text:
Homework 4

Due: April 27, 2018 @ 11:59pm

Instructions

For this homework assignment, you will use statistical inference to answer a question about the National Survey of Family Growth, Cycle 6 dataset published by the National Center for Health Statistics.

Obtain the Github repository you will use to complete homework 4 that contains a starter RMarkdown file named homework_4.Rmd, which you will use to do your work and write-up when completing the questions below. Remember to fill in your name at the top of the RMarkdown document and be sure to save, commit, and push (upload) frequently to Github so that you have incremental snapshots of your work. When you’re done, follow the How to submit section below to setup a Pull Request, which will be used for feedback.

This homework uses the National Survey of Family Growth, Cycle 6 dataset in the file 2002FemPreg.rds, published by the National Center for Health Statistics. Complete descriptions of all the variables can be found in the NSFG Cycle 6: Female Pregnancy File Codebook. Below are selected descriptions of variables that will be used for this homework assignment:

Variable Description
caseid integer ID of the respondent
prglngth integer duration of the pregnancy in weeks
outcome integer code for the outcome of the pregnancy, with a 1 indicating a live birth
birthord serial number for live births; the code for a respondent’s first child is 1, and so on. For outcomes other than live birth, this field is blank

Questions

This homework assignment revolves around answering the following question using this dataset:

Do first born children either arrive early or late when compared with non-first-borns?

The questions in this assignment will guide you through the process of answering this question using statistical inference.

1. Addressing the question “do first born children either arrive early or late when compared with non-first-borns?” means that we should only consider live births in the dataset. Filter the dataset so that it only contains outcomes with live births and assign this result to the variable live_births.

Next, we need to label all births in live_births as either “first” or “other” so that we can easily find the children that are first borns and the ones that are not. There are a couple of different ways that you can label the births:

• Split the dataset into two parts, a first_births dataset and an other_births dataset. Do this by applying a filter to extract the first births, then use mutate() to create a new column called birth_order that labels these rows as “first”. Then repeat this process, except apply a filter to extract all other births and label those as “other” in birth_order. To recombine the datasets into one, use bind_rows().

• Use ifelse() with mutate() to create the birth_order column and the “first” and “other” labels. You can also try using case_when() instead of ifelse() to accomplish this. If you do it this way, you won’t need to use bind_rows().

After labeling the births, remove the extraneous variables from the tibble leaving just the prglngth and birth_order columns. Assign the resulting tibble to a variable named pregnancy_length.

2. Take the pregnancy_length dataset and plot a probability mass function (PMF) histogram of the pregnancy length in weeks that shows “first” births and “other” births on the same plot. Choose a reasonable binwidth for the histogram and add coord_cartesian(xlim = c(27, 46)) to your plot so that the window focuses where most of the data is. After creating the plot, describe the shape, center, and spread of the two distributions. Based on the visualization, do you think the data looks like it supports the statement that “first born children either arrive early or arrive late when compared with non-first-borns”?

3. Group the variable prglngth into “first” and “other” births and compute the summary statistics (mean, median, standard deviation, inter-quartile range, minimum, maximum) for each group. How do the different summary statistics compare between the two distributions? Does it look like there may be a notable difference between the two distributions? Explain.

4. Create theoretical quantile-quantile (q-q) plots to determine whether the pregnancy length distributions for “first” and “other” births are nearly normal. You should make separate q-q plots for “first” births and “other” births (i.e. you should end up with two plots).

Each q-q plot should include a reference line that shows what the theoretical normal distribution looks like so that we can observe deviations from normality. You’ll need to compute this line manually. Adapt the following code to compute the slope and intercept for the theoretical line (you will need to do this twice, once for “first” births and again for “other” births):

qq_x <- qnorm(p = c(0.25, 0.75))
qq_y <- quantile(x = pull(dataset, variable), probs = c(0.25, 0.75), type = 1)
qq_slope <- diff(qq_y) / diff(qq_x)
qq_int <- pluck(qq_y, 1) - qq_slope * pluck(qq_x, 1)

“Adapting the code” means you will have to change the dataset and variable parameters. Once you have found qq_slope and qq_int for “first” and “other” births, use geom_abline() to include the theoretical reference line in your q-q plots.

Based on your plots, does it appear that the pregnancy length distribution is nearly normal for both “first” and “other” births? Why or why not?

5. Returning back to the question of whether or not “first babies arrive early or arrive late when compared with non-first-borns”, plot the cumulative distribution functions (CDFs) of the pregnancy lengths for “first” and “other” births. Plot the CDF for both distributions on the same figure so that we can directly compare them. How do the distributions compare? Does it look like there is there a meaningful difference between the two distributions?

6. If we want to determine whether or not the difference between two distributions is statistically significant, we need to run a hypothesis test. Formalize your analysis by writing down the null hypothesis for the question of whether first babies arrive early or arrive late when compared with non-first-borns. It should be clear from how you write your null hypothesis whether you’re conducting a one-sided or two-sided hypothesis test. You should also restate what the observed value is (this will be a number) that you will be comparing against the null distribution.

7. Use a simulation to generate the null distribution so that you can perform the hypothesis test. Do this using the functions provided in the infer package, specify(), hypothesize(), generate(), and calculate(). To collect enough statistics, you should set the simulation to repeat 10,000 times.

Once you’ve obtained the null distribution, use it to compute the p-value for your hypothesis test. Assuming a significance level of $$\alpha = 0.05$$, state whether we can we reject the null hypothesis.

Finally, visualize the simulated null distribution as a histogram and use geom_vline() to show where the observed value sits relative to it.

8. Use a bootstrap simulation to calculate the 95% confidence interval for your observed value. Do this using the following functions from the infer package, specify(), generate(), and calculate(). To collect enough statistics, you should set the bootstrap simulation to repeat 10,000 times.

Once you’ve obtained the bootstrap distribution, use quantile() to find the upper and lower bounds of the 95% confidence interval. Does the value corresponding to the null result fall within the range of the 95% confidence interval?

Finally, visualize the bootstrap distribution as a histogram and use two geom_vline()s to show the region corresponding to the 95% confidence interval.

9. In addition to hypothesis tests and confidence intervals, we should also consider the effect size, which measures the relative difference between two distributions. The effect size helps us better know how important a given result actually is, not just whether or not we can reject the null hypothesis. One measure of the effect size is called Cohen’s d ( https://en.wikipedia.org/wiki/Effect_size#Cohen.27s_d), which we will use to compute the effect size between the pregnancy lengths for “first” and “other” births. The different ranges of d can be interpreted using the following table:

Effect size d
Very small 0.01
Small 0.20
Medium 0.50
Large 0.80
Very large 1.20
Huge 2.00

The following set of functions should also be preloaded for you: cohens_d_bootstrap(), bootstrap_report(), and plot_ci(). These functions will use bootstrap simulations to compute the confidence interval for the Cohen’s d parameter. Run the bootstrap simulation as follows:

cohens_d_bootstrap(data = pregnancy_length, model = prglngth ~ birth_order)

Be sure to assign the results to a variable, for example bootstrap_results.

To print a report for the bootstrap simulation, run:

bootstrap_report(bootstrap_results)

To visualize the bootstrap distribution and confidence interval, run:

plot_ci(bootstrap_results)

Using the provided table, report how large the effect size is for the difference in pregnancy lengths for “first” and “other” births.

10. Having completed your analysis, write a paragraph that summarizes your results and answers the question “do first born children arrive early or late compared to other children?” Write the summary as if you are an academic or scientific journalist, focusing on how you can answer the question clearly, precisely, and honestly.

How to submit

When you are ready to submit, be sure to save, commit, and push your final result so that everything is synchronized to Github. Then, navigate to your copy of the Github repository you used for this assignment. You should see your repository, along with the updated files that you just synchronized to Github. Confirm that your files are up-to-date, and then do the following steps:

1. Click the Pull Requests tab near the top of the page.

2. Click the green button that says “New pull request”.

3. Click the dropdown menu button labeled “base:”, and select the option starting.

4. Confirm that the dropdown menu button labeled “compare:” is set to master`.

5. Click the green button that says “Create pull request”.

6. Give the pull request the following title: Submission: Homework 4, FirstName LastName, replacing FirstName and LastName with your actual first and last name.

7. In the messagebox, write: My homework submission is ready for grading @shuaibm @jkglasbrenner.

8. Click “Create pull request” to lock in your submission.

Cheatsheets

You are encouraged to review and keep the following cheatsheets handy while working on this assignment:


text:
# The ultimate guide on Virtual Hosts: how to host multiple apps on one server

Virtual hosting is a simple mechanism used by webservers to host multiple websites/web applications using the same server. The main advantage in using Virtual Hosts is that you reduce the number of servers and IP addresses needed to host your services and you can even serve multiple services using the same port.

## Types of Virtual Hosts

Before diving into how to let’s take a look at the different types of Virtual Hosts (bear with me just a few seconds!):

• Name-based: this is the one you’re probably after, you want to host multiple sites using the same ip:port. This virtual hosting method uses names to decide where the traffic will be directed.
• IP-based: this one is actually pretty common and not known as a virtual hosting method. In this scenario a server is bound to multiple IP addresses and uses the IP to decide where the traffic should go. For example site1 is bound to IP1 and site2 is bound to IP2.
• Port-based: this is actually an extension of the previous one and often used together. In this case the port is used to decide where the traffic will go. You can have site1 on ip1:port1 site2 on ip1:port2 and site3 on ip2:port3.

As you might imagine, the Name-based is the most popular since it lets you use the same ip:port combination to serve multiple services. Also you need to specify the port in web browsers when it isn’t 80 or 443, imagine having to tell your users to visit your.domain.tld:9078, it’d be a nightmare!

Important
I take NO responsibility of what you do with your machine; use this tutorial as a guide and remember you can possibly cause data loss if you touch things carelessly.
Tip!
Remember that www.domain.tld and domain.tld are two distinct entities! If you switch from one to the other on an existing site all your site (SE) may suffer!

## Virtual Hosts using Apache

Virtual Hosts in Apache are quite straightforward. You just need to create a file inside one of Apache’s configuration directories. You can call these files however you want, but keep in mind they should end with .conf or they won’t be read!

• For RedHat-based distributions: create a file in /etc/httpd/conf.d/SITENAME.conf
• For Debian-based distributions: create a file in /etc/apache2/sites-available/SITENAME.conf
• (Debian-based only) After creating the file you should issue the following command: # a2ensite SITENAME (this time the SITENAME should be the exact name excluding the .conf extension.)
• For other distributions: follow the RedHat-based instructions as they use upstream configuration.

Let’s now take a look at a sample Virtual Host:

Listen 80
<VirtualHost *:80>
ServerName YOURDOMAIN.TLD
ServerAlias YOURALIAS.TLD
DocumentRoot ROOTDIRECTORY

ErrorLog ${APACHE_LOG_DIR}/yourdomain-error.log CustomLog${APACHE_LOG_DIR}/yourdomain-access.log combined
</VirtualHost>

That’s it! Actually for a Virtual Host to work you just need three things:

• The IP/port,
• The ServerName,
• The DocumentRoot

Now let’s take a look at the block line by line:

• In Line 1 you tell the server to listen on port 80 (change the port to use a different one). Most of the times Apache will be already listening on port 80, you can safely remove this line unless you’re using a different port.
• In Line 2 you define the ip:port. The * stands for “every IP the server can be bound to”. Most of the times you will want to use the asterisk, in other situations where you have multiple networks you may want to restrict the IP addresses your server is bound to.
• Line 3 is the most important one, the ServerName directive is the one used to determine where the traffic will go!
• If you have multiple names and you want to use them you can use ServerAlias.
• ServerAdmin is a directive to specify the administrator email address. This email is mainly used in error pages and when sending emails.
• The DocumentRoot directive tells the server to use the content within the directory to respond requests, it is important you point the server to where your files are! Usually under /var/www/html/something.
• The last two lines within the block are optional, by adding them you can specify where Apache will store the error and access log for that virtual host only. If you’re using a Debian-based distribution you may want to change httpd with apache.

Redhat-basedDebian-based
# systemctl restart httpd
# systemctl restart apache2

### SSL VHost using Apache

A Virtual Host won’t automatically serve SSL requests, that’s why you need another Virtual Host! You can place it in the same file you created. Here’s an example:

Listen 443
<VirtualHost *:443>
ServerName YOURDOMAIN.TLD
ServerAlias YOURALIAS.TLD
DocumentRoot ROOTDIRECTORY

SSLEngine on
SSLCertificateFile /path/to/cert.pem
SSLCertificateKeyFile /path/to/key.pem

ErrorLog ${APACHE_LOG_DIR}/yourdomain-ssl-error.log CustomLog${APACHE_LOG_DIR}/yourdomain-ssl-access.log combined
</VirtualHost>

### Redirecting HTTP traffic to HTTPS

Another common task is to redirect traffic from the HTTP vhost to HTTPS, once again you can use two vhosts. You need mod_rewrite to make it work! The following example will also redirect all traffic to what your ServerName is, remember www vs non-www for SEO!

Redhat-basedDebian-based

No additional steps should be needed, but in case it doesn’t work, check one of the files inside /etc/httpd/conf.modules.d/ contains the following line. If no file contains the line you can add it to 00-base.conf.

LoadModule rewrite_module modules/mod_rewrite.so

Use the following commands:

# a2enmod rewrite
# systemctl restart apache2
Listen 80
Listen 443

<VirtualHost *:80>
ServerName YOURDOMAIN.TLD
ServerAlias YOURALIAS.TLD
DocumentRoot ROOTDIRECTORY

RewriteEngine ON
RewriteCond %{SERVER_NAME} =YOURDOMAIN.TLD [OR]
RewriteCond %{SERVER_NAME} =www.YOURDOMAIN.TLD
RewriteRule ^ https://%{SERVER_NAME}%{REQUEST_URI} [END,NE,R=permanent]

ErrorLog ${APACHE_LOG_DIR}/yourdomain-error.log CustomLog${APACHE_LOG_DIR}/yourdomain-access.log combined
</VirtualHost>

<VirtualHost *:443>
ServerName YOURDOMAIN.TLD
ServerAlias YOURALIAS.TLD
DocumentRoot ROOTDIRECTORY

SSLEngine on
SSLCertificateFile /path/to/cert.pem
SSLCertificateKeyFile /path/to/key.pem

ErrorLog ${APACHE_LOG_DIR}/yourdomain-ssl-error.log CustomLog${APACHE_LOG_DIR}/yourdomain-ssl-access.log combined
</VirtualHost>

## Virtual Hosts (Server blocks) using Nginx

Virtual Hosts in nginx are more often referred as Server Blocks, while Nginx syntax seems harder compared to Apache, the amount of configuration is actually similar! In order to create a server block you just need to create a file inside Nginx configuration directories. You can call these files however you want, but keep in mind they should end with .conf or they won’t be read!

• For RedHat-based distributions: create a file in /etc/nginx/conf.d/SITENAME.conf
• For Debian-based distributions: create a file in /etc/nginx/sites-available/SITENAME.conf
• (Debian-based only) After creating the file you should issue the following command: # ln -s /etc/nginx/sites-available/SITENAME.conf /etc/nginx/sites-enabled/SITENAME.conf(this time the SITENAME should be the exact name excluding the .conf extension.)
• For other distributions: follow the RedHat-based instructions as they use upstream configuration.

Let’s now take a look at a server block:

server {
listen  80;
server_name SERVER_NAME SERVER_ALIAS;

location / {
root  ROOTDIRECTORY;
index  index.html index.htm;
try_files $uri$uri/ =404;
}

error_page  500 502 503 504  /50x.html;
location = /50x.html {
root  /usr/share/nginx/html;
}
}

That’s it! Actually for a server block to work you just need three things:

• The IP/port,
• The server_name,
• The root (directory)

Now let’s take a look at the code line by line:

• In the first line in the block you can specify the IP/port. If you don’t specify the IP (as in this case) nginx will bind to every address it can bind to. If you want to specify an address you may do so using the syntax ip:port. Most of the times you will want to listen on multiple addresses, in other situations where you have multiple networks you may want to restrict the IP addresses your server is bound to.
• In the second line you can specify a server name. This one is the most important since it will decide where your traffic will go. You may also specify a number of server aliases if you want to serve your content under different domain names.
• The location block contains the root directory. You may specify a number of location blocks but you will need at least one with a / (root of the website) for it to work. The root tells the server where to find the content you want to serve.
• The location block also contains a index directive that decides what happens when you visit the directory without specifying a file.
• Inside the location block you can also specify a try_files directive in order to control what happens when there is no resource matching the request (a so-called “404“).
• The last few lines are useful to specify what happens when a server error occurs, they are optional.

Redhat-basedDebian-based
# systemctl restart nginx
# systemctl restart nginx

### SSL Server Block using Nginx

A Server Block won’t automatically serve SSL requests, that’s why you need another server blocks! You can place it in the same file you created. The following example will also redirect all traffic to what your ServerName is, remember www vs non-www for SEO! Here’s the example:

server {
listen  443 ssl;
server_name SERVER_NAME SERVER_ALIAS;

ssl_certificate /path/to/cert.pem;
ssl_certificate_key /path/to/key.pem;

location / {
root  ROOTDIRECTORY;
index  index.html index.htm;
try_files $uri$uri/ =404;
}

error_page  500 502 503 504  /50x.html;
location = /50x.html {
root  /usr/share/nginx/html;
}
}

### Redirecting HTTP traffic to HTTPS

Another common task is to redirect traffic from the HTTP server block to HTTPS, once again you can use two server blocks.

server {
listen  80;
server_name SERVER_NAME SERVER_ALIAS;

return 301 https://$host$request_uri;
}

server {
listen  443 ssl;
server_name SERVER_NAME SERVER_ALIAS;

ssl_certificate /path/to/cert.pem;
ssl_certificate_key /path/to/key.pem;

location / {
root  ROOTDIRECTORY;
index  index.html index.htm;
try_files $uri$uri/ =404;
}

error_page  500 502 503 504  /50x.html;
location = /50x.html {
root  /usr/share/nginx/html;
}
}
Image courtesy of ninita_7

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# azel2uvpat

Convert radiation pattern from azimuth/elevation form to u/v form

## Syntax

``pat_uv = azel2uvpat(pat_azel,az,el)``
``pat_uv = azel2uvpat(pat_azel,az,el,u,v)``
``````[pat_uv,u_pat,v_pat] = azel2uvpat(___)``````

## Description

example

````pat_uv = azel2uvpat(pat_azel,az,el)` expresses the antenna radiation pattern `pat_azel` in u/v space coordinates instead of azimuth/elevation angle coordinates. `pat_azel` samples the pattern at azimuth angles in `az` and elevation angles in `el`. The `pat_uv` matrix uses a default grid that covers u values from –1 to 1 and v values from –1 to 1. In this grid, `pat_uv` is uniformly sampled with a step size of 0.01 for u and v. The function interpolates to estimate the response of the antenna at a given direction. Values in `pat_uv` are NaN for u and v values outside the unit circle because u and v are undefined outside the unit circle.```

example

````pat_uv = azel2uvpat(pat_azel,az,el,u,v)` uses vectors `u` and `v` to specify the grid at which to sample `pat_uv`. To avoid interpolation errors, `u` should cover the range [–1, 1] and `v` should cover the range [–1, 1].```

example

``````[pat_uv,u_pat,v_pat] = azel2uvpat(___)``` returns vectors containing the u and v coordinates at which `pat_uv` samples the pattern, using any of the input arguments in the previous syntaxes.```

## Examples

collapse all

Convert a radiation pattern to u-v space, with the u and v coordinates spaced by 0.01.

Define the pattern in terms of azimuth and elevation.

```az = -90:90; el = -90:90; pat_azel = mag2db(repmat(cosd(el)',1,numel(az)));```

Convert the pattern to u-v space.

`pat_uv = azel2uvpat(pat_azel,az,el);`

Plot the result of converting a radiation pattern to $u/v$ space with the $u$ and $v$ coordinates spaced by 0.01.

The radiation pattern is the cosine of the elevation angle.

```az = -90:90; el = -90:90; pat_azel = repmat(cosd(el)',1,numel(az));```

Convert the pattern to $u/v$ space. Use the $u$ and $v$ coordinates for plotting.

`[pat_uv,u,v] = azel2uvpat(pat_azel,az,el);`

Plot the result.

```H = surf(u,v,mag2db(pat_uv)); H.LineStyle = 'none'; xlabel('u'); ylabel('v'); zlabel('Pattern');```

Convert a radiation pattern to $u/v$ form, with the $u$ and $v$ coordinates spaced by 0.05.

The radiation pattern is cosine of the elevation angle.

```az = -90:90; el = -90:90; pat_azel = repmat(cosd(el)',1,numel(az));```

Define the set of $u$ and $v$ coordinates at which to sample the pattern. Then, convert the pattern.

```u = -1:0.05:1; v = -1:0.05:1; pat_uv = azel2uvpat(pat_azel,az,el,u,v);```

Plot the result.

```H = surf(u,v,mag2db(pat_uv)); H.LineStyle = 'none'; xlabel('u'); ylabel('v'); zlabel('Pattern');```

## Input Arguments

collapse all

Antenna radiation pattern in azimuth/elevation form, specified as a Q-by-P matrix. `pat_azel` samples the 3-D magnitude pattern in decibels, in terms of azimuth and elevation angles. P is the length of the `az` vector, and Q is the length of the `el` vector.

Data Types: `double`

Azimuth angles at which `pat_azel` samples the pattern, specified as a vector of length P. Each azimuth angle is in degrees, between –90 and 90. Such azimuth angles are in the hemisphere for which u and v are defined.

Data Types: `double`

Elevation angles at which `pat_azel` samples the pattern, specified as a vector of length Q. Each elevation angle is in degrees, between –90 and 90.

Data Types: `double`

u coordinates at which `pat_uv` samples the pattern, specified as a vector of length L. Each u coordinate is between –1 and 1.

Data Types: `double`

v coordinates at which `pat_uv` samples the pattern, specified as a vector of length M. Each v coordinate is between –1 and 1.

Data Types: `double`

## Output Arguments

collapse all

Antenna radiation pattern in u/v form, returned as an M-by-L matrix. `pat_uv` samples the 3-D magnitude pattern in decibels, in terms of u and v coordinates. L is the length of the `u` vector, and M is the length of the `v` vector. Values in `pat_uv` are NaN for u and v values outside the unit circle because u and v are undefined outside the unit circle.

u coordinates at which `pat_uv` samples the pattern, returned as a vector of length L.

v coordinates at which `pat_uv` samples the pattern, returned as a vector of length M.

collapse all

### Azimuth Angle, Elevation Angle

The azimuth angle of a vector is the angle between the x-axis and the orthogonal projection of the vector onto the xy plane. The angle is positive in going from the x axis toward the y axis. Azimuth angles lie between –180 and 180 degrees. The elevation angle is the angle between the vector and its orthogonal projection onto the xy-plane. The angle is positive when going toward the positive z-axis from the xy plane. By default, the boresight direction of an element or array is aligned with the positive x-axis. The boresight direction is the direction of the main lobe of an element or array.

Note

The elevation angle is sometimes defined in the literature as the angle a vector makes with the positive z-axis. The MATLAB® and Phased Array System Toolbox™ products do not use this definition.

This figure illustrates the azimuth angle and elevation angle for a vector shown as a green solid line.

### U/V Space

The u and v coordinates are the direction cosines of a vector with respect to the y-axis and z-axis, respectively.

The u/v coordinates for the hemisphere x ≥ 0 are derived from the phi and theta angles by:

`$\begin{array}{l}u=\mathrm{sin}\theta \mathrm{cos}\varphi \\ v=\mathrm{sin}\theta \mathrm{sin}\varphi \end{array}$`

In these expressions, φ and θ are the phi and theta angles, respectively.

To convert azimuth and elevation to u and v use the transformation

`$\begin{array}{l}u=\mathrm{cos}el\mathrm{sin}az\\ v=\mathrm{sin}el\end{array}$`

which is valid only in the range abs(az)≤=90.

The values of u and v satisfy the inequalities

`$\begin{array}{l}-1\le u\le 1\\ -1\le v\le 1\\ {u}^{2}+{v}^{2}\le 1\end{array}$`

Conversely, the phi and theta angles can be written in terms of u and v using

`$\begin{array}{l}\mathrm{tan}\varphi =v/u\\ \mathrm{sin}\theta =\sqrt{{u}^{2}+{v}^{2}}\end{array}$`

The azimuth and elevation angles can also be written in terms of u and v:

`$\begin{array}{l}\mathrm{sin}el=v\\ \mathrm{tan}az=\frac{u}{\sqrt{1-{u}^{2}-{v}^{2}}}\end{array}$`

### Phi Angle, Theta Angle

The phi angle (φ) is the angle from the positive y-axis to the vector’s orthogonal projection onto the yz plane. The angle is positive toward the positive z-axis. The phi angle is between 0 and 360 degrees. The theta angle (θ) is the angle from the x-axis to the vector itself. The angle is positive toward the yz plane. The theta angle is between 0 and 180 degrees.

The figure illustrates phi and theta for a vector that appears as a green solid line.

The coordinate transformations between φ/θ and az/el are described by the following equations

`$\begin{array}{l}\mathrm{sin}el=\mathrm{sin}\varphi \mathrm{sin}\theta \\ \mathrm{tan}az=\mathrm{cos}\varphi \mathrm{tan}\theta \\ \mathrm{cos}\theta =\mathrm{cos}el\mathrm{cos}az\\ \mathrm{tan}\varphi =\mathrm{tan}el/\mathrm{sin}az\end{array}$`

## Version History

Introduced in R2012a


text:
Conservation principles are the Physics´ fundamental laws and they are basic to understand many everyday phenomenom. In particular, the conservation principle of linear momentum is a consequence of the action - reaction principle or Newton´s third law.

Conservation of momentum principle, also known as conservation of quantity of motion, establishes that the resultant of the forces acting on a body or system is void, its linear momentum remains constant in time.

Newton´s cradle, also known as Newton´s pendulum, it ilustrates the conservation of momentum in absence of external forces.

### Demostration

Think of two bodies isolated, A and B, with just one interaction between them. According to the action - reaction principle:

${\stackrel{\to }{F}}_{AB}=-{\stackrel{\to }{F}}_{BA}$

Knowing that $\stackrel{\to }{F}=\frac{∆\stackrel{\to }{p}}{∆t}$, then:

$\frac{∆{\stackrel{\to }{p}}_{A}}{∆t}=\frac{-∆{\stackrel{\to }{p}}_{B}}{∆t}⇒\phantom{\rule{0ex}{0ex}}\frac{∆\left({\stackrel{\to }{p}}_{A}+{\stackrel{\to }{p}}_{B}\right)}{∆t}=0$

This expression tells us the variation of the sum of the momentums is void, thus the total linear momentum of both bodies remains constant:

### Differential notation

We have already explained in several occasions that, in mathematical language, when a magnitude remains constant in time has a derivative equal to zero in relation to that one. So, in this case we may write:

## Collisions and explosions

In physics we say that an isolated system is the one with no interaction with the outside, thus it is not subdue to external forces in relation to it. Particles taking part in crashes, explosions, reaction engines, etc, can be consider isolated systems in which external forces may be disregard opposite to the intensity of the inner ones. Conservation of momentum principle has an important aplication in the study of those phenomenoms, when we don´t know the causes that originate them, since, before and after the phenomenom of linear momentum of the whole system...

Conservation momentum collision

If you throw the green ball against the red one, this gets the linear momentum, the only possibility is the green ball runs off on the direction the image shows and being gain the momentum. That is due to the linear momentum, which is the vector addition (parallelogram rule) of the momentums of each of the balls, it must coincide wit the initial linear momentum, before the collision, which is the one the green ball had.

${\stackrel{\to }{p}}_{\mathrm{before}}={\stackrel{\to }{p}}_{\mathrm{after}}$

## Laws of Newton

As we saw in the previous demonstration, we can consider the conservation of momentum principle as a direct consequence of the Newton´s third law. Therefore, if we apply it on a body whose mass does not vary, it is equivalent to the Newton´s first law:


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# Multiplication

In its most elementary form multiplication is the repeated addition of whole numbers or integers.

For example, $3\times 2 = 2 + 2 + 2 = 6$

The result of a multiplication is the product. The numbers which are multiplied together are called factors.

In this context, it is also one of the most well-known commutative operations: It yields the same result, regardless of placement of numbers.

For example $3\times 2 = 2\times 3$.

Multiplication also possesses the associative property.

The opposite of multiplication is division.

## Properties of Multiplication

• Multiplying any number by 1 yields that same number again. E.g. $8\times 1 = 1$
• Multiplying any number by 0 yields 0. E.g. $7\times 0 = 0$


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plug in with night light 2021


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# Predictions about hydrolysis reactions [duplicate]

Predict whether these $1.0~\mathrm{M}$ solutions are acidic, basic, or neutral. Lets start with $\ce{CH3NH3+NO3-}$

How do I approach a problem such as this?

I certainly do not know all the chemical compounds that exist thus what is my method?

I am guessing that $\ce{NO3-}$ does not hydrolyze and $\ce{CH3NH3+}$ does.

Thus, $\ce{CH3NH3+ + H2O -> CH3NH2 + H3O}$ = ACID

(b) $\ce{NaI~(aq)}$

$\ce{Na}$ does not hydrolyze and neither does iodine, but why?

(c) $\ce{NaNO2}$

$\ce{Na}$ again does not hydrolyze but from the first example neither does $\ce{NO2}$

Does this have something to do with either the solutions have a hydrogen atom or $\ce{OH-}$ molecule?


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# Computing an Expression

I am writing code to evaluate the following expression: $$\frac{(a+b+c)!}{a! b! c!}$$ where $$a$$, $$b$$ and $$c$$ are on the range of $$10$$ to $$500$$. The result is going to be a floating point number. I could use a big number package, but the code will run slowly. I am using 64-bit floating point numbers.

I claim by doing as much of the computation in integer (maybe 64 bit) I will minimize the floating point round off error. Therefore, I claim that if put the integers to be multiplied together in an array, cancel common denominators, and then do the final computation in floating point I will minimize round off error.

Do I have this right?

• "but the code will run slowly" How fast do you need? You might be surprised. – Veedrac Jul 12 at 9:35
• But you shouldn't worry about floating point errors, they're plenty accurate. Rather worry about overflow. – Veedrac Jul 12 at 9:56

You don't need to use integers for any data. Just find the largest of three numbers x=max(a,b,c) and reduce both parts by x!. Then compute in doubles. For numbers as small as 500 both 32-bit ints and 32/64 bit doubles will be precise.
EDIT: Since 64-bit FP isn't enough to deal with 1500!, you can perform computations on (decimal) logarithms of multipliers.


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# PH at which there is no net charge is called

$(a)\;triple\;point\qquad(b)\;electric\;point\qquad(c)\;freezing\;point\qquad(d)\;Isoelectric\;point$

Explanation :
The pH on hydrogen concentration of the solution at which a particular amino acid does not migrate under the influence of an electric field is called isoelectric point of that amino acid .


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# 6.5 Physical applications  (Page 7/11)

 Page 7 / 11

When the reservoir is at its average level, the surface of the water is about 50 ft below where it would be if the reservoir were full. What is the force on the face of the dam under these circumstances?

Approximately 7,164,520,000 lb or 3,582,260 t

To learn more about Hoover Dam, see this article published by the History Channel.

## Key concepts

• Several physical applications of the definite integral are common in engineering and physics.
• Definite integrals can be used to determine the mass of an object if its density function is known.
• Work can also be calculated from integrating a force function, or when counteracting the force of gravity, as in a pumping problem.
• Definite integrals can also be used to calculate the force exerted on an object submerged in a liquid.

## Key equations

• Mass of a one-dimensional object
$m={\int }_{a}^{b}\rho \left(x\right)dx$
• Mass of a circular object
$m={\int }_{0}^{r}2\pi x\rho \left(x\right)dx$
• Work done on an object
$W={\int }_{a}^{b}F\left(x\right)dx$
• Hydrostatic force on a plate
$F={\int }_{a}^{b}\rho w\left(x\right)s\left(x\right)dx$

For the following exercises, find the work done.

Find the work done when a constant force $F=12$ lb moves a chair from $x=0.9$ to $x=1.1$ ft.

How much work is done when a person lifts a $50$ lb box of comics onto a truck that is $3$ ft off the ground?

$150$ ft-lb

What is the work done lifting a $20$ kg child from the floor to a height of $2$ m? (Note that $1$ kg equates to $9.8$ N)

Find the work done when you push a box along the floor $2$ m, when you apply a constant force of $F=100\phantom{\rule{0.2em}{0ex}}\text{N}.$

$200\phantom{\rule{0.2em}{0ex}}\text{J}$

Compute the work done for a force $F=12\text{/}{x}^{2}$ N from $x=1$ to $x=2$ m.

What is the work done moving a particle from $x=0$ to $x=1$ m if the force acting on it is $F=3{x}^{2}$ N?

$1$ J

For the following exercises, find the mass of the one-dimensional object.

A wire that is $2$ ft long (starting at $x=0\right)$ and has a density function of $\rho \left(x\right)={x}^{2}+2x$ lb/ft

A car antenna that is $3$ ft long (starting at $x=0\right)$ and has a density function of $\rho \left(x\right)=3x+2$ lb/ft

$\frac{39}{2}$

A metal rod that is $8$ in. long (starting at $x=0\right)$ and has a density function of $\rho \left(x\right)={e}^{1\text{/}2x}$ lb/in.

A pencil that is $4$ in. long (starting at $x=2\right)$ and has a density function of $\rho \left(x\right)=5\text{/}x$ oz/in.

$\text{ln}\left(243\right)$

A ruler that is $12$ in. long (starting at $x=5\right)$ and has a density function of $\rho \left(x\right)=\text{ln}\left(x\right)+\left(1\text{/}2\right){x}^{2}$ oz/in.

For the following exercises, find the mass of the two-dimensional object that is centered at the origin.

An oversized hockey puck of radius $2$ in. with density function $\rho \left(x\right)={x}^{3}-2x+5$

$\frac{332\pi }{15}$

A frisbee of radius $6$ in. with density function $\rho \left(x\right)={e}^{\text{−}x}$

A plate of radius $10$ in. with density function $\rho \left(x\right)=1+\text{cos}\left(\pi x\right)$

$100\pi$

A jar lid of radius $3$ in. with density function $\rho \left(x\right)=\text{ln}\left(x+1\right)$

A disk of radius $5$ cm with density function $\rho \left(x\right)=\sqrt{3x}$

$20\pi \sqrt{15}$

A $12$ -in. spring is stretched to $15$ in. by a force of $75$ lb. What is the spring constant?

A spring has a natural length of $10$ cm. It takes $2$ J to stretch the spring to $15$ cm. How much work would it take to stretch the spring from $15$ cm to $20$ cm?

$6$ J

A $1$ -m spring requires $10$ J to stretch the spring to $1.1$ m. How much work would it take to stretch the spring from $1$ m to $1.2$ m?

A spring requires $5$ J to stretch the spring from $8$ cm to $12$ cm, and an additional $4$ J to stretch the spring from $12$ cm to $14$ cm. What is the natural length of the spring?

$5$ cm

A shock absorber is compressed 1 in. by a weight of 1 t. What is the spring constant?

A force of $F=20x-{x}^{3}$ N stretches a nonlinear spring by $x$ meters. What work is required to stretch the spring from $x=0$ to $x=2$ m?

$36$ J

Find the work done by winding up a hanging cable of length $100$ ft and weight-density $5$ lb/ft.

For the cable in the preceding exercise, how much work is done to lift the cable $50$ ft?

$18,750$ ft-lb

For the cable in the preceding exercise, how much additional work is done by hanging a $200$ lb weight at the end of the cable?

[T] A pyramid of height $500$ ft has a square base $800$ ft by $800$ ft. Find the area $A$ at height $h.$ If the rock used to build the pyramid weighs approximately $w=100\phantom{\rule{0.2em}{0ex}}{\text{lb/ft}}^{3},$ how much work did it take to lift all the rock?

$\frac{32}{3}\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{9}\phantom{\rule{0.2em}{0ex}}\text{ft-lb}$

[T] For the pyramid in the preceding exercise, assume there were $1000$ workers each working $10$ hours a day, $5$ days a week, $50$ weeks a year. If the workers, on average, lifted 10 100 lb rocks $2$ ft/hr, how long did it take to build the pyramid?

[T] The force of gravity on a mass $m$ is $F=\text{−}\left(\left(GMm\right)\text{/}{x}^{2}\right)$ newtons. For a rocket of mass $m=1000\phantom{\rule{0.2em}{0ex}}\text{kg},$ compute the work to lift the rocket from $x=6400$ to $x=6500$ km. ( Note : $G=6\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-17}\phantom{\rule{0.2em}{0ex}}{\text{N m}}^{2}\text{/}{\text{kg}}^{2}$ and $M=6\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{24}\phantom{\rule{0.2em}{0ex}}\text{kg}\text{.}\right)$

$8.65\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{5}\phantom{\rule{0.2em}{0ex}}\text{J}$

[T] For the rocket in the preceding exercise, find the work to lift the rocket from $x=6400$ to $x=\infty .$

[T] A rectangular dam is $40$ ft high and $60$ ft wide. Compute the total force $F$ on the dam when

1. the surface of the water is at the top of the dam and
2. the surface of the water is halfway down the dam.

a. $3,000,000$ lb, b. $749,000$ lb

[T] Find the work required to pump all the water out of a cylinder that has a circular base of radius $5$ ft and height $200$ ft. Use the fact that the density of water is $62$ lb/ft 3 .

[T] Find the work required to pump all the water out of the cylinder in the preceding exercise if the cylinder is only half full.

$23.25\pi$ million ft-lb

[T] How much work is required to pump out a swimming pool if the area of the base is $800$ ft 2 , the water is $4$ ft deep, and the top is $1$ ft above the water level? Assume that the density of water is $62$ lb/ft 3 .

A cylinder of depth $H$ and cross-sectional area $A$ stands full of water at density $\rho .$ Compute the work to pump all the water to the top.

$\frac{A\rho {H}^{2}}{2}$

For the cylinder in the preceding exercise, compute the work to pump all the water to the top if the cylinder is only half full.

A cone-shaped tank has a cross-sectional area that increases with its depth: $A=\left(\pi {r}^{2}{h}^{2}\right)\text{/}{H}^{3}.$ Show that the work to empty it is half the work for a cylinder with the same height and base.

Answers may vary

#### Questions & Answers

Find the arc length of the graph of f(x) = In (sinx) on the interval [Π/4, Π/2].
mukul Reply
Sand falling freely from a lorry form a conical shape whose height is always equal to one-third the radius of the base. a. How fast is the volume increasing when the radius of the base is (1m) and increasing at the rate of 1/4cm/sec Pls help me solve
ade
show that lim f(x) + lim g(x)=m+l
BARNABAS Reply
list the basic elementary differentials
Chio Reply
Differentiation and integration
Okikiola Reply
yes
Damien
proper definition of derivative
Syed Reply
the maximum rate of change of one variable with respect to another variable
Amdad
terms of an AP is 1/v and the vth term is 1/u show that the sum of uv terms is 1/2(uv+1)
Inembo Reply
what is calculus?
BISWAJIT Reply
calculus is math that studies the change in math, such as the rate and distance,
Tamarcus
what are the topics in calculus
Augustine
what is limit of a function?
Geoffrey Reply
what is x and how x=9.1 take?
Pravin Reply
what is f(x)
Inembo Reply
the function at x
Marc
also known as the y value so I could say y=2x or f(x)= 2x same thing just using functional notation your next question is what is dependent and independent variables. I am Dyslexic but know math and which is which confuses me. but one can vary the x value while y depends on which x you use. also
Marc
up domain and range
Marc
enjoy your work and good luck
Marc
I actually wanted to ask another questions on sets if u dont mind please?
Inembo
I have so many questions on set and I really love dis app I never believed u would reply
Inembo
Hmm go ahead and ask you got me curious too much conversation here
Adri
am sorry for disturbing I really want to know math that's why *I want to know the meaning of those symbols in sets* e.g n,U,A', etc pls I want to know it and how to solve its problems
Inembo
and how can i solve a question like dis *in a group of 40 students, 32 offer maths and 24 offer physics and 4 offer neither maths nor physics , how many offer both maths and physics*
Inembo
next questions what do dy mean by (A' n B^c)^c'
Inembo
The sets help you to define the function. The function is like a magic box where you put inside stuff(numbers or sets) and you get out the stuff but in different shapes (forms).
Adri
I dont understand what you wanna say by (A' n B^c)^c'
Adri
(A' n B (rise to the power of c)) all rise to the power of c
Inembo
Aaaahh
Adri
Ok so the set is formed by vectors and not numbers
Adri
A vector of length n
Adri
But you can make a set out of matrixes as well
Adri
I I don't even understand sets I wat to know d meaning of all d symbolsnon sets
Inembo
Wait what's your math level?
Adri
High-school?
Adri
yes
Inembo
am having big problem understanding sets more than other math topics
Inembo
So f:R->R means that the function takes real numbers and provides real numer. For ex. If f(x) =2x this means if you give to your function a real number like 2,it gives you also a real number 2times2=4
Adri
pls answer this question *in a group of 40 students, 32 offer maths and 24 offer physics and 4 offer neither maths nor physics , how many offer both maths and physics*
Inembo
If you have f:R^n->R^n you give to your function a vector of length n like (a1,a2,...an) where all a1,.. an are reals and gives you also a vector of length n... I don't know if i answering your question. Otherwise on YouTube you havr many videos where they explain it in a simple way
Adri
I would say 24
Adri
Offer both
Adri
Sorry 20
Adri
Actually you have 40 - 4 =36 who offer maths or physics or both.
Adri
I know its 20 but how to prove it
Inembo
You have 32+24=56who offer courses
Adri
56-36=20 who give both courses... I would say that
Adri
solution: In a question involving sets and Venn diagram, the sum of the members of set A + set B - the joint members of both set A and B + the members that are not in sets A or B = the total members of the set. In symbolic form n(A U B) = n(A) + n (B) - n (A and B) + n (A U B)'.
Mckenzie
In the case of sets A and B use the letters m and p to represent the sets and we have: n (M U P) = 40; n (M) = 24; n (P) = 32; n (M and P) = unknown; n (M U P)' = 4
Mckenzie
Now substitute the numerical values for the symbolic representation 40 = 24 + 32 - n(M and P) + 4 Now solve for the unknown using algebra: 40 = 24 + 32+ 4 - n(M and P) 40 = 60 - n(M and P) Add n(M and P), as well, subtract 40 from both sides of the equation to find the answer.
Mckenzie
40 - 40 + n(M and P) = 60 - 40 - n(M and P) + n(M and P) Solution: n(M and P) = 20
Mckenzie
thanks
Inembo
Simpler form: Add the sums of set M, set P and the complement of the union of sets M and P then subtract the number of students from the total.
Mckenzie
n(M and P) = (32 + 24 + 4) - 40 = 60 - 40 = 20
Mckenzie
how do i evaluate integral of x^1/2 In x
ayo Reply
first you simplify the given expression, which gives (x^2/2). Then you now integrate the above simplified expression which finally gives( lnx^2).
Ahmad
by using integration product formula
Roha
find derivative f(x)=1/x
Mul Reply
-1/x^2, use the chain rule
Andrew
f(x)=x^3-2x
Mul
what is domin in this question
noman
all real numbers . except zero
Roha
please try to guide me how?
Meher
what do u want to ask
Roha
?
Roha
the domain of the function is all real number excluding zero, because the rational function 1/x is a representation of a fractional equation (precisely inverse function). As in elementary mathematics the concept of dividing by zero is nonexistence, so zero will not make the fractional statement
Mckenzie
a function's answer/range should not be in the form of 1/0 and there should be no imaginary no. say square root of any negative no. (-1)^1/2
Roha
domain means everywhere along the x axis. since this function is not discontinuous anywhere along the x axis, then the domain is said to be all values of x.
Andrew
Derivative of a function
Waqar
right andrew ... this function is only discontinuous at 0
Roha
of sorry, I didn't realize he was taking about the function 1/x ...I thought he was referring to the function x^3-2x.
Andrew
yep...it's 1/x...!!!
Roha
true and cannot be apart of the domain that makes up the relation of the graph y = 1/x. The value of the denominator of the rational function can never be zero, because the result of the output value (range value of the graph when x =0) is undefined.
Mckenzie
👍
Roha
Therefore, when x = 0 the image of the rational function does not exist at this domain value, but exist at all other x values (domain) that makes the equation functional, and the graph drawable.
Mckenzie
👍
Roha
Roha are u A Student
Lutf
yes
Roha
What is the first fundermental theory of Calculus?
ZIMBA Reply
do u mean fundamental theorem ?
Roha
I want simple integral
aparna Reply
for MSc chemistry... simple formulas of integration
aparna
hello?
funny
how are you
funny
I don't understand integration
aparna
r u insane
aparna
integration is so simple not typical..
funny
tell me any questions about integration then i will solve.
funny
we use integration for whole values or for sum of values any there are some basic rule for integration..
funny
I just formulas
aparna
I just want formulas of integration
aparna
value of log ax cot-x cos-x
aparna
there are many formulas about integration
funny
more then one formula are exist about integration..
funny
so I want simple formulas Because I'm studying MSc chem...Nd have done bsc from bio...
aparna
I am M.sc physics now i am studying in m.phil
funny
so what can i do
aparna
I will send you basic formula for integration after two mint first of all i write then i will send you.
funny
send me your messenger id where i can send you formulas about integration because there is no option for image sending..
funny
integration f(X) dx this is basic formula of integration sign is not there you can look integration sign in methematics form... and f(X) my be any function any values
funny
you send me your any ID where i can send you information about integration
funny
send me SMS at this ID Adnan sathi Adnan sathi
funny
Hi
RIZWAN
I don't understand the formula
Adaeze Reply
who's formula
funny
which formula?
Roha
what is the advantages of mathematical economics
Mubarak

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Home > Windows 10 > Windows 7 Bootcamp Ntfs Error

# Windows 7 Bootcamp Ntfs Error

## Contents

drives needing more space to run faster? As I wanted to put the bootcamp extra $device$ files on it that were downloaded during bootcamp assistant install. permalinkembedsaveparentgive gold[–]Cir0c[S] 0 points1 point2 points 1 year ago(0 children)I genuinely don't have a clue, it's called Bootcamp Assistant. Reply May 4, 2013 at 11:49 am Damien Zander Yeah there seems to be quite a lot of different opinions about it. get redirected here

## Bootcamp Partition Not Ntfs

Whilst others require complicated risqué  Terminal commands. Finally, we will see pop up to encourage us to install Boot Camp on Windows. If everything is ok, then type "w" to write new partition information and exit. 19.

I tried to update bootcamp it is so confusing i don't find boot camp 3.1. Or 60; I only use it for Rosetta Stone (which is an AMAZING program), and playing games. This may help: Boot the windows 7 dvd again. Boot Camp Install Setup What a no go :-/ No wonder their stock value has started to plummet.

Don't try to resize your partition with Windows or a third-party app. Windows 10 Won't Install On Bootcamp Partition After making a backup, open BootCamp, it can be found in the Applications/Utilities folder or by searching for it in spotlight. The selected disk has an MBR partition table. https://support.apple.com/en-us/HT204009 One other possible solution, create another small temporary partition, using EXfat as the partition type.

Disk Utility or other type of applications will not work. Boot Camp We Couldn't Create A New Apple helpline charged me £25 and was unable to resolve. Here is a full guide on how to use it and how to properly burn your DVD: https://neosmart.net/wiki/burning-iso-images-with-imgburn/ 3. i tried several times to install windows using bootcamp but eventually ditched it because it just wouldnt work.

## Windows 10 Won't Install On Bootcamp Partition

download bootcamp drivers and install them in windows to make it functional NB The partition will be called "EFI boot" y default instead of Windows and the logo may be different original site What is an instant of time? \def inside of \def not visible in titles or captions Why is the size of my email about a third bigger than the size of Bootcamp Partition Not Ntfs Verify partitions again by running the verify command. Bootcamp Windows Cannot Be Installed To This Disk Mbr Mack | 18 July, 2015 at 04:59 | Reply Zlop:…one more thing.

Are you running off an ISO? Get More Info NICE - but some advanced games are quirky (mouse control isn't good). so please help me installing mac os x. It all went smoothly afterwards. Bootcamp Ntfs Windows 10

Now when Win 8 installer have EFI boot mode, we actually don't need Bootcamp utility at all. There is a lot more information I suggest a quick google search for “CDBOOT MEMORY OVERFLOW ERROR”. Solve in Web 19,863 views 2:17 Windows cannot be installed to this disk the selected disk is of the gpt partition style itsolutiont - Duration: 3:27. http://3cq.org/windows-10/windows-2000-windows-update-error-0x800b0109.php This happens when the ISO file is simply copied onto the drive/dvd instead of being properly mounted/restored onto it.

So, the external dvd is also included. Bootcamp Windows Cannot Be Installed To Disk 0 Partition 4 Ntfs I'd like to know a bit more about the implementation and implications of this restriction. If we remove the USB drive at this point will it not complain that the USB drive containing the installation media is not present for the installation?

## Risks are inherent in the use of the Internet.

there is a choice ( maybe under advanced options on that screen ) that you pick to indicate to format that partition. Published Date: Mar 27, 2015 Helpful? IF not - I've exhausted all my options. Bootcamp Windows 10 Cannot Be Installed To This Disk I will try again.

DEE Z 8,231 views 4:43 How to Fix Error Partition Table on Hard Disk - Duration: 13:44. Helpful (0) Reply options Link to this post by Kid Dynamic, Kid Dynamic Mar 7, 2012 6:26 PM in response to [email protected] Level 1 (35 points) Mar 7, 2012 6:26 PM And I didThen I clicked NextAng get message "setup was unable to create a new system partitition."Any ideas? this page it seams that it is not configured.

Notify me of new posts by email. Do one of the following: If your Mac has a single internal disk, click Restore. I've tried just about everything, and Bootcamp assistant appeared to work, but windows 10 failed to advance with the dreaded "selected disk is of the GPT partition style" error. Two of my friends are experiencing the same issues.

type "4" (the bootcamp partition) 13. then upgrade to windows 10. Reply February 8, 2014 at 8:04 am Ron Also - I did get the win8 DVD to start to install… it gets to the point where it won't install to a Im fairly sure I partitioned my harddrive correctly because when I click on bootcamp to partition the harddrive again the 100 gigs of space is missing Reply June 30, 2013 at

I now have Windows 10 installed and no OS X. Piracy. For example, I have Macbook Pro Retina, iMac, and Mac Pro. Sign in Share More Report Need to report the video?

Also quick format works too - will save you 2 hours on a 1TB disk. Frédéric Laloup | 14 November, 2015 at 02:28 | Reply Nice job !!!!!!!!!!!!!!!!! Boot camp simply wipes the space and prepares it for the install. permalinkembedsavegive gold[–]Cir0c[S] 0 points1 point2 points 1 year ago(2 children)I've fucked it big time.

Otherwise try copying the drivers to your windows partition while using OS X, this can be done with software such as Tuxera: http://appducate.com/2013/01/read-write-to-windows-ntfs-partition-on-mac/ Reply January 7, 2015 at 11:57 pm Philip entered the correct Disk Identifier to launch gdisk), type "x" to enter the experts menu Type "n" to create a fresh protective MBR; note upon completion gdisk will not confirm a And is it the only hard drive installed into the machine? thanks, Vini Reply February 27, 2014 at 1:51 pm Damien Zander Hey Vini, since your iMac doesn't have a DVD drive you are going to have to create a Windows USB


text:
# 3.3.2.25 GetSaveName

Opens the Save As dialog box.

## Syntax:

getsavename [fileName] .extension

If fileName is specified, it is the default file name in the Save As dialog box. extension is the default file extension. Although extension must be specified, * can be used to leave the choice open.

If you enter a file name and click OK, the file name and the selected path are saved into the string variable %A. If you click Cancel, %A is unchanged.

## Examples:

The following script opens the Save As dialog box and displays *.* in the File Name text box.

getsavename * .*;

The next script opens the Save As dialog box and displays the name of the active window .OGW in the File Name text box.

getsavename %H .ogw;


text:
Question

# Total number of integral solutions of |x|+|y|+|z|=15 is k, then k41=

Solution

## Let x,y,z be positive integers. Then number of solutions = 14C2=91 But x,y,z can be negative too. So, total number of solutions (none of x,y,z is zero) is 91×2×2×2=728     ...(1) Let one of x,y,z is equal to zero. Then number of possible solutions = 14C1=14 But other two can be negative (14×2×2) and one of three can be zero. Hence, number of solutions =14×2×2×3=168     ...(2) Let two of x,y,z is zero, then number of solutions is 6     ...(3) Adding (1),(2) and (3) Total number of integral solutions, k = 902 Hence, k41=90241=22Mathematics

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Journal of Experimental and Theoretical Physics
 HOME | SEARCH | AUTHORS | HELP
 Journal Issues Golden Pages About This journal Aims and Scope Editorial Board Manuscript Submission Guidelines for Authors Manuscript Status Contacts

ZhETF, Vol. 128, No. 6, p. 1201 (December 2005)
(English translation - JETP, Vol. 101, No. 6, p. 1053, December 2005 available online at www.springer.com )

STUDY OF THE PROCESS e+e- \to \pi+\pi- IN THE ENERGY REGION 400<\sqrt{s}<1000 MeV

PACS: 13.66.Bc, 13.66.Jn, 13.25.Jx, 12.40.Vv

 DJVU (282.1K) PDF (855.4K)

The cross section of the process was measured in the spherical neutral detector experiment at the VEPP-2M collider in the energy region MeV. This measurement was based on about 12.4 • 106 selected collinear events, which include 7.4• 106 , 4.5• 106 , and 0.5• 106 selected events. The systematic uncertainty of the cross section determination is 1.3 %. The ρ-meson parameters were determined as MeV, MeV, and nb and the parameters of the G-parity suppressed decay as nb and degree.

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## Algebra and Trigonometry 10th Edition

$x=\pm 9$
$f(x)=x^2-81$ Since we are solving for all the real values of $x$ when $f(x) = 0$, set the function $f(x)=x^2-81$ equal to zero and we get the following equation: $x^2-81=0$ Now add 81 to both sides of the equation so that all of the constants are on the right side of the equation and all of the $x$ terms are on the left side. $x^2-81+81=0+81$ $x^2=81$ Once all of the constants are on the right and all the $x$ terms are on the left, solve for $x$ by taking the square root of both sides. $\sqrt{x^2}=\sqrt{81}$ Note: Remember taking the square root of both sides of the equation results in both a positive and negative answer. This is why the $\pm$ appears in the line below. $x=\pm\sqrt{81}$ $x=\pm 9$


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# Is better to spend parameters on weights or bias?

If a neural network has a limited number of neuron parameters to find, -let's say only 1000 parameters-, it is generally better to spend the parameters on weights or neuron bias?

For example, if each neuron has 2 weights and one bias, it uses 3 parameters per neuron, so only 333 neurons would be available.

But if each neuron uses no bias parameter, then 500 neurons are available with 1000 parameters.

I'm concerned with overfiting by using too many parameters, so I want to minimize the number of parameters meanwhile maximizing the quality of the result.

• Are you just interested in 1. having or not biases or 2. in general, how many connections a neuron has? From your title, it seems like you're trying to understand whether you should or not have biases. However, from the body of your post, it seems like you're also interested in how you should define all the connections (including biases) between neurons (e.g. if a neural network should be sparse or not). – nbro Jun 3 '20 at 16:43
• @nbro I'm asking about the choice between (more neurons) or (less neurons with bias parameters). I guess that more neurons require more computing, and more cycles for convergence, but more neurons can achieve higher accuracy. If the constrain is the number of parameters, then I guess that more neurons should be preferable. – tutizeri Jun 3 '20 at 17:46
• The capacity of a network is proportional to the number of parameters and not necessarily the number of neurons, so I think you're making a possible wrong assumption here. I think your question is more related to the sparsity of the parameters (i.e. how many connections you have and how they affect learning). – nbro Jun 3 '20 at 18:00

## 1 Answer

First of all, your estimates are a bit off. If you have 300 neurons, you won't have just 2 weights per neuron, but much more, assuming full connectivity

Bias isn't just an extra parameter to fit, it is an important adjustable parameter that sets the offset of the separating hyperplane represented by each neuron. Think of the simple equation $$ax+b$$, there's no way to shift the line unless you use the $$b$$ (bias) part.

This would be especially important for small number of nodes and classification tasks (think perceptrons etc)

• Thank you for your answer. I said 300 neurons with 2 weights just as an illustrative example. Do you mean that the bias parameter cannot be replaced by using more neurons without bias? Or just that it is more efficient to use bias than adding neurons? – tutizeri Jun 4 '20 at 18:02
• @tutizeri the bias parameter cannot be replaced by using more neurons without bias, think of it as fitting a line to separate some points, you can rotate the line with the slope (weights) but it still passes through the origin, if your data points are not distributed such that they can be separated by this line, you will need to move the line. This is for one neuron. So, the bias is an important parameter without which your weights can be useless. – ctlr Jun 5 '20 at 11:18