What is the largest positive integer n that satisfies n^200 < 3^500?
(A)13 (B)14 (C)15 (D)16 (E)17
This question is asking what n is. n^200 must be less than 3^500.
The first thing that I tried to do to solve this problem was to punch 3^500 into my calculator. I found out that it didn't work. So instead I found out what 3^5 is which is 243. Then instead of trying to figure out what n is by myself, I just tried the numbers given in the multiple choice answers. I knew that I wouldn't be able to type 13^200 into my calculator so I just typed in 13^2. The answer is 169 which is still pretty low so I tried 14^2 which is 196. I tried 15^2 and 16^2. 15^2 is 225 and 16^2 is 256. 256 is greater than 243 so I knew that answer was (C) 15.
I like this question because it was actually really simple to figure out. All I had to do was think about how to solve it for a minute and then punch some numbers in my calculator. This question looks difficult, but it is actually really easy.
By doing this question I learned that you can not always rely on your calculator. When I tried typing in 3^500 it didn't work so I was stuck for a moment. Then I did some thinking and discovered that this problem was quite easy. My caculator helped me do some of the problem, but if I hadn't thought about the question then I wouldn't have been able to solve it. I need to make sure that I understand math principles because my calculator can not do all the work for me.
Thursday, November 11, 2010
Thursday, October 21, 2010
Who Wants to Be a Mathematician
10 New Things I've Learned About Mathematics
1) Pythagorus probably didn't write the Pythagorean Therom.
2) The Pythagorean Therom is only true on a flat plain.
3) Theroms in mathematics will always remain true.
4) There are an infinite number of Pythagorean Triplets.
5) y^2 = x^3 + ax + b is a million dollar question...literally.
6) Mathematicians are explorers and discoverers.
7) If you add a lot of variables into your equation it gets too confusing to solve.
8) Carl Gauss discovered all of the integers from 1-100.
9) x^3 + y^3 =1 There are no fractions that fit into this equation.
10) Math is hard!
What have you learned from the talk? ...and a Millionaire too...
During the talk I learned that math is really hard! I also learned that math is all about proving answers and formulas. The man showed us many different equations and formulas that proved that they were correct. I found out that there are seven equations that 1 million dollars (US) will be given to the person who can figure out the solution. There are mathematicians that are working on these problems everyday! Near the end of his talk he told us that when you are a millionaire you just have lots of money, but when you are a mathematician you are a discoverer and an explorer. He said that he would definitly choose a mathematician over a millionaire.
How does the workshop help you in future math learning?
During the workshop I learned that sometimes it takes a long time to figure out math problems. You need to be patient and not give up. While doing the math problems I realized that sometimes you just need to use guess and check so that you can figure out the answer. Math is all about expressing mathematic ideas. Math is not always about finding answers, but about learning how the process of getting to the solution works.
1) Pythagorus probably didn't write the Pythagorean Therom.
2) The Pythagorean Therom is only true on a flat plain.
3) Theroms in mathematics will always remain true.
4) There are an infinite number of Pythagorean Triplets.
5) y^2 = x^3 + ax + b is a million dollar question...literally.
6) Mathematicians are explorers and discoverers.
7) If you add a lot of variables into your equation it gets too confusing to solve.
8) Carl Gauss discovered all of the integers from 1-100.
9) x^3 + y^3 =1 There are no fractions that fit into this equation.
10) Math is hard!
What have you learned from the talk? ...and a Millionaire too...
During the talk I learned that math is really hard! I also learned that math is all about proving answers and formulas. The man showed us many different equations and formulas that proved that they were correct. I found out that there are seven equations that 1 million dollars (US) will be given to the person who can figure out the solution. There are mathematicians that are working on these problems everyday! Near the end of his talk he told us that when you are a millionaire you just have lots of money, but when you are a mathematician you are a discoverer and an explorer. He said that he would definitly choose a mathematician over a millionaire.
How does the workshop help you in future math learning?
During the workshop I learned that sometimes it takes a long time to figure out math problems. You need to be patient and not give up. While doing the math problems I realized that sometimes you just need to use guess and check so that you can figure out the answer. Math is all about expressing mathematic ideas. Math is not always about finding answers, but about learning how the process of getting to the solution works.
Monday, October 18, 2010
Problem Set #3
Question #11
Actual Question: Let N=10^3+10^4+10^5+10^6+10^7+10^8+10^9. The sum of the digits of N is
(A) 12 (B) 1 (C) 6 (D) 9 (E) 7
This question is asking that I figure out the answer to the equation above and then add up all of the digits from the answer that I get.
To find the solution to this problem first I need to figure out what the answer to the eqation is. This seems quite difficult because there are so many numbers, but actually it is really simple. 10 to the power of any number will always be 1 with however many zeros behind it. So I figured out the answer to each of the exponents so the equation looked like this:
1,000+10,000+100,000+1,000,000+10,000,000+100,000,000+1,000,000,000=
Now I just added up all of the numbers to solve this equation. The answer I got was 1,111,111,000. Next I added all the digits from my answer and came up with 7. So the answer to question 11 is E) 7.
I like this problem because at first glance it seems really difficult. There are so many numbers and exponents that it is quite confusing. But after reading through the problem I realized that this question really is not that hard.
I learned that when I am solving problems I need to read through the question carefully before I decided whether or not this problem is doable. Sometimes when I do math problems I take one look at the question and decide that I can't do it. This problem showed me that I shouldn't do that anymore, but that I should look the question over, analyze it, try and solve it, and then if I still can't get it ask someone for help. I need to make sure that I do not give up too quickly.
Actual Question: Let N=10^3+10^4+10^5+10^6+10^7+10^8+10^9. The sum of the digits of N is
(A) 12 (B) 1 (C) 6 (D) 9 (E) 7
This question is asking that I figure out the answer to the equation above and then add up all of the digits from the answer that I get.
To find the solution to this problem first I need to figure out what the answer to the eqation is. This seems quite difficult because there are so many numbers, but actually it is really simple. 10 to the power of any number will always be 1 with however many zeros behind it. So I figured out the answer to each of the exponents so the equation looked like this:
1,000+10,000+100,000+1,000,000+10,000,000+100,000,000+1,000,000,000=
Now I just added up all of the numbers to solve this equation. The answer I got was 1,111,111,000. Next I added all the digits from my answer and came up with 7. So the answer to question 11 is E) 7.
I like this problem because at first glance it seems really difficult. There are so many numbers and exponents that it is quite confusing. But after reading through the problem I realized that this question really is not that hard.
I learned that when I am solving problems I need to read through the question carefully before I decided whether or not this problem is doable. Sometimes when I do math problems I take one look at the question and decide that I can't do it. This problem showed me that I shouldn't do that anymore, but that I should look the question over, analyze it, try and solve it, and then if I still can't get it ask someone for help. I need to make sure that I do not give up too quickly.
Subscribe to:
Posts (Atom)