Author Archives: Louwrens

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Math 10: Week 9 – Plotting Points on a Graph

  By Louwrens • April 19, 2022

A point in a plane contains two components where order matters! It comes in the form (,y) where comes first, and  comes second.

  • The -value tells how the point moves either to the right or left along the -axis.
  • The -value tells how the point moves either up or down along the -axis.

A coordinate plane is composed of two lines intersecting at a 90-degree-angle (making them perpendicular lines) at the point (0,0) known as the origin.

here is an illustration of a coordinate plane where the main horizontal line is called the x-axis while the main vertical line is called the y-axis. the x and y-axes intersect at the point (0,0) which is commonly known as the origin. They are perpendicular to each other because they intersect at a 90-degree angle.

  • The x-component of the point (,) moves the point along a horizontal line. If the -value is positive, the point moves “-units” towards the right side. On the other hand, if the -value is negative, the point moves “-units” towards the left.
  • The -component of the point (,) moves the point along a vertical line. If the -value is positive, the point moves “-units” in an upward direction. However, if the -value is negative, the point moves “-units” in a downward direction.

The intersection of the -axis and -axis results to the creation of four (4) sections or divisions

a coordinate plane can be divided into four quadrants. we start counting with the top half of the coordinate plane first. the top right section is considered the first (I) quadrant while the top left section is called the second (II) quadrant. we then continue by moving on to the bottom half of the coordinate plane. below the second quadrant is the third (III) quadrant located on the bottom left section of the plane. right next to it is the last or fourth (IV) quadrant which is located on the bottom right section of the Cartesian plane.

  • The first quadrant is located at the top right section of the plane.
  • The second quadrant is located at the top left section of the plane.
  • The third quadrant is located at the bottom left section of the plane.
  • The fourth quadrant is located at the bottom right section of the plane.

 

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Math 10: Week 8 – What are Negative Exponents

  By Louwrens • April 11, 2022

the exponent of a number tells us how many times we should multiply the base.

For example, 82, 8 is the base, and 2 is the exponent.

We know that 82 = 8 × 8.

A negative exponent tells us, how many times we have to multiply the reciprocal of the base.

Consider the 8-2, here, the base is 8 and we have a negative exponent (-2).

8-2 is expressed as 1/82 = 1/8×1/8.

MORE NEGATIVE EXPONENT EXAMPLES –

5-4= 1/54

x-6= 1/x6

1/y-5= y5

b-6/d-5 = d5/b6

8-9= 1/89

40-4= 1/404

2250-2= 1/22502

 

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Biotechnology – Vaccines, Hormones, and Antibiotics

  By Louwrens • April 9, 2022

In this blog post 3 big questions are answered,

  1. Discuss the greatest advancement with regards to your topic and provide examples.  
  2. How is this form of biotechnology best used? 
  3. How is this form of biotechnology changing the world as we continue to advance towards the future?

1. Vaccines: 

Before, viruses and fatal plagues contaminated Earth’s population, injuring and eventually killing millions of people. Medicine was more of a spiritual thing back then and only a few people had a sliver of ideas on how the body worked. Now, we can provide aid and assistance to people that contract these diseases with vaccines. Vaccines are a type of medicine that helps your body build immunity to certain sicknesses. Scientists use gene therapy to create these liquid protectors by using vectors. Vectors are organisms that carry pathogens (microorganisms that can cause disease) and give those pathogens to other living things. This is helpful because by using vectors, scientists can implant a certain virus or strand of DNA into it and put that into the human body which helps build protective cells for that specific illness. To transport the DNA to the targeted cell within the body, vectors use capsids (virus shell) to transmit a message to the targeted cell on what to do to protect the body. Without this technology, so many more lives would have been lost because of viruses like COVID-19 and what is a global pandemic, could have become global extinction.

1. Hormones:

Recombinant DNA or rDNA is the method used to make hormones by combining two or more DNA molecules to create a hybrid. The techniques used during the rDNA process have helped scientists in identifying what proteins are used in hormones to create more and different kinds. Hormones are used to coordinate processes within the body and can alter growth, fertility, and metabolism. rDNA involves extracting a piece of DNA structure that contains the trait or traits wanted and implanting it into the genome. A genome is in our cells and are the instructions needed to create us and what we need. There are 5 steps involved to create these hormones.

  1. Get the desired trait/genetic material on its own
  2. Make a spot for it in the vector (cut out unwanted material)
  3. Amplify the one gene into millions of the same gene
  4. Join the vector and gene/DNA together
  5. Insert DNA into host (once inserted it gets multiplied)

That DNA is then put into vectors to deliver them to the targeted cell to be multiplied inside the body or to be displayed. This DNA can be engineered to replicate itself inside the body when put in bacteria or yeast. With the DNA inside the bacteria, it can then tell the bacteria to copy itself to make more cells and distribute them throughout the body. This process is called DNA cloning or recombinant DNA. Because of the demand for hormones, this process and technology greatly benefits people all around the world.

1.Antibiotics

Antibiotics are drugs or medication used to kill bacterial infections within the body or delay the effects of it. These drugs are created in a lab where scientists use some of Earth’s resources like fungi who are good at dominating and killing their competition within their habitat and and within their food chain.

2.Vaccines

Vaccines are used to help people by using a small or dead strain of the virus to fight the virus. In some vaccines they use mRNA to fight the virus.  With covid 19 there is multiple vaccines some with a strain of covid and some mRNA vaccines used to kill the virus.

2.Antibiotics

Antibiotics are used to help people that are hurt or sick. Antibiotics are made in large amounts they do this by cultivating and manipulating fungal cells. 

2.Hormones

Hormones are made to help people with there mood or get them stronger with steroids. Scientists have known about stuff like growth hormones since 1920 but they only started using them around  1963.

 

3.Future of Antibiotics:

Transcription, the initial stage in gene expression, is carried out by the enzyme RNA polymerase (RNAP), which is controlled by a number of protein transcription factors. RNAP and its related transcription factors are highly conserved across the bacterial domain, making them ideal targets for the development of broad-spectrum antibacterial agents. Despite the fact that there are countless antibiotics on the market, only two series have been approved to target transcription. The high-resolution identification of the three-dimensional structures of RNAP and transcription complexes during the last 15 years has reignited interest in using rational structure-based techniques to target this critical pathway for antibiotic development.

Because of the rapid rise of high-resolution structural knowledge on RNAP and transcription complexes that is becoming available, more targeted techniques are now conceivable. More rational procedures that require the meticulous building of templates (pharmacophores) around which inhibitors are formed can be used to explore chemical space for the design and development of novel inhibitor molecules. These methods can be utilised to develop/improve drugs that target RNAP’s enzymatic activity as well as protein-protein interactions.

Antibiotics originating from natural products (e.g., penicillin) and synthetic chemicals both have a place in history (e.g., fluoroquinones). What matters most is government and industry commitment and investment to guarantee that all options are thoroughly investigated to ensure the continuous discovery and development of crucial medications. One area where there is a lot of unexplored potential is bacterial transcription targeting.

3.Future of Vaccines:

For more than 25 years, university laboratories have been investigating the use of RNA rather than viruses to strengthen the body’s immune system. According to the researchers, mRNA can be utilised to make a range of vaccinations and medicines in less time and for less money than existing approaches. In the early 1990s, mRNA emerged as a viable alternative to traditional vaccine development. mRNA is a molecule that serves as a blueprint for cells to construct certain proteins. Proteins are essential for a viral infection’s success because they allow the virus to multiply once it has attached to a cell. The vaccines’ theory is that mRNA instructs a cell to produce a protein used by a specific virus, triggering an immune response that strengthens the body’s ability to fight the virus. Throughout the 1990s and early 2000s, the idea showed promise in lab studies and animal trials, with researchers attempting to develop cancer medicines and vaccinations to defend against viral infections like influenza, Ebola, and SARS (severe acute respiratory syndrome). The technology’s effectiveness was hampered by a number of stubborn flaws. Getting mRNA into a cell was challenging, as mRNA generated acute inflammation and was swiftly eliminated by the body. Using synthetic RNA that the body’s immune system doesn’t recognise and encasing it in lipid nanoparticles (fat bubbles) that easily slide into cells, mRNA researchers consider this a milestone. Human trials for mRNA vaccines against HIV, influenza, Zika, and rabies began in 2017. A pandemic can strike at any time, but the advent of COVID-19 in December 2019 provided an ideal opportunity for mRNA research. Just as the world sorely needed a vaccine to be created faster than ever, the technology was ready for a real-world test. Malaria, tuberculosis, hepatitis B, and cystic fibrosis are just a few of the diseases that researchers believe will benefit from mRNA vaccines and therapies in the future. Scientists are still looking into mRNA therapies for a variety of cancers. According to University of Texas MD Anderson Cancer Center experts, mRNA tells a patient’s cells to generate protein fragments depending on a tumor’s genetic alterations, causing the immune system to seek out other cells that have the mutant proteins and target the tumour cells that remain. At the same time, the researchers caution against setting unrealistic expectations. Although confirmed adverse effects from COVID-19 mRNA vaccinations have been modest in all but a few cases thus far, there is still much to learn. To gain public acceptance, effective education regarding the negative effects and misinformation, such as that mRNA can modify someone’s genetic composition, will be required. Other issues exist outside of the realm of science, few diseases can elicit the kind of worldwide response that COVID-19 did in terms of finance, commitment of top-tier scientific resources, collaboration, and public support.

3.Future of Hormones:

The reduction of sex steroid hormones with age has been linked to an increased risk of Alzheimer’s disease (AD) in both men and women. The principal female hormone oestrogen and the primary male hormone testosterone have a number of preventive effects in the brain that are relevant to the prevention of Alzheimer’s disease, such as increasing neuron survival, reducing – amyloid buildup, and reducing tau hyperphosphorylation. As a result, it’s been proposed that a rapid decrease of these hormones, whether due to menopause or normal ageing, can increase vulnerability of a AD pathogenesis. The discovery of selective oestrogen and androgen receptor modulators may be one of the most promising translational tools thus far. However, more study is needed to improve these and other integrative approaches in order to successfully use hormone therapy in both men and women to postpone, prevent, or treat Alzheimer’s disease.

 

 

 

 

Works Cited

9 September 2020. Government of Canada. Web. 4 April 2022. <https://www.canada.ca/en/health-canada/services/drugs-health-products/biologics-radiopharmaceuticals-genetic-therapies/activities/fact-sheets/regulation-vaccines-human-canada.html>.

Boundless, General Microbiology at. 7.1H: Production of Vaccines, Antibiotics, and Hormones. 5 March 2021. Web. 1 April 2022. <https://bio.libretexts.org/Bookshelves/Introductory_and_General_Biology/Book%3A_General_Biology_(Boundless)/17%3A_Biotechnology_and_Genomics/17.1%3A_Biotechnology/17.1H%3A_Production_of_Vaccines_Antibiotics_and_Hormones#title>.

Boyle, Patrick. mRNA technology promises to revolutionize future vaccines and treatments for cancer, infectious diseases. 29 March 2021. Web. 4 April 2022. <https://www.aamc.org/news-insights/mrna-technology-promises-revolutionize-future-vaccines-and-treatments-cancer-infectious-diseases>.

Carroll, Jenna C. and Emily R. Rosario. The potential use of hormone-based therapeutics for the treatment of Alzheimer’s disease. 9 January 2012. Web. 8 April 2022. <https://pubmed.ncbi.nlm.nih.gov/22329650/>.

Kabir. Vaccines, Antibiotics, and hormones. 8 may 2020. Web. 30 March 2022. <https://myriverside.sd43.bc.ca/kabirm2018/2020/05/08/vaccines-antibiotics-and-hormones/>.

Ma, Cong, Xaio Yang and Peter J. Lewis. Bacterial Transcription as a Target for Antibacterial Drug Development. 13 January 2016. Web. 8 April 2022. <https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4771368/>.

Organization, World Health. How are vaccines developed. 8 December 2020. Web. 4 April 2022. <https://www.who.int/news-room/feature-stories/detail/how-are-vaccines-developed>.

Petechuk, David. Genetics. Ed. Katherine H., Nemeh and Jacqueline L. Longe. 2021. Gale, a Cengage Company. Web. 30 March 2022. <https://go.gale.com/ps/retrieve.do?tabID=Reference&resultListType=RESULT_LIST&searchResultsType=MultiTab&hitCount=2&searchType=BasicSearchForm&currentPosition=1&docId=GALE%7CCX8124401091&docType=Topic+overview&sort=Relevance&contentSegment=ZXAR-VRL&prodId>.

Table 2 Clinical trials with mRNA vaccines against infectious diseases. 29 March 2021. Nature Portfolio. Web. 4 April 2022. <https://www.nature.com/articles/nrd.2017.243/tables/2>.

Vectors 101. 11 May 2021. Web. 4 April 2022. <https://patienteducation.asgct.org/gene-therapy-101/vectors-101>.

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Math 10: Week 7 – Polynomials with Algebra Tiles

  By Louwrens • April 3, 2022

Algebra tiles are tiles of different colors and sizes. Each size corresponds to a degree of the different monomials of the polynomial.

This tile represents a unit. Polinomios

This represents ‘x’.Polinomios

this represents ‘x2‘.Polinomios

if we want to represent the polynomial 2x2 + 4x + 5 it’s as easy as arranging the corresponding tiles:

Polinomios

We’ve got 2 tiles of ‘x2‘, 4 tiles of ‘x’, and 5 tiles that represent a unit.

Adding polynomials with algebra tiles

Adding polynomials is just as simple as representing them. In this case we’ll use polynomials with all positive monomials. We’ll take the polynomial that we represented before, 2x2 + 4x + 5 and we will add x2 + 2x + 3.

Polynomials

Polynomials

Now we add the like tiles to find the result…

Polynomials

The polynomial result of the addition is 3x2 + 6x + 8.

 

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Math 10: Week 6 – Polynomials

  By Louwrens • March 25, 2022

Polynomial comes from poly- (meaning “many”) and -nomial (in this case meaning “term”) … so it says “many terms”.

A polynomial can have:

constants (like 3, −20, or ½)
variables (like x and y)
exponents (like the 2 in y2), but only 0, 1, 2, 3, … etc. are allowed

that can be combined using addition, subtraction, multiplication and division.

Polynomial or Not?

polynomial

These are polynomials:

  • 3x
  • x − 2
  • −6y2 − (79)x
  • 3xyz + 3xy2z − 0.1xz − 200y + 0.5
  • 512v5 + 99w5
  • 5

(Yes, “5” is a polynomial, one term is allowed, and it can be just a constant!)

These are not polynomials

  • 3xy-2 is not, because the exponent is “-2” (exponents can only be 0,1,2,…)
  • 2/(x+2) is not, because dividing by a variable is not allowed
  • 1/x is not either 

But these are allowed:

  • x/2 is allowed, because you can divide by a constant
  • also 3x/8 for the same reason
  • √2 is allowed, because it is a constant (= 1.4142…etc)

 

 

 

 

sources

https://www.mathsisfun.com/algebra/polynomials.html

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Math 10: Week 5 – Inverse Sine, Cosine, Tangent

  By Louwrens • March 8, 2022

sin vs sin-1

The sine function sin takes angle θ and gives the ratio opposite over hypotenuse 

The inverse sine function sin-1 takes the ratio opposite over hypotenuse  and gives angle θ

And cosine and tangent follow a similar idea.

Example (lengths are only to one decimal place):

triangle 2.8 4.0 4.9 has 35 degree angle

sin(35°)= Opposite / Hypotenuse

= 2.8/4.9

= 0.57…

sin-1(Opposite / Hypotenuse)= sin-1(0.57…)

= 35°

Inverse Sine Function

sometimes it is the angle we need to find.

This is where “Inverse Sine” comes in.

It answers the question “what angle has sine equal to opposite/hypotenuse?”

The symbol for inverse sine is sin-1, or sometimes arcsin.

example: Find the angle “a”

trig ship example 30m and 18.88m

We know

The distance down is 18.88 m.

The cable’s length is 30 m.

And we want to know the angle “a”

 

Start with sin (a) = opposite/hypotenuse

sin (a) = 18.88/30

The Inverse Sine will tell us what angle a is equal to

Inverse Sine: a° = sin-1 (18.88/30)

Use a calculator to find sin-1(18.88/30)

a° = 39.0° (to 1 decimal place)

The angle “a” is 39.0°

what about “cos” and “tan”

Cosine

The Cosine of angle θ is:

cos(θ) = Adjacent / Hypotenuse

And Inverse Cosine is :

cos-1 (Adjacent / Hypotenuse) = θ

Tangent

The Tangent of angle θ is:

tan(θ) = Opposite / Adjacent

So Inverse Tangent is :

tan-1 (Opposite / Adjacent) = θ

 

 

 

 

sources

https://www.mathsisfun.com/algebra/trig-inverse-sin-cos-tan.html

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Math 10: Week 4 – Pythagoras’ Theorem

  By Louwrens • February 28, 2022

Pythagoras was a Greek philosopher who lived over 2500 years ago. He is credited with a number of important mathematical and scientific discoveries, arguably the most significant of which has become known as Pythagoras’ Theorem.

It is an important rule that applies only to right-angled triangles. It says that ‘the square on the hypotenuse is equal to the sum of the squares on the other two sides.’

That sounds rather complicated, but it is actually quite a simple concept when we see it in a diagram:

Pythagoras' Theorem. Demonstating that the square on the hypotenuse is equal to the sum of the squares on the other two sides of a right-angled triangle.

 

Pythagoras’ Theorem says :

a2 + b2 = c2

So, if we know the length of two sides of a triangle and we need to calculate the third, we can use Pythagoras’ Theorem.

Let’s see if it really works using an example.

Example: A “3, 4, 5” triangle has a right angle in it.

triangle 3 4 5 Let’s check if the areas are the same:

32 + 42 = 52

Calculating this becomes:

9 + 16 = 25

It works like Magic!

However, if we know only one side length and one of the internal angles, then Pythagoras is no use to us on its own and we need to use trigonometry.

 

 

 

 

sources

https://www.skillsyouneed.com/num/trigonometry.html

https://www.mathsisfun.com/pythagoras.html

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Math 10: Week 3 – Trigonometry

  By Louwrens • February 22, 2022 ,

Trigonometry, as the name might suggest, is all about triangles.

More specifically, trigonometry is about right-angled triangles, where one of the internal angles is 90°. Trigonometry is a system that helps us to work out missing or unknown side lengths or angles in a triangle.

A right-angled triangle has a single right angle. By definition, that means that all sides cannot be the same length. A typical right-angled triangle is shown below.

Right-angled triangle showing the Opposite, Adjacent and Hypotenuse

  • The right angle is indicated by the little box in the corner.
  • The other angle that we (usually) know is indicated by θ (theta).
  • The side opposite the right angle, which is the longest side, is called the hypotenuse.
  • The side opposite θ is called the opposite.
  • The side next to θ which is not the hypotenuse is called the adjacent.

Introducing Sine, Cosine and Tangent:

There are three basic functions in trigonometry, each of which is one side of a right-angled triangle divided by another.

The three functions are:

Name Abbreviation Relationship to sides of the triangle
Sine Sin Sin (θ) = Opposite/hypotenuse
Cosine Cos Cos (θ) = Adjacent/hypotenuse
Tangent Tan Tan (θ) = Opposite/adjacent

Calculating Sine, Cosine and Tangent

You may find it helpful to remember Sine, Cosine and Tangent as SOH CAH TOA.

Remembering trigonometric functions can be difficult and confusing to begin with. Even SOH CAH TOA can be tricky. You could try making up a funny mnemonic to help you remember. Just keep each group of three letters in the same order.

For example, TOA SOH CAH could be ’The Old Archaeologist Sat On His Coat And Hat’.

 

 

 

 

sources

https://www.skillsyouneed.com/num/trigonometry.html

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Math 10: Week 2 – Exponent Rules

  By Louwrens • February 14, 2022

What is an exponent?

An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means:

2 x 2 x 2 = 8.

23 is not the same as 2 x 3 = 6.

Remember that a number raised to the power of 1 is itself. For example,

a1 = a

51 = 5.

There are some special cases:

1. a0 = 1

When an exponent is zero, as in 60, the expression is always equal to 1.

a0 = 1

60 = 1

14,3560 = 1

You can have a variable to a given power, such as a3, which would mean a x a x a. 

The Rules.

There are five rules for working with exponents:

1. am * an = a(m+n)

2. (a * b)n = an * bn

3. (am)n = a(m * n)

4. am / an = a(m-n)

5. (a/b)n = an / bn

am * =an  a(m+n) says that when you take a number, a, multiplied by itself m times, and multiply that by the same number a multiplied by itself n times, it’s the same as taking that number a and raising it to a power equal to the sum of m + n.

Here’s an example where

a = 3
m = 4
n = 5

34 * 35 = 3(4+5) = 39 = 19,683

(a * b)n = an * bn says that when you multiply two numbers, and then multiply that product by itself n times, it’s the same as multiplying the first number by itself n times and multiplying that by the second number multiplied by itself n times.

Let’s work out an example where

a = 3
b = 6
n = 5

(3 * 6)5 = 35 * 65

185 = 35 * 65 = 243 * 7,776 = 1,889,568

(am)n = a(m * n) says that when you take a number, a , and multiply it by itself m times, then multiply that product by itself n times, it’s the same as multiplying the number a by itself m * n times.

Let’s work out an example where

a = 3
m = 4
n = 5

(34)5 = 3(4 * 5) = 320 = 3,486,784,401

am / an = a(m-n) says that when you take a number, a, and multiply it by itself m times, then divide that product by a multiplied by itself n times, it’s the same as a multiplied by itself m–n times.

Here’s an example where

a = 3
m = 4
n = 5

34 / 35 = 3(4-5) = 3-1 (Remember how to raise a number to a negative exponent.)

34 / 35 = 1 / 31 = 1/3

(a/b)n = an / bn says that when you divide a number, a by another number, b, and then multiply that quotient by itself n times, it is the same as multiplying the number by itself n times and then dividing that product by the number b multiplied by itself n times.

Let’s work out an example where

a = 3
m = 4
n = 5

(3/6)5 = 35 / 65

Remember 3/6 can be reduced to 1/2. So we have:

(1/2)5 = 243 / 7,776 = 0.03125

 

 

 

 

sources

  1. http://www.mclph.umn.edu/mathrefresh/exponents.html
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Math 10: Week 1 – Prime Numbers

  By Louwrens • February 7, 2022 ,

Intro:

Prime numbers are numbers that have only 2 factors: 1 and themselves. For example, the first 5 prime numbers are 2, 3, 5, 7, and 11. on the contrary, numbers with more than 2 factors are called composite numbers.

Prime Number Facts:

  • The only even prime number is 2. All other even numbers can be divided by 2.
  • If the sum of a number’s digits is a multiple of 3, that number can be divided by 3.
  • No prime number greater than 5 ends in 5. Any number greater then 5 that ends in a 5 can be divided by 5.
  • Zero and 1 are not considered prime numbers.
  • Except for 0 and 1, a number is either a prime number or a composite number. A composite number is defined as any number, greater than 1, that is not a prime.
  • A prime number can be divided, without a remainder, only by itself and by 1. For example, 17 can be divided only by 17 and by 1.

How to prove is a number is a prime number:

To prove whether a number is a prime number, first try dividing it by 2, and see if you get a whole number. If you do, it can’t be a prime number. If you don’t get a whole number, next try dividing it by prime numbers: 3, 5, 7, 11 (9 is divisible by 3) and so on, always dividing by a prime number

(see table below).