:0cm" class="MsoNormal"><font face="Calibri" size="3">By searching the weird and wonderful internet we can find answers for the speed of light and varying speeds in which we are moving in relation to all the above rest frames. </font></p><p style="margin-top:0cm;margin-left:0cm;margin-right:0cm" class="MsoNormal"><font face="Calibri" size="3">Thought experiment: <span> </span>if we measure the speed of light, in direction A, B and C, knowing we are flying through space at massive speed (100’s km/s) and knowing the speed of light is constant, should not the measurements be dramatically different? <span> </span>In fact couldn’t we infer our exact speed and direction through space just by measuring the speed at which light takes to travel the same distance in 3 directions?</font></p> <div class="Discussion_UserSignature"> <p align="center"><font color="#808080">-------------- </font></p><p align="center"><font size="1" color="#808080"><em>Let me start out with the standard disclaimer ... I am an idiot, I know almost nothing, I haven’t taken calculus, I don’t work for NASA, and I am one-quarter Bulgarian sheep dog. With that out of the way, I have several stupid questions... </em></font></p><p align="center"><font size="1" color="#808080"><em>*** A few months blogging can save a few hours in research ***</em></font></p> </div>
M
#### MeteorWayne
##### Guest
Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>Everyone knows we are moving, our continents are drifting, our earth is spinning, the earth is orbiting the sun, the sun is orbiting the Milky Way, the Milky Way is moving in our local galactic cluster, and our galactic cluster is moving compared to the cosmic background radiation. By searching the weird and wonderful internet we can find answers for the speed of light and varying speeds in which we are moving in relation to all the above rest frames. Thought experiment: if we measure the speed of light, in direction A, B and C, knowing we are flying through space at massive speed (100’s km/s) and knowing the speed of light is constant, should not the measurements be dramatically different? In fact couldn’t we infer our exact speed and direction through space just by measuring the speed at which light takes to travel the same distance in 3 directions? <br />Posted by Manwh0re</DIV><br /><br />That is what was expected back before the 20th century. But in fact, light measures exavtly the same speed in all directions. Google the Michelson-Morley experiment. This discover was the foundation of Einsteins theories of relativity. <div class="Discussion_UserSignature"> <p><font color="#000080"><em><font color="#000000">But the Krell forgot one thing John. Monsters. Monsters from the Id.</font></em> </font></p><p><font color="#000080">I really, really, really, really miss the "first unread post" function</font><font color="#000080"> </font></p> </div>
D
#### DrRocket
##### Guest
<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>Everyone knows we are moving, our continents are drifting, our earth is spinning, the earth is orbiting the sun, the sun is orbiting the Milky Way, the Milky Way is moving in our local galactic cluster, and our galactic cluster is moving compared to the cosmic background radiation. By searching the weird and wonderful internet we can find answers for the speed of light and varying speeds in which we are moving in relation to all the above rest frames. Thought experiment: if we measure the speed of light, in direction A, B and C, knowing we are flying through space at massive speed (100’s km/s) and knowing the speed of light is constant, should not the measurements be dramatically different? In fact couldn’t we infer our exact speed and direction through space just by measuring the speed at which light takes to travel the same distance in 3 directions? <br />Posted by Manwh0re</DIV></p><p>As Wayne noted, the Michelson-Morley experiment was undertaken to find just the effect that you described, but instead found no effect whatever. Einstein's theory of special relativity took that one step further and adopted as a fundamental postulate that the speed of light is a constant, independent of the inertial reference frame in which it is measured.</p><p>While this result may seem counter-intuitive, it has been verified experimentally many times since the Michelson-Morley experiment and has profound implications for our understanding of physics. Among other things it shows that the concept of time is also dependent on the reference frame in which it is measured and this correction for time is important in our use of the Global Positioning System, which relies on very precise time measurements. </p><p>When you "Google" the Michelson-Morely experiment, I suggest that you also look at Special Relativity.<br /></p> <div class="Discussion_UserSignature"> </div>
D
#### derekmcd
##### Guest
<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>Everyone knows we are moving, our continents are drifting, our earth is spinning, the earth is orbiting the sun, the sun is orbiting the Milky Way, the Milky Way is moving in our local galactic cluster, and our galactic cluster is moving compared to the cosmic background radiation. By searching the weird and wonderful internet we can find answers for the speed of light and varying speeds in which we are moving in relation to all the above rest frames. Thought experiment: if we measure the speed of light, in direction A, B and C, knowing we are flying through space at massive speed (100’s km/s) and knowing the speed of light is constant, should not the measurements be dramatically different? In fact couldn’t we infer our exact speed and direction through space just by measuring the speed at which light takes to travel the same distance in 3 directions? <br /> Posted by Manwh0re</DIV></p><p> </p><p>I think the only way this might be possible if the astronaut was travelling in a closed circle and the photons also travel the same path within the closed circle. No matter what speed the astronaut is travelling, should he/she emit two photons when at the "12 o'clock" position (one released in the direction being travelled, and the other in the opposite direction), both photons will circumnavigate the circle at the same speed and still meet at the point they were released. However, due to closing speed, the astronaut will meet the photon that was released from behind sooner than the one that was released in the forward direction. From this, the speed of the craft could be determined.</p><p>Unfortunately, this can't happen in the real world because photons can't travel in a circle unless you can somehow get the photon to fall into orbit around a black hole right on the event horizon. Not sure any astronauts wan't to go there. </p> <div class="Discussion_UserSignature"> <div> </div><br /><div><span style="color:#0000ff" class="Apple-style-span">"If something's hard to do, then it's not worth doing." - Homer Simpson</span></div> </div>
D
#### DrRocket
##### Guest
<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'> I think the only way this might be possible if the astronaut was travelling in a closed circle and the photons also travel the same path within the closed circle. No matter what speed the astronaut is travelling, should he/she emit two photons when at the "12 o'clock" position (one released in the direction being travelled, and the other in the opposite direction), both photons will circumnavigate the circle at the same speed and still meet at the point they were released. However, due to closing speed, the astronaut will meet the photon that was released from behind sooner than the one that was released in the forward direction. From this, the speed of the craft could be determined.Unfortunately, this can't happen in the real world because photons can't travel in a circle unless you can somehow get the photon to fall into orbit around a black hole right on the event horizon. Not sure any astronauts wan't to go there. <br />Posted by derekmcd</DIV></p><p>My head is starting to hurt on this one, but you can get light to go in a circle. Just use fiber optics. The speed will be a bit slower than c but it will be pretty close. However, you still will not be able to detect uniform motion or determine any sort of preferred rest frame. Without going through the problem in detail I'm pretty certain that your scenario will run into trouble determining when the astronaut intercepts the photon -- basically running into the issue of relativity of simultaneity.<br /></p> <div class="Discussion_UserSignature"> </div>
D
#### derekmcd
##### Guest
<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>My head is starting to hurt on this one, but you can get light to go in a circle. Just use fiber optics. The speed will be a bit slower than c but it will be pretty close. However, you still will not be able to detect uniform motion or determine any sort of preferred rest frame. Without going through the problem in detail I'm pretty certain that your scenario will run into trouble determining when the astronaut intercepts the photon -- basically running into the issue of relativity of simultaneity. <br /> Posted by DrRocket</DIV></p><p>A photon travelling in a fiber optic cable made into a circle wouldn't be travelling in a circle. The beam of light, as whole, would be, but the individual photons are not. </p><p>Simultaneity still confuses me a bit, but for the astronaut travelling in a closed circle, I'm not sure if it would be an issue. Wouldn't the astronaut's entire reference frame be contracted. The distance all the way up to his exhaust pipe would be contracted. I would think that if the astronaut can "see" the entire circular path, then the whole path in the direction he is travelling would be contracted. This might mean there would be no issues. Honestly, I'm not quite sure.</p><p>I was thinking more along the line of non-relativistic speeds. Like 2 cars on a race track and me jogging in one direction. I'm going to meet the car travelling the opposite direction first, but the cars will meet where they started. I was just trying to provide a simple picture.</p> <div class="Discussion_UserSignature"> <div> </div><br /><div><span style="color:#0000ff" class="Apple-style-span">"If something's hard to do, then it's not worth doing." - Homer Simpson</span></div> </div>
B
#### BoJangles
##### Guest
<p style="margin:0cm0cm10pt" class="MsoNormal"><font face="Calibri" size="3">Thanks I appreciate all your comments</font></p> <div class="Discussion_UserSignature"> <p align="center"><font color="#808080">-------------- </font></p><p align="center"><font size="1" color="#808080"><em>Let me start out with the standard disclaimer ... I am an idiot, I know almost nothing, I haven’t taken calculus, I don’t work for NASA, and I am one-quarter Bulgarian sheep dog. With that out of the way, I have several stupid questions... </em></font></p><p align="center"><font size="1" color="#808080"><em>*** A few months blogging can save a few hours in research ***</em></font></p> </div>
M
#### Mee_n_Mac
##### Guest
<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>A photon travelling in a fiber optic cable made into a circle wouldn't be travelling in a circle. The beam of light, as whole, would be, but the individual photons are not. Simultaneity still confuses me a bit, but for the astronaut travelling in a closed circle, I'm not sure if it would be an issue. Wouldn't the astronaut's entire reference frame be contracted. The distance all the way up to his exhaust pipe would be contracted. I would think that if the astronaut can "see" the entire circular path, then the whole path in the direction he is travelling would be contracted. This might mean there would be no issues. Honestly, I'm not quite sure.<u>I was thinking more along the line of non-relativistic speeds. Like 2 cars on a race track and me jogging in one direction. I'm going to meet the car travelling the opposite direction first, but the cars will meet where they started. I was just trying to provide a simple picture.</u> <br />Posted by <strong>derekmcd</strong></DIV><br /><br />This is the basic operating priniciple behing a ring laser (or fiber optic) gyro. There's Doppler shift in those devices as well but I see no reason, given a long enough path length, that relative timing between 2 photons or packets of photons couldn't be used to determing rotation rate of the detector (astronaut). I think the grey dots in this wiki animation show what you're trying to say. </p><p>BTW this doesn't answer the OP's question. Let me ponder that for a bit but my inclination is say no you can't measure your velocity his way.</p> <div class="Discussion_UserSignature"> <p>-----------------------------------------------------</p><p><font color="#ff0000">Ask not what your Forum Software can do do on you,</font></p><p><font color="#ff0000">Ask it to, please for the love of all that's Holy, <strong>STOP</strong> !</font></p> </div>
Status
Not open for further replies. | 3,296 | 14,056 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3 | 3 | CC-MAIN-2023-06 | latest | en | 0.760701 |
https://www.physicsforums.com/threads/volume-of-a-solid-with-known-cross-sections.307230/ | 1,701,989,048,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100705.19/warc/CC-MAIN-20231207221604-20231208011604-00415.warc.gz | 1,029,616,816 | 13,949 | # Volume of a solid with known cross sections
## Homework Statement
Any cross sectional slice of a certain solid in a plane perpendicular to the x-axis is a square with side AB, with A lying on the curve $$y^2 = 4x$$ and B on the curve $$x^2 = 4y$$. Find the volume of the solid lying between the points of intersection of these two curves.
## Homework Equations
$$\int ^{b}_{a} A(x)dx$$
## The Attempt at a Solution
I'm not sure if I'm going in the right direction, but so far I've put the curves in terms of y, leaving me with $$y = 2\sqrt{x}$$ and $$y = \frac{x^2}{4}$$. After graphing, I also know that the limits of integration will be from 0 to 4 since the points of intersection are at (0, 0) and (4, 4). From here on, I'm completely lost.
Thanks :)
The area of a square is s^2 where s is the length of one side. So, what is the length of one side? The distance from A to B, so find that from your graph (at an arbitrary x value and the expression should be in terms of y.) | 271 | 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": 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} | 3.8125 | 4 | CC-MAIN-2023-50 | latest | en | 0.943818 |
https://brainmass.com/statistics/confidence-interval/calculating-probabilities-normally-distributed-data-546552 | 1,716,262,366,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058383.61/warc/CC-MAIN-20240521025434-20240521055434-00632.warc.gz | 123,349,360 | 6,648 | Purchase Solution
# Calculating probabilities for normally distributed data
Not what you're looking for?
plastic bags used for packing are manufactured so that the breaking strength
of the bag is distributed by N(5pounds, 2.2 pounds), if a sample of 25 bags is selected.
1. what is the chance that the sample mean of breaking 3 pound strength is larger than 5.3 pounds
2. what is the chance that the breaking strength is larger than 6.0 pounds.
3. between what two values symmetrically distributed around the mean will 95% of the sample mean of breaking strength fall?
4. between what two values symmetrically distributed around the mean will 95% of the breaking strength fall?
5. what is the sample size for finding a population if confidence is 99% and the sampling error is +/- 0.04
##### Solution Summary
The solution gives detailed steps on calculating probabilities for normally distributed data. All the formula and calcuations are shown and explained.
##### Solution Preview
1. what is the chance that the sample mean of breakin3 pound strength is larger than 5.3 pounds
2. what is the chance that the ...
##### Measures of Central Tendency
Tests knowledge of the three main measures of central tendency, including some simple calculation questions. | 271 | 1,268 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.046875 | 3 | CC-MAIN-2024-22 | latest | en | 0.922466 |
http://kamus.landak.com/cari?emang=decimal%20fraction | 1,566,684,659,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027321786.95/warc/CC-MAIN-20190824214845-20190825000845-00348.warc.gz | 106,030,161 | 7,245 | Kamus Online suggested words
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Hasil cari dari kata atau frase: decimal fraction (0.01715 detik)
Found 3 items, similar to decimal fraction.
English → Indonesian (quick) Definition: decimal fraction desimal
English → English (WordNet) Definition: decimal fraction decimal fraction n : a proper fraction whose denominator is a power of 10 [syn: decimal]
English → English (gcide) Definition: Decimal fraction Fraction \Frac"tion\, n. [F. fraction, L. fractio a breaking, fr. frangere, fractum, to break. See Break.] 1. The act of breaking, or state of being broken, especially by violence. [Obs.] [1913 Webster] Neither can the natural body of Christ be subject to any fraction or breaking up. --Foxe. [1913 Webster] 2. A portion; a fragment. [1913 Webster] Some niggard fractions of an hour. --Tennyson. [1913 Webster] 3. (Arith. or Alg.) One or more aliquot parts of a unit or whole number; an expression for a definite portion of a unit or magnitude. [1913 Webster] Common fraction, or Vulgar fraction, a fraction in which the number of equal parts into which the integer is supposed to be divided is indicated by figures or letters, called the denominator, written below a line, over which is the numerator, indicating the number of these parts included in the fraction; as 1/2, one half, 2/5, two fifths. Complex fraction, a fraction having a fraction or mixed number in the numerator or denominator, or in both. --Davies & Peck. Compound fraction, a fraction of a fraction; two or more fractions connected by of. Continued fraction, Decimal fraction, Partial fraction, etc. See under Continued, Decimal, Partial, etc. Improper fraction, a fraction in which the numerator is greater than the denominator. Proper fraction, a fraction in which the numerator is less than the denominator. [1913 Webster] Decimal \Dec"i*mal\, a. [F. d['e]cimal (cf. LL. decimalis), fr. L. decimus tenth, fr. decem ten. See Ten, and cf. Dime.] Of or pertaining to decimals; numbered or proceeding by tens; having a tenfold increase or decrease, each unit being ten times the unit next smaller; as, decimal notation; a decimal coinage. [1913 Webster] Decimal arithmetic, the common arithmetic, in which numeration proceeds by tens. Decimal fraction, a fraction in which the denominator is some power of 10, as 2/10, [frac25x100], and is usually not expressed, but is signified by a point placed at the left hand of the numerator, as .2, .25. Decimal point, a dot or full stop at the left of a decimal fraction. The figures at the left of the point represent units or whole numbers, as 1.05. [1913 Webster]
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# If x and y are integers, is xy even?
SORT BY:
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90090 posts | 607 | 1,814 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.078125 | 3 | CC-MAIN-2023-50 | latest | en | 0.79785 |
https://pkg.go.dev/sort@go1.12beta1 | 1,632,303,845,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780057337.81/warc/CC-MAIN-20210922072047-20210922102047-00295.warc.gz | 492,543,290 | 16,139 | # sort
package standard library
Version: go1.12beta1 Latest Latest
This package is not in the latest version of its module.
Go to latest
Published: Dec 18, 2018 License: BSD-3-Clause
## Documentation ¶
### Overview ¶
Package sort provides primitives for sorting slices and user-defined collections.
Example
package main
import (
"fmt"
"sort"
)
type Person struct {
Name string
Age int
}
func (p Person) String() string {
return fmt.Sprintf("%s: %d", p.Name, p.Age)
}
// ByAge implements sort.Interface for []Person based on
// the Age field.
type ByAge []Person
func (a ByAge) Len() int { return len(a) }
func (a ByAge) Swap(i, j int) { a[i], a[j] = a[j], a[i] }
func (a ByAge) Less(i, j int) bool { return a[i].Age < a[j].Age }
func main() {
people := []Person{
{"Bob", 31},
{"John", 42},
{"Michael", 17},
{"Jenny", 26},
}
fmt.Println(people)
// There are two ways to sort a slice. First, one can define
// a set of methods for the slice type, as with ByAge, and
// call sort.Sort. In this first example we use that technique.
sort.Sort(ByAge(people))
fmt.Println(people)
// The other way is to use sort.Slice with a custom Less
// function, which can be provided as a closure. In this
// case no methods are needed. (And if they exist, they
// are ignored.) Here we re-sort in reverse order: compare
// the closure with ByAge.Less.
sort.Slice(people, func(i, j int) bool {
return people[i].Age > people[j].Age
})
fmt.Println(people)
}
Output:
[Bob: 31 John: 42 Michael: 17 Jenny: 26]
[Michael: 17 Jenny: 26 Bob: 31 John: 42]
[John: 42 Bob: 31 Jenny: 26 Michael: 17]
Example (SortKeys)
ExampleSortKeys demonstrates a technique for sorting a struct type using programmable sort criteria.
package main
import (
"fmt"
"sort"
)
// A couple of type definitions to make the units clear.
type earthMass float64
type au float64
// A Planet defines the properties of a solar system object.
type Planet struct {
name string
mass earthMass
distance au
}
// By is the type of a "less" function that defines the ordering of its Planet arguments.
type By func(p1, p2 *Planet) bool
// Sort is a method on the function type, By, that sorts the argument slice according to the function.
func (by By) Sort(planets []Planet) {
ps := &planetSorter{
planets: planets,
by: by, // The Sort method's receiver is the function (closure) that defines the sort order.
}
sort.Sort(ps)
}
// planetSorter joins a By function and a slice of Planets to be sorted.
type planetSorter struct {
planets []Planet
by func(p1, p2 *Planet) bool // Closure used in the Less method.
}
// Len is part of sort.Interface.
func (s *planetSorter) Len() int {
return len(s.planets)
}
// Swap is part of sort.Interface.
func (s *planetSorter) Swap(i, j int) {
s.planets[i], s.planets[j] = s.planets[j], s.planets[i]
}
// Less is part of sort.Interface. It is implemented by calling the "by" closure in the sorter.
func (s *planetSorter) Less(i, j int) bool {
return s.by(&s.planets[i], &s.planets[j])
}
var planets = []Planet{
{"Mercury", 0.055, 0.4},
{"Venus", 0.815, 0.7},
{"Earth", 1.0, 1.0},
{"Mars", 0.107, 1.5},
}
// ExampleSortKeys demonstrates a technique for sorting a struct type using programmable sort criteria.
func main() {
// Closures that order the Planet structure.
name := func(p1, p2 *Planet) bool {
return p1.name < p2.name
}
mass := func(p1, p2 *Planet) bool {
return p1.mass < p2.mass
}
distance := func(p1, p2 *Planet) bool {
return p1.distance < p2.distance
}
decreasingDistance := func(p1, p2 *Planet) bool {
return distance(p2, p1)
}
// Sort the planets by the various criteria.
By(name).Sort(planets)
fmt.Println("By name:", planets)
By(mass).Sort(planets)
fmt.Println("By mass:", planets)
By(distance).Sort(planets)
fmt.Println("By distance:", planets)
By(decreasingDistance).Sort(planets)
fmt.Println("By decreasing distance:", planets)
}
Output:
By name: [{Earth 1 1} {Mars 0.107 1.5} {Mercury 0.055 0.4} {Venus 0.815 0.7}]
By mass: [{Mercury 0.055 0.4} {Mars 0.107 1.5} {Venus 0.815 0.7} {Earth 1 1}]
By distance: [{Mercury 0.055 0.4} {Venus 0.815 0.7} {Earth 1 1} {Mars 0.107 1.5}]
By decreasing distance: [{Mars 0.107 1.5} {Earth 1 1} {Venus 0.815 0.7} {Mercury 0.055 0.4}]
Example (SortMultiKeys)
ExampleMultiKeys demonstrates a technique for sorting a struct type using different sets of multiple fields in the comparison. We chain together "Less" functions, each of which compares a single field.
package main
import (
"fmt"
"sort"
)
// A Change is a record of source code changes, recording user, language, and delta size.
type Change struct {
user string
language string
lines int
}
type lessFunc func(p1, p2 *Change) bool
// multiSorter implements the Sort interface, sorting the changes within.
type multiSorter struct {
changes []Change
less []lessFunc
}
// Sort sorts the argument slice according to the less functions passed to OrderedBy.
func (ms *multiSorter) Sort(changes []Change) {
ms.changes = changes
sort.Sort(ms)
}
// OrderedBy returns a Sorter that sorts using the less functions, in order.
// Call its Sort method to sort the data.
func OrderedBy(less ...lessFunc) *multiSorter {
return &multiSorter{
less: less,
}
}
// Len is part of sort.Interface.
func (ms *multiSorter) Len() int {
return len(ms.changes)
}
// Swap is part of sort.Interface.
func (ms *multiSorter) Swap(i, j int) {
ms.changes[i], ms.changes[j] = ms.changes[j], ms.changes[i]
}
// Less is part of sort.Interface. It is implemented by looping along the
// less functions until it finds a comparison that discriminates between
// the two items (one is less than the other). Note that it can call the
// less functions twice per call. We could change the functions to return
// -1, 0, 1 and reduce the number of calls for greater efficiency: an
// exercise for the reader.
func (ms *multiSorter) Less(i, j int) bool {
p, q := &ms.changes[i], &ms.changes[j]
// Try all but the last comparison.
var k int
for k = 0; k < len(ms.less)-1; k++ {
less := ms.less[k]
switch {
case less(p, q):
// p < q, so we have a decision.
return true
case less(q, p):
// p > q, so we have a decision.
return false
}
// p == q; try the next comparison.
}
// All comparisons to here said "equal", so just return whatever
// the final comparison reports.
return ms.less[k](p, q)
}
var changes = []Change{
{"gri", "Go", 100},
{"ken", "C", 150},
{"glenda", "Go", 200},
{"rsc", "Go", 200},
{"r", "Go", 100},
{"ken", "Go", 200},
{"dmr", "C", 100},
{"r", "C", 150},
{"gri", "Smalltalk", 80},
}
// ExampleMultiKeys demonstrates a technique for sorting a struct type using different
// sets of multiple fields in the comparison. We chain together "Less" functions, each of
// which compares a single field.
func main() {
// Closures that order the Change structure.
user := func(c1, c2 *Change) bool {
return c1.user < c2.user
}
language := func(c1, c2 *Change) bool {
return c1.language < c2.language
}
increasingLines := func(c1, c2 *Change) bool {
return c1.lines < c2.lines
}
decreasingLines := func(c1, c2 *Change) bool {
return c1.lines > c2.lines // Note: > orders downwards.
}
// Simple use: Sort by user.
OrderedBy(user).Sort(changes)
fmt.Println("By user:", changes)
// More examples.
OrderedBy(user, increasingLines).Sort(changes)
fmt.Println("By user,<lines:", changes)
OrderedBy(user, decreasingLines).Sort(changes)
fmt.Println("By user,>lines:", changes)
OrderedBy(language, increasingLines).Sort(changes)
fmt.Println("By language,<lines:", changes)
OrderedBy(language, increasingLines, user).Sort(changes)
fmt.Println("By language,<lines,user:", changes)
}
Output:
By user: [{dmr C 100} {glenda Go 200} {gri Go 100} {gri Smalltalk 80} {ken C 150} {ken Go 200} {r Go 100} {r C 150} {rsc Go 200}]
By user,<lines: [{dmr C 100} {glenda Go 200} {gri Smalltalk 80} {gri Go 100} {ken C 150} {ken Go 200} {r Go 100} {r C 150} {rsc Go 200}]
By user,>lines: [{dmr C 100} {glenda Go 200} {gri Go 100} {gri Smalltalk 80} {ken Go 200} {ken C 150} {r C 150} {r Go 100} {rsc Go 200}]
By language,<lines: [{dmr C 100} {ken C 150} {r C 150} {r Go 100} {gri Go 100} {ken Go 200} {glenda Go 200} {rsc Go 200} {gri Smalltalk 80}]
By language,<lines,user: [{dmr C 100} {ken C 150} {r C 150} {gri Go 100} {r Go 100} {glenda Go 200} {ken Go 200} {rsc Go 200} {gri Smalltalk 80}]
Example (SortWrapper)
package main
import (
"fmt"
"sort"
)
type Grams int
func (g Grams) String() string { return fmt.Sprintf("%dg", int(g)) }
type Organ struct {
Name string
Weight Grams
}
type Organs []*Organ
func (s Organs) Len() int { return len(s) }
func (s Organs) Swap(i, j int) { s[i], s[j] = s[j], s[i] }
// ByName implements sort.Interface by providing Less and using the Len and
// Swap methods of the embedded Organs value.
type ByName struct{ Organs }
func (s ByName) Less(i, j int) bool { return s.Organs[i].Name < s.Organs[j].Name }
// ByWeight implements sort.Interface by providing Less and using the Len and
// Swap methods of the embedded Organs value.
type ByWeight struct{ Organs }
func (s ByWeight) Less(i, j int) bool { return s.Organs[i].Weight < s.Organs[j].Weight }
func main() {
s := []*Organ{
{"brain", 1340},
{"heart", 290},
{"liver", 1494},
{"pancreas", 131},
{"prostate", 62},
{"spleen", 162},
}
sort.Sort(ByWeight{s})
fmt.Println("Organs by weight:")
printOrgans(s)
sort.Sort(ByName{s})
fmt.Println("Organs by name:")
printOrgans(s)
}
func printOrgans(s []*Organ) {
for _, o := range s {
fmt.Printf("%-8s (%v)\n", o.Name, o.Weight)
}
}
Output:
Organs by weight:
prostate (62g)
pancreas (131g)
spleen (162g)
heart (290g)
brain (1340g)
liver (1494g)
Organs by name:
brain (1340g)
heart (290g)
liver (1494g)
pancreas (131g)
prostate (62g)
spleen (162g)
### Constants ¶
This section is empty.
### Variables ¶
This section is empty.
### Functions ¶
#### func Float64s ¶
func Float64s(a []float64)
Float64s sorts a slice of float64s in increasing order (not-a-number values are treated as less than other values).
Example
package main
import (
"fmt"
"math"
"sort"
)
func main() {
s := []float64{5.2, -1.3, 0.7, -3.8, 2.6} // unsorted
sort.Float64s(s)
fmt.Println(s)
s = []float64{math.Inf(1), math.NaN(), math.Inf(-1), 0.0} // unsorted
sort.Float64s(s)
fmt.Println(s)
}
Output:
[-3.8 -1.3 0.7 2.6 5.2]
[NaN -Inf 0 +Inf]
#### func Float64sAreSorted ¶
func Float64sAreSorted(a []float64) bool
Float64sAreSorted tests whether a slice of float64s is sorted in increasing order (not-a-number values are treated as less than other values).
Example
package main
import (
"fmt"
"sort"
)
func main() {
s := []float64{0.7, 1.3, 2.6, 3.8, 5.2} // sorted ascending
fmt.Println(sort.Float64sAreSorted(s))
s = []float64{5.2, 3.8, 2.6, 1.3, 0.7} // sorted descending
fmt.Println(sort.Float64sAreSorted(s))
s = []float64{5.2, 1.3, 0.7, 3.8, 2.6} // unsorted
fmt.Println(sort.Float64sAreSorted(s))
}
Output:
true
false
false
#### func Ints ¶
func Ints(a []int)
Ints sorts a slice of ints in increasing order.
Example
package main
import (
"fmt"
"sort"
)
func main() {
s := []int{5, 2, 6, 3, 1, 4} // unsorted
sort.Ints(s)
fmt.Println(s)
}
Output:
[1 2 3 4 5 6]
#### func IntsAreSorted ¶
func IntsAreSorted(a []int) bool
IntsAreSorted tests whether a slice of ints is sorted in increasing order.
Example
package main
import (
"fmt"
"sort"
)
func main() {
s := []int{1, 2, 3, 4, 5, 6} // sorted ascending
fmt.Println(sort.IntsAreSorted(s))
s = []int{6, 5, 4, 3, 2, 1} // sorted descending
fmt.Println(sort.IntsAreSorted(s))
s = []int{3, 2, 4, 1, 5} // unsorted
fmt.Println(sort.IntsAreSorted(s))
}
Output:
true
false
false
#### func IsSorted ¶
func IsSorted(data Interface) bool
IsSorted reports whether data is sorted.
func Search(n int, f func(int) bool) int
Search uses binary search to find and return the smallest index i in [0, n) at which f(i) is true, assuming that on the range [0, n), f(i) == true implies f(i+1) == true. That is, Search requires that f is false for some (possibly empty) prefix of the input range [0, n) and then true for the (possibly empty) remainder; Search returns the first true index. If there is no such index, Search returns n. (Note that the "not found" return value is not -1 as in, for instance, strings.Index.) Search calls f(i) only for i in the range [0, n).
A common use of Search is to find the index i for a value x in a sorted, indexable data structure such as an array or slice. In this case, the argument f, typically a closure, captures the value to be searched for, and how the data structure is indexed and ordered.
For instance, given a slice data sorted in ascending order, the call Search(len(data), func(i int) bool { return data[i] >= 23 }) returns the smallest index i such that data[i] >= 23. If the caller wants to find whether 23 is in the slice, it must test data[i] == 23 separately.
Searching data sorted in descending order would use the <= operator instead of the >= operator.
To complete the example above, the following code tries to find the value x in an integer slice data sorted in ascending order:
x := 23
i := sort.Search(len(data), func(i int) bool { return data[i] >= x })
if i < len(data) && data[i] == x {
// x is present at data[i]
} else {
// x is not present in data,
// but i is the index where it would be inserted.
}
As a more whimsical example, this program guesses your number:
func GuessingGame() {
var s string
fmt.Printf("Pick an integer from 0 to 100.\n")
answer := sort.Search(100, func(i int) bool {
fmt.Printf("Is your number <= %d? ", i)
fmt.Scanf("%s", &s)
return s != "" && s[0] == 'y'
})
}
Example (DescendingOrder)
This example demonstrates searching a list sorted in descending order. The approach is the same as searching a list in ascending order, but with the condition inverted.
package main
import (
"fmt"
"sort"
)
func main() {
a := []int{55, 45, 36, 28, 21, 15, 10, 6, 3, 1}
x := 6
i := sort.Search(len(a), func(i int) bool { return a[i] <= x })
if i < len(a) && a[i] == x {
fmt.Printf("found %d at index %d in %v\n", x, i, a)
} else {
fmt.Printf("%d not found in %v\n", x, a)
}
}
Output:
found 6 at index 7 in [55 45 36 28 21 15 10 6 3 1]
#### func SearchFloat64s ¶
func SearchFloat64s(a []float64, x float64) int
SearchFloat64s searches for x in a sorted slice of float64s and returns the index as specified by Search. The return value is the index to insert x if x is not present (it could be len(a)). The slice must be sorted in ascending order.
#### func SearchInts ¶
func SearchInts(a []int, x int) int
SearchInts searches for x in a sorted slice of ints and returns the index as specified by Search. The return value is the index to insert x if x is not present (it could be len(a)). The slice must be sorted in ascending order.
#### func SearchStrings ¶
func SearchStrings(a []string, x string) int
SearchStrings searches for x in a sorted slice of strings and returns the index as specified by Search. The return value is the index to insert x if x is not present (it could be len(a)). The slice must be sorted in ascending order.
#### func Slice ¶ added in go1.8
func Slice(slice interface{}, less func(i, j int) bool)
Slice sorts the provided slice given the provided less function.
The sort is not guaranteed to be stable. For a stable sort, use SliceStable.
The function panics if the provided interface is not a slice.
Example
package main
import (
"fmt"
"sort"
)
func main() {
people := []struct {
Name string
Age int
}{
{"Gopher", 7},
{"Alice", 55},
{"Vera", 24},
{"Bob", 75},
}
sort.Slice(people, func(i, j int) bool { return people[i].Name < people[j].Name })
fmt.Println("By name:", people)
sort.Slice(people, func(i, j int) bool { return people[i].Age < people[j].Age })
fmt.Println("By age:", people)
}
Output:
By name: [{Alice 55} {Bob 75} {Gopher 7} {Vera 24}]
By age: [{Gopher 7} {Vera 24} {Alice 55} {Bob 75}]
#### func SliceIsSorted ¶ added in go1.8
func SliceIsSorted(slice interface{}, less func(i, j int) bool) bool
SliceIsSorted tests whether a slice is sorted.
The function panics if the provided interface is not a slice.
#### func SliceStable ¶ added in go1.8
func SliceStable(slice interface{}, less func(i, j int) bool)
SliceStable sorts the provided slice given the provided less function while keeping the original order of equal elements.
The function panics if the provided interface is not a slice.
Example
package main
import (
"fmt"
"sort"
)
func main() {
people := []struct {
Name string
Age int
}{
{"Alice", 25},
{"Elizabeth", 75},
{"Alice", 75},
{"Bob", 75},
{"Alice", 75},
{"Bob", 25},
{"Colin", 25},
{"Elizabeth", 25},
}
// Sort by name, preserving original order
sort.SliceStable(people, func(i, j int) bool { return people[i].Name < people[j].Name })
fmt.Println("By name:", people)
// Sort by age preserving name order
sort.SliceStable(people, func(i, j int) bool { return people[i].Age < people[j].Age })
fmt.Println("By age,name:", people)
}
Output:
By name: [{Alice 25} {Alice 75} {Alice 75} {Bob 75} {Bob 25} {Colin 25} {Elizabeth 75} {Elizabeth 25}]
By age,name: [{Alice 25} {Bob 25} {Colin 25} {Elizabeth 25} {Alice 75} {Alice 75} {Bob 75} {Elizabeth 75}]
#### func Sort ¶
func Sort(data Interface)
Sort sorts data. It makes one call to data.Len to determine n, and O(n*log(n)) calls to data.Less and data.Swap. The sort is not guaranteed to be stable.
#### func Stable ¶ added in go1.2
func Stable(data Interface)
Stable sorts data while keeping the original order of equal elements.
It makes one call to data.Len to determine n, O(n*log(n)) calls to data.Less and O(n*log(n)*log(n)) calls to data.Swap.
#### func Strings ¶
func Strings(a []string)
Strings sorts a slice of strings in increasing order.
Example
package main
import (
"fmt"
"sort"
)
func main() {
s := []string{"Go", "Bravo", "Gopher", "Alpha", "Grin", "Delta"}
sort.Strings(s)
fmt.Println(s)
}
Output:
[Alpha Bravo Delta Go Gopher Grin]
#### func StringsAreSorted ¶
func StringsAreSorted(a []string) bool
StringsAreSorted tests whether a slice of strings is sorted in increasing order.
### Types ¶
#### type Float64Slice ¶
type Float64Slice []float64
Float64Slice attaches the methods of Interface to []float64, sorting in increasing order (not-a-number values are treated as less than other values).
#### func (Float64Slice) Len ¶
func (p Float64Slice) Len() int
#### func (Float64Slice) Less ¶
func (p Float64Slice) Less(i, j int) bool
#### func (Float64Slice) Search ¶
func (p Float64Slice) Search(x float64) int
Search returns the result of applying SearchFloat64s to the receiver and x.
#### func (Float64Slice) Sort ¶
func (p Float64Slice) Sort()
Sort is a convenience method.
#### func (Float64Slice) Swap ¶
func (p Float64Slice) Swap(i, j int)
#### type IntSlice ¶
type IntSlice []int
IntSlice attaches the methods of Interface to []int, sorting in increasing order.
#### func (IntSlice) Len ¶
func (p IntSlice) Len() int
#### func (IntSlice) Less ¶
func (p IntSlice) Less(i, j int) bool
#### func (IntSlice) Search ¶
func (p IntSlice) Search(x int) int
Search returns the result of applying SearchInts to the receiver and x.
#### func (IntSlice) Sort ¶
func (p IntSlice) Sort()
Sort is a convenience method.
#### func (IntSlice) Swap ¶
func (p IntSlice) Swap(i, j int)
#### type Interface ¶
type Interface interface {
// Len is the number of elements in the collection.
Len() int
// Less reports whether the element with
// index i should sort before the element with index j.
Less(i, j int) bool
// Swap swaps the elements with indexes i and j.
Swap(i, j int)
}
A type, typically a collection, that satisfies sort.Interface can be sorted by the routines in this package. The methods require that the elements of the collection be enumerated by an integer index.
#### func Reverse ¶ added in go1.1
func Reverse(data Interface) Interface
Reverse returns the reverse order for data.
Example
package main
import (
"fmt"
"sort"
)
func main() {
s := []int{5, 2, 6, 3, 1, 4} // unsorted
sort.Sort(sort.Reverse(sort.IntSlice(s)))
fmt.Println(s)
}
Output:
[6 5 4 3 2 1]
#### type StringSlice ¶
type StringSlice []string
StringSlice attaches the methods of Interface to []string, sorting in increasing order.
#### func (StringSlice) Len ¶
func (p StringSlice) Len() int
#### func (StringSlice) Less ¶
func (p StringSlice) Less(i, j int) bool
#### func (StringSlice) Search ¶
func (p StringSlice) Search(x string) int
Search returns the result of applying SearchStrings to the receiver and x.
#### func (StringSlice) Sort ¶
func (p StringSlice) Sort()
Sort is a convenience method.
#### func (StringSlice) Swap ¶
func (p StringSlice) Swap(i, j int) | 6,089 | 20,708 | {"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-2021-39 | latest | en | 0.573188 |
https://www.esaral.com/q/express-each-of-the-following-product-as-a-monomials-and-verify-the-result-in-each-case-for-x-1-67904 | 1,719,002,950,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862157.88/warc/CC-MAIN-20240621191840-20240621221840-00329.warc.gz | 668,685,595 | 11,989 | # Express each of the following product as a monomials and verify the result in each case for x = 1:
Question:
Express each of the following product as a monomials and verify the result in each case for x = 1:
(x2)3 × (2x) × (−4x) × (5)
Solution:
We have to find the product of the expression in order to express it as a monomial.
To multiply algebraic expressions, we use commutative and associative laws along with the laws of indices, i.e., $a^{m} \times a^{n}=a^{m+n}$ and $\left(a^{m}\right)^{n}=a^{m n}$
We have:
$\left(x^{2}\right)^{3} \times(2 x) \times(-4 x) \times 5$
$=\left(x^{6}\right) \times(2 x) \times(-4 x) \times 5$
$=\{2 \times(-4) \times 5\} \times\left(x^{6} \times x \times x\right)$
$=\{2 \times(-4) \times 5\} \times\left(x^{6+1+1}\right)$
$=-40 x^{8}$
$\therefore\left(x^{2}\right)^{3} \times(2 x) \times(-4 x) \times 5=-40 x^{8}$
Substituting x = 1 in LHS, we get:
LHS $=\left(x^{2}\right)^{3} \times(2 x) \times(-4 x) \times 5$
$=\left(1^{2}\right)^{3} \times(2 \times 1) \times(-4 \times 1) \times 5$
$=1^{6} \times 2 \times(-4) \times 5$
$=1 \times 2 \times(-4) \times 5$
$=-40$
Putting x = 1 in RHS, we get:
$\mathrm{RHS}=-40 x^{8}$
$=-40(1)^{8}$
$=-40 \times 1$
$=-40$
$\because L H S=R H S$ for $x=1$; therefore, the result is correct
Thus, the answer is $-40 x^{8}$. | 525 | 1,325 | {"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} | 4.59375 | 5 | CC-MAIN-2024-26 | latest | en | 0.567165 |
https://www.askmehelpdesk.com/math-sciences/true-false-315720.html | 1,696,016,482,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510528.86/warc/CC-MAIN-20230929190403-20230929220403-00757.warc.gz | 703,292,620 | 9,171 | P-Will Posts: 1, Reputation: 1 New Member #1 Feb 10, 2009, 11:49 AM
True or false
True or false: In a unit circle, the radian measure of a central angle and the length of the intercepted arc are equal.
True or false: In a unit circle, the degree measure of a central angle and the length of the intercepted arc are equal.
ebaines Posts: 12,131, Reputation: 1307 Expert #2 Feb 10, 2009, 12:09 PM
You should learn and memorize that the arc length s is equal to:
$
s = R \theta
$
where $\theta$ is the angle measured in radians.
Further, to convert an angle measurement from radians to degrees multiply radians by $180 /\pi$
You now have enough information to answer thee questions yourself.
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Is an e'mail traceable back to the sender?
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Is a cell of animals prokaryotes | 297 | 1,206 | {"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": 3, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.765625 | 3 | CC-MAIN-2023-40 | latest | en | 0.854246 |
https://www.physicsforums.com/threads/trig-question.284723/ | 1,544,988,030,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376827992.73/warc/CC-MAIN-20181216191351-20181216213351-00478.warc.gz | 1,020,174,438 | 12,684 | # Homework Help: Trig question
1. Jan 13, 2009
### bobby1
1. The problem statement, all variables and given/known data
A ship in distress sends up flares that are visible to two other ships. The athabasca notes that the flares are a N41 degrees E of its position. The Britiannia, which is 12.7 nautical miles due east of the athabasca sees the flares at a bearing of 310 degrees. will the athabasca or the britannia reach the ship in distress first if they travel at equal speeds. Where do I start.
2. Relevant equations
3. The attempt at a solution
2. Jan 13, 2009
### gabbagabbahey
Start by drawing a picture!
I suggest putting the athabasca at the origin, letting North represent the positive y-direction and East, the positive x-direction.
Then label the position of the Britiannia and draw a vector pointing from the athabasca in the direction N 41 deg East and from the Britiannia at a bearing of 310 degrees. The point where those two vectors intersect is the location of the ship in distress. Find that location, then calculate which ship is closer.
3. Jan 13, 2009 | 277 | 1,085 | {"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-2018-51 | latest | en | 0.912438 |
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