I find myself in an algebraic loop and can't get out...

[nflchamp]

No its

3. For what values of h and k is the following system consistent?

2x1 - x2 = h

6x1 + 3x2 = k

Hint: begin by representing the system as a matrix.

I'm sorry I'm late to the party, I'll try to get this done for you.

If you didn't understand the problem, they want to know what h and k can be such that there is an x1 and x2 that solve the system.

Representing the system as a matrix

[2    -1     h
6     3     k]

I eventually solve that to be

[1     0     (h/2)+((k-3h)/12)
0     1     (k-3h)/6]

That means x1=(h/2)+((k-3h)/12) and x2=(k-3h)/6 for all h,k. The only reason this system would be inconsistent was if one of these equations was unsolvable for some reason. These equations are solvable for all values of h and k, therefore the system is consistent for all values of h and k.

[nflchamp]

they only taught me volume of solids rotating on vertical and horizontal axis, I don't know how to calculate it in a diagonal axis :/

Why don't you just shift the axis?

[ragnell.]

I am not completely sure, but that only works of the solid is right next to the axis, if there is an empty space between the axis and the solid it is not correct. Or I could be wrong and it does not matter

Edited October 4, 2012 by ragnell.

[Zanarkin]

Thank you ragnell and nflchamp. will look at both suggestions tomorrow (later today?) as i must go to sleep now... I overslept today and woke up at 12:10... oh god...

[nflchamp]

Thank you ragnell and nflchamp. will look at both suggestions tomorrow (later today?) as i must go to sleep now... I overslept today and woke up at 12:10... oh god...

We really just said the same thing - h and k can be anything. PM me or something if you need me to explain what I'm saying. I'm not working so I could actually respond timely.

@ragnell. - So long as you change the equation appropriately, it should work fine. I'd probably have to relook at rotating solids to give a better answer. Can't say for certain you need to do anything specific for a diagonal axis of rotation.

[ragnell.]

You made me remember that I have to take a look to my older notes. Currently I am seeing series and next week I begin differential equations.

[shadowofchaos]

Screw Algebra.

Geometry is where it's at:

Edited October 4, 2012 by shadowofchaos

[Quintessence]

^ lol

[Zanarkin]

well I decided to just state that h and k can be any element of the reals so long as the condition k+3h=0 is met. Hopefully that will be good enough because i can't see a way to get a value and according to the help i got here, there really isn't a definite value as an infinite number of things fit k+3h=0.

[nflchamp]

well I decided to just state that h and k can be any element of the reals so long as the condition k+3h=0 is met. Hopefully that will be good enough because i can't see a way to get a value and according to the help i got here, there really isn't a definite value as an infinite number of things fit k+3h=0.

Well, I can prove that wrong.

Example: h=1, k=1

if x1= 1/3 and x2 = -1/3 then we have

2(1/3) - (-1/3) = 1

6(1/3) + 3(-1/3) = 1.

Simplifying gets

2/3 + 1/3 = 1

2 - 1 = 1

which leaves the obviously true statements

1 = 1

1 = 1.

Therefore x1=1/3 and x2=-1/3 is a solution for the system and the system is consistent for h=1, k=1.

[Zanarkin]

Well, I can prove that wrong.

Example: h=1, k=1

if x1= 1/3 and x2 = -1/3 then we have

2(1/3) - (-1/3) = 1

6(1/3) + 3(-1/3) = 1.

Simplifying gets

2/3 + 1/3 = 1

2 - 1 = 1

which leaves the obviously true statements

1 = 1

1 = 1.

Therefore x1=1/3 and x2=-1/3 is a solution for the system and the system is consistent for h=1, k=1.

ugh you had to go ahead and prove me wrong :(

thanks!

[Percivalé]

ＤＯ ＹＯＵ ＷＡＮＴ ＴＯ ＴＡＬＫ ＡＢＯＵＴ ＬＯＯＰＳ ＴＨＡＴ ＹＯＵ ＣＡＮ'Ｔ ＥＳＣＡＰＥ ＦＲＯＭ

[Esme]

ＤＯ ＹＯＵ ＷＡＮＴ ＴＯ ＴＡＬＫ ＡＢＯＵＴ ＬＯＯＰＳ ＴＨＡＴ ＹＯＵ ＣＡＮ'Ｔ ＥＳＣＡＰＥ ＦＲＯＭ

fruit loops

loop de loops

[Zanarkin]

ＤＯ ＹＯＵ ＷＡＮＴ ＴＯ ＴＡＬＫ ＡＢＯＵＴ ＬＯＯＰＳ ＴＨＡＴ ＹＯＵ ＣＡＮ'Ｔ ＥＳＣＡＰＥ ＦＲＯＭ

sure...?