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Question-70838

Question Number 70838 by A8;15: last updated on 08/Oct/19 Answered by mind is power last updated on 08/Oct/19 $${X}^{\mathrm{3}} −\mathrm{1}=\left({X}−\mathrm{1}\right)\left({X}^{\mathrm{2}} +{X}+\mathrm{1}\right) \\ $$$${X}^{\mathrm{3}} +\mathrm{1}=\left({X}+\mathrm{1}\right)\left({X}^{\mathrm{2}} −{X}+\mathrm{1}\right)…

A-bowl-contains-carefully-shredded-confetti-6-of-which-are-blue-and-the-remaining-12-are-red-Each-piece-of-confetti-is-either-circular-triangular-or-rectangular-in-shape-and-are-in-the-ratio-1-3-2-f

Question Number 136375 by nadovic last updated on 22/Mar/21 $$\mathrm{A}\:\mathrm{bowl}\:\mathrm{contains}\:\mathrm{carefully}\:\mathrm{shredded} \\ $$$$\mathrm{confetti},\:\mathrm{6}\:\mathrm{of}\:\mathrm{which}\:\mathrm{are}\:\mathrm{blue}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{remaining}\:\mathrm{12}\:\mathrm{are}\:\mathrm{red}. \\ $$$$\mathrm{Each}\:\mathrm{piece}\:\mathrm{of}\:\mathrm{confetti}\:\mathrm{is}\:\mathrm{either}\:\mathrm{circular} \\ $$$$\mathrm{triangular}\:\mathrm{or}\:\mathrm{rectangular}\:\mathrm{in}\:\mathrm{shape}\:\mathrm{and} \\ $$$$\mathrm{are}\:\mathrm{in}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{1}:\mathrm{3}:\mathrm{2}\:\mathrm{for}\:\mathrm{each}\:\mathrm{colour} \\ $$$$\mathrm{respectively}.\:\mathrm{If}\:\mathrm{they}\:\mathrm{are}\:\mathrm{thrown}\:\mathrm{up}\: \\ $$$$\boldsymbol{\mathrm{thrice}}\:\mathrm{in}\:\mathrm{a}\:\mathrm{certain}\:\mathrm{competition}\:\mathrm{and}\:\mathrm{a} \\…

Question-70834

Question Number 70834 by Maclaurin Stickker last updated on 08/Oct/19 Answered by mind is power last updated on 08/Oct/19 $$\sum_{{k}=\mathrm{1}} ^{{n}−\mathrm{1}} \frac{\mathrm{1}}{{log}_{{x}} \left(\mathrm{2}^{{k}} \right){log}_{{x}} \left(\mathrm{2}^{\left.{k}+\mathrm{1}\right)}…

letf-x-x-3-arctan-pi-x-1-calculate-f-n-x-2-calculate-f-n-1-3-developp-f-at-integer-serie-

Question Number 136370 by mathmax by abdo last updated on 21/Mar/21 $$\mathrm{letf}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{3}} \:\mathrm{arctan}\left(\frac{\pi}{\mathrm{x}}\right) \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right) \\ $$$$\left.\mathrm{2}\right)\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{1}\right) \\ $$$$\left.\mathrm{3}\right)\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integer}\:\mathrm{serie} \\ $$ Answered by…

dx-sin-x-cos-x-

Question Number 136365 by liberty last updated on 21/Mar/21 $$\int\:\frac{{dx}}{\mathrm{sin}\:{x}\:\sqrt{\mathrm{cos}\:{x}}}\:=? \\ $$ Answered by mathmax by abdo last updated on 21/Mar/21 $$\mathrm{I}\:=\int\:\frac{\mathrm{dx}}{\mathrm{sinx}\sqrt{\mathrm{cosx}}}\:\:\mathrm{we}\:\mathrm{do}\:\mathrm{the}\:\mathrm{changement}\:\mathrm{cosx}=\mathrm{t}^{\mathrm{2}} \:\Rightarrow\mathrm{x}=\mathrm{arcos}\left(\mathrm{t}^{\mathrm{2}} \right) \\…

Question-70831

Question Number 70831 by ajfour last updated on 08/Oct/19 Commented by ajfour last updated on 08/Oct/19 $${Stick}\:{of}\:{mass}\:{m},\:{length}\:{b}\:{is} \\ $$$${released}\:{as}\:{shown}.\:{As}\:{it}\:{slides} \\ $$$${down}\:{and}\:{breaks}\:{contact}\:{with} \\ $$$${hemisphere},\:{the}\:{top}\:{end}\:{is}\:{at} \\ $$$${angular}\:{position}\:\beta.\:{Assume}…

A-circle-has-been-drawn-with-one-unit-opened-compass-on-surface-of-a-sphere-of-one-unit-radius-What-will-be-the-area-of-the-circle-

Question Number 5291 by Rasheed Soomro last updated on 05/May/16 $$\mathrm{A}\:\mathrm{circle}\:\mathrm{has}\:\mathrm{been}\:\mathrm{drawn}\:\mathrm{with}\:\mathrm{one} \\ $$$$\mathrm{unit}\:\mathrm{opened}\:\mathrm{compass}\:\mathrm{on}\:\:\mathrm{surface} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{sphere}\:\mathrm{of}\:\mathrm{one}\:\mathrm{unit}\:\mathrm{radius}.\: \\ $$$$\mathrm{What}\:\mathrm{will}\:\mathrm{be}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}? \\ $$ Commented by Yozzii last updated on…