https://liberty.io/can-decimal-numbers-be-considered-even-or-odd.htmlBuzz Spill Dailyen2026-08-14T03:33:45-04:00Can decimal numbers be considered "even" or "odd"?https://liberty.io/the-number-of-integers-039-a-039-1-leq-a-leq-200-such-that-a-a-is-a-pe.htmlBuzz Spill Dailyen2026-08-14T03:32:05-04:00The number of integers &#039;a&#039; ($1\leq a\leq 200$) such that a^a is a perfect square are:$ A). 105$ $ B) 103$ $C)107$ $D)109?$https://liberty.io/simplifying-finding-the-natural-log-of-two-terms-without-logarithm-law.htmlBuzz Spill Dailyen2026-08-14T03:22:44-04:00Simplifying/Finding the natural log of two terms without logarithm laws.https://liberty.io/cayley-table-for-d-4-langle-r-2-rangle.htmlBuzz Spill Dailyen2026-08-14T03:11:08-04:00Cayley table for $D_4/\langle r^2\rangle$.https://liberty.io/interior-extremum-theorem.htmlBuzz Spill Dailyen2026-08-14T02:59:29-04:00Interior Extremum Theoremhttps://liberty.io/in-simple-english-what-does-it-mean-to-be-transcendental.htmlBuzz Spill Dailyen2026-08-14T02:58:42-04:00In simple English, what does it mean to be transcendental?https://liberty.io/partial-orders-and-hasse-diagrams-totally-confused.htmlBuzz Spill Dailyen2026-08-14T02:38:20-04:00Partial Orders and Hasse Diagrams: Totally confusedhttps://liberty.io/how-can-i-find-the-value-of-ln-x-without-using-the-calculator.htmlBuzz Spill Dailyen2026-08-14T02:34:52-04:00How can I find the value of $\ln( |x|)$ without using the calculator?https://liberty.io/upside-down-triangle-symbol-on-function.htmlBuzz Spill Dailyen2026-08-14T02:32:17-04:00Upside-down triangle symbol on functionhttps://liberty.io/principal-branch-of-logarithm.htmlBuzz Spill Dailyen2026-08-14T02:29:11-04:00Principal branch of logarithmhttps://liberty.io/negation-of-if-and-only-if.htmlBuzz Spill Dailyen2026-08-14T02:25:38-04:00Negation of if and only if?https://liberty.io/equidistant-points-on-a-circle.htmlBuzz Spill Dailyen2026-08-14T02:25:19-04:00Equidistant points on a circlehttps://liberty.io/relative-version-of-kunneth-theorem-for-cw-pairs.htmlBuzz Spill Dailyen2026-08-14T02:25:05-04:00Relative version of Kunneth Theorem for $CW$ pairs.https://liberty.io/what-is-the-relationship-between-cubic-b-splines-and-cubic-splines.htmlBuzz Spill Dailyen2026-08-14T02:21:34-04:00What is the relationship between cubic B-splines and cubic splines?https://liberty.io/find-a-point-on-a-line-segment-which-is-the-closest-to-other-point-not.htmlBuzz Spill Dailyen2026-08-14T02:05:33-04:00Find a point on a line segment which is the closest to other point not on the line segmenthttps://liberty.io/how-to-study-abstract-algebra.htmlBuzz Spill Dailyen2026-08-14T02:05:11-04:00How to study abstract algebrahttps://liberty.io/find-number-of-vertices-when-given-number-of-edges.htmlBuzz Spill Dailyen2026-08-14T02:03:30-04:00Find number of vertices when given number of edgeshttps://liberty.io/the-definition-of-the-absolute-value.htmlBuzz Spill Dailyen2026-08-14T01:56:05-04:00The Definition of the Absolute Valuehttps://liberty.io/skew-lines-and-what-039-s-between-them.htmlBuzz Spill Dailyen2026-08-14T01:53:23-04:00Skew lines and what&#039;s between themhttps://liberty.io/determine-direction-of-an-arc-cw-ccw.htmlBuzz Spill Dailyen2026-08-14T01:46:39-04:00Determine Direction of an Arc (CW/CCW)https://liberty.io/how-is-a-sin-theta-b-cos-theta-c-sin-theta-phi-derived.htmlBuzz Spill Dailyen2026-08-14T01:44:49-04:00How is $A\sin\theta +B\cos\theta = C\sin(\theta + \phi)$ derived?https://liberty.io/gaussian-elimination-with-4x-3y-11-and-x-3y-1.htmlBuzz Spill Dailyen2026-08-14T01:44:43-04:00Gaussian elimination with $4x-3y=11$ and $x-3y=-1$https://liberty.io/why-do-we-call-it-a-sigma-algebra.htmlBuzz Spill Dailyen2026-08-14T01:35:42-04:00Why do we call it a $\sigma$-algebra?https://liberty.io/trace-of-a-matrix-times-outer-product.htmlBuzz Spill Dailyen2026-08-14T01:30:01-04:00Trace of a matrix times outer producthttps://liberty.io/quadruple-integral-int-limits-0-1-int-limits-0-1-int-limits-0-1-int-li.htmlBuzz Spill Dailyen2026-08-14T01:28:46-04:00Quadruple Integral $\int\limits_0^1\!\!\int\limits_0^1\!\!\int\limits_0^1\!\!\int\limits_0^1\frac1{1-xyzw}\,dw\,dz\,dy\,dx$https://liberty.io/cummulative-probability-5-chance-per-iteration.htmlBuzz Spill Dailyen2026-08-14T01:20:32-04:00Cummulative Probability 5% chance per iterationhttps://liberty.io/express-the-following-invertible-matrix-a-as-a-product-of-elementary-m.htmlBuzz Spill Dailyen2026-08-14T01:17:28-04:00Express the following invertible matrix A as a product of elementary matriceshttps://liberty.io/heat-equation-for-a-cylinder-in-cylindrical-coordinates.htmlBuzz Spill Dailyen2026-08-14T01:14:36-04:00Heat equation for a cylinder in cylindrical coordinateshttps://liberty.io/how-prove-this-tan-frac-2-pi-13-4-sin-frac-6-pi-13-sqrt-13-2-sqrt-13.htmlBuzz Spill Dailyen2026-08-14T01:13:46-04:00How prove this $\tan{\frac{2\pi}{13}}+4\sin{\frac{6\pi}{13}}=\sqrt{13+2\sqrt{13}}$https://liberty.io/i-have-3-quarters-2-dimes-and-2-pennies-if-i-select-at-least-one-coin-.htmlBuzz Spill Dailyen2026-08-14T01:10:33-04:00I have 3 quarters, 2 dimes, and 2 pennies. If I select at least one coin, how many different amounts of money can I make?https://liberty.io/from-a-vector-to-a-skew-symmetric-matrix.htmlBuzz Spill Dailyen2026-08-14T01:06:30-04:00From a vector to a skew symmetric matrixhttps://liberty.io/let-l-be-a-linear-form-is-l-continuous.htmlBuzz Spill Dailyen2026-08-14T01:03:25-04:00let $L$ be a linear form, is $L$ continuous?https://liberty.io/is-xy-0-a-function.htmlBuzz Spill Dailyen2026-08-14T00:58:32-04:00Is $xy=0$ a function?https://liberty.io/induction-help-prove-2n-1-2-n-for-all-n-greater-than-or-equal-to-3.htmlBuzz Spill Dailyen2026-08-14T00:46:41-04:00Induction Help: prove $2n+1< 2^n$ for all $n$ greater than or equal to $3$.https://liberty.io/regarding-understanding-of-the-following-svd-code-in-matlab.htmlBuzz Spill Dailyen2026-08-14T00:45:47-04:00Regarding understanding of the following SVD code in matlabhttps://liberty.io/a-and-b-are-solutions-of-frac-1-x-2-10x-29-frac-1-x-2-10x-45-frac-2-x-.htmlBuzz Spill Dailyen2026-08-14T00:42:14-04:00$a$ and $b$ are solutions of $ \frac{1}{x^{2} - 10x-29} + \frac{1}{x^{2} - 10x-45} - \frac{2}{x^{2} - 10x-69} = 0 $, $a+b=?$https://liberty.io/representation-of-null-set-or-empty-set.htmlBuzz Spill Dailyen2026-08-14T00:30:08-04:00Representation of null set or empty set?https://liberty.io/how-many-options-are-there-for-15-student-to-divide-into-3-equal-sized.htmlBuzz Spill Dailyen2026-08-14T00:28:26-04:00How many options are there for 15 student to divide into 3 equal sized groups?https://liberty.io/interpretation-of-svd-for-text-mining-topic-analysis.htmlBuzz Spill Dailyen2026-08-14T00:23:01-04:00interpretation of SVD for text mining topic analysishttps://liberty.io/find-the-point-on-the-line-y-2x-1-that-is-closest-to-the-point-5-2.htmlBuzz Spill Dailyen2026-08-14T00:14:03-04:00Find the point on the line $y = 2x + 1$ that is closest to the point $(5, 2)$?https://liberty.io/how-to-prove-these-product-to-sum-trig-identities-closed.htmlBuzz Spill Dailyen2026-08-14T00:12:20-04:00How to Prove these Product to Sum Trig Identities [closed]https://liberty.io/how-to-derive-the-volume-and-surface-area-formula-for-truncated-cylind.htmlBuzz Spill Dailyen2026-08-14T00:12:10-04:00How to derive the volume and surface area formula for truncated cylinder without calculus?https://liberty.io/sequence-that-converges-to-0-but-its-function-diverges.htmlBuzz Spill Dailyen2026-08-14T00:12:04-04:00Sequence that converges to 0 but its function divergeshttps://liberty.io/suppose-we-draw-two-cards-without-replacement-out-of-a-standard-deck-o.htmlBuzz Spill Dailyen2026-08-14T00:06:59-04:00Suppose we draw two cards without replacement out of a standard deck of 52 cardshttps://liberty.io/change-of-basis-for-a-polynomial.htmlBuzz Spill Dailyen2026-08-13T23:59:57-04:00Change of basis for a polynomialhttps://liberty.io/for-what-values-of-t-the-solution-for-this-equation-exist.htmlBuzz Spill Dailyen2026-08-13T23:54:51-04:00For what values of t, the solution for this equation existhttps://liberty.io/the-description-of-abelian-lie-groups.htmlBuzz Spill Dailyen2026-08-13T23:53:41-04:00The description of abelian Lie groupshttps://liberty.io/what-is-the-antiderivative-of-e-x-2.htmlBuzz Spill Dailyen2026-08-13T23:47:31-04:00What is the antiderivative of $e^{-x^2}$https://liberty.io/what-is-the-difference-of-pure-strategic-equilibria-and-nash-equilibri.htmlBuzz Spill Dailyen2026-08-13T23:38:09-04:00What is the difference of pure strategic equilibria and nash equilibria?https://liberty.io/how-to-change-the-limits-of-a-summation-when-the-index-k-is-replaced-b.htmlBuzz Spill Dailyen2026-08-13T23:23:54-04:00How to change the limits of a summation when the index $k$ is replaced by $-k$?https://liberty.io/what-exactly-is-in-the-standart-atlas-of-r-n.htmlBuzz Spill Dailyen2026-08-13T23:11:42-04:00What exactly is in the standart atlas of $R^n$?https://liberty.io/can-navier-stokes-equation-be-derived-from-cauchy-momentum-equation.htmlBuzz Spill Dailyen2026-08-13T23:08:43-04:00Can Navier-Stokes equation be derived from Cauchy momentum equation?https://liberty.io/let-g-be-a-group-and-a-in-z-g-prove-that-langle-a-rangle-is-a-normal-s.htmlBuzz Spill Dailyen2026-08-13T23:00:10-04:00Let G be a group and $a\in Z(G)$. Prove that $\langle a\rangle$ is a normal subgroup of G.https://liberty.io/how-to-find-a-conserved-quantity-in-this-differential-equation.htmlBuzz Spill Dailyen2026-08-13T22:58:23-04:00How to find a conserved quantity in this differential equation.https://liberty.io/confusion-regarding-log-x-and-ln-x.htmlBuzz Spill Dailyen2026-08-13T22:55:23-04:00Confusion regarding $\log(x)$ and $\ln(x)$https://liberty.io/tiling-a-square-problem.htmlBuzz Spill Dailyen2026-08-13T22:53:33-04:00Tiling a square problemhttps://liberty.io/dividing-divergent-and-convergent-sequences.htmlBuzz Spill Dailyen2026-08-13T22:51:21-04:00Dividing Divergent and Convergent Sequenceshttps://liberty.io/how-far-does-a-free-falling-object-fall-in-the-3-rd-second.htmlBuzz Spill Dailyen2026-08-13T22:45:50-04:00How far does a free-falling object fall in the $3$rd second?https://liberty.io/ellipse-word-problem.htmlBuzz Spill Dailyen2026-08-13T22:43:58-04:00Ellipse Word Problemhttps://liberty.io/changing-from-quadratic-formula-to-standard-form.htmlBuzz Spill Dailyen2026-08-13T22:39:45-04:00Changing from quadratic formula to standard form.https://liberty.io/where-does-r-1-2-cos-theta-have-tangents.htmlBuzz Spill Dailyen2026-08-13T22:32:28-04:00Where does $r = 1 + 2\cos(\theta)$ have tangents?https://liberty.io/how-should-i-approach-finding-the-derivative-using-the-limit-process-f.htmlBuzz Spill Dailyen2026-08-13T22:29:18-04:00How should I approach finding the derivative using the limit process, for $f(x) = 8/(x^{1/2})$?https://liberty.io/proof-of-the-least-upper-bound-or-completeness-axiom-corollary-greates.htmlBuzz Spill Dailyen2026-08-13T22:25:51-04:00Proof of the least upper bound or completeness axiom corollary (greatest lower bound)https://liberty.io/how-to-show-that-the-sequence-frac-n-2-n-1-2n-2-4n-1-converges-to-frac.htmlBuzz Spill Dailyen2026-08-13T22:25:35-04:00How to show that the sequence $\frac{n^2+n+1}{2n^2-4n+1}$ converges to $\frac{1}{2}$ by the $\epsilon-N$ definition?https://liberty.io/proof-by-induction-cup-n-1-infty-a-n-is-countable-for-countable-a-n.htmlBuzz Spill Dailyen2026-08-13T22:20:53-04:00Proof by induction: $\cup_{n=1}^\infty A_n$ is countable, for countable $A_n$https://liberty.io/evaluation-of-surface-integral-over-the-unit-disk-and-plane-in-xy-axis.htmlBuzz Spill Dailyen2026-08-13T22:11:18-04:00evaluation of surface integral over the unit disk and plane in $xy$ axishttps://liberty.io/question-about-bearings-and-trig.htmlBuzz Spill Dailyen2026-08-13T22:08:05-04:00Question about Bearings and Trighttps://liberty.io/finding-the-turning-point-of-a-parabola.htmlBuzz Spill Dailyen2026-08-13T22:04:09-04:00Finding the turning point of a parabolahttps://liberty.io/what-is-the-difference-between-closed-form-expression-and-analytic-exp.htmlBuzz Spill Dailyen2026-08-13T21:57:28-04:00What is the difference between closed-form expression and analytic expression?https://liberty.io/series-expansion-for-e-x-2.htmlBuzz Spill Dailyen2026-08-13T21:52:22-04:00Series expansion for $e^{- x^2}$https://liberty.io/how-to-find-a-minimal-polynomial-field-theory.htmlBuzz Spill Dailyen2026-08-13T21:48:23-04:00How to find a minimal polynomial (field theory)https://liberty.io/is-a-matrix-a-with-an-eigenvalue-of-0-invertible.htmlBuzz Spill Dailyen2026-08-13T21:45:56-04:00Is a matrix $A$ with an eigenvalue of $0$ invertible?https://liberty.io/why-is-the-sum-over-all-positive-integers-equal-to-1-12-duplicate.htmlBuzz Spill Dailyen2026-08-13T21:37:51-04:00Why is the sum over all positive integers equal to -1/12? [duplicate]https://liberty.io/direct-sum-vs-direct-product-vs-tensor-product-closed.htmlBuzz Spill Dailyen2026-08-13T21:35:01-04:00Direct Sum vs. Direct Product vs. Tensor Product [closed]https://liberty.io/mississippi-problem.htmlBuzz Spill Dailyen2026-08-13T21:33:32-04:00MISSISSIPPI problemhttps://liberty.io/cosine-integral.htmlBuzz Spill Dailyen2026-08-13T21:27:14-04:00cosine integralhttps://liberty.io/imo-1988-problem-6.htmlBuzz Spill Dailyen2026-08-13T21:25:47-04:00IMO 1988, problem 6https://liberty.io/using-the-definition-of-derivative-to-find-tan-2x.htmlBuzz Spill Dailyen2026-08-13T21:24:15-04:00Using the definition of derivative to find $\tan^2x$https://liberty.io/understanding-kleene-star-in-relation-to-regular-expressions.htmlBuzz Spill Dailyen2026-08-13T20:59:25-04:00Understanding Kleene star in relation to regular expressionshttps://liberty.io/basis-of-fundamental-cycles.htmlBuzz Spill Dailyen2026-08-13T20:53:42-04:00Basis of fundamental cycleshttps://liberty.io/vector-space-vs-subspace.htmlBuzz Spill Dailyen2026-08-13T20:53:21-04:00Vector Space vs Subspacehttps://liberty.io/finding-limits-of-rational-functions-as-x-to-infty-duplicate.htmlBuzz Spill Dailyen2026-08-13T20:44:56-04:00Finding limits of rational functions as $x\to\infty$ [duplicate]https://liberty.io/odds-of-being-correct-x-times-in-a-row.htmlBuzz Spill Dailyen2026-08-13T20:40:25-04:00Odds of being correct X times in a rowhttps://liberty.io/explanation-of-the-bounded-convergence-theorem.htmlBuzz Spill Dailyen2026-08-13T20:36:57-04:00Explanation of the Bounded Convergence Theoremhttps://liberty.io/to-prove-that-f-n-x-frac-nx-1-n-2x-2-does-not-uniformly-converge-to-f-.htmlBuzz Spill Dailyen2026-08-13T20:26:42-04:00To prove that $f_n(x) = \frac{nx}{1+n^2x^2}$ does not uniformly converge to $f(x) = 0$ on $[0,1]$https://liberty.io/subtracting-exponents-with-same-base.htmlBuzz Spill Dailyen2026-08-13T20:25:08-04:00Subtracting exponents with same basehttps://liberty.io/how-do-i-write-code-for-solving-partial-derivatives-numerically.htmlBuzz Spill Dailyen2026-08-13T20:17:02-04:00How do I write code for solving partial derivatives numerically?https://liberty.io/why-frac-log-x-log-y-gives-the-same-value-as-frac-ln-x-ln-y.htmlBuzz Spill Dailyen2026-08-13T20:11:39-04:00Why $\frac{\log(x)}{\log(y)}$ gives the same value as $\frac{\ln(x)}{\ln(y)}$https://liberty.io/line-dividing-closed-plane-figure-into-congruent-parts.htmlBuzz Spill Dailyen2026-08-13T20:10:51-04:00Line dividing closed plane figure into congruent partshttps://liberty.io/determine-if-a-triangle-is-right-angled-with-only-coordinates-duplicat.htmlBuzz Spill Dailyen2026-08-13T20:03:29-04:00Determine if a triangle is right angled with only coordinates [duplicate]https://liberty.io/is-the-number-0-2343434343434-rational-duplicate.htmlBuzz Spill Dailyen2026-08-13T19:54:35-04:00Is the number 0.2343434343434.. rational? [duplicate]https://liberty.io/what-is-the-optimal-value-for-x-in-a-1-1000-random-number-generator-2-.htmlBuzz Spill Dailyen2026-08-13T19:49:07-04:00What is the optimal value for x in a 1-1000 random number generator 2 stage algorithm where x is the "split point".https://liberty.io/how-many-sewings-are-there-on-a-soccer-ball.htmlBuzz Spill Dailyen2026-08-13T19:41:56-04:00How many sewings are there on a soccer ball?https://liberty.io/smoothness-of-a-function-is-independent-from-the-chart.htmlBuzz Spill Dailyen2026-08-13T19:39:53-04:00Smoothness of a function is independent from the charthttps://liberty.io/what-is-the-geometric-interpretation-of-the-transpose.htmlBuzz Spill Dailyen2026-08-13T19:32:00-04:00What is the geometric interpretation of the transpose?https://liberty.io/negative-area-below-x-axis-and-above-f-x.htmlBuzz Spill Dailyen2026-08-13T19:22:41-04:00Negative area below x-axis and above $f(x)$https://liberty.io/a-mod-b-when-b-is-greater-than-a.htmlBuzz Spill Dailyen2026-08-13T19:21:23-04:00a mod b, when b is greater than ahttps://liberty.io/permutation-test-for-one-way-anova.htmlBuzz Spill Dailyen2026-08-13T19:16:41-04:00permutation test for one-way ANOVA?https://liberty.io/riemann-rearrangement-theorem.htmlBuzz Spill Dailyen2026-08-13T19:15:56-04:00Riemann rearrangement theoremhttps://liberty.io/symmetric-matrix-multiplication.htmlBuzz Spill Dailyen2026-08-13T19:01:14-04:00Symmetric matrix multiplication