Question Number 4942 by prakash jain last updated on 24/Mar/16 $$\mathrm{If}\:{p}\:\mathrm{is}\:\mathrm{a}\:\mathrm{prime}\:\mathrm{number}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{5},\:\mathrm{the}\:\mathrm{prove} \\ $$$$\mathrm{that}\:{p}\:\mathrm{mod}\:\mathrm{6}\:\equiv\mathrm{1}\:\mathrm{or}\:{p}\:\mathrm{mod}\:\mathrm{6}\equiv\mathrm{5}. \\ $$$$\mathrm{i}.\mathrm{e}.\:\mathrm{All}\:\mathrm{prime}\:\mathrm{numbers}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{5}\:\mathrm{leave}\:\mathrm{a} \\ $$$$\mathrm{remainder}\:\mathrm{of}\:\mathrm{1}\:\mathrm{or}\:\mathrm{5}\:\mathrm{when}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{6}. \\ $$ Commented by Yozzii last updated on…
Question Number 4941 by madscientist last updated on 25/Mar/16 $${if}\:{i}\:{had}\:{a}\:{grid}\:{with}\:\mathrm{4}\:{quadrants}\:{and}\:{i}\:{shaded}\:{a}\:\: \\ $$$${quarter}\:{of}\:{it}\:{and}\:{chose}\:{one}\:{of}\:{the}\:\mathrm{4}\:{quadrants}\:{to}\:{form}\:{a}\:{new}\:{grid} \\ $$$${and}\:{shaded}\:{it}\:{and}\:{repeated}\:{the}\:{process}\:{infinitly}\:{what}\: \\ $$$${is}\:{the}\:{amount}\:{of}\:{the}\:{shaded}\:{area}? \\ $$$${and}\:{what}\:{formula}\:{will}\:{solve}\:{it}? \\ $$ Answered by FilupSmith last updated…
Question Number 4939 by Yozzii last updated on 24/Mar/16 $$\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\left(−\mathrm{1}\right)^{{k}+\mathrm{1}} {k}^{\mathrm{2}} }{{k}^{\mathrm{3}} +\mathrm{1}}\right)=? \\ $$ Commented by prakash jain last updated on 24/Mar/16…
Question Number 136008 by liberty last updated on 17/Mar/21 $$\:\mathrm{cos}\:{x}\:\sqrt{\mathrm{tan}\:{x}}\:=\:\mathrm{sin}\:^{\mathrm{3}} {x}+\mathrm{cos}\:^{\mathrm{3}} {x} \\ $$ Answered by MJS_new last updated on 17/Mar/21 $${t}=\sqrt{\mathrm{tan}\:{x}}\:\wedge{t}\geqslant\mathrm{0} \\ $$$$\frac{{t}}{\left({t}^{\mathrm{4}} +\mathrm{1}\right)^{\mathrm{1}/\mathrm{2}}…
Question Number 70473 by Tinku Tara last updated on 04/Oct/19 $$ \\ $$$$\mathrm{While}\:\mathrm{posting}\:\mathrm{photos}\:\mathrm{of}\:\mathrm{printed}\:\mathrm{material} \\ $$$$\mathrm{please}\:\mathrm{use}\:\mathrm{app}\:\left(\mathrm{like}\:\mathrm{camscanner}\right)\:\mathrm{so} \\ $$$$\mathrm{that}\:\mathrm{picture}\:\mathrm{will}\:\mathrm{look}\:\mathrm{clean}. \\ $$$$\mathrm{Also}\:\mathrm{please}\:\mathrm{crop}\:\mathrm{pictures}\:\mathrm{and}\:\mathrm{upload} \\ $$$$\mathrm{in}\:\mathrm{correct}\:\mathrm{orientation}. \\ $$$$ \\ $$$$\mathrm{In}\:\mathrm{built}\:\mathrm{editor}\:\mathrm{support}\:\mathrm{near}\:\mathrm{all}\:\mathrm{maths}…
Question Number 136005 by Raxreedoroid last updated on 17/Mar/21 $$\mathrm{challenge}\:\mathrm{question} \\ $$$$ \\ $$$$\mathrm{Let}\:{R}\left({m},{n}\right)={R}\left({m},{n}−\mathrm{1}\right)+{R}\left({m}+\mathrm{1},{n}−\mathrm{1}\right) \\ $$$$\mathrm{if}\:{R}\left(\mathrm{1},\mathrm{1}\right)=\mathrm{19},{R}\left(\mathrm{2},\mathrm{1}\right)=\mathrm{9},{R}\left(\mathrm{3},\mathrm{1}\right)=−\mathrm{2} \\ $$$$\mathrm{and}\:\forall{n}\:\mathrm{s}.\mathrm{t}.\:{R}\left(\mathrm{4},{n}\right)=\mathrm{0} \\ $$$$ \\ $$$$ \\ $$$$\left.{a}\right)\:\mathrm{Find}\:{R}\left(\mathrm{1},\mathrm{33}\right) \\…
Question Number 136006 by liberty last updated on 17/Mar/21 $$ \\ $$What are the dimensions of the rectangle of maximum area that can be inscribed…
Question Number 136000 by physicstutes last updated on 17/Mar/21 $$\mathrm{A}\:\mathrm{room}\:\mathrm{has}\:\mathrm{5}\:\mathrm{doors},\:\mathrm{if}\:\mathrm{a}\:\mathrm{person}\:\mathrm{enters}\:\mathrm{through}\:\mathrm{a}\:\mathrm{dooor}, \\ $$$$\mathrm{that}\:\mathrm{person}\:\mathrm{cannot}\:\mathrm{leave}\:\mathrm{through}\:\mathrm{that}\:\mathrm{same}\:\mathrm{door}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\: \\ $$$$\mathrm{of}\:\mathrm{ways}\:\mathrm{that}\:\mathrm{person}\:\mathrm{can}\:\mathrm{enter}\:\mathrm{and}\:\mathrm{leave}\:\mathrm{that}\:\mathrm{room}. \\ $$ Answered by liberty last updated on 17/Mar/21 $$\mathrm{5}×\mathrm{4}=\mathrm{20} \\…
Question Number 136003 by physicstutes last updated on 17/Mar/21 $$\mathrm{let}'\mathrm{s}\:\mathrm{define}\:\mathrm{a}\:\mathrm{relation}\:\boldsymbol{{R}}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\:_{{a}} {R}_{{b}} \:\Leftrightarrow\:{a}\:\leqslant\:{b} \\ $$$$\mathrm{is}\:\mathrm{this}\:\mathrm{relation}\:\mathrm{reflexive},\:\mathrm{symmetic}\:\mathrm{and}\:\mathrm{transitive}?\:\left(\mathrm{equivalence}\:\mathrm{relation}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 136002 by physicstutes last updated on 17/Mar/21 $$\mathrm{A}\:\mathrm{man}\:\mathrm{has}\:\mathrm{a}\:\mathrm{set}\:\mathrm{of}\:\mathrm{5}\:\mathrm{balls},\:\mathrm{in}\:\mathrm{which}\:\mathrm{3}\:\mathrm{are}\:\mathrm{red}\:\mathrm{and}\:\mathrm{2}\:\mathrm{are}\:\mathrm{blue} \\ $$$$\mathrm{what}\:\mathrm{are}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{these}\:\mathrm{5}\:\mathrm{balls}\:\mathrm{can}\:\mathrm{be}\:\mathrm{arranged}\:\mathrm{in}\:\mathrm{a}\: \\ $$$$\mathrm{line}. \\ $$ Answered by liberty last updated on 17/Mar/21 $$\frac{\mathrm{5}!}{\mathrm{2}!.\mathrm{3}!} \\…