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nelson90 11 years ago
  1. 250 (g of cream cheese)=2*125 = 2 pounds
200 (g of powdered sugar) = 1/5 kg = 0.5 pounds
total 2.5 pounds (I don't know the value of the pound in Euros, but I have the impression that the glazing could be more expensive that the cake itself!)

Extra question, for the fun :)
first boat: x=5t, y=4+12t
second boat: x=10-3u, y=4u (I have to use another variable for the parameter, because they are independent).

The intersection occurs when
5t=10-3u
4+12t=4u

5t+3u=10 ==> 20t+12u=40
12t-4u=-4 ==> 36t-12u=-12

Making the sum of both equations, I get 20t+36t=40-12
then 56t=28 ==> t=1/2
4u=4+12t=4+6=10 ==> u=5/2

The intersection is: x=5t=5/2 y=4+12t=10
SimonM 11 years ago
  That's the same Ferrari
200/cbrt(2)+50*cbrt(4)= [200+50*cbrt(4)*cbrt(2)]/cbrt(2)=[200+50*cbrt*(8)]=300/cbrt(2)
woops I made a little fault. I forgot to multiple 50 with 2...

The first curve is given by r(t) = (5t)x + (4+12t)y and the second as s(u) = (10-3u)x + (4u)y. (the x and y used here are unit vector pointing along the x-axis and y-axis) Then we have to solve r(t) = s(u) to u and t, so we get this set of equations:
|5t = 10-3u
|4+12t = 4u

To solve this we can use a matrix:
( 5 3 | 10)
(12 -4 | -4)
An echelon form is:
(5 3 | 10)
(0 2 | 5)
So u = 5/2 and t = (10-3u)/5 = 1/2
Then fill in the t and u to get the intersection point(s).
I get the intersection is (5/2, 10).
Btw is this for homework or just interested? :)
Ferrari12 11 years ago
  First question is correct, third question is cotrrect, but one the second question; how do you get 200/cbrt(2)+50*cbrt(4) to become 250/cbrt(2)? They aren't the same, are they?

200/cbrt(2)+50*cbrt(4)=238,1101 ... (Which is the correct answer)
250/cbrt(2)=198,4251 ...

Or is my calculator lying again? I will deduct no points either way. Even if there is a mistake there it is so small compared to the task in its eniterity, so I don't think it's fair to penalize it.
alanliu12121 11 years ago
  Brain burst X_X
SimonM 11 years ago
  First question: x=25 and y=10. First subsitute y=35-x in first equation. You'll get 35-x=2sqrt(x). Thus x = 25. So then y = 10.


Second question: Name x the width of the base and y the height of the box.
The volume is given by 4x^2*y=200 Thus y=50/(x^2).
The surface is given by 2*4x*y+2*x*y+2*x*4x=10xy+8x^2

Then subsitute y=50/(x^2) so you get 500/x + 8x^2.

Now differentiate this so you become -500/(x^2)+16x.

To get a extremum equalize it to 0. so -500/(x^2)+16x=0. So -500+16x^3=0 So x=cbrt(500/16)= (5/2)*cbrt(2).

Now the surface is 500/[(5/2)*cbrt(2)]+8*[(5/2)*cbrt(2)]^2=200/cbrt(2)+50*cbrt(4)=250/cbrt(2)

(where cbrt(x) is the cube root of x)

third question: Say OH = time from Oslso to Hamar and HM = time from Hamar to Molde and OM = time from Oslo to Molde. Then is 4*OH=HM. OM = 7,5 hour. Then is OH+HM=OM So 5*OH=OM. Thus OH= 1,5 hour which is 1 hour and thirthy minutes.
Ferrari12 11 years ago
  Interesting. I have only solved it the way Nelson did!

Anyway, three new questions are up :)
SimonM 11 years ago
  The proportion is similar to the construction of the golden ratio.

You could also prove the second question in a different way:

a/|AD|=cos(A) and x/|AD|=sin(A) so a/x=cot(A).
The same way we find x/|CD|=sin(C) and b/|CD|=cos(C) so x/b=tan(C).

Because the triangle ACD is rectangle we know C = 90°-A. So x/b = tan(C)= tan(90°-A) = cot(A) = a/x. Thus a/x = x/b.

edit: gave second solution for fun. :)
nelson90 11 years ago
  1. The volume of a pyramid is equal to (base area)*height/3

V=230^2*146/3=52900*146/3=2574466.667 m3, about 2574467 m3

2. A triangle in a semi-circle is rectangle:
AD^2+DC^2=AC^2=(a+b)^2

Since BD is perpendicular to AC, the triangles ABD and DBC are rectangle:
AD^2=AB^2+BD^2=a^2+x^2
CD^2=DB^2+BC^2=x^2+b^2

From the three equations, we get:
a^2+x^2+x^2+b^2=(a+b)^2=a^2+2ab+b^2 ==> 2x^2=2ab ==> a/x=x/b

Sorry, I don't know the English term.
Ferrari12 11 years ago
  Actually, I have made a typo in the question. Alternative E should have been 1043, and then 5011 would've been the only possible answer. Your reasoning is 100% correct, so I'm going to give you the points, of course :)

And, I guess my calculator was the problem then, tricking me to believe that the parametric equations were for two different lines. Bad Calculator! :/
nelson90 11 years ago
  Again about the parametric equations, your graphic calculator seems to give strange results:
- [-3t-1, -t+2] and [-3t+2, -t+3] have the same derivative [-3, -1]
- the point [-1, +2] belongs to both curves, first curve for t=0, second curve for t=1

Concerning the suite 3938 - 7606 - 9170 - 3217 - 2234, I have remarked that the sums of the digits of each number are
3+9+3+8 = 23
7+6+0+6 = 19
9+1+7+0 = 17
3+2+1+7 = 13
2+2+3+4 = 11
These numbers are all prime numbers, the following being 7. The problem is that 5011 and 1042 have both 7 for sum. Could it be that your problem has 2 solutions? Maybe I am missing something or my solution is totally wrong.
SimonM 11 years ago
  When I plotted them, they were the same, but for a certain value of t, you won't get the same point. But because for a parametric equation of a straight line the variable goes from -infinity to infinity. So basically you get the same collection of points, so it represents the same.
Ferrari12 11 years ago
  PineappleDude gave the correct answer to task 1, and Nelson answered task 2 correctly. Well done!

Back to the parametres, I know there is an infinite number of parametric equations for the same line, but when I plotted my answer and your answer in on my graphic calculator, I got two different lines. I thought this meant that they don't represent the same object. If someone could explain why this is happening, then I would be grateful :) And just to be sure, I'll plot them in one more time, to make sure I didn't put in the worng number or something.
nelson90 11 years ago
  About the parametric equations, I agree with Simon, I got exactly the same result at first try.

Concerning the suite 3456 - 9801 - 11781 - 22959, the following number is 115254. Explanation:
3456+6345=9801
9801+1980=11781
11781+11178=22959
22959+92295=115254
The number to add is obtained by circular permutation : just move the last digit at first position.
PineappleDude 11 years ago
  Cocktail question: Onnly way this is possible is if all of the fanta is used. If all 1.5 liters of fanta is used, 1 liter of coke will be used. That is 2.5 liters in total, or 10 glasses :)
SimonM 11 years ago
  Btw Ferrari there are hundreds of parametric equations of the same object. You can for example subsitute t by 2s or something and you would get a parametric equation in s.
Ferrari12 11 years ago
  I'm not going to be very persistant here, so unless there are any protest I can happily give you your four points Simon :)

And Pineappledude gets one point as well!
PineappleDude 11 years ago
  One icecube weighs 180/3=60/2= 30g ^^
SimonM 11 years ago
  That's rather strange, it's the standard procedure. I also got the derivation right and the t0. And for the i, j, k stuff, that's the international convention.

edit:
my tangent and your tangent

I think they are just the same except I got another parameter representation. proof of the same line. So give me my points :).
Ferrari12 11 years ago
  I actually get x=2-3t and y=3-t, and so does the book I got the task from. I also found a list of known flaws in the book, and there should be nothing wrong with that task.

Regarding the i, j, k ... thing, I'm presenting my questions the way I have been taught. Maybe they teach a different setup in other countries, I don't know :/

Psychomaster: I can make an easy question for you now, and I can make sure that whenever I add new questions, I can add an easy one too :)
psychomaster 11 years ago
  I wish there were a few easy questions, too.
SimonM 11 years ago
  Let's say x(t)=t^2-t and y(t)=t^3-4t and let's say t0 is the value of t in point (2,3) which is -1. Then the tangent line is given by
| x=x(t0)+x'(t0)*(t-t0)=2-3*(t+1)
| y=y(t0)+y'(t0)*(t-t0)=3-1*(t+1)

(x'(t)=2t-1 and y'(t)=3t^2-4)

So the parameter equation of the tangent is given by [-3t-1, -t+2].

btw for vectors they mostly use i, j, k, ... unit vectors instead of [ ].
Ferrari12 11 years ago
  That's correct!
nelson90 11 years ago
  The speed is the derivative of the position versus time: [40, 20-10t]. At t=0, the speed vector is [40,20] ==> its module is sqrt(40^2+20^2) = sqrt(2000) = 20*sqrt(5) m/s, about 44.721 m/s or 160.997 km/h.
Ferrari12 11 years ago
  Simon got the answer I was looking for, and since this obviously was a bit tougher than the previous one, I'll make it a 4p question instead.
gameinsky 11 years ago
  1; 3,5; 5; 6,5
2/2 7/2 10/2 13/2

Everyting points for 11 to me.
SimonM 11 years ago
  This new sequence is pretty difficult.
Could 8 be the next number(probably not)
nelson90 11 years ago
  I fully agree with both of you, I have found this question very easy. Don't hesitate to reduce my score. Anyway, I don't care about the score, my main pleasure is to try to solve the problems :)
Ferrari12 11 years ago
  Maybe not, how about three points? I'm not especially good at these kind of questions, so I may have over-estimated its difficulty.
SimonM 11 years ago
  Damnit I always see the question after Nelson solved it... But I don't think this question deserves 4 points.
nelson90 11 years ago
  And the kind of question I am very fond of!

If we multiply each number by 2, we get 1 - 8 - 27 - 64, that is 1^3 - 2^3 - 3^3 - 4^3.

The next number is 5^3/2 = 125/2 = 62.5

General

First post of the topic

Ferrari12 11 years ago
  I thought I'd be fun to revive this little quiz-topic, orginally done by AK, who unfortunately is no longer active. The rules are more or less the same as in the old version, but if you are not familiar with them, here is how the game works:
- I post maths questions, and then it's up to you guys to find the answer(s), preferably with some kind of explanation.
- The first to post the correct answer, gets the points.
- The number of points any question gives, is stated along with the question itself. Few points → Easy question, and oposite.
- New questions will be added whenever the previous one(s) have been answered correctly.

CURRENT QUESTION(S):

What is the average score of Math Whiz Quiz Game V2? (1p)

LEADERBOARD:
Nelson90: 72p
SimonM: 46p
Jim674: 7p
Gameinsky: 3p
PineappleDude: 3p
Demonicyoshi: 1p
Psychomaster: 1p
Treazer: 1p

Signs explanation
SPOILER
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