The DW Math Thread

Graviora - Dreamweaver

Are you a math teacher or something?

Dakuken - Dreamweaver

Graviora - Dreamweaver wrote: »

Are you a math teacher or something?

Nope, he just has a math fetish and a lot of time

Decus - Dreamweaver

Graviora - Dreamweaver wrote: »

Are you a math teacher or something?

Dakuken - Dreamweaver wrote: »

Nope, he just has a math fetish and a lot of time

Actually, I am a music teacher. However, my degree is in music and mathematics, as well

I am also certified to teach both music and mathematics (in most states of the US, due to reciprocal certification in my home state) and tutor college math.

b:pleased

Cheze - Lost City

it's singular. r1 + r2 - r5 = r6, not linearly independent

Decus - Dreamweaver

Cheze - Lost City wrote: »

it's singular. r1 + r2 - r5 = r6, not linearly independent

Your work isn't done b:quiet

Cheze - Lost City

row space:
[ 1 1 0 0 1 1]
[ 0 1 1 0 0 1]
[ 0 0 1 1 0 0]
[ 0 0 0 1 1 1]
[ 0 0 0 0 1 1]

column space:
first 5 columns

nullspace:
-1
1
0
0
1
1

left nullspace:
1 1 0 0 -1 1
ops

MageFizban - Lost City

imma just put in matlab bc that's too big of a matrix to write down.

A=sym([1 1 0 0 1 1; 0 0 1 1 0 0; 0 1 1 0 0 1; 1 0 1 0 1 0; 0 0 0 1 1 1; 1 1 1 0 0 0]);
Col = colspace(A);
Row = colspace(A')';
Null1=null(A);
Null2=null(A')';

Column Space:

[ 1, 0, 0, 0, 0]
[ 0, 1, 0, 0, 0]
[ 0, 0, 1, 0, 0]
[ 0, 0, 0, 1, 0]
[ 0, 0, 0, 0, 1]
[ 1, 1, 0, 0, -1]

Row Space:

[ 1, 0, 0, 0, 0, -1]
[ 0, 1, 0, 0, 0, 1]
[ 0, 0, 1, 0, 0, 0]
[ 0, 0, 0, 1, 0, 0]
[ 0, 0, 0, 0, 1, 1]

Nubsauce:

1
-1
0
0
-1
1

Other nubsauce:

[ -1, -1, 0, 0, 1, 1]

I started using rref(A) and doing it first, but that just felt like too much work. Although "first 5 columns" would have been a much easier answer right? I don't even feel like double checking.

DTK - Dreamweaver

oh look its the unit I'm doing horribly in right now o.o

Kswizzled - Dreamweaver

b:bye

I'm learning about vectors now in precalculus and I'm a bit confizzled.

last question on my homework assignment:

83) Navigation An airplane is flying in the direction of 148 degrees with an airspeed of 875 kilometers per hour. because of the iwnd, its groundspeed and direction are 800 kilometers and 140 degrees, respectively (see figure). Find the direction and speed of the wind.

The Figure

Textbook Example

I feel like im thinking too much into this >.<, and its actually really simple. Has that ever happened to you? I'd love any help

this thread is godly. b:byeb:thanks

Cheze - Lost City

Kswizzled - Dreamweaver wrote: »

b:bye

I'm learning about vectors now in precalculus and I'm a bit confizzled.

last question on my homework assignment:

83) Navigation An airplane is flying in the direction of 148 degrees with an airspeed of 875 kilometers per hour. because of the iwnd, its groundspeed and direction are 800 kilometers and 140 degrees, respectively (see figure). Find the direction and speed of the wind.

The Figure

Textbook Example

I feel like im thinking too much into this >.<, and its actually really simple. Has that ever happened to you? I'd love any help

this thread is godly. b:byeb:thanks

change both velocities in terms of x and y instead of radian, then subtract to find the difference which is the wind.

MageFizban - Lost City

Cheze - Lost City wrote: »

change both velocities in terms of x and y instead of radian, then subtract to find the difference which is the wind.

And make sure you subtract final - initial otherwise your sign will be incorrect.

Decus - Dreamweaver

Kswizzled - Dreamweaver wrote: »

b:bye

I'm learning about vectors now in precalculus and I'm a bit confizzled.

last question on my homework assignment:

83) Navigation An airplane is flying in the direction of 148 degrees with an airspeed of 875 kilometers per hour. because of the iwnd, its groundspeed and direction are 800 kilometers and 140 degrees, respectively (see figure). Find the direction and speed of the wind.

The Figure

Textbook Example

I feel like im thinking too much into this >.<, and its actually really simple. Has that ever happened to you? I'd love any help

this thread is godly. b:byeb:thanks

Sorry I took some days off!

Looks like you'll need to first convert out of polar coordinates and subtract to find the difference (like Cheze and Fiz said).

So, let's do that!

Conversions from polar coordinates to rectangular are pretty simple. Keep in mind that, in polar coords, we have points in the form of (r,q) where r is the radius from the origin (in this case, the magnitude of the vector) and q is the measure of the angle.

So, from polar -> rectangular

x = r*cos q and y = r*sin q

Now we convert the two velocities we were given. If we say the first velocity is v1 and the second is v2, then

v1 = (x,y)

where x = 875*cos(148) ~ -742
y = 875*sin(148) ~ 464.7

AND

v2 = (x,y)

where x = 800*cos(140) ~ -612.8
y = 800*sin(140) ~ 514.2


(I'm rounding to the nearest tenth)

So now we have our vectors in rectangular coordinates, we can now just subtract to find the difference between the two.

v2 - v1 = (-612.8, 514.2) - (-742, 464.7) = (-612.8 - (-742) , 514.2 - 464.7) = (129.2, 49.5)

Now we have the vector in rectangular coords for the wind, but we need to go back to radians to find the direction and magnitude.

So let's remember that, in polar coords, r = sqrt(x^2 + y^2) and that tan(q) = y/x

Accordingly:

r = sqrt((192.2)^2 + (49.5)^2) ~ 198.5 <--- this is the speed of the wind (or magnitude of the wind vector)

and, since tan(q) = y/x, then q = arctan(y/x)

Therefore, q = arctan(49.5/192.2) ~ 14.4 deg <--- this is the direction of the wind (or angle of the wind vector)


Comprende? (Am I way off the mark?) b:question

And yes, this thread is godly. Glad you enjoyed it. b:thanks

Tearle - Dreamweaver

Decussss

I want to thank you for the help you gave me. We had a major test over the junk I asked you about and I managed to pass it (barely but helluva lot better than my previous grades). Between you and Tep helping me I've held my spot in the class rankings in the top 20 and qualify for some scholarships that I hadn't before (amazing what one math grade can do ._.)

Just wanted to say thanks and appreciate the help quite a bit.

Escorian - Dreamweaver

@.@ i clicked this by accident and read decus' last post and now my brain is all over the walls from my head exploding.

MageFizban - Lost City

Escorian - Dreamweaver wrote: »

@.@ i clicked this by accident and read decus' last post and now my brain is all over the walls from my head exploding.

Not surprised.

Kswizzled - Dreamweaver

Decus! Thank you so much . I posted that at like 4AM my time, and skipped the problem. I loaded this page on my blackberry when I woke up and was able to figure out what you were saying on the way to school. b:chuckle

My teacher was reallyy impressed, because he didn't mean for any of us to get it since he didn't teach it yet. I just told him I had a pretty badass 'teacher' myself

Thank you very much! I'll make it up to you! b:laugh

oooh and Escorian, I freaked the hell out the first time I read it too. You are not alone x.x

Escorian - Dreamweaver

MageFizban - Lost City wrote: »

Not surprised.

what because im not good at math? big whoop. when are you actually gonna use this **** irl anyways?

Decus - Dreamweaver

Tearle - Dreamweaver wrote: »

Just wanted to say thanks and appreciate the help quite a bit.

My pleasure! Glad I could help!
Not that I did a whole lot... Tepp-chan probably did most of the work

Kswizzled - Dreamweaver wrote: »

Decus! Thank you so much ...
I'll make it up to you! b:laugh

You're welcome, it's why the thread is here! No need to make up anything to me, I do it purely for fun.

b:pleased




AND to Fiz and Esco: Play nicely, please, as I'd like to keep this thread open b:cute

MageFizban - Lost City

Escorian - Dreamweaver wrote: »

what because im not good at math? big whoop. when are you actually gonna use this **** irl anyways?

Hmm maybe if you learned about physics. You know . . . like science.

Decus - Dreamweaver wrote: »

AND to Fiz and Esco: Play nicely, please, as I'd like to keep this thread open b:cute

Only for you my item-dropping cleric frand. Where's this week's problem? I'm sure cheze can't wait to solve it first.

Decus - Dreamweaver

MageFizban - Lost City wrote: »

Only for you my item-dropping cleric frand. Where's this week's problem? I'm sure cheze can't wait to solve it first.

Glad to see people still remember me for dropping items. Boy I miss the days when I was a big, bright red pinata.
b:chuckle

Also, I haven't thought up a problem yet. Though you take the prize for last week's problem since Cheze's nullspace (and obviously, left nullspace) was wrong.

Maybe this week will be an algebra problem...

MageFizban - Lost City

Decus - Dreamweaver wrote: »

Glad to see people still remember me for dropping items. Boy I miss the days when I was a big, bright red pinata.
b:chuckle

Also, I haven't thought up a problem yet. Though you take the prize for last week's problem since Cheze's nullspace (and obviously, left nullspace) was wrong.

Maybe this week will be an algebra problem...

I cheated. MATLAB did the math for me. I think I even posted my code. Forgot.

Kswizzled - Dreamweaver

I aced my math test today (: Thanks for the vector help haha

Decus - Dreamweaver

MageFizban - Lost City wrote: »

I cheated. MATLAB did the math for me. I think I even posted my code. Forgot.

Yea well it seems I cannot avoid people not doing the work :<

Kswizzled - Dreamweaver wrote: »

I aced my math test today (: Thanks for the vector help haha

I did nothing, it was all you. Way to go!


New week; very late new problem!

Since I am late in giving the problem to you all, I'll make it a word problem and make it fairly easy. After this week, I think I'll up the difficulty some but then also offer a second, easier problem since I don't have many takers on solving the ones I have given so far.

Have at it, mathies!

Two trains are 2 miles apart and are traveling towards each other on the same
track, each train going 30 mph. A fly going 60 mph starts at the nose of one train,
flies toward the other train, and upon reaching the second train immediately turns
around and flies back towards the first train. The fly buzzes back and forth until all
three collide. How far did the fly fly?

MageFizban - Lost City

Decus - Dreamweaver wrote: »

Yea well it seems I cannot avoid people not doing the work :<



I did nothing, it was all you. Way to go!


New week; very late new problem!

Since I am late in giving the problem to you all, I'll make it a word problem and make it fairly easy. After this week, I think I'll up the difficulty some but then also offer a second, easier problem since I don't have many takers on solving the ones I have given so far.

Have at it, mathies!

Two trains are 2 miles apart and are traveling towards each other on the same
track, each train going 30 mph. A fly going 60 mph starts at the nose of one train,
flies toward the other train, and upon reaching the second train immediately turns
around and flies back towards the first train. The fly buzzes back and forth until all
three collide. How far did the fly fly?

Well my intuition said 2 miles. But I wasn't satisfied in just doing that.

So I thought about it and got 4/3 * summation of (1/3)^n from 0 to infinity. Which evaluates to 4/3 * [1-(1/3)^inf] / (1-1/3) which gives me 2 miles as well.

inb4 i got the wrong answer twice hahah

Cheze - Lost City

or just say the fly flew for the same period of time as the trains moved, the trains moved at relative speed of 60 and moved 2 miles, so the fly also flew for 2 miles.

Yhumy - Dreamweaver

a+b=c
2a-a+2b-b=2c-c
2a+2b-2c=a+b-c
2(a+b-c)=a+b-c
2=1

o.0

Now then, whoever is decent at calculus, derive this:

(∀x)[(∃y)(Kby & Qxy) ⊃(∃z)(~Hz & Qxz)]

From

(∀y)(Kby ⊃~Hy)

Go! Should only take 14 or so steps.

MageFizban - Lost City

Cheze - Lost City wrote: »

or just say the fly flew for the same period of time as the trains moved, the trains moved at relative speed of 60 and moved 2 miles, so the fly also flew for 2 miles.

Yeah, what I did at first but so boring.

Yhumy - Dreamweaver wrote: »

Now then, whoever is decent at calculus, derive this:

(∀x)[(∃y)(Kby & Qxy) ⊃(∃z)(~Hz & Qxz)]

From

(∀y)(Kby ⊃~Hy)

Go! Should only take 14 or so steps.

Proofs are boring as well.

Yhumy - Dreamweaver

If so boring, answer it. btw. not a proof. its a derivation question. and can anyone see the fault in that algebraic question showing 1=2?

MageFizban - Lost City

Yhumy - Dreamweaver wrote: »

If so boring, answer it. btw. not a proof. its a derivation question. and can anyone see the fault in that algebraic question showing 1=2?

a+b = c
a+b-c = 0

Anything times 0 is 0. You have 2(0) = 0. Then say 0/0 = 1 which it doesn't.

And derivations are just as bad. What's the point of deriving something when you already have your desired result? Good practice? nty.

HexOmega - Dreamweaver

i know cheze was an archer back in the day

but fizzie is archer too?