Acmlm's Board - I2 Archive - Brain Teasers - Strange Math Riddles
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Dylan
Posts: 683/1407 |
I bet the word problems are from a site or book, I doubt he would take the time to create a tough word problem that turns out logical. Now if we could only find that site... ha. HA. 
Actually, I'd prefer to solve them myself, thats the whole point of a brain teaser.  |
Grey the Stampede
Posts: 635/3770 |
It's 100, but I'm dropping out to play Mindtrap and 20 Questions...
I'd still love to see what JJ can throw at us though, some of these questions are pretty challenging. |
Heian-794
Posts: 379/896 |
Maybe he's building up the suspense of the 22-22 tie for the lead!
How many questions are in this one? A hundred? When it's over, I might want to start my own math quiz. |
Dylan
Posts: 643/1407 |
I guess JJ is on vacation. He needs to give us a question soon before this gets buried.  |
Heian-794
Posts: 373/896 |
7x� + 2x� - 9x - 246 = 0
I didn't know the formula for solving cubic equations so I had to look it up. Here goes:
We need to first define three intermediate-step numbers f, g, and h:
f = [(3c/a) - (b�/a�] /3 = .25853
g = [(2b�/a� - (9bc/a� + (27d/a)] / 27 = 41.1445
h = (g�/4) + (f�/27) = 423.2288
If h is positive (which it is), we then define three more intermediate numbers:
R = -(g/2) + sqrt(h) = .000275 (note that the square root of H is really close to -1/2 of G, meaning that we have to worry about rounding error)
S = (R)^(1/3) = .06504
T = -(g/2) - (h) = -443.80105
U = T^(1/3) = -7.6277
Now:
X1 = (S + U) - (b/3a)
X2 = -(S + U)/2 - (b/3a) + i*(S-U)*sqrt(3)/2
X3 = -(S + U)/2 - (b/3a) - i*(S-U)*sqrt(3)/2 (this is -X2)
Which gives us:
3.3101 and -1.7979 +/- 2.7174i
Edit: I won't be able to post for three days or so starting tomorrow. Don't score too many points while I'm gone! |
JJ64
Posts: 917/919 |
I first ended up with your answer also, Heian, now I realize my mistake...
Scores
1st. Grey-22 points
1st. Heian-794-22 points
3rd. NSNick-10 points
4th. Kirby all the way-8 points
5th. wolfman2000-5 points
6th. ziratha-4 points
7th. Emptyeye-1 point
7th. RavenX-1 point
7th. Slash Dafter-1 point
7th. Xkeeper-1 point
11th. neotransotaku-0 points
11th. Gb boy-0 points
11th. Teddylot-0 points
Question 75 (1 point)-
Solve for x:
7x^3+2x^2-9x+7=253
ziratha
Posts: 22/231 |
You mean... im not an idiot? ... ahem yay yay ayyaay, I was certain i was gonna get a bag over the head point in this quiz game too... anyway thanks heian.  ... I'm really tired.. Im not sure IF ill be back today ... |
Heian-794
Posts: 366/896 |
JJ, it looks like I missed a minus sign in the quadratic formula and that Ziratha's answer of b = (-9 +/- sqrt(2001)) / 24 is correct (i. e. 2001 under the root sign, not -1839). This makes X (after some reducing) (9 +/- sqrt(2001)) / 6. Did you make the same mistake?
The square root of 2001 is 44.7325, so we've got 1.4889 or -2.2389 for B and 8.9554 or -5.955 for X
Pairing the first B with the first X, and the second B with the second X, gives us 40 to three decimal places.
So the only problem with Ziratha's answer was that he rounded too quickly, whereas I missed a whole minus sign. I think he should have the point on this one. |
ziratha
Posts: 21/231 |
Damn i look like an idiot.... o well, im used to it.
I'm gonna run our answers through my calculatot, figure out where i miscalculated
anyway this part of his math seems wrong, or did i totally forget the quadratic equation??? i looked at heians work and this is what i came up with, would somebody please tell me what im doing wrong, i really cant for the life of me.
from heians...
12b2 + 9b - 40 = 0
Using the quadratic formula, we arrive at:
b = (-9 +/- sqrt(-1839)) / 24
b = (-3 +/- 613i)/8
12b2 + 9b - 40 = 0
the quadratic equation should be
(-b+-/squrt(b^2-4*a*c))/2a
right? or am i totally wrong????????
(-9+-/squrt(9^2-4*12*-40))/24
0=(-9 +/- sqrt(-1839)) / 24
how can -4*9*-40 = a negative number???
-4*-40=160
and
12*160=1920
1920+81=2001...
,.....
......
I must be doing something, wrong, can anybody point it out? cause if i am i want to know so that i can get questions right. This is really bothering me....
anyway ill check his answers on my calculator cause i did mine and they seemed right, ill check them after i check his.....
his answers are:
b = (-3 +/- 613i)/8
and
x = [(-3 +/- 613i)/2] + 3 = (3 +/- 613i)/2
abx+2abx=40a
8b+6=2x
3bx=40
3((-3+613i)/2)*((3+613i)/2)= -3(-9/2-1839i/2+1839i/2+375769i^2)=-3(-9/2-375769/2)=-563667?????what am i doing wrong..???????/ i must be a total idiot....
3((-3-613i)/2)*((3-613i)/2)= -3(-9/2=1839i/2-1839i/2+375769i^2)=-3(-9/2-375769/2)=-563667????? seems to come to the same answer. im realllyyy confused.....
|
JJ64
Posts: 914/919 |
Heian-794 has the point, my browser is having problems, I can't post anything longer than a line, so you'll get the next question later... |
ziratha
Posts: 20/231 |
abx+2abx=40a
8b+6=2x
4b+3=x
ab(4b+3)+2ab(4b+3)=40a
12ab^2+9ab=40a
12b^2+9b=40
(-9+-(81-4*12*-40)^.5)/24
(-9+-(2001)^0.5)/24
ignore this, apparently im wrong....(heian, i think u did: ,(81+4*12*-40)=-1839,ill look really stupid if im wrong now...)
(-9+-44.73)/24
(-3+-14.91)/8
ill divide and round to 2 decimal places
b=11.91/8=1.48875=1.49,x=5.96+3=8.96 Or
b=-17.91/8,=-2.23875=-2.24,x= -8.96+3= -5.96
now to check.
bx+2bx=40
1.49*8.96*3=38.8443, close to 40, seems right with the rounding. Or
-2.24*-5.96*3=40.0512, even closer. |
Heian-794
Posts: 362/896 |
(1) abx+2abx=40a
(2) 8b+6=2x
Let's look at (2) first since it'll be simpler (I actually did it the opposite way in the beginning).
8b+6=2x
4b+3=x
Now let's substitute X into the other equation:
The A's can be eliminated right away, so we get:
3bx=40
and consequently
3b(4b+3) = 40
then
12b2 + 9b - 40 = 0
Using the quadratic formula, we arrive at:
b = (-9 +/- sqrt(-1839)) / 24
b = (-3 +/- 613i)/8
and
x = [(-3 +/- 613i)/2] + 3 = (3 +/- 613i)/2
|
JJ64
Posts: 911/919 |
The last time you had the right answer, ziratha.
Scores
1st. Grey-22 points
1st. Heian-794-22 points
3rd. NSNick-10 points
4th. Kirby all the way-8 points
5th. wolfman2000-5 points
6th. ziratha-3 points
7th. Emptyeye-1 point
7th. RavenX-1 point
7th. Slash Dafter-1 point
7th. Xkeeper-1 point
11th. neotransotaku-0 points
11th. Gb boy-0 points
11th. Teddylot-0 points
Question 74 (1 point)-
Solve the system of equations (for b and x only):
abx+2abx=40a
8b+6=2x
ziratha
Posts: 16/231 |
Lol sorry, if it helps, It took me almost 2 hours, it wouldn't have been so long but i havent worked with absolute values much. so it tooke me some time to see how i could manipulate them. I was able to get a vague idea of the values based on the equations, which helped a lot. my origional estimate was +/-10,2/7 but that wasn't quite right.
well, hope another riddle comes soon. good luck to us both... |
Heian-794
Posts: 360/896 |
Dagnabbit, Ziratha, I was in the middle of solving this! |
ziratha
Posts: 15/231 |
ok, heres the answer, it took a long time to come up with.
first failed attempt.
|4x|=7y+42
|4xy+x-y|=21
7y=|4x|-42
y=(|4x|-42)/7
y=4|x|/7-6
humm
now that gives me.
|4x*(|x|4/7-6) +x -(|x|4/7-6)|=21
|x16|x|/7+x-4|x|/7|=21
|16x^2 /7+x-4|x|/7|=21
|16x^2 /7+3x/7|=21
-b+-(b^2-4ac)^(1/2)
x^2+3x/16-(9+3/16)
note, if x>0 x^2= posative, ifx <0 x^2= negative.
y=|x|4/7-6
so lets say x has the following values,
+/-(7,3.5,10).
|4*7|=7*-2+42 ,1
|4*+/-7*-2++/-7- -2|=21,0
56-14=42
correct answer. (I hope, i almost messed up the quadratic equation.)
7y=|4x|-42
y=|x|4/7-6
|4x|=7y+42
|4xy-y+x|=21
|y(4x-1)+x|=21
|y(7y+42-1)+x|=21
|7yy+41y+7/4y+10.5-21|=0
|7yy+42 3/4y-10.5|=0
(-42 3/4 +-((42+3/4)^2-4*7*-10.5)^0.5)/14
y=.24
x= 10.91 |
JJ64
Posts: 900/919 |
Although your answer is right, try to show at least a little work, ziratha.
Scores
1st. Grey-22 points
1st. Heian-794-22 points
3rd. NSNick-10 points
4th. Kirby all the way-8 points
5th. wolfman2000-5 points
6th. Emptyeye-1 point
6th. RavenX-1 point
6th. Slash Dafter-1 point
6th. Xkeeper-1 point
6th. ziratha-1 point
11th. neotransotaku-0 points
11th. Gb boy-0 points
11th. Teddylot-0 points
It's been two days with no answer, so the point value is upgraded!
Question 73 (2 points)-
Solve the system of equations:
|4x|=7y+42
|4xy+x-y|=21
ziratha
Posts: 14/231 |
x=aprox 2.51
|
JJ64
Posts: 891/919 |
At least you realized your mistake, NSNick. Anyway, it's now a tie!
Scores
1st. Grey-22 points
1st. Heian-794-22 points
3rd. NSNick-10 points
4th. Kirby all the way-8 points
5th. wolfman2000-5 points
6th. Emptyeye-1 point
6th. RavenX-1 point
6th. Slash Dafter-1 point
6th. Xkeeper-1 point
11th. neotransotaku-0 points
11th. Gb boy-0 points
11th. Teddylot-0 points
Question 72 (1 point)-
Solve the equation:
|x^3+2x^2+7x-46|=0
NSNick
Posts: 803/3875 |
Yeah, I didn't have the full prime factorization. |
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