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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 AntwortMathematicsvor 6 JahrenWhat would be the edge length in cm of one cubic shaped US tablespoon?
3 AntwortenMathematicsvor 6 JahrenHow many prime divisors does (10^263-1)/9 have?
2 AntwortenMathematicsvor 6 JahrenComputational 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 AntwortMathematicsvor 6 JahrenI 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 AntwortYahoo Answersvor 6 JahrenIs 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 AntwortMathematicsvor 6 Jahren
Prove the following identity involving the golden ratio (see picture)?
1 AntwortMathematicsvor 6 JahrenQuestion 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 AntwortenMathematicsvor 6 Jahren
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 AntwortenMathematicsvor 6 JahrenFive 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 AntwortMathematicsvor 6 JahrenIs it true that on this site a+b/c+d means (a+b) / (c+d)?
4 AntwortenMathematicsvor 6 JahrenIs 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 AntwortMathematicsvor 6 JahrenCan 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 AntwortenMathematicsvor 6 JahrenIs n a power of 3 if and only if x^(2n) + x^n + 1 is irreducible?
Either prove or give a counterexample.
2 AntwortenMathematicsvor 6 JahrenIs antibiotic resistance and example of evolution?
5 AntwortenBiologyvor 6 JahrenShow 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 AntwortMathematicsvor 6 JahrenIs 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 AntwortenMathematicsvor 6 JahrenA 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 AntwortenMathematicsvor 6 Jahren
