Month: February 2018

Pre-Calculus 11 Week 4 – Adding and Subtracting Square Roots

alexr2015

This week, we discussed adding and subtracting numbers with square roots, such as 2\sqrt{2} + 3\sqrt{2}

The easiest way to learn how to add these numbers is simply looking at them the same way you would look at 2x + 3x in algebra. You can simplify this expression. 2x + 3x = 5x

But you wouldn’t be able to add, say, 2x + 2y together. The expression is already simplified. The same thing applies to roots!

You can add 2\sqrt{2} + 3\sqrt{2} together to make 5\sqrt{2}!

However, you are unable to simplify 4\sqrt{2} + 5\sqrt{3}, because the radicands aren’t the same.

If our square root is really big, like \sqrt {128} + 3\sqrt{2}, we can still add them together! We just need to simplify the square root first. In this case, \sqrt {128} simplifies into 8\sqrt {2}. Our steps are as follows:

\sqrt {128} + 3\sqrt{2}

 

\sqrt {8*8*2} + 3\sqrt{2}

 

8\sqrt{2} + 3\sqrt{2}

 

11\sqrt{2}

 

All these rules apply to subtraction as well.

7\sqrt {3} - 3\sqrt{3} = 4\sqrt{3}

and

\sqrt {243} - 3\sqrt{3}

 

9\sqrt {3} - 3\sqrt{3}

 

6\sqrt{3}

Pre-Calculus 11 Week 3 – Absolute Value of a Real Number

alexr2015

This week, we looked at what absolute values were. Absolute values are the distance that the number is from zero. In class, we used the analogy of attempting to throw crumpled paper balls into a garbage bin. One person made the shot, others missed and landed a certain distance from the trash can. While some paper balls will have landed in different positions, their distance from the trash can could be the same as another paper ball. Absolute values are written like so:

|-5| = 5

The answer is 5 because -5 is 5 away from 0.

|5| = 5

The answer is also 5 because 5 is 5 away from -5.

Numbers beside these terms act as coefficients. Like so:

3|-5|

3×5

=15

Or if there is an expression within the lines, you do those first before completing the equation:

3|-3+6|

3|3|

3*3

= 9

You can almost think of the lines like brackets.

 

Capital Punishment within the short story, “The Two Fishermen”

alexr2015

Capital Punishment within the short story, “The Two Fishermen”

Capital punishment is the legally authorized killing of someone as punishment for a crime. This was used for anyone who committed murder, rape, and treason. Canada used to have capital punishment for a while, up until 1976, where it was removed from the Canadian Criminal Code. The death penalty was life imprisonment, along with no chance of parole for 25 years for first-degree murders. Capital punishment remained within the Canadian National Defence Act, only for the most serious military offences until 1998.

If this story took place in Canada, the crime would have been committed between 1865-1961. This was the time when crimes of murder, rape, and treason all carried the death penalty. Then the events that happened in the story would be allowed to take place in Canada, and Thomas Delaney would be handed capital punishment for murdering the man molesting his wife.

Thomas Delaney should not have been hanged. Capital punishment was not appropriate for the crime he committed. He may have killed someone, but it was a) in the heat of the moment, b) to protect his wife, and c) the crime was really voluntary manslaughter, not murder. There was a fight between the two men, that was started by Matthew Rinehart  This resulted in one of them dying. This for sure warrants jail time, along with recuperating with therapy sessions or something. Either way, death was not the proper punishment for the crime he committed.

Gallows cartoons, Gallows cartoon, funny, Gallows picture, Gallows pictures, Gallows image, Gallows images, Gallows illustration, Gallows illustrations

Sources:

https://www.thoughtco.com/history-of-capital-punishment-in-canada-508141

https://www.cartoonstock.com/directory/g/gallows.asp

 

 

Pre-Calculus 11 Week 2 – Geometric Sequences

alexr2015

This week, I focused on geometric sequences.

Geometric sequences share similar characteristics to arithmetic sequences. For one, geometric sequences are patterns, just like our arithmetic sequences from last week! Arithmetic sequences have common differences, such as this one: “5, 10, 15, 20, 25, 30…” You can tell the pattern here is that 5 is being added for every new term!

Geometric sequences, however, have common ratios. Like so: “2, 4, 8, 16, 32, 64…” You should be able to see a pattern here. What’s the pattern? The terms are being multiplied by 2 each time! This is very different from our arithmetic sequence, where numbers were being added as the pattern was continuing. The ratio is determined like so: tn/(tn-1)=r.

The ratio is a very important number. It’s as important to geometric sequences as the common difference, d, is to arithmetic sequences, so get used to finding it!

There are a number of ways that you can utilize the common ratio, r. Say, you wanna find the 9th term in our geometric sequence here. Looks something like this:

t1*r^(n-1) = t9

2*2^(9-1) = t9

2*2^8 = t9

2*256 = t9

512 = t9

The general formula for geometric sequences is t1*r(n-1)=tn

Pre-Calculus 11 Week 1 – Arithmetic Sequences

alexr2015

First week of Pre-Calc 11! This week, I learned about Arithmetic Sequences.

Arithmetic sequences are like patterns, they look something like this: 5, 7, 9, 11, 13….

For a pattern to be an arithmetic sequence, all the numbers must have a common difference between them all. The common difference is how much it goes up or down. For our pattern here, the common difference is 2! You see how the pattern continues to increase by 2? This is an arithmetic sequence.

If you wanted to find the 20th term in that pattern, you would use the following formula:

t_10=t_1+9d

 

t_10 = 5 + 9(2)

 

t_10 = 5 + 18

 

t_10 = 23

With this formula, we’re saying that we’re going to take the first term in the arithmetic sequence, add the common difference (2) NINE times to get the 10th term. Let’s count it, and make sure my work is correct.

5, 7, 9, 11, 13, 15, 17, 19, 21, 23

Look at that, the 10th term really is 23! For this formula, you don’t have to use t1. You can use any term you already have. If we only had t4, the formula would look like this:

t_10=t4+6d

 

23 = 11 + 6(2)

 

23= 11 + 12

 

23 = 23

You can find a general formula for tn as well. It looks like this” $latex t_n = t1 + (n-1)d    For example:

t_23 = 5 + (23-1)d

 

t_23 = 5 + (22)2

 

t_23 = 5 + 44

 

t_23 = 49

 

Restaurant Reivew – Rosa’s Cucina Italiana

alexr2015

The household turned restaurant is small, but never felt cramped. Tables are spaced out nicely, while still making the most out of the space. There’s chatter amongst the tables, but it never overpowers your ears. Flags hang from the kitchen doors and around the restaurant, showing their nationality proudly. The walls are adorned, no, completely covered with pictures that Rosa has taken with many noteworthy people over the course of her life. They’re all signed by their respective celebrity, too. Michael Bublé, Wayne Gretzky, Bobby Hull, and many others. The only one that makes you a little uncomfortable is a picture of Ron Jeremy by the washroom doors with his, erhm, devilish smile. At least the picture was taken during his better years.

You and your friends sit down at a table, half of you sitting in booth seats, the others in chairs opposite of you. You feel comfortable in the leather seats that span the whole side of the restaurant wall. You order your food, and then are greeted by warm bread and butter while the main course is being prepared. Picking up the bread, you notice it is warm to the touch, but not burning your palm. Spreading butter on the bread, it melts perfectly on top. The bread warms your mouth. A crispy crust, but a fluffy inside. Perfect.

Finally, your dish arrives, catered to you by the waitress. The dish hasn’t even met your eyes, yet you can see the steam floating into the air from it. And it lands in front of you. Spaghetti covered with tomato sauce. Parmesan cheese splashed on top of the tomatoes, with some basil leaves on top to give it a splash of colour. A single, warm slice of garlic bread is set to the side of the dish. You smell the tomato sauce filling your nose with warmth. The scent of the garlic bread mixes with the rest of the dish nicely. The whole thing is such a pleasure to look at, you can hardly bring yourself to eat it! But you haven’t eaten anything since your 6-inch Subway sandwich for lunch, so you’re kinda hungry. You grab your fork and spoon, the required equipment for enjoying such a fine culinary creation. You wrap the spaghetti around your fork, raise it to your mouth, and bite.

The spaghetti itself; not too hard, but not practically made of mush. The perfect density. The tomato sauce and parmesan cheese compliment each other wonderfully. The tomato sauce brings your taste buds to a fiery awakening, while the parmesan cheese almost cools your mouth down and brings a second taste. The whole meal, instantly enjoyable, makes you feel like you’re in a restaurant in Italy. While your meal makes your wallet much lighter, your stomach and brain are only getting fuller. Full of enjoyable food and memories with your friends.