Question Number 5609 by FilupSmith last updated on 22/May/16 $$\lfloor{x}\rfloor\:=\:\mathrm{floor}\:\mathrm{function} \\ $$$$\lceil{x}\rceil\:=\:\mathrm{ceiling}\:\mathrm{function} \\ $$$$ \\ $$$$\mathrm{I}\:\mathrm{have}\:\mathrm{seen}\:\mathrm{somewhere}\:\mathrm{either}: \\ $$$$\lfloor{x}\rceil\:\:\mathrm{or}\:\:\lceil{x}\rfloor\:\:\:\left(\mathrm{i}\:\mathrm{dont}\:\mathrm{remember}\:\mathrm{which}\right) \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{it}/\mathrm{are}\:\mathrm{they}? \\ $$ Terms of Service…
Question Number 71115 by TawaTawa last updated on 11/Oct/19 Answered by mind is power last updated on 11/Oct/19 $$\mathrm{A}.\left(\mathrm{999994}\right)……\left(\mathrm{1000002}\right)=\mathrm{1}\left(\mathrm{1000003}\right) \\ $$$$\mathrm{used}\:\mathrm{wilson}\:\mathrm{theorem}\:\left(\mathrm{p}−\mathrm{1}\right)!=\mathrm{1}\left(\mathrm{p}\right) \\ $$$$\Rightarrow \\ $$$$\Rightarrow\mathrm{A}\left(−\mathrm{1}\right).\left(−\mathrm{2}\right)……\left(−\mathrm{9}\right)=\mathrm{1}\left(\mathrm{1000003}\right)…
Question Number 136640 by jahar last updated on 24/Mar/21 $${if}\:\frac{{x}+{y}}{\mathrm{3}{a}−{b}}=\:\frac{{y}+{z}}{\mathrm{3}{b}−{c}}=\frac{{z}+{x}}{\mathrm{3}{c}−{a}}\:{then}\: \\ $$$${prove}\:{that}\:,\frac{{x}+{y}+{z}}{{a}+{b}+{c}}\:=\:\:\:\frac{{ax}+{by}+{cz}}{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 5519 by FilupSmith last updated on 17/May/16 $${P}=\underset{{i}=\mathrm{1}} {\overset{{n}} {\prod}}\frac{{a}^{{i}} }{{b}^{{i}} }\:\:\:\:\:\:\:\:{a}\neq{b},\:{b}\neq\mathrm{0} \\ $$$${P}=?? \\ $$ Commented by Yozzii last updated on 17/May/16…
Question Number 136516 by metamorfose last updated on 22/Mar/21 $${find}\:{all}\:{integers}\:\left({x},{y}\right)\::\:\mathrm{5}^{{x}} =\mathrm{3}^{{x}} +\mathrm{2021}{y} \\ $$ Answered by MJS_new last updated on 23/Mar/21 $$\mathrm{solution}:\:{x}=\mathrm{322}{n}\wedge{y}=\frac{\mathrm{5}^{\mathrm{322}{n}} −\mathrm{3}^{\mathrm{322}{n}} }{\mathrm{2021}}\forall{n}\in\mathbb{N} \\…
Question Number 136500 by rexford last updated on 22/Mar/21 Answered by Dwaipayan Shikari last updated on 22/Mar/21 $${a}−\mathrm{2}{d}+{a}−{d}+{a}+{a}+{d}+{a}+\mathrm{2}{d}+{a}+\mathrm{3}{d}=\mathrm{78} \\ $$$$\Rightarrow\mathrm{6}{a}+\mathrm{3}{d}=\mathrm{78}\Rightarrow\mathrm{2}{a}+{d}=\mathrm{26} \\ $$$${since}\:{a}−\mathrm{2}{d}>\mathrm{1}\Rightarrow{a}>\mathrm{2}{d}+\mathrm{1}\:\:{Greatest}\:{possible}\:{when}\:{a}=\mathrm{2}{d}+\mathrm{1} \\ $$$$\mathrm{2}{a}+{d}=\mathrm{26}\Rightarrow\mathrm{5}{d}+\mathrm{2}=\mathrm{26}\Rightarrow\Rightarrow{d}=\frac{\mathrm{24}}{\mathrm{5}} \\…
Question Number 136478 by liberty last updated on 22/Mar/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 70898 by Henri Boucatchou last updated on 09/Oct/19 $$\boldsymbol{{Solve}}\::\: \\ $$$$\left.\mathrm{1}.\right)\:\:\sqrt{\boldsymbol{{x}}−\mathrm{2}}\:+\:\sqrt{\mathrm{4}−\boldsymbol{{x}}}\:=\:\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{6}\boldsymbol{{x}}+\mathrm{11} \\ $$$$\left.\mathrm{2}.\right)\:\:\boldsymbol{{x}}^{\mathrm{4}} \:+\:\boldsymbol{{x}}^{\mathrm{3}} \:−\:\mathrm{2}\boldsymbol{{ax}}^{\mathrm{2}} \:−\:\boldsymbol{{ax}}\:+\:\boldsymbol{{a}}^{\mathrm{2}} \:=\:\mathrm{0} \\ $$ Answered by MJS…
Question Number 5274 by sanusihammed last updated on 03/May/16 $${Please}\:{help}\: \\ $$$$ \\ $$$${The}\:{stock}\:\:{of}\:{umar}\:{pharmacy}\:{in}\:{january}\:{was}\:\mathrm{20240}\:{items}. \\ $$$${its}\:{stock}\:{decline}\:{by}\:\mathrm{20}\:{percent}\:{in}\:{may}\:{due}\:{to}\:{increase}\:{sales}. \\ $$$${What}\:{is}\:{the}\:{amount}\:{of}\:{stock}\:{in}\:{may}\:.\: \\ $$ Commented by Rasheed Soomro last…
Question Number 70780 by MJS last updated on 08/Oct/19 $$\frac{\mathrm{1}}{{t}+\sqrt{{u}}+\sqrt{{v}}}= \\ $$$$=\frac{\left({t}−\sqrt{{u}}+\sqrt{{v}}\right)\left({t}+\sqrt{{u}}−\sqrt{{v}}\right)\left({t}−\sqrt{{u}}−\sqrt{{v}}\right)}{\left({t}+\sqrt{{u}}+\sqrt{{v}}\right)\left({t}−\sqrt{{u}}+\sqrt{{v}}\right)\left({t}+\sqrt{{u}}−\sqrt{{v}}\right)\left({t}−\sqrt{{u}}−\sqrt{{v}}\right)}= \\ $$$$=\frac{{t}^{\mathrm{3}} −\left(\sqrt{{u}}+\sqrt{{v}}\right){t}^{\mathrm{2}} −\left(\sqrt{{u}}−\sqrt{{v}}\right)^{\mathrm{2}} {t}+\left({u}−{v}\right)\left(\sqrt{{u}}−\sqrt{{v}}\right)}{{t}^{\mathrm{4}} −\mathrm{2}\left({u}+{v}\right){t}^{\mathrm{2}} +\left({u}−{v}\right)^{\mathrm{2}} } \\ $$$$ \\ $$$$\frac{\mathrm{1}}{{t}+\sqrt[{\mathrm{3}}]{{u}}+\sqrt[{\mathrm{3}}]{{v}}}= \\…