Question Number 69162 by Learner-123 last updated on 20/Sep/19 $${Find}\:{the}\:{local}\:{extreme}\:{values}\:{of} \\ $$$${the}\:{function}\:: \\ $$$${f}\left({x},{y}\right)=\:{xy}−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{2}{y}+\mathrm{4}. \\ $$ Answered by MJS last updated on 20/Sep/19…
Question Number 134693 by Engr_Jidda last updated on 06/Mar/21 $$\int{sec}^{\mathrm{4}} {xtanxdx}?? \\ $$ Answered by john_santu last updated on 06/Mar/21 $$\mathcal{X}=\int\left(\mathrm{tan}\:^{\mathrm{2}} {x}+\mathrm{1}\right)\mathrm{tan}\:{x}\:\mathrm{sec}\:^{\mathrm{2}} {x}\:{dx} \\ $$$${let}\:\mathrm{tan}\:{x}\:=\:\rho\:…
Question Number 69159 by Rio Michael last updated on 20/Sep/19 $${please}\:{help}\: \\ $$$$\:{A}\:\mathrm{7}.\mathrm{38}\:{g}\:{sample}\:{of}\:{magnesium}\:{sulfate}\:{MgSO}_{\mathrm{4}} .\:{X}\:{H}_{\mathrm{2}} {O}\:{lost}\:\mathrm{3}.\mathrm{78}{g}\:{of} \\ $$$${water}\:{on}\:{heating},\:{find}\:{the}\:{value}\:{of}\:{X}. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 134694 by Engr_Jidda last updated on 06/Mar/21 $$\int{sin}^{\mathrm{4}} {xdx} \\ $$ Answered by john_santu last updated on 06/Mar/21 $$\mathcal{J}\:=\:\int\:\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\mathrm{2}{x}\right)^{\mathrm{2}} {dx} \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{4}}\int\left(\mathrm{1}+\mathrm{cos}\:\mathrm{2}{x}\right)^{\mathrm{2}} \:{dx}…
Question Number 134689 by benjo_mathlover last updated on 06/Mar/21 $$\:\frac{\mathrm{2}^{\mathrm{289}} +\mathrm{1}}{\mathrm{2}^{\mathrm{17}} +\mathrm{1}}\:=\:\mathrm{2}^{{a}_{\mathrm{1}} } \:+\:\mathrm{2}^{{a}_{\mathrm{2}} } \:+\:\mathrm{2}^{{a}_{\mathrm{3}} } \:+\:…\:+\:\mathrm{2}^{{a}_{{k}} } \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{k}. \\ $$ Answered by…
Question Number 3617 by Rasheed Soomro last updated on 16/Dec/15 $${If}\:\:{the}\:{G}.{M}.\:{between}\:{two}\:{numbers}\: \\ $$$${a}\:,\:{b}\:\:\:{is}\:\:{G}\:{and}\:{the}\:{two}\:{A}.{M}.'{s}\:{between} \\ $$$${them}\:{are}\:{p}\:\:{and}\:\:{q}\:,\:{then}\:{prove}\:{that} \\ $$$${G}^{\mathrm{2}} =\left(\mathrm{2}{p}−{q}\right)\left(\mathrm{2}{q}−{p}\right). \\ $$ Commented by Yozzii last updated…
Question Number 3615 by Rasheed Soomro last updated on 16/Dec/15 $${Find}\:{the}\:{value}\:{of}\:{n}\:{so}\:{that} \\ $$$$\frac{{a}^{{n}+\mathrm{1}} +{b}^{{n}+\mathrm{1}} }{{a}^{{n}} +{b}^{{n}} } \\ $$$${may}\:{become}\:{the}\:{H}.{M}.\:{between} \\ $$$${a}\:\:\:{and}\:\:\:\:{b}. \\ $$ Commented by…
Question Number 3607 by Rasheed Soomro last updated on 16/Dec/15 $${Construct}\:{a}\:{line}\:{segment}\:{of}\:\boldsymbol{{a}}^{\mathrm{2}} \:{units}\: \\ $$$${using}\:{ruler}\:{and}\:\:{compass}\:{only},\:{when} \\ $$$${a}\:{line}\:{segment}\:{of}\:\boldsymbol{{a}}\:{units}\:{is}\:{given}. \\ $$ Answered by prakash jain last updated on…
Question Number 134676 by mohammad17 last updated on 06/Mar/21 Answered by benjo_mathlover last updated on 06/Mar/21 $$\left(\mathrm{2}\right)\frac{\mathrm{d}}{\mathrm{dx}}\:\left[\:\mathrm{e}^{\mathrm{xy}} \:+\mathrm{3ln}\:\left(\mathrm{xy}\right)+\mathrm{cos}\:\left(\mathrm{xy}\right)\:\right]=\:\mathrm{1} \\ $$$$\Rightarrow\left(\mathrm{y}+\mathrm{xy}'\right)\mathrm{e}^{\mathrm{xy}} +\mathrm{3}\left(\frac{\mathrm{y}+\mathrm{xy}'}{\mathrm{xy}}\right)−\left(\mathrm{y}+\mathrm{xy}'\right)\mathrm{sin}\:\left(\mathrm{xy}\right)=\mathrm{1} \\ $$$$ \\ $$…
Question Number 69143 by ajfour last updated on 20/Sep/19 $${x}^{\mathrm{4}} +{ax}^{\mathrm{3}} +{bx}^{\mathrm{2}} +{cx}+{d}=\mathrm{0} \\ $$$${let}\:\:{x}={f}\left({t}\right)\:\:{linear}\:{perhaps} \\ $$$${t}^{\mathrm{4}} +{At}^{\mathrm{3}} +{Bt}^{\mathrm{2}} +{Ct}+{D}=\mathrm{0} \\ $$$${can}\:{we}\:{have}\:\: \\ $$$$\:\:\:\mathrm{4}{AB}={A}^{\mathrm{3}} +\mathrm{8}{C}\:\:{solving}\:{at}\:{most}…