https://liberty.io/finding-magnitude-of-a-function.htmlBuzz Spill Dailyen2026-08-18T18:29:02-04:00Finding magnitude of a functionhttps://liberty.io/swing-twist-decomposition-for-quaternion-rotations-verification.htmlBuzz Spill Dailyen2026-08-18T18:15:28-04:00Swing-Twist decomposition for quaternion rotations (verification)https://liberty.io/what-is-the-maximum-norm-induced-by-the-maximum-norm-for-mathbb-r-n.htmlBuzz Spill Dailyen2026-08-18T18:10:31-04:00What is the maximum norm induced by the maximum norm for $\mathbb{R}^n$?https://liberty.io/how-is-the-joint-proportionality-joint-variation-equation-i-e-y-kxz-lo.htmlBuzz Spill Dailyen2026-08-18T18:10:19-04:00How is the joint proportionality (joint variation) equation (i.e. $y = kxz$) logically correct?https://liberty.io/does-the-series-sum-frac-1-n-ln-n-3-2-converge-or-diverge.htmlBuzz Spill Dailyen2026-08-18T18:03:03-04:00Does the series $\sum \frac{1}{n\ (\ln(n))^{3/2}}$ converge or diverge?https://liberty.io/derivative-of-arcsin-x-in-1.htmlBuzz Spill Dailyen2026-08-18T18:01:01-04:00Derivative of $\arcsin(x)$ in $-1$https://liberty.io/rolling-a-fair-die.htmlBuzz Spill Dailyen2026-08-18T18:00:25-04:00Rolling a fair diehttps://liberty.io/find-the-area-common-to-the-inside-of-the-cardioid-r-1-sin-theta-and-t.htmlBuzz Spill Dailyen2026-08-18T18:00:14-04:00Find the area common to the inside of the cardioid $r = 1+\sin \theta$ and the outside of the cardioid $r = 1 + \cos \theta$.https://liberty.io/prove-sinh-x-x-for-all-x-0.htmlBuzz Spill Dailyen2026-08-18T17:57:25-04:00Prove $\sinh x > x$ for all $x >0$https://liberty.io/find-arcsin-frac-4-5-arccos-frac-1-sqrt-50.htmlBuzz Spill Dailyen2026-08-18T17:55:25-04:00Find $\arcsin(\frac{4}{5})+\arccos(\frac{1}{\sqrt{50}})$https://liberty.io/property-of-a-kite-inscribed-in-a-square.htmlBuzz Spill Dailyen2026-08-18T17:41:45-04:00Property of a kite inscribed in a squarehttps://liberty.io/what-distinguishes-039-family-039-vs-039-set-039-of-functions.htmlBuzz Spill Dailyen2026-08-18T17:41:18-04:00What distinguishes 'family' vs. 'set' of functions?https://liberty.io/a-question-about-irreducible-representations-of-so-3-group.htmlBuzz Spill Dailyen2026-08-18T17:34:26-04:00A question about irreducible representations of SO(3) grouphttps://liberty.io/evaluating-int-2x-2-1-e-x-2-dx.htmlBuzz Spill Dailyen2026-08-18T17:18:29-04:00Evaluating $\int(2x^2+1)e^{x^2}dx$https://liberty.io/pentation-notation-how-does-it-work-duplicate.htmlBuzz Spill Dailyen2026-08-18T17:10:43-04:00Pentation Notation - How does it work? [duplicate]https://liberty.io/is-there-a-way-to-solve-an-equation-with-both-sine-and-cosine-in-it.htmlBuzz Spill Dailyen2026-08-18T17:06:23-04:00Is there a way to solve an equation with both Sine and Cosine in it?https://liberty.io/what-is-the-difference-between-a-unit-simplex-and-a-probability-simple.htmlBuzz Spill Dailyen2026-08-18T16:57:16-04:00What is the difference between a unit simplex and a probability simplex?https://liberty.io/solving-ax-b-when-x-and-b-are-given.htmlBuzz Spill Dailyen2026-08-18T16:55:53-04:00Solving $Ax=b$ when $x$ and $b$ are given.https://liberty.io/calculate-average-wind-direction.htmlBuzz Spill Dailyen2026-08-18T16:51:40-04:00Calculate average wind directionhttps://liberty.io/finding-final-velocity-when-initial-velocity-distance-travelled-and-ac.htmlBuzz Spill Dailyen2026-08-18T16:45:33-04:00Finding final velocity when initial velocity, distance travelled and acceleration are known?https://liberty.io/trapezium-midsegment-theorem.htmlBuzz Spill Dailyen2026-08-18T16:35:48-04:00Trapezium Midsegment Theoremhttps://liberty.io/what-does-round-off-error-in-double-arithmetic-mean.htmlBuzz Spill Dailyen2026-08-18T16:32:15-04:00What does round-off error in double arithmetic mean?https://liberty.io/given-a-number-039-n-039-find-how-many-how-many-numbers-are-there-betw.htmlBuzz Spill Dailyen2026-08-18T16:25:05-04:00Given a number '$N$' find how many how many numbers are there between $1$ to $N$ that doesn't contain the digit $3$?https://liberty.io/given-that-the-customer-has-filed-a-claim-what-is-the-probability-that.htmlBuzz Spill Dailyen2026-08-18T16:22:15-04:00Given that the customer has filed a claim, what is the probability that the customer is a good riskhttps://liberty.io/what-does-3-3-mean.htmlBuzz Spill Dailyen2026-08-18T16:20:43-04:00What does $ ^3 3$ mean?https://liberty.io/which-of-the-following-expressions-completes-the-identity-1-sec-2-x.htmlBuzz Spill Dailyen2026-08-18T16:15:22-04:00Which of the following expressions completes the identity 1 + sec^2 x?https://liberty.io/gale-stewart-theorem-open-games-are-determined-implies-closed-games-ar.htmlBuzz Spill Dailyen2026-08-18T16:11:28-04:00Gale-Stewart Theorem (open games are determined) implies closed games are determinedhttps://liberty.io/how-to-factor-a-four-term-polynomial-without-grouping.htmlBuzz Spill Dailyen2026-08-18T16:08:51-04:00How to factor a four term polynomial without grouping?https://liberty.io/rotate-graph-of-function-by-180.htmlBuzz Spill Dailyen2026-08-18T16:08:12-04:00rotate graph of function by 180https://liberty.io/what-is-the-geodesic-between-a-point-and-a-line-geodesic-between-two-p.htmlBuzz Spill Dailyen2026-08-18T16:03:32-04:00What is the geodesic between a point and a line (geodesic between two points) on an oblate spheroid?https://liberty.io/find-the-least-positive-value-of-alpha-for-the-following-trignometric-.htmlBuzz Spill Dailyen2026-08-18T15:59:49-04:00Find the least positive value of alpha for the following trignometric equationhttps://liberty.io/how-to-calculate-the-area-of-a-parabolic-dish.htmlBuzz Spill Dailyen2026-08-18T15:54:20-04:00How to calculate the area of a parabolic dishhttps://liberty.io/high-dimensional-optimization-algorithm.htmlBuzz Spill Dailyen2026-08-18T15:50:30-04:00High Dimensional Optimization Algorithm?https://liberty.io/find-a-formula-for-the-area-of-the-triangle-with-vertices-in-polar-coo.htmlBuzz Spill Dailyen2026-08-18T15:47:54-04:00Find a formula for the area of the triangle with vertices (in polar coordinates) $(r_1,\theta_1)$, $(r_2, \theta_2)$, and $(r_3,\theta_3)$.https://liberty.io/defining-a-plane-using-only-2-points-and-an-axis.htmlBuzz Spill Dailyen2026-08-18T15:43:06-04:00Defining a plane using only 2 points (and an axis)https://liberty.io/for-how-many-natural-numbers-a-is-the-expression-sqrt-frac-a-64-a-64-a.htmlBuzz Spill Dailyen2026-08-18T15:39:21-04:00For how many natural numbers $a$ is the expression $\sqrt{\frac{a+64}{a-64}}$ also a natural number? [closed]https://liberty.io/how-to-find-the-length-of-diagonal-of-a-rhombus.htmlBuzz Spill Dailyen2026-08-18T15:36:28-04:00How to find the length of diagonal of a rhombushttps://liberty.io/how-do-i-solve-this-square-root-problem.htmlBuzz Spill Dailyen2026-08-18T15:31:40-04:00How do I solve this square root problem?https://liberty.io/extending-the-p-adic-valuation.htmlBuzz Spill Dailyen2026-08-18T15:26:55-04:00Extending the p-adic valuationhttps://liberty.io/how-to-find-the-n-th-term-of-the-series-1-22-333-4444-55555.htmlBuzz Spill Dailyen2026-08-18T15:22:57-04:00How to find the $n$-th term of the series 1, 22, 333, 4444, 55555..........?https://liberty.io/on-when-and-when-not-to-divide-by-tan-theta.htmlBuzz Spill Dailyen2026-08-18T15:22:28-04:00On When And When Not To Divide By $\tan(\theta)$https://liberty.io/having-a-unique-solution-for-a-rectangular-matrix.htmlBuzz Spill Dailyen2026-08-18T15:18:55-04:00Having a unique solution for a rectangular matrixhttps://liberty.io/how-or-why-are-implicit-functions-actually-functions.htmlBuzz Spill Dailyen2026-08-18T15:13:54-04:00How or why are implicit functions actually functions?https://liberty.io/jacobian-calculation-with-homographic-coordinates.htmlBuzz Spill Dailyen2026-08-18T15:03:33-04:00Jacobian Calculation with Homographic Coordinateshttps://liberty.io/third-order-differential-equations.htmlBuzz Spill Dailyen2026-08-18T15:03:15-04:00Third Order Differential Equationshttps://liberty.io/why-do-we-need-prime-ideals-in-the-spectrum-of-a-ring.htmlBuzz Spill Dailyen2026-08-18T15:01:00-04:00Why do we need prime ideals in the spectrum of a ring?https://liberty.io/cauchy-039-s-formula-for-repeated-integrals-proof-by-induction.htmlBuzz Spill Dailyen2026-08-18T14:59:31-04:00Cauchy's formula for repeated integrals proof by inductionhttps://liberty.io/is-there-a-way-to-reverse-factorials-duplicate.htmlBuzz Spill Dailyen2026-08-18T14:53:48-04:00Is there a way to reverse factorials? [duplicate]https://liberty.io/given-a-point-p-outside-equilateral-delta-abc-but-inside-angle-abc-if-.htmlBuzz Spill Dailyen2026-08-18T14:50:35-04:00Given a point $P$ outside equilateral $\Delta ABC$ but inside $\angle ABC$, if the distance between $P$ to $BC,CA,AB$ are $h_1,h_2,h_3$ respectively.https://liberty.io/show-that-sin45-sin15-sin75.htmlBuzz Spill Dailyen2026-08-18T14:29:04-04:00Show that $\sin45°+\sin15°=\sin75°$https://liberty.io/how-do-we-write-the-derivation-of-distance-formula-of-two-points-from-.htmlBuzz Spill Dailyen2026-08-18T14:24:09-04:00How do we write the derivation of distance formula of two points from two different quadrants in a cartesian plane?https://liberty.io/asymptotic-and-exact-confidence-interval.htmlBuzz Spill Dailyen2026-08-18T14:17:41-04:00asymptotic and exact confidence intervalhttps://liberty.io/how-to-calculate-distance-run-on-athletics-track.htmlBuzz Spill Dailyen2026-08-18T14:17:04-04:00How to calculate distance run on athletics trackhttps://liberty.io/how-to-calculate-a-weighted-gpa.htmlBuzz Spill Dailyen2026-08-18T14:05:11-04:00How to Calculate a Weighted GPAhttps://liberty.io/set-of-algebraic-integers-is-closed-under-addition-and-multiplication.htmlBuzz Spill Dailyen2026-08-18T14:05:06-04:00Set of algebraic integers is closed under addition and multiplicationhttps://liberty.io/what-is-the-ratio-of-the-area-of-a-circle-to-its-radius-closed.htmlBuzz Spill Dailyen2026-08-18T14:03:11-04:00What is the ratio of the area of a circle to its radius? [closed]https://liberty.io/how-were-the-sine-cosine-and-tangent-tables-originally-calculated.htmlBuzz Spill Dailyen2026-08-18T14:00:57-04:00How were the sine, cosine and tangent tables originally calculated?https://liberty.io/learning-how-to-flip-equations.htmlBuzz Spill Dailyen2026-08-18T13:56:04-04:00Learning how to flip equationshttps://liberty.io/calculating-running-time-in-seconds-of-algorithms-of-a-given-complexit.htmlBuzz Spill Dailyen2026-08-18T13:51:51-04:00Calculating Running Time (in seconds) of algorithms of a given complexityhttps://liberty.io/difference-between-continuity-and-uniform-continuity.htmlBuzz Spill Dailyen2026-08-18T13:50:49-04:00Difference between continuity and uniform continuityhttps://liberty.io/is-the-present-king-of-france-is-bald-studied-by-maths.htmlBuzz Spill Dailyen2026-08-18T13:50:30-04:00Is "The present King of France is bald" studied by maths?https://liberty.io/symbol-of-a-partition.htmlBuzz Spill Dailyen2026-08-18T13:50:01-04:00Symbol of a partitionhttps://liberty.io/buchberger-039-s-algorithm.htmlBuzz Spill Dailyen2026-08-18T13:43:28-04:00Buchberger's algorithmhttps://liberty.io/min-and-max-of-a-product.htmlBuzz Spill Dailyen2026-08-18T13:35:40-04:00Min and max of a product.https://liberty.io/a-proportionality-puzzle-if-half-of-5-is-3-then-what-039-s-one-third-o.htmlBuzz Spill Dailyen2026-08-18T13:34:08-04:00A proportionality puzzle: If half of $5$ is $3$, then what's one-third of $10$?https://liberty.io/probability-of-of-an-event-happening-at-least-once-in-a-sequence-of-in.htmlBuzz Spill Dailyen2026-08-18T13:31:53-04:00Probability of of an event happening at least once in a sequence of independent events?https://liberty.io/integration-over-a-triangle.htmlBuzz Spill Dailyen2026-08-18T13:31:13-04:00Integration over a trianglehttps://liberty.io/find-the-nth-power-of-a-matrix.htmlBuzz Spill Dailyen2026-08-18T13:20:38-04:00Find the nth power of a matrixhttps://liberty.io/dodecahedron-proof-on-number-of-vertices-edges-and-faces.htmlBuzz Spill Dailyen2026-08-18T13:08:55-04:00dodecahedron proof on number of vertices, edges, and faceshttps://liberty.io/can-the-poisson-distribution-be-used-to-find-the-expected-value-of-tim.htmlBuzz Spill Dailyen2026-08-18T13:08:41-04:00Can the Poisson Distribution be used to find the expected value of time of arrival given an expected arrivals per unit time?https://liberty.io/matrix-representations-of-parabola.htmlBuzz Spill Dailyen2026-08-18T12:59:22-04:00Matrix representations of parabola.https://liberty.io/how-to-evaluate-the-following-integral.htmlBuzz Spill Dailyen2026-08-18T12:54:35-04:00How to evaluate the following integral.https://liberty.io/what-is-the-equation-of-a-3d-cone-with-generalised-tilt.htmlBuzz Spill Dailyen2026-08-18T12:49:06-04:00What is the equation of a 3D cone with generalised tilt?https://liberty.io/the-definition-of-ln-x.htmlBuzz Spill Dailyen2026-08-18T12:43:58-04:00The definition of $\ln(x)$https://liberty.io/how-many-different-arrangements-are-possible-with-3-digits-numbers-fro.htmlBuzz Spill Dailyen2026-08-18T12:43:38-04:00How many different arrangements are possible with 3 digits numbers from 1-9 if we have to arrange them in ascending order?https://liberty.io/get-the-inverse-of-ratio-what-is-the-mathematical-term.htmlBuzz Spill Dailyen2026-08-18T12:34:58-04:00Get the inverse of ratio, what is the mathematical term?https://liberty.io/operation-that-is-commutative-but-not-associative-duplicate.htmlBuzz Spill Dailyen2026-08-18T12:32:32-04:00operation that is commutative but not associative [duplicate]https://liberty.io/how-to-calculate-the-surface-area-of-parametric-surface.htmlBuzz Spill Dailyen2026-08-18T12:25:53-04:00How to calculate the surface area of parametric surface?https://liberty.io/rational-solutions-for-x-2-y-2-3.htmlBuzz Spill Dailyen2026-08-18T12:23:35-04:00Rational solutions for $x^2+y^2=3$https://liberty.io/why-is-sphere-non-euclidean-space.htmlBuzz Spill Dailyen2026-08-18T12:13:25-04:00Why is sphere non-euclidean space?https://liberty.io/size-of-eigenvalues-and-diagonal-dominance.htmlBuzz Spill Dailyen2026-08-18T12:03:01-04:00Size of eigenvalues and diagonal dominancehttps://liberty.io/finding-roots-of-z-3-8.htmlBuzz Spill Dailyen2026-08-18T11:56:00-04:00Finding roots of $z^3 = 8$https://liberty.io/when-to-stop-checking-if-a-transition-matrix-is-regular.htmlBuzz Spill Dailyen2026-08-18T11:53:03-04:00When to stop checking if a transition matrix is regular?https://liberty.io/how-to-show-that-if-f-2-x-is-uniformly-continous-function-then-f-is-un.htmlBuzz Spill Dailyen2026-08-18T11:45:35-04:00How to show that if $f^2(x)$ is uniformly continous function then f is uniformly continoushttps://liberty.io/what-is-the-limit-of-lim-x-1-x-1-x-when-x-approaches-infinity-without-.htmlBuzz Spill Dailyen2026-08-18T11:35:18-04:00What is the limit of $ \lim ((x-1)/(x+1))^x$ when $x$ approaches infinity (without l'Hôpital's rule)?https://liberty.io/how-to-find-net-torque-closed.htmlBuzz Spill Dailyen2026-08-18T11:31:13-04:00How to find net torque? [closed]https://liberty.io/proving-lim-x-n-a-n-as-x-goes-to-a-from-definition.htmlBuzz Spill Dailyen2026-08-18T11:28:56-04:00Proving $\lim x^n = a^n$ as $x$ goes to $a$ from definitionhttps://liberty.io/proof-that-there-are-infinitely-many-primes-congruent-to-1-mod-3.htmlBuzz Spill Dailyen2026-08-18T11:28:22-04:00proof that there are infinitely many primes congruent to $1$ mod $3$https://liberty.io/notation-convention-for-integer-in-a-certain-range.htmlBuzz Spill Dailyen2026-08-18T11:12:06-04:00Notation Convention for integer in a certain rangehttps://liberty.io/calculating-the-divergence-of-a-tensor.htmlBuzz Spill Dailyen2026-08-18T11:09:36-04:00Calculating the Divergence of a Tensorhttps://liberty.io/find-the-derivative-of-y-2-x-as-a-function-of-y.htmlBuzz Spill Dailyen2026-08-18T11:06:19-04:00Find the derivative of y^2=x as a function of y.https://liberty.io/where-does-b-2a-come-from.htmlBuzz Spill Dailyen2026-08-18T11:03:44-04:00Where does $-b/2a$ come from?https://liberty.io/how-can-you-prove-that-1-5-9-cdots-4n-3-2n-2-n-without-using-induction.htmlBuzz Spill Dailyen2026-08-18T10:50:29-04:00How can you prove that $1+ 5+ 9 + \cdots +(4n-3) = 2n^{2} - n$ without using induction?https://liberty.io/how-to-simplify-a-sum-of-exponential-equation.htmlBuzz Spill Dailyen2026-08-18T10:49:36-04:00How to simplify a sum of exponential equation?https://liberty.io/prove-that-if-f-n-in-o-g-n-then-g-n-in-omega-f-n.htmlBuzz Spill Dailyen2026-08-18T10:47:54-04:00Prove that if $f(n) \in O(g(n))$ then $g(n) \in \Omega(f(n))$https://liberty.io/what-is-the-practical-application-of-factorials.htmlBuzz Spill Dailyen2026-08-18T10:33:18-04:00What is the practical application of factorialshttps://liberty.io/natural-deduction-proof-problem-with-existential-elimination.htmlBuzz Spill Dailyen2026-08-18T10:30:16-04:00Natural deduction proof - problem with existential eliminationhttps://liberty.io/25-chance-of-happening-but-has-to-happen-4-times-in-a-row-what-is-the-.htmlBuzz Spill Dailyen2026-08-18T10:16:05-04:0025% chance of happening but has to happen 4 times in a row, what is the real chance of happening?https://liberty.io/difference-between-state-space-and-sample-space.htmlBuzz Spill Dailyen2026-08-18T10:08:55-04:00Difference between State Space and Sample Spacehttps://liberty.io/which-value-goes-on-which-axis-in-plot-a-against-b.htmlBuzz Spill Dailyen2026-08-18T10:07:49-04:00Which value goes on which axis in "plot $a$ against $b$"?