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Showing posts from September, 2019

Advice to Teachers conducting lessons remotely

A lot of WhatsApp groups for delivering tutorials have surfaced recently in the wake of the corona virus pandemic.  This was necessitated by the need to mitigate the effects of keeping schools closed for an extended period of time. Most students were falling behind on their studies before the mushrooming of such WhatsApp groups.
E-learning is not a new phenomenon to Zimbabwe but measures to curb the spread of Covid-19 ,like lockdown and minimizing of gatherings , have seen an upsurge in the number of tutors embracing the internet as a mode of delivering lessons. This article will look at the best  platforms available which teachers can use in their endeavor to continue educating people in these trying times.
In the Zimbabwean context, WhatsApp is likely the first option which comes to many people's minds when they think of distance learning solutions. This is mainly due to the great number of users on the platform. Many, if not all, smartphone owners have WhatsApp installed and also…

C Programming - file manipulation

Access Modes
“r” File is opened for reading only, does not create a file.
“w” File is opened for writing only (start from the beginning of the file, wipes any stored data)
“a” File is opened for appending only (start from the end of the file without deleting anything)
“r+” File is opened for reading plus (read and insert (overwrite) starting from the beginning of the file, can not create a new file)
“w+” File is opened for writing (create, read and write, wipes any stored data)
“a+” File is opened for appending (read the whole file or writing at the end

Structure of a C Program

A C Program has the following sections;

Documentation: This is where the name of the writer is placed as well as a description of the program.
Preprocessor/Link: This is where C libraries are called so that certain functions are able to work in the program.
Global declaration: The functions and global variables, those variables which should be available to all statements in the program are placed under this section.
Definitions: Constants are defined in this section. The declaration is not a statement and therefore should not be terminated by a semicolon. Capital letters are used to represent a constant.
Main Function: Program execution begins in the main function.
Sub Programs: These are user-defined functions
Local Variables: These are variables declared in a function and only that function can access the variable.

Below is sample code demonstrating recursion as well as showing the full structure of a C Program.

C Program to Arrange Numbers in Ascending Order

The following is the source code for a c program which arranges numbers in ascending order.

Comments
 The integer n is for capturing the value of arryA[j] before swapping the numbers. Failure to capture that number before its value changes will result in all numbers defaulting to the maximum or lowest number in the list depending on the condition stated in the if statement.

Gradient of a Straight Line

Gradient of a line AB = increase in y from A to B divided by increase in x from A to B

In A level mathematics we use differentiation to calculate gradient or a formula similar to the one stated above. It will then be stated as ∆y/∆x that is change in y over change in x.

Given two points on a line, we can calculate its gradient.

Given the gradient of a line and the coordinates of a point it passes through, we can write the equation of the line.

Rounding Off Numbers

Rounding Off Numbers
Rough estimates are not accurate but they are useful in calculations as they can give us some idea of the size of the correct results.

 Numbers can be rounded off to the nearest hundred, ten, whole number or to a given number of decimal places

1, 2, 3 and 4 are rounded down while 5, 6, 7, 8 and 9 are rounded up.

Significant Figures
The significance of a digit depends on its position in the number. The first significant figure in a decimal fraction is the first non-zero digit. For example in 0.00356, the first significant figure is 3.

Example

Round off 136,78 to (a) 1 significant figure (b) 2 significant figures (b) 4 significant figures.

Solution
(a) 136,78 = 100 to 1 significant figure
(b)136,78 = 140 to 2 significant figures
(c)136,78 = 136,8 to 4 significant figures



Example

Round off 136,78 to (a) 2 decimal places  (b) to the  nearest whole number (b) to the nearest hundred

Solution
(a) 136,78 = 136,9 to 1 decimal place
(b)136,78 = 137 to the nearest whole number
(c)136,78 = 10…

Ways of Increasing Traffic to Your Website

Organic Traffic
First and foremost, your site should be indexed by search engines so that it can start appearing on Search Engine Result Pages (SERPs). For your site to be quickly indexed you need to submit a site map to each of the major Search Engines like Google, Binge and Yandex. Do not worry about Yahoo as it is a meta search engine which means that it uses other search engines to provide search results. Yahoo has its own website crawlers but it supplements that with the Binge search engine. Therefore submitting a site map to Binge will make your website to also appear on Yahoo SERP. Referrals
Create and curate content for social media which can grow your brand as well drive traffic to your website. You need a social media strategy in order to be effective. This might include a Social Media Management tool and a buyer persona. The first one will help you schedule posts and the latter guides you in posting content which is relevant to your audience. You can also create back links …

Set Theory Rules

Question 

Show that

`A cup (A^c cap B) = A cup B`

Solution

`A cup (A^c cap B) = (A cup A^c) cap (A cup B)` (distributive law)

`xi = A cup B`

`xi  = A cup A^c `

`(A cup A^c) cap (A cup B)`

`(A cup B) cap (A cup B)`
`=A cup B` (shown)

The following is a complete list of rules

1.
2.
3.






Application of Set Theory

Question 1 (8 marks)

A survey of 73 customers was taken at a bookstore regarding the type of book purchased. The survey found out that 42 customers purchased mysteries, 33 purchased science fiction and 27 purchased romance novels. If 17 purchased mysteries and science fiction, 14 purchased mysteries and romance novels, 8 purchased fiction and romance and 4 purchased all three types.

(a) How many of the surveyed customers purchased only romance novels? [4]

(b) How many purchased mysteries and science fiction, but not romance? [4]

Solution

Using a Venn diagram we can find the answers
(a) We need to find `(M cup S)^c cap R` which is equal to 9.
      Nine customers purchased books on romance only.

(b) We need to find `(M cap S) cap R^c ` which is equal to 13.
Thirteen customers purchased books on mysteries and science fiction but not romance.


Question 2

In a group of 60 students, 25 play table tennis, 16 do swimming and 22 play cricket, 8 play table tennis and do swimming, 6 play cricket and do s…

Inverse of a 3×3 Matrix

To find the inverse of a 3x3 matrix, first calculate the determinant of the matrix. If the determinant is 0, the matrix has no inverse. Next, transpose the matrix by rewriting the first row as the first column, the middle row as the middle column, and the third row as the third column. If `A = [[a,b,c], [d,e,f], [g,h,I]]` Then `A^T = [[a,d,g], [b,e,h], [c,f,I]]`

Set Theory

A set does not have the following properties
• frequency
• order

Therefore a set A= {1, 4, 3, 2,3, 1}
is equivalent to A={1, 2, 3,4}
The number of times the elements appear does not have any effect on the set. Set Theory is all about belonging.

If a set B= {2, 4, 6, 8}

The intersection of A and B is a set which contains elements that appear in both A and B

The intersection  is denoted by `cap`

`A cap B = {2,4}`

The union of A and B is a set which contains al elements from A and B

The union  is denoted by `cup`

`A cup B = {1,2,3,4,6,8}`

Inverse of a Matrix

2×2 Matrices

Example
 `A= [[3,-5], [2,4]]`

The transpose `A^T = [[3,2],[-5,4]]`

The determinant of A  which is |A|= `( 3×4)-(-5×2)`

To find the inverse of a 2x2 matrix: `[[a,b], [c,d]]` swap the positions of a and d, put negatives in front of b and c, and divide everything by the determinant (ad-bc).
The inverse of A which is denoted by `A^-1 `= `frac{1}{22}[[4,5],[-2,3]]`

Quadratic Equations

Quadratic Formula

`x= ( -b +- sqrt(b^2-4ac))/(2a)`


Solve `x^2+8x+16=0`

`a=1 `
`b=8`
` c= 16`

By substitution:

`x = (-8 +- sqrt(8^2 -(4×1×16)))/(2×1)`
`x=+-4`


By factorisation:

`x^2+4x+4x+16=0`
`x(x+4)+4(x+4)=0`
 `(x+4)^2=0`
`x=+-4=0`


More Maths Problems and Solutions

Exercise 1Solve the equation
`x^2+5x+6=0`

Solution
`x^2+2x+3x+6=0`
`x(x+2)+3(x+6)=0`
`(x+2)(x+3)=0`

`x=-2, -3` 
Explanation A quadratic equation has a general form denoted by
`ax^2+bx+c`
To factorise such an expression we multiply the coefficient of `x^2` by the constant ` c` to get `ac`. Next step is finding factors of `ac` which when added together gives us `b` which is the coefficient of `x`.  We then rewrite the quadratic equation in the form below:
`ax^2 + (` factors of  `c` which add up to `b` `)x+ c` 

 In the question above we used factorisation to get the answers.
To factorise, multiply the coefficient of `x^2` which is 1 by the constant which is 6. Then find factors of `6x` which when summed up gives us `5x`. The factors are `2x and 3x`. Replace `5x` with the factors and simplify the resulting expression.
Question 2Solve the equation
`x^2-9x+18=0`

Solution
`x^2-6x-3x+18=0`
`x(x-6)-3(x-6)=0`
`(x-6)(x-3)=0`

`x=6, 3`

Question 3

If `xi = `{all cars}, M={modern cars} , S={cars with seat belts} , H…

Limitations of the Internet, A Zimbabwean Perspective

Internet has its pros and cons. This article is about the disadsvantages or limitations of the internet in a Zimbabwean context. Language. English is the main language of the internet. Zimbabweans are ranked as one of the nations with the highest literacy rates. However, the thrill of reading articles in your own vernacular language can not be compared to anything else. Unfiltered content. There is fake news being peddled on the internet. The amount of rumours and speculation makes it difficult to to know what to believe. There is uncensored content like violence and pornography as well which can cause moral degradation. Teenagers who are still in school are now attending to Vuzu parties where they get involved in group sex and take drugs. This behavior is said to have emanated from South Africa. Internet can speed up such cultural interchange which can be detrimental to a society. Broadband and Dial Up. The internet speeds range from very low to high. Some parts of Zimbabwe can not acc…

Email Signature Generator

Email Signature Generator

FIRST NAME

LAST NAME

MOBILE NUMBER

EMAIL

JOB TITLE

DEPARTMENT

COMPANY

WEBSITE

OFFICE FAX

ADDRESS LINE 1

ADDRESS LINE 2

LOGO/AVATAR (you can upload image to Google Drive and create link )

Apply Signature
Your email signature will appear here. Copy and paste it in the Gmail app.
StewartMukonziFreelance Digital MarketerMarketingTimid CoderP: +263999210M: +263F:  +263999210A: ZRP Borrowdale Camp199 HebronW: http://www.stewartmukonzi.blogspot.comE: 

Alternative to a tripod- canon DSLR cameras

There are times when we have to use a slow shutter speed when taking photographs. However, we might end up with blurry images if we do no use the appropriate equipment. In this article I write about two alternatives which you can adopt.

When should you use a tripod? If your shutter speed is greater than 2 seconds you should use a tripod as camera shake is then likely to occur no matter how steady you hold the camera. Another way to know if you are likely to experience camera shake is to check the focal length of your lense. If the focal length is say 55mm then you should keep your shutter speed less than 1/55 seconds. It is just a rough estimate and if you can keep even less it will be ideal. The following are alternatives to a tripod.

Remote trigger. You can opt for a remote trigger. Place your camera on a flat surface facing the subject. Make all the necessary adjustments in terms of aperture, ISO and shutter speed etc,  on the  camera and compose your image. When satisfied plug in …

Photography Styles

There are quite a number of styles of photography which one can explore. I would like to share a few of them and the main techniques they use.



Macro photography. It is used to take life size or greater than life sizes images of small objects like insects. It is also used for taking photographs of products which is a lucrative business and is also important to master if you need to succeed in e-commerce. There is a phenomenon known as focus breathing and also blurring of some parts of an image taken  using a macro lens. To fix that  one has to take multiple shots and overlay them in a photo editing software to come up with a perfect image. Street Photography. This is accomplished by taking candid or unposed photos of people, usually strangers, often while they are  unaware on the streets. Tourist do the same with ease, however, for a local it might be challenging as not all people enjoy having their photos taken without permission. Therefore, to avoid being shouted at, street photograp…

Use A Grey Card to Master A DSLR's Manual Mode

The purpose of upgrading from a point and shoot camera to a Digital Single Lense Reflex (DSLR) is usually to improve the quality of photographs that you can take and the ability to be more creative. However, quite a number of people end up getting frustrated after seeing no change in their photographs after the upgrade. In this article I write about one important tip you need to  try to start enjoying taking great photographs again, that is the use of a grey card.

A DSLR camera when operated in automatic mode rarely brings changes to your photography. Though you might benefit from the ability to capture more details due to the increase in pixels, it will not be long till you start to view your DSLR as cumbersome and therefore not ideal to carry around when you travel. This happens when you have not mastered operating the  camera in manual mode. There are a few things you need to learn first before you can be comfortable using the manual mode but the most important concept is that of …

Techniques and Tools To Improve Smartphone Photography

Most photos be it of families on vacation or for use on websites either by individuals or journalists and bloggers are now being shot using smartphones. Therefore there is a need for learning some techniques and tools which can ultimately enhance smartphone photography.

White Balance. Professional photographers know that White Balance (WB) sometimes needs to be corrected but those who have never heard about that tip might not know how it adjusting the WB can dramatically improve your photos.

HDR. Indoor photos and photographs of buildings usually comprise both areas of highlights and shadows. An experienced photographer knows that most all cameras can not capture properly both highlights and shadows correctly without compromising on some details. To avoid loss of detail in your composition you should turn on HDR on your smartphone's camera. You will notice a great improvement instantly.

Tools (mobile apps for editing photos)
Snapseed
Photoshop Express

How To List Your Business Online

Have you created an online strategy yet? If yes, I bet listing your business is among some of your top priorities as an online presence is essential for any business to thrive in this digital era. In this article I will show you how to list your business in a few minutes. But before I do that, let me delve into the advantages first.

Advantages
I will give a few examples of some of the benefits of listing your business starting with touch points.

Increase in Touch Points. You create more touch points or chance of people interacting with you business. This also means an increase in lead generation

Convenience to Existing Customers.  Technology makes our lives easier. By embracing technology as a business, you tend to bring convenience to your customers. This improves customer retention. Satisfied customers are likely to recommend your services or products by word of mouth (WOM).

Cutting down on Expenses. The traditional form of advertising is more expensive than digital marketing. There by …