You are here:

Advanced Math/problem solving

Advertisement

Expert: - 3/30/2009


Question
1. For which integers k, if any, is x^2+k a factor of x^4-3x^3+6x^2-3xk+8?

2. A man began an evening with $10. He visited 10 casinos and doubled his money at each casino. Upon exiting one of the casinos, he found a couple of paper bills on the ground of U.S. currency. If he left the last casino with $10,656, can we determine exactly how much money he found on the ground and when he found it?

. the hint on both problems is work backwards, thank you.

Answer
1. Look at it as dividing x²+k into x^4 - 3x^3 + 6x^2 - 3kx + 8.

This, in long division form, is
(1 0 1) into (1 -3 6 -3k 8).

If the first factor is 1,
then we subtract 1(1 0 1) from the first part of (1 -3 -3k 8).

This leaves us with (0 -3 6-k -3k 8)
The next factor is -3, so multiplying by 3 and adding on gives
(-3 6-k -3k 8) + (3 0 3k 0) = (0 6-k 0 8).

Now we know that 6-k must be 8, since the x²+1 must divide evenly.
This means that k = -2.


2. If he started with 10 and doubled at 10 casinos,
he would end with 10,240 (that's 2^10 * 10).  
Now 10,656 - 10,240 = 416.  Since he doubled at each casino,
how many times can 2 go into 416?  If you keep dividing by 2,
you get 208, 104, 52, 26, and 13.

The 208 is 6 bills (2 @ 100, 4 @ 2),
the 104 is 3 bills (1 @ 100, 2 @ 2),
The 52 is 2 bills - yeah, we found it - a 50 and a 2.
The only other choices would be a 20 plus 3-s's = 26 (4 bills)
or a 10, a 2, and a 1 = 13 (3 bills).

So looking back at the question, he found 52 dollars.
He ended up with 416 extra.  That means if he found it 2 casinos ago and bet it, it would amount to 104 there, 1 casino ago it would amounted to 208, and it this casino, as soon as he was done, it would have been 416.

So the answer is 2 casinos ago.

Maybe that's the one to hit - just look around on the floor...

Advanced Math

All Answers

Answers by Expert:

Ask Experts

Volunteer

Scott A Wilson

Expertise

I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can even tell you it takes me over 2,000 steps to go a mile, but is that relevant?

Experience

Experience in the area; I have tutored people in the above areas of mathematics for almost two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree almost 25 years ago. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

Publications
My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

Education/Credentials
Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

Awards and Honors
I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

Past/Present Clients
My clients have been students at OSU, people nearby, friends with math questions, and several people every day on the PC, and you're probably make one more.

©2012 About.com, a part of The New York Times Company. All rights reserved.