Advice to Next Year’s Seventh Grade

Seventh grade is a difficult year. You experience a sudden increase in homework and the courses also get difficult as time progresses. So for the last (graded) blog post of the year, I have compiled a list of useful tips to keep in your mind during your seventh grade year.

  • Stay well organized:

Throughout seventh grade, you will be experiencing a larger amount of homework. So a good way to be able to turn in your homework on time is to have everything well organized. Keep things in separate folders or binders and label everything. Even though this may seem like a big waste of time and energy, it will slowly repay you overtime. Keeping a well organized binder will enable you to find homework and worksheets without much of a hassle.

  • Keep your locker organized:

Similar to keeping your binder neat and well organized, keeping your locker organized and secured is just as important. Having random things in your locker (such as old sandwiches) attracts unwanted bugs (such as ants and cockroaches) and can make a mess. Avoid leaving food in your locker over the weekends and clean out your locker every few months.

  • Turn in your homework:

Even though homework grades are only 10% (give or take some percentage) of your grade, they are really important. Homework is your skill assessment after a lesson and helps you study for quizzes and tests. Getting zeros on homework will eventually affect your grade because the percentages pile up and total to almost a major. So do your homework!!! It’s essential to getting straight A’s and maintaining good grades.

 

Seventh grade can be either a blast to you, or may seem really difficult. Whatever it is, just keep everything well organized and participate in class. You won’t regret it!

Denesting Nested Radicals –Square Roots Within a Square Root

I just recently learned about denesting radicals, and I thought they were somewhat interesting… So I wrote a blog post about denesting them, because they can be very useful in solving some problems such as $x\sqrt[3]{10+6\sqrt{3}}+x\sqrt[3]{10-6\sqrt{3}}=\sqrt[4]{49+20\sqrt{6}}+\sqrt[4]{20-\sqrt{6}}$.

Rewriting nested radicals, such as $\sqrt{5+2\sqrt{6}}$, in simplified form where no radicals exist under another radical is called denesting. To denest a radical, you first have to assume that it can be rewritten as the sum of two radicals in the form $\sqrt{a+b\sqrt{c}}=\sqrt{d}+\sqrt{e}$.

Squaring both sides gives us $a+b\sqrt{c}=d+e+2\sqrt{de}$. From there, we can group $d$ and $e$ together to equal $a$, and set $2\sqrt{de}=b\sqrt{c}$. For $2\sqrt{de}=b\sqrt{c}$, we can isolate $de$ by dividing by $2$ and squaring both sides to get: $2\sqrt{de}=b\sqrt{c}\iff\sqrt{de}=\frac {b\sqrt{c}}{2}\iff de=\frac {b^2c}{4}$. So really, you just need to find two numbers that sum to $a$ and have a product equal to $\frac {b^2c}{4}$.

For example, in $\sqrt{5+2\sqrt{6}}$, setting that equal to $\sqrt{a+b\sqrt{c}}$, we see that $a=5$, $b=2$ and $c=6$ for the equation to be true! From there, we need to find two numbers that sum $a$ ($5$), and have a product of $\frac {2^2\cdot 6}{4}=6$. Playing around with numbers, we see that $d=3$ and $e=2$ because $3+2=5$ and $3\cdot 2=6$. So, $\sqrt{5+2\sqrt{6}}=\sqrt{3}+\sqrt{2}$.

Another example: $\sqrt{10-4\sqrt{6}}$.

To solve this, we need to find two numbers that sum to $10$ and multiply out to $\frac {4^2\times 6}{4}=24$. Numbers $4$ and $6$ work! But which do we place first?

In subtraction, you always want to place the larger of the two because radicals cannot be negative. You would get an imaginary number instead. So $\sqrt{10-4\sqrt{6}}=\sqrt{6}-\sqrt{4}=\sqrt{6}-2$.

 

Generalizing it:

You can rewrite a nested radical in the form $\sqrt{a+b\sqrt{c}}$ and setting that equal to $\sqrt{d}+\sqrt{e}$ gives us $\sqrt{a+b\sqrt{c}}=\sqrt{d}+\sqrt{e}$. Squaring both sides (like before) gives us:

$a+b\sqrt{c}=d+e+2\sqrt{de}$

From this, we can see that $d+e=a$ so $e=a-d$ and $2\sqrt{de}=b\sqrt{c}\rightarrow 4de=b^2c$. Substituting $e$ gives us a Quadratic Equation $4d(a-d)=b^2c\rightarrow 4d^2-4ad+b^2c=0$. Using the Quadratic Formula, we get:

$d=\frac {4a\pm\sqrt{(4a)^2-4(4)(b^2c)}}{2\times 4}$ which simplifies into $d=\frac {a\pm\sqrt{a^2-b^2c}}{2}$

Since $d+e=a$, $e$ is the conjugate of $d$. So $e=\frac {a-\sqrt{a^2-b^2c}}{2}$ and $d=\frac {a+\sqrt{a^2-b^2c}}{2}$.

The Squid

The Squid

A Poem by Frank

His body was torpid

And sleek

And light-orange

And as he passed by a school of fish

He shot foreword

And encased a victim in his tentacles

It was now dead and half eaten

And I saw a strong, straight, stream of water

And a flap of his fins

And a reach of his tentacles

Slippery, sleek, smart

Then out through the school of fish

With gleaming eyes

Slowly

Gracefully

He swam away

Inspired by The Shark by Edwin John Pratt

The Night Sky

Pixabay CC0

Pixabay CC0

While I sat away the beautiful calm spring night,
Alone with the stars, I had only your smile in sight,
With it my plum, you have set my world alight.
Ablaze this gentle soul embarks today, on a journey, a plight,
To be the man of your dreams with all my might
By now you know it all, you are my Mrs. Right.

Yours my angel, is a place indented to my left; my Heart,
Oh! When it beats only for you, it is rhythmic art.
Nothing quiet matches the sting of your glances that cut,
Right through my tenderness to rip the silk of my gut
Painless beautiful feelings I dearly miss when we are apart.
And I know nothing will fade away this endless feeling,
Of a knights passion and heart drenched in your needing.
And if I die tonight leaving behind the memories of a fated meeting
My love of you lives on in and through this piece of writing…

 

— Kudakwashe Maynard Manyowa

I cherish this poem because I admire the vivid details put into this poem and how poetic it sounds. It also has rhyme! Which gives it a “beat” when you’re reading this.

Top 3 Tourist Attractions You Should Visit

If you are a fervor tourist and love to see famous tourist attractions, travel no further! This blog post contains some of the most fascinating places around Texas! You won’t regret it!

alamo-360829_1280

Pixabay CC0

The Alamo:

This historical landmark marked an important battle in Texas History. This is the exact place where William B. Travis fought against Santa Anna during the Texas Revolution. Enjoy and take pictures of the many compartments and defense points in the Alamo!

The Alamo

Barton Springs Pool - Austin, TexasCreative Commons License Todd Dwyer via Compfight

Barton Springs:

Whether you are a competitive swimmer, of just an amateur who swims for fun, Barton Springs Pool is the perfect place to visit during the hot, hot summer! It’s cool $71.6^{\circ}$ F will keep you cool the entire time while you swim around racing your friend, or play fun water games!

Barton Springs

Storybook Land Castle Peter Lee via Compfight

Disney Land:

With hundreds of attractions and places to visit, Disney land makes a perfect place to visit during the summer! With rides and entertainment, it will keep your children (and you) entertained all day!

Disney Land

Deriving The Binomial Theorem

I was bored, so I decided to write a post about something “mathy”. Since I just learned about the Binomial Theorem, I decided to write this post about it.

The Binomial Theorem is a formula that you use where you can find $x+y$ to the $n^{th}$ power. We are going to derive it with Algebra. But before we attempt to derive it, there is something that you should know; this notation: $\left(\begin{array}{c}n\\ r\end{array}\right)$. It is pronounced $n$ choose $r$ and is equal to $\frac {n!}{r!(n-r)!}$. This kind of expression is called a combination. It is just another way of representing how many ways we can rearrange something. For example, $\left(\begin{array}{c}4\\ 1\end{array}\right)x^3y=4$ because there are $4$ different ways that we can rearrange $x^3y$. We can rearrange it as $xxxy$, $xxyx$, $xyxx$ and $yxxx$.

The $!$ mark isn’t an exclamation mark in Math, but means the product of all the numbers less than $n$ including $n$. So $n!=n\times (n-1)\times (n-2)\cdots 2\times 1$. We call this a factorial.

Now, on with the formula. If we go ahead and list out the first four powers of $x+y$, we have $(x+y)^{0}=1$, $(x+y)^1=x+y$, $(x+y)^2=x^2+2xy+y^2$, $(x+y)^3=x^3+3x^2y+3xy^2+y^3$ and $(x+y)^4=x^4+4x^3y+6x^2y^2+4xy^3+y^4$.

Focusing on the coefficients and the powers of $x$ and $y$, we see a pattern! The sum of the coefficients of the coefficients above give the new coefficient. In other words, the coefficient of $x^3$ and $3x^2y$ in $(x+y)^3$ give us $4x^3y$ for $(x+y)^4$. This is Pascal’s Triangle.Pascal's Triangle

With this, we can derive the Binomial Theorem. Looking at the $4^{th}$ row, we see that we can write $1$ as $\left(\begin{array}{c}4\\ 0\end{array}\right)$ because there is only one way to arrange $x^4$. Continuing on, we can write $4$ as $\left(\begin{array}{c}4\\ 1\end{array}\right)$, $6$ as $\left(\begin{array}{c}4\\ 2\end{array}\right)$ all the way until we get back to $1$ ($\left(\begin{array}{c}4\\ 4\end{array}\right)$).

Now, we have the general rule. Now, we can replace $4$ with $n$ to get our formula. So, $(x+y)^{n}=\left(\begin{array}{c}n\\ 0\end{array}\right)x^n+\left(\begin{array}{c}n\\ 1\end{array}\right)x^{n-1}y+\cdots +\left(\begin{array}{c}n\\ n\end{array}\right)y^{n}$.

This is the Binomial Theorem! A simply check with plugging in $n=3$ gives us $(x+y)^{3}=\left(\begin{array}{c}3\\ 0\end{array}\right)x^3+\left(\begin{array}{c}3\\ 1\end{array}\right)x^2y+\left(\begin{array}{c}3\\ 2\end{array}\right)xy^2+\left(\begin{array}{c}3\\ 3\end{array}\right)y^3$. Which further simplifies into $x^{3}+3x^{2}y+3xy^{2}+y^{3}$, which is exactly what we wrote before.

Creative Commons License philosophygeek via Compfight

Ways To Tell If Someone Is Lying

Sometimes, people will lie (this is supposed to be obvious by the way)! Lying is used to get someone out of trouble. But there are ways to tell if someone is lying, or they are just trying to get off scot-free. So I have collected on ways to spot a lie:

  • Avoiding the term “I”
If someone is lying, they will sometimes avoid saying words like “I”, or “me”. Instead, they start speaking about themselves in third person. Doing this keeps the person at a distance from the lie. But don’t get too carried away. It really depends on how they speak.
  • The person has an explanation for everything
When asked for what they did at a certain time, people usually pause and think about what they say, before actually telling the story. So if someone has an explanation for anything, as if they rehearsed it and practiced it, then that is almost a dead giveaway that they are lying.
  • Inconsistency

If someone says a lie, and part of it is inconsistent, or doesn’t quite fit like the rest, then the story is much more like a lie. For example, if someone says that she heard gunshots, didn’t look, but just run away and hide, then there is most likely a lie. At the sound of a gunshot, most people look back and try to gather what is going on.

  • Repeat the story, backwards

If someone is telling you a lie, about what they were doing while you were away (or something like that), wait for them to tell the whole story, and then tell them to repeat everything backwards. If they hesitate and can’t recite the story backwards properly without making lots of mistakes, then they are most likely lying. It is (in a way) like getting tangled in your own webbing.

FRAUDS!!!

I hope this helped you discern truths from lies better than before. Note that trying to make someone smile and laugh is a very ineffective way to tell if someone is lying because they could have simply laughed for many different reasons. But how would you know?

Photo is by Pixabay CC0

Clash of Clans War Bases

Clash of Clans is an awesome game! The game is mainly about you, having a village and defending it against attacks from other people. But at the same time, you attack other people to gain loot and upgrade your buildings and whatnot. The game now has many features such as clan wars, where clans (groups of players together) can war with another clan and the winner gets loot, to leaderboards! Many Youtubers also play Clash of Clans; some of which include Beaker’s Lab, Clash of Clans Attacks and Godson.

That was the introduction! What I really am writing about are 3 anti 3 star bases that I have made. These designs are based off of some Town Hall 8 designs and therefore, aren’t technically my creation, but they are still my creation. (What?) There are three things that all anti 3 star bases should be good against: Dragons, Hog Riders, and GoWiPe. The Town Hall the bases are at are Town Hall 7, so GoWiPe isn’t a problem at this level (thankfully).

Dragons:

  • To protect against Dragons: in the recent update, Supercell (the developers of Clash of Clans) added an extra Air Defense (a defense tower that defends the base against air troops! More info here!) to Town Hall 7. So now, we have 3 Air Defenses instead of 2! My advice is to arrange your Air Defenses in an equilateral triangle shape, so that if the attacker destroys one Air Defense, it’ll take the same amount to destroy the other 2. Arranging them in a triangle shape also maximizes airspace covered by the Air Defense. Another strategy is to put high hit-point structures near the Air Defenses to stall and give the Air Defense more time to destroy incoming air troops. You’ll see that in the bases.

Hog Riders:

  • Protection against Hog Riders isn’t that bad. Placing two double giant bombs together make a great way to kill Hog Riders. Now, all you need to do is direct them so that they are all bunched up and making them run toward a giant bomb. Best bet is placing both giant bombs between two defenses so that they immediately hop to the closest one: the one guarded by traps!

The bases:

The bases are still in the testing mode. The sole purpose of them is just to waste enemy attacks and incapacitate their lower leveled players. So the top leveled players will need to spend their attack on low leveled people, instead of destroying higher leveled people. This is crucial because if you get more stars than the enemy, you win!

Blog Post

Blog Post 2

Blog Post 3
Photos taken by me!

Feel free to copy! Copy at your own risk though! The middle and bottom one haven’t been tested. The topmost base has been tested in war. Someone got 49% first try, but was then 3 starred by a Town Hall 8.

Band Blazer Tag Event

On Wednesday, January 27, 2016, I went to Blazer Tag with my friends.

Everyone who was going to Blazer Tag met at the Band Hall just after Wild Cat Time! We were waiting for the buses to get here. All in all, we were going to take three buses. Each could seat about 47 students. I’ll save you the math, we had approximately 141 people attending. Give of take for various reasons. About halfway through, Mrs. Glover took attendance and happily announced that we were all here! Now, we were waiting for the sluggish buses to arrive here.

The bus ride there was really boring. So I’ll ignore that part. When we got to Blazer Tag, the first thing everyone did was crowd around to get tokens for the arcades. I donated all of my tokens to Hunter and helped him get a jackpot in the Galactic arcade game. Fortunately, the 7th grade game of Blazer Tag was beginning, so all the 7th graders hurried to the briefing room to watch the brain-frying video that we all have to watch. After the video, we suited up and the game started.

Ever see those people who just run around on the bottom floor getting overrun with lasers? Well, here’s my advice: DON’T DO THAT!! What I do is find the highest level that I can reach, and start sniping people as much as possible. It is way more effective than running around shooting anyone you see, and following the same guy over and over again. The first game, I got 5th place with this strategy. My problem was that people would sneak up behind me and surprise-attack me. Next time, I swore to myself that I would be more careful.

The next game, I did immensely better than my last game. I got first place and even beat Bryan! It was awesome. The only problem was how I teamed up with a couple of people, and then they started backstabbing me. That wasn’t fun. But it was necessary to the Frank-doesn’t-die idea that I was working on.

The last game, I got second place and I think! I think I beat Bryan again. Although I’m not sure.

After 3 games, Mrs. Glover told us to get back to the buses and prepare for the long, boring trip back to West Ridge. I had a lot of fun at Blazer Tag. I hope I go back there again sometime!

Hoverboards –The Pros and The Cons

I’ve noticed a couple of people wanting this thing called a Hoverboard (Not sure why it’s called a Hoverboard, it doesn’t even hover) for their birthday or for Christmas, so I decided to look into the aspects of it and have found a couple of pros and cons about it.

 

Pros:

  • Looks cool when riding it around on the sidewalk
  • No leg movement involved! Just stand and move!
  • Easily stowed in backpacks for a quick getaway back home! (Assuming you live close by)
  • Doesn’t take very long to get used to it

Cons:

  • Catch on fire easily, which means lots of damage, property loss and a hospital
  • Due to danger of fire, most states have them banned
  • If you crash into something and fall off, you have virtually no way to turn your Hoverboard off again!
  • Falling off can result in injuries (duh)

 

I can’t think of anymore Pros and Cons. Comment something if you can think of a Pro or Con!

 

I don’t think that these things are worth the money. They range between $1 800 to $2 000 for a little skateboard that can’t even hover! Did I ever mention that they can catch on fire easily? It’s the battery that is catching it on fire. The Hoverboard uses a Lithium Ion Battery. If the batteries are used too much, they over heat and catch on fire, resulting in a bonfire. Things that can catch the battery on fire would be over-excessive charging and playing around with it too much.

Point is, don’t spend your money on this. Just buy something else that is fun to do… I’ll leave that up to you!