Week 14 Math Post

This week we learned about how to use substitution to find the solution of two linear relations. The substitution method is essentially where you take one equasion and input it into the second one. The solution is the point where the two relations would cross if they were graphed. It is possible to have lines with one solution (where the two lines cross at one point on the graph), no solutions (if the lines are parallel and the slopes are the same) and infinite solutions (if the two lines are on top of one another and have identical equations). To find the solution using the substitution method you’d need to follow the following steps. I’ll use the equations (x+4y=-3) and (3x-7y=29) as an example.

  1. First you would need to isolate a variable. Select a variable from either equation that seems the easiest to work with. The variable that seems the easiest to work with in these equations is the x from the first equasion (x+4y=-3) as it does not have a base associated with it. After you have chosen your variable, you can isolate it by subtracting 4y from both sides of the equal sign. The rearranged equation should look like this: (x=-4y-3).
  2. Next you can take (-4y-3) and substitute it into the second equation (3x-7y=29). Since x in the first equation is equal to (-4y-3) you would replace the x in the second equation with that same answer. Now the second equation should look like this: (3(-4y-3)-7y=29).
  3. After that you can solve the equation. Take the 3 and use the distributive law first to get rid of the brackets. The equation then becomes (-12y-9-7y=29). Then, simplify the (-12y) and the (-7y) so that the equation becomes (-19y-9=29). After you can add 9 to both sides of the equal sign so the equation becomes (-19y=38). Finally divide both sides by (-19) to get (y=-2). Now you have the y coordinate of the solution. All we need is to find the x.
  4. To do that, substitute the y coordinate (-2) back into the rearranged version of the first equation (x=-4y-3) so that it becomes (x=-4(-2)-3). Solve this equation to find x. (-4(-2)) is equal to (8) and (8-3) is equal to (5). Therefore, (x=5).

Now you know that the solution of these two equations and you can write it as an ordered pair (5, -2). You can verify this by using a graphing calculator or by inputting the two numbers back into one or both of the original equations, (x+4y=-3) and (3x-7y=29). If we use the first one, it would be (5-8=-3) so we know it is accurate. You can also see on the graph showed here that the two lines cross at (5, -2).

Rester en sécurité au travail

Dans le futur je veux travailler comme une astrochimiste dans un planétarium ou musée. Il y a quelques risques assossiés avec cet emploi. Voici 3 choses que je vais faire pour rester en sécurité pendant que je travail:

Je vais savoir tout les risques et dangers des machines technologiques que je vais utiliser, par exemple les microscopes et téléscopes. Il y a beaucoup de risques quand on travaille avec les machines, même s’ils sont stationnaires et ne semblent pas dangereux. Par exemple, les petites microscopes deviennent très chaude et ils peuvent façilement me brûler si je ne fait pas attention. Les Machines plus grands comme les téléscopes et les machines utilisés pour mesurer le radiation peuvent aussi être très dangereux. Savoir comment ces machines fonctionnent et les types de dangers assossiés avec eux va m’aider à éviter les accidents et blessures au travail. Je serais informé et aussi prete à prendre action si quelque chose arrive.

Ensuite, je vais porter toujours l’équipement de sécurité quand je fais des expériences avec des produits chimiques, analyse un objet ou n’importe autre projet scientifique. Les produits chimiques en particulière peuvent aussi être extrêmement dangereux. Plusieurs substances sont corrosifs et peuvent dissoudre la peau et le métal s’il entre en contact. Les autres sont flammables ou toxique si tu l’ingeste. Par exemple, si par accident je renverse un contenant d’acide sulfirique ça peut brûler ma peau si je le touche, causer l’aveuglement si ça entre dans mes yeux et manger un trou dans ma gorge et poumons si je le respire. Avoir le propre équipement est essentiel si j’utilise les produits chimiques.

Finalement, je vais demander de l’aide ou refuser de faire les choses à quels je ne suis pas comfortables. Quelque fois, les scientifiques qui étudient l’espace font des excursions pour recueillir l’information sur des objets spécifiques. Pour faire cela, ils doivent souvent assembler des grands machines lourds. Si, par exemple quelqu’un me demande d’assembler un de ces machines et je ne sais pas comment le faire, je vais demander à quelqu’un d’autre pour m’aider ou refuser de le faire. Assembler ces machines sans expérience peut être dangereux parce qu’ils ont besoin de beaucoup d’électricité qui vient des générateurs électriques ou des battéries. Si je ne branche pas correctement, quelqu’un peut être électrocuté ou ça peut commencer un feu. Je dois me rappeler que demander pour de l’aide n’est pas un mauvais chose surtout quand ça peut prévenir un accident.

Voici deux choses que je vais faire pour protèger les autres au travail:

Je vais être concient de mon environnement, surtout quand je fais des expériences chimiques. Un grand hazard pour les scientifiques est le feu. Ils utilisent souvent des bruleurs buntzen pour chauffer les produits chimiques. Si quelqu’un oublie de les enlever de la bruleur ou oublie d’éteindre le bruleur ça peut causer un grand feu surtout s’il y a des autres produits flammables dans le laboratoire. Cela est dangereux pas juste pour moi mais pour tout les personnes dans le batiment aussi et les pompiers qui viendraient pour éteindre le feu. C’est pourquoi je dois toujours faire attention à ce que je fais, parce que une petite faute peut être catastrophique pour beaucoup de personnes.

Je vais aussi parler à mes collègues s’ils ont besoin d’aide ou ne font pas un tâche proprement. Les nouveaux employées ne sont pas expériencés et peuvent oublier ou pas savoir les propre mesures de sécurités. Même des petites choses peuvent mener à des grands problèmes. Par exemple, si tu réchauffe une fiole avec du liquide là-dans et tu oublie d’enlèver le bouchon, le pressure peut s’accumuler et le flacon peut exploser. C’est important de rappeler à tes collègues des petits mesures de sécurités comme ceci pour que les autres ne soient pas blessés.

L’histoire la plus marquant pour moi était l’un de Grant De Patie. Il avait 24 ans et il travaillait à un station d’essence. Un jour, quelqu’un a essayé de remplir leur voiture avec l’essence sans payer. Grant a essayé de l’arrêté mais il est devenue coincé sous la voiture de la personne qui l’a ensuite conduit pour 7 kilomètres. Grant avait crié mais la personne n’a pas arrêté la voiture. C’est marquant pour moi parce que la personne dans la voiture savait probablement que Grant était sous son voiture mais il a continué à conduire comme rien était de mal. Il a montré aucun décence humaine et s’enfichait de la fait que Grant était en train de souffrir. Il pouvait facilement arrêter la voiture ou, encore mieux ne pas voler de l’essence du tout.

Après l’accident un nouveau loi était mis en place. Les gens doivent payer pour l’essence AVANT de remplir leurs voitures.

Week 13 math post

This week we learned how to change an equation from point slope form to general form. Point slope form is where the equation should look like this: m(x-x)=y-y. This form is useful because it gives a lot of information about the equation. You can immediately see the slope of the equation (slope = m) , the ordered pair being used (the second x and y variables would be the coordinates) and it can be rearranged easily to other forms like general form and slope y intercept form. General form is not very useful but you can easily tell if the equation is linear by seeing if the highest degree is 1 (making sure the variable has no exponents higher than 1). General form must only include integers (no fractions) it’s leading coefficient must be positive and the equation must equal to 0. To change point slope form to general form you can follow the steps and use the equation 9(x-2)=y-3.

1. Add 3 on both sides of the equal sign. Our goal is to get the equation equal to 0 so we start getting rid of the y and the -3. The equation should now look like this: 9(x-2)+3=y.

2. Simplify the equation. Use distributive law to simplify the 9(x-2) so that it becomes 9x-18+3=y. Then, simplify it further by adding the -18 and 3. It should then look like this: 9x-15=y.

3. Subtract y from both sides of the equal sign. We do this to make the equation equal 0 by cancelling out the y on the right side. The y should go right after the x value. Your final answer should be: 9x-y-15=0.

As long as you remember your algebra, distributive property and BEDMAS you should be able to use these steps to rearrange a variety of equations into general form.

Week 12 blog post

This week we learned how to calculate the slope of a line. Slope is a number that states how steep a line is. To calculate slope from a graph, you need to find the rise and the run. Those are numbers that describe how to get from one nice point (points on the given line that are not decimals or fractions). The formula for calculating slope is rise over run. It is the same concept if you want to calculate the slope between ordered pairs.

If you take (3,12) and (5,22) as an example, this is how you would calculate the slope.

Calculate the rise and run to get from one nice point to the next. Rise is the rate the line goes up by on the y axis and run is the rate that the line goes horizontally on the x axis. The two ordered pairs (3,12) and (5,22) are both nice points which makes it easier to calculate. Use a slightly modified formula: y1 – y2 over x1 – x2 (the 1 and 2 are refering to the ordered pairs, for example (3,12) is pair one and (5,22) is pair 2). Written out, it should be 12 – 22 over 3 – 5. This should end up becoming -10 over -2. Once you have that you divide -10 by -2 to get an exact answer for the slope. If you graph the two points and the line that passes through them you can verify if the slope is correct. It should look like this:

The slope is 5 over 1 which means to get from one “nice point” to the next closest one you would need to go up 5 units and over 1.

Week 11 Math Post

Something I found interesting this week is that equations can be represented in so many different ways. For example you have ordered pairs, table of values, arrow diagram, mapping notation, function notation and much more. To show what some of those listed would look like, we can use 3x+4 as an example.

Ordered pairs: (1, 7) (2, 10) (3, 13) etc.

The x in the example equation represents the input value, the first number in each ordered pair (which can also be any number you choose). What you get after solving the of the equation (in this case multiplying the input by 3 and adding 4) is the y value or output. You can then write the input and output numbers in brackets which give you ordered pairs. These are good if you want to graph the numbers on a cartesian plane.

Table of values:

X | Y
1    7
2   10
3   13

The table of values has the same numbers as the ordered pairs, only instead of matching the corresponding x and y values together in pairs, you would write all the x values together and all the y values together. This is good if you want to find the rule (3x+4) and if you want to find x intercepts (the x value when y is equal to zero) and y intercepts (the y value when x is equal to zero)

Function notation: f(x)=3x+4

For function notation, you can take the general rule (3x+4) and state the name (f) and input value (x) at the beginning. To be more specific with numbers, you can write: f(1)=7 where 1 is the input and 7 is the output. Function notation is good when you want to show that the relation is a function (only one input value per output).

There are many more ways of representing equations, each meaning the same thing but being written differently. They are critical to solving different types of problems and in different situations.

Week 10 Math post

This week we learned about function notation. It is a specific way of writing functions, which is a special type of relation where every x value only has one y value.

Written out, function notation looks something like this:

F(x)=2x+3

In the equation F is the name of the function and x is the input value. You could input a number into the equation and you would get a specific answer after you solve it.

To write a function from a table of values where, for example the x values are 1, 2, 3 and the y values are 5, 7, 9 you would follow these steps.

First, find out the rule. To do that, select a pair of x and y values to work with (let’s say 1 and 5). Then take the difference between the each y value (for example in the equation the y values increase by 2) and multiply that by the x value you chose (2×1). Then take the new number and see what you would do to it to get the original y value chosen (2+?=5). After that, write it out as an equation: (y=2x+3)

Now that you have the rule, you can write it in function notation. Write the name of the function, (usually f) then write x in parentheses to represent an input value. Finally write out the rule (2x+3). The final form should look like this: f(x)=2x+3.

Week 9 Math Post

This week we reviewed how to graph inequalities on a number line. For example, if you had the equation x > 2 this is how you’d display it properly.

1. Take the number(s) in the equation and find them on the number line. In this case the number is 2.

2. Look at the symbol(s). In the equation, it states that x is larger than 2, using the > sign.

3. Draw either a filled-in circle or a hollow circle on the number. The filled-in circle means that x is greater than or equal to/ less than or equal to the number. The hollow circle means that x is either greater or less than the number. In the example equation, x is greater than 2 so you would put a hollow circle around the 2.

4. Draw an arrow stating if x is greater than or less than the number. In the equation we know x is greater than 2 so you would need to draw an arrow pointing to the right of, and along all the numbers greater than 2.

The end result should look like the picture above.