UIL D

[hello]

37. If x + y = 11 and xy = 4, then x^3 + y^3 = ?
Answer: 1199

49. Find the units digit of (2012)^2011.
Answer: 8

I also need help on 25, 44, 54. Thanks.

[redhawk2015]

37. [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula]. So [unparseable or potentially dangerous latex formula].

[ohernandez]

37. x + y = 11
xy = 4
x^3 + y^3 = (sum)^3 - 3(sum)(product) = 11^3 - (3)(11)(4) = 1199

A similar question:
x - y = 4
xy = 3
x^3 - y^3 = (difference)^3 + 3(difference)(product) = 4^3 + 3(4)(3) = 100

[nsguy1350]

[FabensMath]

What if it asks for tens digits, hundreds, 10^-6, etc.?

[nsguy1350]

Well, young one, in that case, you skip.
One does not simply find the tens digit without the answer key.
Or, you use something to do with Euler that I have forgotten. Something with relatively prime integers.

[hello]

So, number 34 on the TMSCA State test (What is the digit in the tens place of (11)^(2012)?) is only doable with Euler's thing?

[PokémonMaster]

Actually,if I'm not mistaken, 11^x has a tens digit of the ones digit of x.Like if you wanted 11^23, the tens digit is 3

[nsguy1350]

PokemonMaster is correct, but they give you numbers besides 11. That question tripped me up on the TMSCA State test, but I guessed it correctly :p

[hello]

I think you might be right, PokemonMaster. Thanks!

Instead of making another post, I'm just going to add on to this one. The following questions are from yesterday's TMSCA State meet.

8. A dog trainer wants to build a rectangular pen for to hold his dogs. He wants to separate the pen into three equal sections. The length of the pen is 4 times as long as its width. He has 72 feet of fencing. What is the largest possible area of each section?
Answer: 48 sq. feet.

17. If sin(2x) = -sqrt(3)/2 and cos(4x) = -1/2, then cos(2x) is:
Answer: sin(11x/4).

Also, is a glide reflection just a translation, then a reflection? If so, would that mean that a glide is the same as a translation?

[rcelsom]

A way to do 49. is divide it into different exponents.

So if your solving for the tens digit in 2012^2011, divide it into (2012^500 mod 100)*4*(2012^11 mod 100)
It gives you the tens and ones digit.

[hello]

I have district tomorrow, so can someone please help. Thanks.

[redhawk2015]

One more from TMSCA State.

42 (Abridged). An NS team has 4 people. What is the probability that two were born on the same day of the week?

[007math]

I wasn't there at TMSCA state and I recently took the math test. What were the issues on it? I just wanted to confirm these:

#17) Seemed like there were two answers.
#34) Seemed like the answer on the answer key was incorrect.
#44) It wasn't a hyperbola.

I heard #44 was thrown out, but what about #17 and #34?

On a side note, I failed that test.

[nsguy1350]

How did you do? I will check on those 2 problems.

[nsguy1350]

17. I got it correct with B. What was the second answer?

34. I got it correct (guess) with C.

[Capybara]

We called Mr. White, and he confirmed two changes:
#17 we accepted both B and E
#34 was changed to C

#44... He didn't do anything about it at the end.
I also wasn't sure if #26 could have another correct answer.
And I JUST now understood that the "Will I. When" in #25 is a name... I thought it was some extremely strange capitalization/punctuation/grammar...

[007math]

#17 was B and E? I got the second answer to be D....let [unparseable or potentially dangerous latex formula]

That test seemed to be pretty bad in the number of errors it had. Nothing happened to #44? I thought it should be omitted since I looked at it and saw hyperbola and thought you had to factor out a negative when completing the square to make it one...I clearly wasn't thinking during the test but it was highly misleading.

Assuming I got #17 right, I would have had a 310. I had missed way too many problems due to misreading errors.

I had a 267 on calculator. Let's not talk about NS...I thought that NS test was time consuming then I saw that Bobby had a 382..........

[Salvadoramerican]

can someone answer 42 i really want to know how to do that one