Question Number 221863 by fantastic last updated on 11/Jun/25 $${If}\:{a}\:{and}\:{b}\:{are}\:{whole}\:{numbers}\:{such}\:{a}^{{b}} =\mathrm{121} \\ $$$${then}\:{find}\:{the}\:{value}\:{of}\:\left({a}−\mathrm{1}\right)^{{b}+\mathrm{1}} \\ $$ Commented by Tawa11 last updated on 11/Jun/25 $$\mathrm{11}^{\mathrm{2}} \:\:=\:\:\mathrm{121} \\…
Question Number 221831 by Nicholas666 last updated on 11/Jun/25 $$\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\:\:\frac{\sqrt{{x}}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:+\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\:{dx} \\ $$$$ \\ $$ Answered by MathematicalUser2357 last updated on 25/Jun/25…
Question Number 221856 by ajfour last updated on 11/Jun/25 Commented by ajfour last updated on 11/Jun/25 Commented by ajfour last updated on 11/Jun/25 Commented by…
Question Number 221788 by Tawa11 last updated on 10/Jun/25 Answered by mr W last updated on 10/Jun/25 Commented by mr W last updated on 10/Jun/25…
Question Number 221791 by hardmath last updated on 10/Jun/25 Commented by hardmath last updated on 10/Jun/25 $$\mathrm{ABC}\:-\:\mathrm{equilateral}\:\mathrm{triangle} \\ $$$$\mathrm{MK}\:\parallel\:\mathrm{AB} \\ $$$$\mathrm{MN}\:\parallel\:\mathrm{AC} \\ $$$$\mathrm{ML}\:\bot\:\mathrm{AB} \\ $$$$\mathrm{AC}\:=\:\mathrm{a}…
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Question Number 221786 by wewji12 last updated on 10/Jun/25 $$\:\mathrm{Express}\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:{z}^{{z}^{{z}^{\iddots} } } \:\mathrm{d}{z}\:\:\mathrm{closed}\:\mathrm{form}… \\ $$$${z}\upuparrows^{\infty} ={z}^{{z}^{{z}^{\iddots} } } \\ $$ Terms of Service…
Question Number 221787 by efronzo1 last updated on 10/Jun/25 $$\:\:\sqrt{\frac{\mathrm{1}−\mathrm{4x}\sqrt{\mathrm{1}−\mathrm{4x}^{\mathrm{2}} }}{\mathrm{2}}}\:=\:\mathrm{1}−\mathrm{8x}^{\mathrm{2}} \\ $$$$\:\:\mathrm{x}=?\: \\ $$ Answered by mr W last updated on 11/Jun/25 $$\mathrm{1}−\mathrm{4}{x}^{\mathrm{2}} =\mathrm{1}−\left(\mathrm{2}{x}\right)^{\mathrm{2}}…
Question Number 221814 by Tawa11 last updated on 10/Jun/25 Answered by wewji12 last updated on 11/Jun/25 $$\mathrm{log}_{{a}} \left({b}\right)=\frac{\mathrm{log}_{{b}} \left({c}\right)}{\mathrm{log}_{{a}} \left({c}\right)} \\ $$$$\frac{\mathrm{ln}\left(\mathrm{2}\right)}{\mathrm{ln}\left({x}+\mathrm{1}\right)}+\frac{\mathrm{ln}\left(\mathrm{3}\right)}{\mathrm{ln}\left({x}+\mathrm{2}\right)}+\frac{\mathrm{ln}\left(\mathrm{4}\right)}{\mathrm{ln}\left({x}+\mathrm{3}\right)}=\mathrm{3} \\ $$$$\mathrm{if}\:{x}=\mathrm{1}\: \\…
Question Number 221782 by fantastic last updated on 10/Jun/25 $$\left(\sqrt[{\sqrt[{\mathrm{3}^{{a}} }]{\mathrm{27}}}]{\mathrm{81}}\right)^{\sqrt{\mathrm{4}}} \\ $$$${where}\:{a}=\mathrm{4}^{\mathrm{0}^{\mathrm{4}^{\mathrm{3}} } } {and}\:{b}=\underset{{n}=\mathrm{1}} {\overset{\mathrm{6}} {\sum}}{n} \\ $$ Terms of Service Privacy Policy…