Question Number 71073 by TawaTawa last updated on 11/Oct/19 Commented by Prithwish sen last updated on 11/Oct/19 $$\mathrm{a}^{\mathrm{2}} =\:\mathrm{b}^{\mathrm{2}} +\mathrm{c}^{\mathrm{2}} +\mathrm{2bc} \\ $$$$\therefore\:\boldsymbol{\mathrm{bc}}\:=\:\frac{\boldsymbol{\mathrm{a}}^{\mathrm{2}} −\boldsymbol{\mathrm{b}}^{\mathrm{2}} −\boldsymbol{\mathrm{c}}^{\mathrm{2}}…
Question Number 136607 by EDWIN88 last updated on 23/Mar/21 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} \:\mathrm{if}\:\mathrm{ax}+\mathrm{by}=\mathrm{3} \\ $$$$\mathrm{bx}−\mathrm{ay}\:=\:\mathrm{4}\:\mathrm{and}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{4} \\ $$ Answered by MJS_new last updated on 24/Mar/21…
Question Number 5532 by Rasheed Soomro last updated on 18/May/16 $$\mathrm{Volume}\:\mathrm{of}\:\mathrm{a}\:\mathrm{cube}\:\mathrm{and}\:\mathrm{its}\:\mathrm{surface}-\mathrm{area} \\ $$$$\mathrm{are}\:\mathrm{numerically}\:\mathrm{equal}.\mathrm{What}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{measure}\:\mathrm{of}\:\mathrm{the}\:\mathrm{side}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cube}? \\ $$$$ \\ $$ Commented by FilupSmith last updated on…
Question Number 5531 by Rasheed Soomro last updated on 18/May/16 $$\mathrm{Once}\:\mathrm{I}\:\mathrm{opened}\:\mathrm{an}\:\mathrm{algebra}-\mathrm{book}.\mathrm{Instead} \\ $$$$\mathrm{of}\:\mathrm{individual}\:\mathrm{page}\:\mathrm{numbers}\:\mathrm{there}\:\mathrm{was} \\ $$$$\mathrm{written}:“{sum}\:{of}\:{page}\:{numbers}\:\:{infront} \\ $$$${of}\:{you}\:{is}\:\mathrm{x}''.\mathrm{Determine}\:\mathrm{the}\:\mathrm{page}\:\mathrm{numbers} \\ $$$$\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{x}. \\ $$ Commented by prakash jain…
Question Number 5525 by sanusihammed last updated on 17/May/16 $${Expand}\:\:{f}\left({z}\right)\:=\:{cos}\left({z}\right) \\ $$$${about}\:{point}\:\:{z}\:=\:\Pi/\mathrm{3} \\ $$$$ \\ $$$$ \\ $$ Commented by Yozzii last updated on 18/May/16…
Question Number 5508 by selene rmz. last updated on 17/May/16 $$\mathrm{24}\boldsymbol{\div}\mathrm{56} \\ $$ Answered by Abdul Haque Soomro last updated on 20/May/16 $$\mathrm{3}\boldsymbol{\div}\mathrm{7} \\ $$…
Question Number 5498 by Yozzii last updated on 16/May/16 $$\left(\mathrm{1}+{abc}\right)^{\mathrm{3}} \geqslant{abc}\left(\mathrm{1}+{a}\right)\left(\mathrm{1}+{b}\right)\left(\mathrm{1}+{c}\right)\: \\ $$$${if}\:{a},{b},{c}>\mathrm{0}? \\ $$ Answered by Rasheed Soomro last updated on 17/May/16 Commented by…
Question Number 5495 by FilupSmith last updated on 16/May/16 $$\mathrm{Why}\:\mathrm{does}: \\ $$$$\mathrm{cos}^{\mathrm{2}} {x}=\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{cos}\left(\mathrm{2}{x}\right)+\mathrm{1}\right) \\ $$ Commented by Yozzii last updated on 16/May/16 $${Let}\:\boldsymbol{{a}}=\begin{pmatrix}{{cosA}}\\{{sinA}}\end{pmatrix}\:,\boldsymbol{{b}}=\begin{pmatrix}{{cosB}}\\{−{sinB}}\end{pmatrix}. \\ $$$${For}\:{all}\:\mathrm{0}<{A},{B}<\mathrm{2}\pi,\:{the}\:{angle}\:{between}\:\boldsymbol{{a}}\:{and}\:\boldsymbol{{b}}\:{is}\:{A}+{B}…
Question Number 70997 by A8;15: last updated on 10/Oct/19 Answered by MJS last updated on 10/Oct/19 $$\mathrm{trying}\:\mathrm{first} \\ $$$$\mathrm{for}\:\mathrm{an}\:\mathrm{easy}\:\mathrm{solution}\:\mathrm{both}\:{a}+\mathrm{24}\:\mathrm{and}\:{a}+\mathrm{12} \\ $$$$\mathrm{must}\:\mathrm{be}\:\mathrm{square}\:\mathrm{numbers} \\ $$$$\Rightarrow\:{a}=−\mathrm{8}\:\Rightarrow\:{x}=−\mathrm{2} \\ $$…
Question Number 70969 by TawaTawa last updated on 10/Oct/19 Answered by mind is power last updated on 10/Oct/19 $${first}\:{find}\:{how}\:{many}\:{zero}\:{ends}\:\mathrm{80}! \\ $$$${n}=\left[\frac{\mathrm{80}}{\mathrm{5}}\right]+\left[\frac{\mathrm{80}}{\mathrm{25}}\right]=\mathrm{16}+\mathrm{3}=\mathrm{19} \\ $$$${so}\:{we}\:{have} \\ $$$$\mathrm{80}!={d}\ast\mathrm{10}^{\mathrm{19}}…