Question Number 149568 by mathdanisur last updated on 06/Aug/21 $${solve}\:{the}\:{equation}: \\ $$$$\mathrm{20}{z}\left[{z}\right]\:-\:\mathrm{21}\left\{{z}\right\}\:=\:\mathrm{2021} \\ $$$${where}\:\left\{\ast\right\}\:{is}\:{GIF}\:\:{and}\:\:\left\{{z}\right\}\:=\:{z}\:-\:\left[{z}\right] \\ $$ Answered by Olaf_Thorendsen last updated on 06/Aug/21 $$\mathrm{20}{z}\left[{z}\right]−\mathrm{21}\left\{{z}\right\}\:=\:\mathrm{2021}\:\:\:\:\left(\mathrm{1}\right) \\…
Question Number 149567 by mathdanisur last updated on 06/Aug/21 $${if}\:\:\boldsymbol{{q}}\:\:{is}\:{prime}\:{number}\:{fixed},\:{then} \\ $$$${solve}\:{for}\:{natural}\:{numbers}\:{the}\:{equation}: \\ $$$$\frac{\mathrm{1}}{{q}}\:=\:\frac{\mathrm{1}}{{x}}\:+\:\frac{\mathrm{1}}{{y}}\:-\:\frac{\mathrm{1}}{{z}} \\ $$ Commented by Rasheed.Sindhi last updated on 07/Aug/21 $$\mathrm{My}\:\mathrm{answer}\:\mathrm{is}\:\mathrm{too}\:\mathrm{lengthy}. \\…
Question Number 84014 by redmiiuser last updated on 08/Mar/20 $${find}\:{the}\:{no}.\:{of}\:{positivve} \\ $$$${integral}\:{solutions}\:{of} \\ $$$${x}+{y}+\mathrm{2}{z}=\mathrm{89} \\ $$$${x}>\mathrm{10} \\ $$$${y}>\mathrm{20} \\ $$$${z}>\mathrm{2} \\ $$ Commented by redmiiuser…
Question Number 84002 by M±th+et£s last updated on 08/Mar/20 $$\frac{{sin}\left({x}\right)}{\:\sqrt{\mathrm{2}{sin}^{\mathrm{2}} \left({x}\right)+{cos}^{\mathrm{2}} \left({x}\right)}}\:+\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}={csc}\left({x}\right)\sqrt{\mathrm{2}{sin}^{\mathrm{2}} \left({x}\right)+{cos}^{\mathrm{2}} \left({x}\right)} \\ $$$${show}\:{that} \\ $$$${x}=\left\{\frac{\pi}{\mathrm{2}}+\mathrm{2}\pi{n}\right\}\:{and}\:{x}=\left\{{cos}^{−\mathrm{1}} \left(\sqrt{\mathrm{3}}\right)−\pi+\mathrm{2}\pi{n}\right\} \\ $$$${and}\:{x}=\left\{−{cos}^{−\mathrm{1}} \left(\sqrt{\mathrm{3}}\right)+\mathrm{2}\pi{n}\right\} \\ $$$$ \\…
Question Number 84005 by redmiiuser last updated on 08/Mar/20 $${find}\:{atleast}\:\mathrm{7}\:{solutions} \\ $$$${of}\:{the}\:{equation}. \\ $$$$\mathrm{900}{x}+\mathrm{7689}{y}=\mathrm{109876} \\ $$$${CAN}\:{ANYONE}\:{SOLVE} \\ $$$${THIS} \\ $$$${now}\:{lets}\:{find}\:\mathrm{7}\:{integral} \\ $$$${solutions} \\ $$ Commented…
Question Number 149516 by mathdanisur last updated on 05/Aug/21 $$\Omega\:=\:\underset{\:\mathrm{0}} {\overset{\:\mathrm{3}} {\int}}\:\left(\sqrt{\left({x}\:+\:\mathrm{2}\right)^{\mathrm{2}} \:-\:\mathrm{8}{x}}\right)\:{dx}\:=\:? \\ $$ Answered by Ar Brandon last updated on 05/Aug/21 $$\:\:=\int_{\mathrm{0}} ^{\mathrm{3}}…
Question Number 149505 by mathdanisur last updated on 05/Aug/21 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\mathrm{n}\:+\:\mathrm{3}}{\mathrm{n}\:+\:\mathrm{1}}\right)^{\mathrm{n}} =\:? \\ $$ Commented by EDWIN88 last updated on 06/Aug/21 $$\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\frac{{n}+\mathrm{3}}{{n}+\mathrm{1}}\right)^{{n}} =\:{e}^{\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\frac{{n}+\mathrm{3}}{{n}+\mathrm{1}}−\mathrm{1}\right){n}}…
Question Number 18432 by Joel577 last updated on 21/Jul/17 $$\mathrm{Find}\:\mathrm{interval}\:{p}\:\mathrm{so} \\ $$$$\left({p}\:−\:\mathrm{2}\right){x}^{\mathrm{2}} \:+\:\mathrm{2}{px}\:+\:{p}\:−\:\mathrm{1}\:=\:\mathrm{0} \\ $$$$\mathrm{have}\:\mathrm{negative}\:\mathrm{roots} \\ $$ Answered by 433 last updated on 21/Jul/17 $$…
Question Number 149503 by mathdanisur last updated on 05/Aug/21 $$\mathrm{Calcular}: \\ $$$$\mathrm{3sin}\centerdot\left(\mathrm{150}\:-\:\boldsymbol{\alpha}\right)\:-\:\mathrm{2cos}\centerdot\left(\mathrm{60}\:-\:\boldsymbol{\alpha}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Answered by MJS_new last updated on 05/Aug/21 $$\Leftrightarrow \\ $$$$\mathrm{3sin}\:\left(\alpha+\mathrm{30}\right)\:−\mathrm{2sin}\:\left(\alpha+\mathrm{30}\right)\:=\frac{\mathrm{1}}{\mathrm{2}} \\…
Question Number 149481 by mathdanisur last updated on 05/Aug/21 Answered by mr W last updated on 05/Aug/21 $${say}\:{AB}={CK}={x},\:{BM}={BK}=\mathrm{1} \\ $$$${AC}={x}−\mathrm{1}+{x}=\mathrm{2}{x}−\mathrm{1} \\ $$$$\left(\mathrm{2}{x}−\mathrm{1}\right)^{\mathrm{2}} ={x}^{\mathrm{2}} +\left({x}+\mathrm{1}\right)^{\mathrm{2}} \\…