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[(a+(a^1/2))^1/2] + [(a-(a^1/2))^1/2] = 2. What is the value of a?
4 AnswersMathematics1 decade agoConsider the following equation:?
2a + 5b = ab - 1
How many sets of integer pairs (a,b) solve this equation?
1 AnswerMathematics1 decade ago[(a+(a^1/2))^1/2] + [(a+(a^1/2))^1/2] = 2. What is the value of a?
10 points for best answer!
7 AnswersMathematics1 decade agoA park has 100 rocks. Each rock is either 1 pound, 10 pounds or 50 pounds.?
The total weight of these rocks is 500 pounds. If x is the number of 10-pound rocks, how many different values of x are possible?
9 AnswersMathematics1 decade agoBest music-player?
I personally prefer Winamp but what does everyone out there use?
1 AnswerMusic1 decade agoWhat's your favorite deo-spray?
2 AnswersOther - Beauty & Style1 decade agoLet <a> be a sequence satisfying a(1)=1, a(2)=8 and a(n)=a(n-1)+2a(n-2) for n≥3.?
Prove that a(n) = 3.2^[n-1] + 2[-1]^[n] for nЄN.
Note: The things within the parentheses stand for subscripts.
2 AnswersMathematics1 decade agoLet n be an integer between 1 and 999. Written as three decimal digits, let n be abc (i.e. n=100a+10b+c)?
Let the reverse of a three-digit decimal number with digits αβγ be the three-digit number with digits γβα. Suppose that a=/=c (either may be 0). Let x be the difference between n and its reverse. Prove that x and its reverse sum to 1089.
10 points for best answer!
4 AnswersMathematics1 decade agoBalance scale problem involving bijection/induction?
Consider a balance scale plus k objects of known weights 1, 3, ... , 3^(k-1) (the first k powers of 3). Prove by induction on k that every unknown weight in the set {1, ... , ((3^k)-1)/2} can be balanced.
1 AnswerMathematics1 decade agoDetermine the set of natural numbers n such that every sum of n consecutive natural numbers is divisible by n?
how do you find this out? =S
4 AnswersMathematics1 decade agoFind out if this statement is true or false. If true, provide a proof. If false, provide a counterexample?
For nЄN,
[2n-18]/[(n^2)-8n+8] < 1
I think this has to be done with induction? I'm not sure how to do it though. Could someone help?
3 AnswersMathematics1 decade agoCan you prove these two statements given the condition...?
If <a> is a sequence satisfying a(n) = 2a(n-1) + 3a(n-2) for n>=3.
(i) Given that a(1), a(2) are odd, prove that a(n) is odd for nЄN.
(ii) Given that a(1)=a(2)=1, prove that a(n)=(1/2)*[3^(n-1)-(-1)^n] for nЄN.
Note: a(n) means n is the subscript.
Any help would be nice :)
2 AnswersMathematics1 decade agoIf nЄN, prove the following?
(from i=1 to n)Σ i(i+1) = (n)(n+1)(n+2)/3 (whole divided by 3)
Could someone help me out with this problem?
2 AnswersMathematics1 decade agoIs this statement true or false? If true, give a proof. If false, give a counterexample?
nЄN, 2n-8<(n^2)-8n+17
6 AnswersMathematics1 decade agoObtain a simple formula for the number of closed intervals...?
with integer endpoints contained in the interval [1, n] (including one-point intervals).
3 AnswersMathematics1 decade agoDetermine the set of natural numbers that can be expressed as...?
the sum of some non-negative number of 3s and some nonnegative number of 10s.
Anyone know how to get this?
1 AnswerMathematics1 decade agoAlgorithm to calculate the first day of any month of any year?
Does anyone know a "simple" algorithm to find out the first day of any month of any given year? I've searched the internet but some of the algorithms out there haven't been that helpful.
Hope someone can help me out here.
3 AnswersMathematics1 decade agoCan you prove the following statements?
(i) For all real numbers y, b, m with m≠0, there is a unique real number x such that y=mx+b
(ii) For all real numbers y, m, there exist b, xЄR such that y=mx+b
3 AnswersMathematics1 decade ago