Question Number 201144 by sts313 last updated on 30/Nov/23 $$\left(\frac{\mathrm{14}}{\mathrm{15}}\right)^{\mathrm{6}} ×\left(\frac{\mathrm{45}}{\mathrm{28}}\right)^{\mathrm{6}} = \\ $$ Answered by mathlove last updated on 01/Dec/23 $$\left(\frac{\mathrm{14}}{\mathrm{15}}\right)^{\mathrm{6}} ×\left(\frac{\mathrm{3}×\mathrm{15}}{\mathrm{2}×\mathrm{14}}\right)^{\mathrm{6}} =\frac{\cancel{\mathrm{14}^{\mathrm{6}} }}{\cancel{\mathrm{15}^{\mathrm{6}}…
Question Number 201146 by ajfour last updated on 30/Nov/23 Commented by ajfour last updated on 30/Nov/23 $${How}\:{far}\:{is}\:{J}\:{from}\:{center}\:{of}\:{circle}? \\ $$ Commented by mr W last updated…
Question Number 201140 by Calculusboy last updated on 30/Nov/23 $$\boldsymbol{{If}}\:\underset{−} {\boldsymbol{{R}}}=\boldsymbol{{x}}^{\mathrm{2}} \boldsymbol{{y}}\underset{−} {\boldsymbol{{i}}}−\mathrm{2}\boldsymbol{{y}}^{\mathrm{2}} \boldsymbol{{z}}\underset{−} {\boldsymbol{{j}}}+\boldsymbol{{xy}}^{\mathrm{2}} \boldsymbol{{z}}^{\mathrm{2}} \underset{−} {\boldsymbol{{k}}},\:\boldsymbol{{find}}\:\mid\frac{\boldsymbol{{d}}^{\mathrm{2}} \boldsymbol{{R}}}{\boldsymbol{{dx}}^{\mathrm{2}} }×\frac{\boldsymbol{{d}}^{\mathrm{2}} \boldsymbol{{R}}}{\boldsymbol{{dy}}^{\mathrm{2}} }\mid\:\: \\ $$$$\boldsymbol{{at}}\:\boldsymbol{{the}}\:\boldsymbol{{point}}\:\left(\mathrm{2},\mathrm{1},−\mathrm{2}\right) \\…
Question Number 201139 by cherokeesay last updated on 30/Nov/23 Commented by Frix last updated on 30/Nov/23 $${x}\approx\mathrm{6395}.\mathrm{12283}\wedge{y}\approx\mathrm{171}.\mathrm{458282} \\ $$$$\mathrm{Exact}\:\mathrm{solution}: \\ $$$${x}=\mathrm{32}\left(\mathrm{8}\left(\mathrm{5}{r}^{\mathrm{2}} +\mathrm{6}{r}+\mathrm{9}\right)\sqrt{{r}−\mathrm{1}}+\mathrm{16}{r}^{\mathrm{2}} +\mathrm{29}{r}+\mathrm{38}\right) \\ $$$${y}=\mathrm{16}\left(\mathrm{4}\left({r}^{\mathrm{2}}…
Question Number 201133 by mnjuly1970 last updated on 30/Nov/23 $$ \\ $$$$ \\ $$$$\:\:\:\Omega=\:\int_{\mathrm{1}} ^{\:\mathrm{3}} \frac{\:\mathrm{1}}{\:\sqrt{\left({x}−\mathrm{1}\:\right)^{\mathrm{3}} }\:+\:\sqrt{\left({x}+\mathrm{1}\:\right)^{\mathrm{3}} }}\:{dx}=\:?\:\:\: \\ $$$$ \\ $$ Commented by Frix…
S-Area-of-AB-C-in-AB-C-a-2-4S-1-2-cot-B-cot-C-a-2-4S-a-2-4-1-2-bc-sin-A-4R-2-sin-2-A-8R-2-sin-B-sin-
Question Number 201134 by mnjuly1970 last updated on 30/Nov/23 $$\: \\ $$$$\:\:\:\:\:\:{S}\::\:\:{Area}\:\:{of}\:\:\:{A}\overset{\Delta} {{B}C} \\ $$$$\:\:\:\:\:{in}\:\:\:\:{A}\overset{\Delta} {{B}C}\:\::\:\:\:\frac{{a}^{\:\mathrm{2}} }{\mathrm{4}{S}}\:\overset{?} {=}\:\frac{\mathrm{1}}{\mathrm{2}}\:\left({cot}\left({B}\right)+{cot}\left({C}\right)\right) \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\frac{{a}^{\:\mathrm{2}} }{\mathrm{4}{S}}\:=\:\frac{\:{a}^{\:\mathrm{2}} }{\mathrm{4}\:\left(\frac{\mathrm{1}}{\mathrm{2}}\:{bc}\:{sin}\left({A}\right)\right)}=\frac{\mathrm{4}{R}^{\mathrm{2}} {sin}^{\:\mathrm{2}}…
Question Number 201135 by 281981 last updated on 30/Nov/23 Answered by MM42 last updated on 30/Nov/23 $${SX}+{SM}=\left({m}+{n}\right)\left(\mathrm{4}{a}−{b}\right) \\ $$$$\frac{\mathrm{9}}{\mathrm{5}}{SM}=\left({m}+{n}\right)\left(\mathrm{4}{a}−{b}\right) \\ $$$$\frac{\mathrm{9}}{\mathrm{5}}\left({SP}+{PQ}+{QM}\right)=\left({m}+{n}\right)\left(\mathrm{4}{a}−{b}\right) \\ $$$$\frac{\mathrm{9}}{\mathrm{5}}\left(\frac{\mathrm{4}{a}−{b}}{\mathrm{2}}\right)=\left({m}+{n}\right)\left(\mathrm{4}{a}−{b}\right) \\ $$$$\Rightarrow{m}+{n}=\frac{\mathrm{9}}{\mathrm{10}}\:\:\checkmark\:\:\left(\mathrm{1}\right)…
Question Number 201112 by cherokeesay last updated on 29/Nov/23 Answered by Frix last updated on 29/Nov/23 $$\mathrm{Approximation}\:\mathrm{only} \\ $$$${x}\approx−.\mathrm{581935060421} \\ $$$${x}\approx\mathrm{8}.\mathrm{44603068951} \\ $$ Terms of…
Question Number 201081 by Calculusboy last updated on 29/Nov/23 Answered by Rasheed.Sindhi last updated on 29/Nov/23 $$\mathrm{AnOther}\:\mathrm{Way} \\ $$$$\mathrm{2}{x}^{\mathrm{3}} −{x}^{\mathrm{2}} −\mathrm{22}{x}−\mathrm{24}=\mathrm{0} \\ $$$${let}\:{the}\:{two}\:{roots}\:{are}\:\mathrm{3}{a}\:\&\:\mathrm{4}{a}\:{where}\:{a}\neq\mathrm{0} \\ $$$$\bullet\mathrm{2}\left(\mathrm{3}{a}\right)^{\mathrm{3}}…
Question Number 201108 by SLVR last updated on 29/Nov/23 Commented by SLVR last updated on 29/Nov/23 $${Now}\:{ok}\:{sir} \\ $$ Commented by mr W last updated…