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Convert the point $(0,3)$ in rectangular coordinates to polar coordinates. Enter your answer in the form $(r,\theta),$ where $r > 0$ and $0 \le \theta < 2 \pi.$ | [
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Define
\[p = \sum_{k = 1}^\infty \frac{1}{k^2} \quad \text{and} \quad q = \sum_{k = 1}^\infty \frac{1}{k^3}.\]Find a way to write
\[\sum_{j = 1}^\infty \sum_{k = 1}^\infty \frac{1}{(j + k)^3}\]in terms of $p$ and $q.$ | [
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"If $f(x) = \\frac{3x-2}{x-2}$, what is the value of $f(-2) +f(-1)+f(0)$? Express your answer as a c(...TRUNCATED) | [2679,400,69,2075,8,284,1124,37018,90,18,87,12,17,15170,87,12,17,31716,11,1128,374,279,897,315,400,6(...TRUNCATED) | [33975,33975,33975,33975,33975,33975,33975,33975,33975,33975,33975,33975,33975,33975,33975,33975,339(...TRUNCATED) | [[[50,33,54,52,21,15,26,5],[50,54,4,52,7,23,21,33],[28,32,9,41,34,2,4,27],[52,3,12,54,13,7,40,15],[1(...TRUNCATED) | [[[32,35,7,24,47,57,54,11],[32,35,7,24,47,54,57,11],[32,35,7,24,47,54,57,11],[32,35,7,24,47,54,57,11(...TRUNCATED) |
How many positive whole-number divisors does 196 have? | [
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"The results of a cross-country team's training run are graphed below. Which student has the greates(...TRUNCATED) | [785,3059,315,264,5312,55871,2083,594,4862,1598,525,4771,291,3685,13,15920,5458,702,279,12196,5461,4(...TRUNCATED) | [54275,12669,198,2,18614,279,6010,9761,553,1817,22259,518,1817,882,9873,198,19348,38087,291,284,2278(...TRUNCATED) | [[[33,8,44,16,5,1,11,18],[8,18,44,33,21,3,27,1],[36,43,2,16,29,54,11,1],[51,34,24,35,38,9,17,0],[46,(...TRUNCATED) | [[[38,42,6,3,55,39,37,22],[38,24,13,55,40,17,54,33],[42,39,32,44,55,8,35,21],[6,34,15,54,10,21,47,32(...TRUNCATED) |
"A regular hexagon can be divided into six equilateral triangles. If the perimeter of one of the tri(...TRUNCATED) | [32,5792,12371,6113,646,387,17779,1119,4743,3232,42939,42446,13,1416,279,46342,315,825,315,279,42446(...TRUNCATED) | [33975,33975,33975,33975,33975,33975,33975,33975,33975,33975,198,1249,1477,279,46342,315,264,5792,12(...TRUNCATED) | [[[1,33,36,35,16,46,11,40],[1,36,35,39,16,3,40,55],[56,53,57,58,11,1,16,22],[54,47,27,52,48,14,24,13(...TRUNCATED) | [[[32,35,7,24,47,11,17,27],[32,35,7,24,47,11,17,27],[32,35,7,24,47,11,17,27],[32,35,24,7,47,11,17,27(...TRUNCATED) |
"What is the smallest positive perfect cube that can be written as the sum of three consecutive inte(...TRUNCATED) | [
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"The set of points $(x,y,z)$ that satisfy\n\\[2x = 3y = -z\\]is a line.\n\nThe set of points $(x,y,z(...TRUNCATED) | [785,738,315,3501,4930,87,7358,22669,15087,429,26553,198,78045,17,87,284,220,18,88,284,481,89,59,60,(...TRUNCATED) | [82345,9885,700,1782,9210,1948,279,5128,304,12348,11,448,279,8660,429,279,1156,1555,3643,458,9210,57(...TRUNCATED) | [[[33,8,44,16,5,1,11,18],[8,18,44,21,35,50,16,5],[29,53,30,55,25,57,54,43],[51,34,3,15,55,29,50,47],(...TRUNCATED) | [[[25,41,26,57,51,19,39,55],[25,41,26,19,39,2,34,51],[15,10,49,30,16,50,47,40],[52,47,15,10,25,54,0,(...TRUNCATED) |
"What is the distance, in units, between the points $(2, -6)$ and $(-4, 3)$? Express your answer in (...TRUNCATED) | [3838,374,279,6010,11,304,8153,11,1948,279,3501,4930,17,11,481,21,15087,323,400,4080,19,11,220,18,15(...TRUNCATED) | [33975,33975,33975,25046,3,33975,25046,3,33975,25046,3,33975,66426,785,6010,400,67,3,1948,1378,3501,(...TRUNCATED) | [[[33,4,32,26,24,30,23,0],[4,32,24,11,33,49,54,27],[40,37,24,11,35,48,44,17],[8,46,5,44,40,55,57,11](...TRUNCATED) | [[[32,35,7,24,47,54,57,17],[32,35,7,24,47,39,54,11],[32,35,7,24,47,39,54,17],[32,35,11,24,23,21,7,17(...TRUNCATED) |
"The expression $2\\cdot 3 \\cdot 4\\cdot 5+1$ is equal to 121, since multiplication is carried out (...TRUNCATED) | [785,7493,400,17,59,50853,220,18,1124,50853,220,19,59,50853,220,20,10,16,3,374,6144,311,220,16,17,16(...TRUNCATED) | [33975,33975,33975,33975,33975,374,6144,311,198,59,7265,90,6612,9,532,5,17,59,50853,220,18,59,50853,(...TRUNCATED) | [[[33,8,44,16,5,1,11,18],[8,18,44,21,50,1,4,2],[36,2,19,23,41,17,35,27],[28,12,19,58,41,2,27,23],[14(...TRUNCATED) | [[[32,35,24,47,7,11,54,48],[32,35,24,7,47,11,54,17],[32,35,24,7,47,11,54,17],[32,35,24,7,47,11,54,17(...TRUNCATED) |
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