Question Number 224069 by MirHasibulHossain last updated on 17/Aug/25 $$\mathrm{If}\:\mathrm{x}^{\mathrm{32}} =\mathrm{2}^{\mathrm{x}} \:\mathrm{then}\:\mathrm{solve}\:\mathrm{for}\:\mathrm{x}. \\ $$ Answered by mr W last updated on 17/Aug/25 $${x}=\pm\mathrm{2}^{\frac{{x}}{\mathrm{32}}} \\ $$$${x}=\pm{e}^{\frac{\left(\mathrm{ln}\:\mathrm{2}\right){x}}{\mathrm{32}}}…
Question Number 224054 by ajfour last updated on 17/Aug/25 $${For}\:{kids} \\ $$ Commented by ajfour last updated on 17/Aug/25 Commented by fantastic last updated on…
Question Number 224071 by MirHasibulHossain last updated on 17/Aug/25 $$\mathrm{Two}\:\mathrm{masses}\:\mathrm{of}\:\mathrm{3}\:\mathrm{kg}\:\mathrm{and}\:\mathrm{6}\:\mathrm{kg}\:\mathrm{are}\:\mathrm{placed}\:\mathrm{2}\:\mathrm{m}\:\:\mathrm{apart}\:\mathrm{in}\:\mathrm{space}. \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{gravitational}\:\mathrm{force}\:\mathrm{between}\:\mathrm{them}. \\ $$$$\left(\mathrm{Take}\:\mathrm{G}=\mathrm{6}.\mathrm{673}×\mathrm{10}^{−\mathrm{11}} \:\mathrm{Nm}^{\mathrm{2}} \mathrm{kg}^{−\mathrm{2}} \right) \\ $$ Answered by MrAjder last updated on…
Question Number 224065 by MirHasibulHossain last updated on 17/Aug/25 $$\mathrm{Find}\:\mathrm{x},\:\sqrt{\mathrm{3}}\mathrm{x}−\mathrm{3x}\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }=\mathrm{1}\:. \\ $$ Commented by Ghisom_ last updated on 17/Aug/25 $$\mathrm{you}\:\mathrm{can}\:\mathrm{only}\:\mathrm{pproximate} \\ $$$$\mathrm{see}\:\mathrm{question}\:\mathrm{224029} \\ $$$$\left[\right.…
Question Number 224067 by fantastic last updated on 17/Aug/25 $$ \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{diagonal}\:\mathrm{of}\:\mathrm{image}\:\mathrm{formed}\:\mathrm{by} \\ $$$$\mathrm{line}\:\mathrm{segment}\:\mathrm{connecting}\:\mathrm{the} \\ $$$$\mathrm{points}\:\left(\mathrm{2},\mathrm{3}\right)\:\mathrm{and}\:\left(\mathrm{4},\mathrm{5}\right)\:\mathrm{in}\:\mathrm{sequence} \\ $$$$\mathrm{with}\:\mathrm{their}\:\mathrm{respective} \\ $$$$\mathrm{reflection}\:\mathrm{point}\:\mathrm{with}\:\mathrm{respect}\:\mathrm{to} \\ $$$$\:\mathrm{x}−\mathrm{axis}. \\…
Question Number 224049 by MASANJAJJ last updated on 16/Aug/25 Answered by RedstoneGG4 last updated on 17/Aug/25 $${O}\:=\:\left(\mathrm{0},\mathrm{0}\right) \\ $$$$ \\ $$$${T}\left({O}\right)\:=\:\left(\mathrm{3},-\mathrm{2}\right) \\ $$$${S}\left({O}\right)\:=\:\left(-\mathrm{2},\mathrm{1}\right) \\ $$$$\left(\mathrm{a}\right)\:\left({S}\:\circ\:{T}\right)\left({O}\right)\:=\:\left(\mathrm{1},-\mathrm{1}\right)…
Question Number 224028 by behi834171 last updated on 15/Aug/25 Answered by Rasheed.Sindhi last updated on 15/Aug/25 $$\frac{\left({x}+{c}^{\mathrm{2}} \right)\left({x}−{ab}\right)}{\left({x}+{a}^{\mathrm{2}} \right)\left({x}+{b}^{\mathrm{2}} \right)}=\frac{{c}}{{a}+{b}} \\ $$$$\left({a}+{b}\right)\left({x}^{\mathrm{2}} +\left(−{ab}+{c}^{\mathrm{2}} \right){x}−{abc}^{\mathrm{2}} \right)…
Question Number 224029 by behi834171 last updated on 15/Aug/25 Answered by Ghisom last updated on 15/Aug/25 $$\mathrm{you}\:\mathrm{can}\:\mathrm{only}\:\mathrm{approximate} \\ $$ Answered by fantastic last updated on…
Question Number 224030 by behi834171 last updated on 15/Aug/25 Answered by Rasheed.Sindhi last updated on 15/Aug/25 $${x}^{\mathrm{3}} \geqslant\mathrm{18}\Rightarrow{x}\neq\mathrm{1},\mathrm{2} \\ $$$$\mathrm{3}^{\mathrm{3}} =\mathrm{3}^{\mathrm{3}} +\mathrm{17}\:× \\ $$$$\mathrm{3}^{\mathrm{4}} =\mathrm{4}^{\mathrm{3}}…
Question Number 224041 by Tawa11 last updated on 15/Aug/25 Answered by mr W last updated on 19/Aug/25 $${say}\:{f}\left({x}\right)=\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{kx}^{{k}} \\ $$$${since}\:{a}_{\mathrm{1}} ,\:{a}_{\mathrm{2}} ,\:…,\:{a}_{{n}} \:{are}\:{the}\:{roots}\:{of}…