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#1 2008-08-11 03:01:01

espeon
Real Member
Registered: 2006-02-05
Posts: 2,586

Algebra (lol)

Im studying during my summer holidays in preparation for my ks3 SATZ (likes to get organized early) xD

My beloved parents bought me some practise tests (Jettz) xD and I have no idea what was on the math one ._. Well, some of them =o

So I need majorrrr help XD *really wants to make her parents happy :<)

I have trouble working out the formula for number patterns and I am really really thick when it comes to answering questions which are simple -.-

I have no problem solving inequalities or equations which I hope is something good T^T

I think there were 3 questions which I struggled on a lot :x

*goes afk to go onto paint and copy them =o*

*comes back*

*goes afk to go put them onto Imageshack*

*comes back*

*goes afk to find out the IMG code thingy and how to work it*

*doesnt come back*

Stupid code thingy lol :'D

trianglethingyttos5.jpg
This one is the one I couldnt answer at all xDDD *stuppid girl* DX


circlethingyttnh1.jpg
I guessed this one, so I guess I could answer it o.o

numberpuzzleta1.jpg
This one I uh... On the B) i) I answered some huge mumbo jumbo thingy when apparantly I was only supposed to repeat what the question was -.-

Pl0x help <3

You will earn my wuvvvvvvvv D': touched

x~Saku~x

Edit: I worked out the code thingy! lol ._. *used italics*

Last edited by espeon (2008-08-11 03:01:53)


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#2 2008-08-11 03:10:49

makar92
Member
Registered: 2008-08-10
Posts: 6

Re: Algebra (lol)

in the last one i think you must come up with two equations and then you must break out 1 variable and put in that equation in the other one. so if you break out "x" in one equation you put the whole expression in the other equation, where it is x.
try it, maybe i'm wrong.

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#3 2008-08-11 03:16:11

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

Re: Algebra (lol)

the angles in a triangle always add to 180 degrees. so you have;

x + (2x+10) + (3x+20) = 180
6x = 150
x = 25

which gives the 3 angles as: 25°, 60°, 95°


-----------

assuming the circles from left to right are the values A to E; you should be able to really do this in your head to state which are true, but as a detailed breakdown you could have;

for first one; A > D
n-3 > n/3
3n - 9 > n
2n > 9

if n is between 0 and 1, then at most, 2n can be 2, which is not more than 9. thereofre A > D is false.

second one; B = C
well... to be perfectly honest, n3 makes absolutely no sense at all unless it has a multiplication sign between them, you can only use notation like that if the number comes before the letter like the previous one 3n. but assuming it does mean n×3, then yes, 3×n is the same as n×3. so B=C is true

third one; C > E
n×3 > 3/n
3n² > 3  (n is not negative, so sign doesn't change)
n² > 1. if n is between 0 and 1, then at most n² is equal to 1, which is not greater than 1, therefore C > E is false.

fourth one; E > 1
3/n > 1
3 > n. if n is between 0 and 1, then at most n is 1, since 3 is greater than 1, E > 1 is true.

---

so the answer is b) and d) are true.

----------------

if the first number is x, and second is 3 times x. then the second number is 3x, since the third number is less than the second, we could right it as being 3x-n. where n is greater than 0.

if they add to 46, then you have that
x + 3x + 3x-n = 46
7x = 46+n
x = (46+n)/7

since x is a prime number, it must be an integer aswell, so 46+n must be a multiply of 7, the nearest one is given by n = 3 -> x = 49/7 = 7. 7 is a prime number so this works, you can see this is the only solution that gives a prime value for x, because if 46+n where any larger a multiple of 7, then when dividing by 7 you would be able to write it as (some number)×7 and since n must be greater than 0, you cannot go down to a smaller multiple. so the answer is x = 7. then the second number is 3×7 = 21. and since n = 3, the third number is 18.

Last edited by luca-deltodesco (2008-08-11 03:17:57)


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#4 2008-08-11 03:56:41

espeon
Real Member
Registered: 2006-02-05
Posts: 2,586

Re: Algebra (lol)

Wow o_o Thankies so much you two ='] *worships* xD I ist writing this all down into mynotebook :'D *huggles both* XD

Edit:Oops >_< the n3 was supposed to be a cubed x.x Sowwie T^T

Last edited by espeon (2008-08-11 04:16:18)


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#5 2008-08-11 07:28:26

espeon
Real Member
Registered: 2006-02-05
Posts: 2,586

Re: Algebra (lol)

I have two more from the same test paper which I couldnt work out either >_< I think this test paper hates me or something x.x

nthshapegg3.jpg

Its EVIL LOL T_T

locusthingyht5.jpg

Waaaa evil locus thingy >>'' It reminds me of swarming bee's for some reason o.o

*cries and screams from terror*

Someone help meeeeeeeeeeee big_smile *will reward with cookies* -And my love*

kiss


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#6 2008-08-11 08:19:32

MooseofDoom
Member
Registered: 2008-08-10
Posts: 13

Re: Algebra (lol)

Locus? is that suppose to mean focus? CoNfUsEd!


π≈ 3.141 592 653 589 793 238 462 643 383 279 502 884 197 169 399 375 105 820 974 944 592 307 816 406 286 208 998 628 034 825 342 117 067 982 148 086 513 282 306 647 093 844 609 550 582 231 725 359 408 128 481 117 450 284 102 701 938 521 105 559 644 622 948 954 930...

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#7 2008-08-11 08:45:06

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

Re: Algebra (lol)

for the squares, note that each one going clockwise from top is just counting, so first is 1,2,3 and 4. the next one is 3,4,5 and 6. and then 5,6,7 and 8.

so you need only look for a pattern in the top number in which case you have 1,3,5.... etc. each one is seperated by a common value of 2. so you have the form 2n+a. where a is a constant, if you put n=1 for first cross you get 2×1+a = 1 for first cross, so a is -1.

so for the n'th cross you have numbers.  2n-1, 2n, 2n+1, 2n+2. which add together for middle number to give 8n+2

i'm not entirely sure what it means for the second question, it doesn't make sense to me.

Last edited by luca-deltodesco (2008-08-11 08:54:44)


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#8 2008-08-11 08:59:35

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

Re: Algebra (lol)

oh wait i think i know what it means now

http://img359.imageshack.us/img359/6451/losjd0.png

i think it means like that, so if you form a new triangle with the point a2 being on a circle around a, what is the radius of that circle such that any triangle formed has area 16


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#9 2008-08-11 09:55:15

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Algebra (lol)

Locus is a confusing word, but the question isn't too hard. Points B and C are fixed, and you can move point A around freely.

The question just wants to know at what points A can be, such that the triangle's area is 16. In most questions like this, the points that meet the condition will join up to make a line, circle or some other shape (here it's two lines). That shape is the "locus".


Why did the vector cross the road?
It wanted to be normal.

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#10 2008-08-12 05:18:01

espeon
Real Member
Registered: 2006-02-05
Posts: 2,586

Re: Algebra (lol)

Everyone but moose gets a cookie big_smile w00t XD

Only joking :3 *gives moose a cake instead*

Edit: I found out the thingy with the locus point, I bugged my dad (Math and physics teacher (I wuvvvv my daddy :3)) and he got confuzzled too XD First of all, the triangle that was drawn onto my test paper was half in scale half not in scale (LOL) and the locus was just a parallel line to the line BC XD (Dad told me how to work it out)

In the answer book it was was

'Line parallel to BC,
Passing through A'

Can someone enlighten me on the question with the  5 circles and algebra please T_T Im so sorry to luca for giving the wrong information >_< The n3 is supposed to be a n³ hoorah for the

Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

Under the header XD

The answer book told me but I have no idea how Im supposed to work it out still for cube thingies T_T

I uh ran out of cookies but I have a shoe! *puts shoe on a velvet pillow as the prize* XD

kiss

Last edited by espeon (2008-08-12 06:04:44)


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#11 2008-08-12 08:17:26

MooseofDoom
Member
Registered: 2008-08-10
Posts: 13

Re: Algebra (lol)

ah no cookie, oh but a cake! Yay! Smashs face in cake:..

Last edited by MooseofDoom (2008-08-12 08:18:32)


π≈ 3.141 592 653 589 793 238 462 643 383 279 502 884 197 169 399 375 105 820 974 944 592 307 816 406 286 208 998 628 034 825 342 117 067 982 148 086 513 282 306 647 093 844 609 550 582 231 725 359 408 128 481 117 450 284 102 701 938 521 105 559 644 622 948 954 930...

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#12 2008-08-12 21:06:09

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

Re: Algebra (lol)

in that case espeon:

second one; B = C
3n = n³
3 = n², so this is only true if n = √3, already you could say that b) is not true, since it must be true for a range of n, but even so √3 is already more than 1 eitherway. so B=C is not true.

third one; C > E
n³ > 3/n
3n[sup]4[/sup] > 3  (n is not negative, so sign doesn't change)
n[sup]4[/sup] > 1. if n is between 0 and 1, then at most n[sup]4[/sup] is equal to 1, which is not greater than 1, therefore C > E is still false.

---

so now only d) is true.

Last edited by luca-deltodesco (2008-08-12 21:06:36)


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