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| ArbitraryRenaissance
ArbitraryRenaissance
♂️
[21747461]
[2012-04-16 20:25:39 +0000 UTC]
"You can call me Arby, though."
(United States)
# Statistics
Favourites: 127; Deviations: 31; Watchers: 43
Watching: 47; Pageviews: 18957; Comments Made: 1248; Friends: 47
# Comments
Comments: 104
👍: 0 ⏩: 0
I don't know who you are. The only person I blocked recently was someone who spams FFN story posters with copy/paste PSAs about a group of bullies, and I want no part in that drama. If that's you, then unless if you're actually interested in me or my story, please leave me alone, or I'm going to block you here too.
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(heavily vibrating eyes emoji)
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I saw you look at my profile with DA's creepy stalker feature that lets you see when people view your profile XD
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Do you mean the "visitors" box that shows a record of page visits from others?
I was wondering whether it was by pure coincidence that you commented on my profile only a moment after I popped into your profile.
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Oh! It might be a core only thing, but whenever you (or anyone else) visits my profile page and I'm on Deviantart, a little box pops up in my lower left hand corner saying "ArbitraryRenaissance has visited your profile". So I can in real time tell who is looking at my profile, it's a bit creepy. (Like right now the box popped up).
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Thank you, Zira!
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Thank you, my little square friend.
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I hear you're a pokemon writer. Nice!
I tend to write a few Pokemon stories myself, though lately, I've been writing stories about dragons.
Anyways, I might gjve a view at your work. From one Pokemon fan to another.
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Hey, glad to hear! It's always nice to hear from a fellow writer. Thanks for stopping by.
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Happy birthday! Was hoping to review AoS Ch 2 & 3 as a gift, but something came up today. :(
Have a good one!
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Don't worry about it. I've been so entrenched in my later chapters lately anyway, so you're free to take your time with those reviews.
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I sure did. Thanks!
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Happy birthday, AR! I hope you enjoy your day, and have a good time with your family and friends.
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Thank you friendly friend!
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Happy birthday! Here's hoping you can do another stream sometime that I can actually watch!
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Thank you! I've got two more Friday livestreams left in me before I return to the old college campus--this time with a roommate--and I only plan on playing Stardrew Valley, which should basically be a spoiler-free game.
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Just add them to your deviantWATCH. They automatically get added to your friends list.
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How do you become popular and make friends on this platform?
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Don't ask me. I never really paid attention to popularity. I'm also not particularly popular. If you want to get to know someone, though, just say hi to them on their profile and ask them a question or two. We're all friendly.
(By the way, if you're looking at that comment on my profile, that's just copypasta spam that I decided not to delete. That person posted the same thing on a bunch of other people's profiles.)
👍: 0 ⏩: 1
Uh, hello there!
So uh this is really embarrassing 
I've been watching you from afar for awhile.
When I first saw your profile, I felt something.
At first I didn't understand what it what it was, but now I understand.
It was love.
I've loved you since the first time I viewed your profile and to this day I still love you.
I would DIE for you!
My love for you is deeper than the ocean itself, wider than the Galaxy, shining brighter than the sun!
I love you!
I understand you may not feel the same way, but I had to be honest.
Your personality, talent and EVERYTHING about you attracted me so much.
I know we probably will never meet in real life but...
You're my soulmate~
👍: 0 ⏩: 1
I had a Word document written out for your coordinate geometry problem, but it ended up being over 1 page long, so I'll simplify it as much as possible.
The first 2 altitudes are the side lengths of the legs of the right triangle: 12 and 5.
Since the 3rd altitude will be perpendicular to the hypotenuse, its slope will be the negative reciprocal of the hypotenuse's slope. The hypotenuse's slope is found from the axis intercepts; it is -12/5. Therefore the altitude's slope is 5/12.
To put the altitude into a line equation, we can use slope-intercept form. The corner opposite of the hypotenuse is at the origin, so the y-intercept is 0. The altitude's line equation is y=(5/12)x+0, or simply y=(5/12)x.
To find the length of the altitude, we need to solve the 2 equations 12x+5y=60 and y=5/12x. Rearranging the first equation in terms of y gives us:
12x+5y=60
5y=60-12x
y=12-(12/5)x
(note that at this point rearranging for y=-(12/5)x+12 gives us the slope-intercept form of the hypotenuse, verifying that our slope is indeed -12/5.)
both equations are in terms of y now, so we can solve for x:
12-(12/5)x=(5/12)x
12=(5/12)x+(12/5)x
12=(5x/12)+(12x/5)
12=(25x/60)+(144x/60)
12=169x/60
720=169x
720/169=x
Now we can substitute our x-value into the equation to solve for y:
y=(5/12)x
y=(5/12)(720/169)
y=3600/2028
y=30/169
These 2 equations gave us the intersection point of the altitude line and the hypotenuse. It is at (720/169, 30/169). We can make a right triangle with leg lengths of 720/169 and 30/169, and the hypotenuse will be the length of our altitude. Using the Pythagorean Theorem:
A^2+b^2=c^2
(720/169)^2+(30/169)^2=c^2
518400/28561+900/28561=c^2
519100/28561=c^2
C=√(59100)/√(28561)
C=10√(591)/169
Therefore, out 3rd altitude has a length of 10√(591)/169. Finding the sum of the 3 altitudes:
12+5+10√(591)/169
17+10√(591)/169
2873/169+10√(591)/169
(2873+10√(591))/169
The sum of the 3 altitudes is (2873+10√(591))/169. In numerical format this is ≈18.438.
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y=3600/2028
y=30/169Try reducing this again, and I think you'll get the right solution.
👍: 0 ⏩: 1
Argh, an error in my ways!
y=3600/2028
y=300/169
then, with the Pythagorean Theorem:
A^2+b^2=c^2
(720/169)^2+(300/169)^2=c^2
518400/28561+90000/28561=c^2
608400/28561=c^2
c=780/169
c=60/13
Finding the sum:
12+5+(60/13)
(156/13)+(65/13)+(60/13)
281/13
The sum of the 3 altitudes is therefore 281/13, or ≈21.615
Can't believe I missed a 0 >.<
👍: 0 ⏩: 1
Correct!
Alternate solution:
The area of this triangle is (1/2)*5*12 = 30.
We can use the hypotenuse as another base to find the third height. This is a (5, 12, 13) right triangle, so the hypotenuse is of length 13. Let a be the third altitude that we wish to find. Then the area of the triangle is equal to a times the hypotenuse divided by 2. Thus,
30 = 13 * a / 2
which implies a = 60/13. Hence, the sum of the altitudes is 5 + 12 + 60/13 = 281/13.
👍: 0 ⏩: 2
I'm all for harder questions, I like things that challenge me to think in different ways. Especially if it's concerning probabilities or number theories.
Side note: I think it's great that you had a different path to the solution. Anytime you have 2 or more paths to the solution of a problem, there's almost always some sort of link between the 2 paths. Finding the parallelism between those paths can often teach you more about the subject than actually solving the problem, as you end up with a more general approach to the problem.
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Harder it is. We've got a three now.
The way I gauge difficulties is roughly along the lines of this:
1 means I can answer the question in my head. 1.5 is the same, although it will take more strain.
2 means I'll probably need some paper, but I can still immediately work out how to solve the problem by looking at it. 2.5 means there's a bit more work, or I think the solution is a little bit more abstract.
3 means I won't immediately know how to answer the question by looking at it, but after a few minutes of noodling on paper, I'll work it out. 3.5 is the same, but if the main idea behind the solution is more clever or counter-intuitive, it'll be here.
4 means that I personally struggled a bit with the problem. It took me a bit of brain bashing to figure out how to solve it, but I worked it out in, say, less than an hour. 4.5 just means I struggled more.
5 means that even if I solved it, I probably didn't fully understand the method that I used. I could probably get the right answer, but I couldn't formally explain why or how. 5.5 is probably the upper limit to my personal ability. A problem of this difficulty probably has multiple intermediary steps towards the solution. Each step might be straightforward enough when isolated, but weaving it all together is very tricky.
6's I probably can't solve no matter how long I stare at them. I just don't have enough enough experience in mathematical tactics to work them out. However, if I looked at a clean solution, I could probably work out the process used for solving the problem and I could translate that to the layperson fairly cleanly. A 6.5 would be similar, but it would probably require a bit more comprehension on my end.
7 means that somewhere, you're going to probably need to know some useful theorem that you've never heard of before, like Vandermonde's Identity or Lucas's Theorem or Power of a Point. Make it a 7.5 if the problem is tough to visualize.
8 would mean that I couldn't even tell you how to start if I looked at the problem. It's too far above my level for me to even comprehend. Consequentially, I can't tell the difference between an 8 and any higher difficulty.
I probably won't put in anything harder than a 6. If I can't tell you how to solve it, there's no point. If you're so good at math that you can work it out yourself, you'll know where to get more problems that are harder for you.
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I see what you did there, your solution as actually a lot shorter than mine. I kinda wish I'd seen that, but at the same time I kind of like taking the long way around. I use math to keep my mind busy, so taking the longer way can be a bit enjoyable, as weird as that sounds.
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I personally prefer the most elegant method. Of course, that tends to be the shortest one as well.
I tend to keep these questions up until about a day after the first person solves it, then I replace it with another one. Since you solved this, I'll ask: do you want a harder question or an easier question next time? I think I'll pull away from geometry next time and do a probability or combinatorics or number theory problem. Something like that.
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Honestly, I couldn't solve a problem like this (I mean, "Regarding the above image.."). I must to admit that I'm really bad in maths (like so many people). And I hope someday became just good on this, snif.
Whatever, thanks for being one of my friends from the page (even we don't often talk, hehe), I'm actually new on this and I don't know how does this work yet. So, I'm very glad you were one of the first person on this. I wish to you a very cool 2017, HAPPY NEW YEAR TO YOU and merry Christmas! 
All inspiration is for you 
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I'll give you a hint for the problem above if you're interested. The altitude of a triangle is the perpendicular line segment from one point to the opposite side. Since the triangle created in the above image is a right triangle (the right angle is the coordinate axes!), then the two legs of this triangle are two of the altitudes. You can do some algebra to find the lengths of these sides.
The third altitude is a bit trickier to work out, but if you can find the length of the hypotenuse of this triangle (Pythagorean theorem). Remember that the area of a triangle is base times height over two. If you let the base be one of the sides of the triangle then the height is the altitude of the opposite point. You can calculate the area, and then use that to determine the last altitude.
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{\fonttbl\f0\fnil\fcharset0 TrebuchetMS;}
{\colortbl;\red255\green255\blue255;\red0\green0\blue0;}
\deftab720
\pard\pardeftab720\sl440\partightenfactor0
\f0\fs32 \cf2 \expnd0\expndtw0\kerning0
\outl0\strokewidth0 \strokec2 I could try to solve this...\
\
...But sometimes I feel like I can't, haha ^^'. I'm gonna try anyways, it's not impossible, I just have to make my brain move and I'll reach it! Thank you so much!
👍: 0 ⏩: 0
Let variables b, n, k, and s represent the quantity of blueberries, nanab berries, kiwis, and strawberries respectively.
Givens:
280 berries total
b = 2n
s = 3k
n = 4s
Objective: Find value of s.
From these, the equation:
280 = b + n + s + k
since each variable represent a quantity, and 280 is the sum of all quantities.
To answer, solve for s.
To solve for s, substitute thusly:
280 = 2n + 4s + s + (s/3)
280 = 2(4s) + 4s + s + (s/3)
Simplify:
280 = 8s + 5s + (s/3)
280 = 13s + (s/3)
840 = 39s + s
840 = 40s
s = 21
There are 21 strawberries in this fruit salad.
———
True story, I saw your comment on Shane Killan's encryption videos , and was inspired to check your page since I see you around a lot. Glad we both have a passion for math. ^^ Since it's winter break for me, I was hoping to take a look at your stories as well. Looking forward to seeing what you've got!
👍: 0 ⏩: 1
Hmm, nope, that's not what I got. There are twice as many nanab berries as blueberries, not twice as many blueberries as nanab berries. You have the right idea, but you need to read the question just a bit more carefully.
Heh, yeah, if you know where to look, you'll see me around quite a bit. I've run into familiar faces in the past myself.
👍: 0 ⏩: 1
Ah I get it now.
If there are twice as many nanab berries as blueberries, then if there are 3 blueberries, there must be 6 nanab berries.
In other words:
3b = 6n
Simplification yields b = 2n.
However, this is false because the equation suggests whatever quantity n I have, I must multiply by two to have a quantity equal to b—which means there are twice as many blueberries as nanab berries.
The equation should instead be n = 2b since one must double the number of blueberries for both quantities to be equal. To use the earlier example, I must double 3 blueberries to match 6 nanab berries.
In that case, all the equations are reversed.
n = 2b
k = 3s
s = 4n
Re-solve!
280 = b + n + s + k
280 = (n/2) + (s/4) + s + 3s
280 = (s/8) + (s/4) + 4s
280 = (3s/8) + 4s
2240 = 3s + 32s
2240 = 35s
s = 64
👍: 0 ⏩: 1
Excellent! My solution was similar. Keeping the equations, we have:
b + n + k + s = 280
n = 2b
k = 3s
s = 4n
Just for illustrative purposes, I'm going to reorder the last three equations:
2b = n
4n = s
3s = k
From here, we can substitute:
4n = 4(2b) = 8b = s
and
3s = 3(4n) = 3(4(2b)) = 24b = k.
And now we have n, s, and k in terms of b. We then get:
b + n + k + s = 280
b + 2b + 24b + 8b = 280
35b = 280
b = 8
and since s = 8b, it follows that there are 64 strawberries in the fruit salad. Q.E.D.
I don't like fractions, so I tend to take slightly less direct alternatives in order to avoid them.
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