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Rita the dog
My name is Rita. I am only a dog. I used to have a blog, but it has languished with no new entries for months. It's not easy being a dog. The new Yahoo Answers sucks.
Show that cos78° = √(7-√5-√(30-6√5)) / 4?
1 AnswerMathematics6 years agoHow many prime divisors does (10^263-1)/9 have?
2 AnswersMathematics6 years agoComputational challenge?
Find the smallest positive real number x such that
sin(355x/113) - sin(πx) = 1
Your answer should be accurate at least to 5 places after the decimal point.
Note: I have an answer to this question, but I would like to have it corroborated.
1 AnswerMathematics6 years agoI keep getting the message:?
Your criteria doesn't [sic] match any questions
when I click on the "Mathematics" section. Is this a general problem with Y!A or is there something wrong because of my location or something else specific to me?
1 AnswerYahoo Answers6 years agoIs the sum of this infinite series zero?
The series starts:
1 - 1/2 - 1/3 + 1/4 - 1/5 + 1/6 - 1/7 - 1/8 + 1/9 + 1/10 - 1/11 - 1/12 - 1/13 + 1/14 + ...
The sign in front of 1/n is negative if the prime factorization of n has an odd number of factors (counted with multiplicity) and is positive otherwise. For example 12 = 2 * 2 * 3, so the prime factorization of 12 has 3 factors, so it is -1/12 in the sum.
Please provide proof that the infinite sum is zero, or explain why it is not zero.
1 AnswerMathematics6 years agoQuestion about a double tangent to a curve.?
What is the equation of the tangent line to the curve x^4 + xy + y^2 + x = 7 that is tangent to the curve at a point in the first quadrant and is also tangent to the curve at a point in the second quadrant?
[this question is motivated by a question of Andrew]
2 AnswersMathematics6 years ago
Question about decomposing an equilateral triangle into two triangles?
What are all possible positive integer pairs (m, n) that validate the picture exactly?
Note:
the smallest solution is (m, n) = (7, 4).
2 AnswersMathematics6 years agoFive angles whose sum is exactly ninety degrees?
Show that
π/2 = arcsin(12/37) + arcsin(57/185) + arcsin(3232/10457) + arcsin(7735/25033) + arcsin(385468067/1308850405)
exactly.
1 AnswerMathematics6 years agoIs it true that on this site a+b/c+d means (a+b) / (c+d)?
4 AnswersMathematics6 years agoIs this an identity, i.e. exactly true, or is it only an approximation?
2π =
arctan(35 / 12) + arctan(176 / 57) + arctan(9945 / 3232) + arctan(23808 / 7735) + arctan(1250801244 / 385468067)
1 AnswerMathematics6 years agoCan you find a more golden Pythagorean triangle?
Pythagorean triangle: a right triangle with integer side lengths.
Golden triangle: a right triangle whose legs are in the golden ratio.
Golden ratio: (1+√5)/2 : 1
There is no golden Pythagorean triangle because the golden ratio is irrational.
However the right triangle (a,b,c) = (262353, 424496, 499025) is almost golden because b:a = 1.6180337:1 is almost the golden ratio.
Can you find a more golden right triangle than the one just given?
2 AnswersMathematics6 years agoIs n a power of 3 if and only if x^(2n) + x^n + 1 is irreducible?
Either prove or give a counterexample.
2 AnswersMathematics6 years agoIs antibiotic resistance and example of evolution?
5 AnswersBiology6 years agoShow that each tetrahedron in this sequence has the same altitude to its equilateral base (see details)?
For non-negative integers n define
a(0) = -1, a(1) = 1, a(n) = 4a(n-1) - a(n-2) and
b(0) = 1, b(1) = 1, b(n) = 4b(n-1) - b(n-2).
Each positive integer n, let T(n) be the tetrahedron whose base is the equilateral triangle each of whose sides is b(n), and whose other three edges each equal a(n). Show that each of these tetrahedra has the same length of altitude to its base.
[note -- I deleted an earlier version of this question, which was misstated]
1 AnswerMathematics6 years agoIs the greatest common divisor of n^2+1000 and (n+1)^2+1000 always 1?
For each positive integer n = 1, 2, 3, ..., 1000 the gcd of n^2+1000 and and (n+1)^2+1000 is 1. Is this always true?
[Note: I know the answer, but I was surprised. This is based on a similar question someone else asked. Sorry, I don't have the link.]
3 AnswersMathematics6 years agoA tetrahedron has edge lengths 4,4,4,4,4,x. What should x be to maximize the volume?
I know the answer, but I just thought it was a cute problem that some others might like, and perhaps the answer may surprise some.
2 AnswersMathematics6 years ago
