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Question Number 224150 by behi834171 last updated on 23/Aug/25 Commented by behi834171 last updated on 23/Aug/25 $$\boldsymbol{{x}};\:\boldsymbol{{in}}\:\boldsymbol{{terms}}\:\boldsymbol{{of}}:\:\left(\boldsymbol{{a}}\:\boldsymbol{{and}}\:\boldsymbol{{b}}\right)\in\boldsymbol{{R}} \\ $$ Commented by Ghisom_ last updated on…
Question Number 224146 by hardmath last updated on 22/Aug/25 $$\boldsymbol{\mathrm{a}}\:=\:\mathrm{12}^{\mathrm{223}} \:\centerdot\:\mathrm{7}^{\mathrm{56}} \:+\:\mathrm{19}^{\mathrm{25}} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{last}\:\mathrm{digit}\:\mathrm{of}\:\mathrm{the}\:\mathrm{number}? \\ $$ Answered by Ghisom_ last updated on 23/Aug/25 $$\mathrm{12}^{\mathrm{223}} \:\mathrm{has}\:\mathrm{the}\:\mathrm{same}\:\mathrm{last}\:\mathrm{digit}\:\mathrm{as}\:\mathrm{2}^{\mathrm{223}}…
Question Number 224095 by fitraha last updated on 19/Aug/25 $${how}\:{to}\:{prove}\:{that}\:\:{x}\:+\:\mathrm{9}\:=\:{x}\:{is}\:{not}\:{has}\:{solution} \\ $$$${because}\: \\ $$$$\left({x}\:+\:\mathrm{9}\right)^{\mathrm{2}} \:=\:{x}^{\mathrm{2}} \\ $$$${x}^{\mathrm{2}} \:+\:\mathrm{18}{x}\:+\:\mathrm{81}\:=\:{x}^{\mathrm{2}} \\ $$$$\mathrm{18}{x}\:=\:−\mathrm{81} \\ $$$${x}\:=\:−\:\frac{\mathrm{81}}{\mathrm{18}}\:=\:−\frac{\mathrm{9}}{\mathrm{2}} \\ $$ Commented…
Question Number 224076 by MrAjder last updated on 18/Aug/25 $$ \\ $$$${D}=\sqrt{\left({m}−\frac{{n}^{\mathrm{2}} }{\mathrm{4}}\right)^{\mathrm{2}} +\left({e}^{{m}} −{n}\right)^{\mathrm{2}} }+\frac{{n}^{\mathrm{2}} }{\mathrm{4}}\left({m},{n}\in{R}\right),{D}_{\mathrm{min}} =? \\ $$ Answered by MrAjder last updated…
Question Number 224078 by OmoloyeMichael last updated on 18/Aug/25 $$\boldsymbol{{Evaluate}}\:\underset{\mathrm{0}} {\int}^{\frac{\boldsymbol{\pi}}{\mathrm{2}}} \boldsymbol{{sinxdx}}\:\boldsymbol{{with}}\:\boldsymbol{{h}}=\frac{\boldsymbol{\pi}}{\mathrm{12}},\boldsymbol{{correct}}\:\boldsymbol{{to}} \\ $$$$\mathrm{5}\:\boldsymbol{{decimal}}\:\boldsymbol{{places}},\boldsymbol{{using}} \\ $$$$\left(\mathrm{1}\right)\boldsymbol{{Trapezoidal}}\:\boldsymbol{{rule}} \\ $$$$\left(\mathrm{2}\right)\boldsymbol{{Newton}}−\boldsymbol{{Cotes}}\:\boldsymbol{{formula}}\:\boldsymbol{{for}}\:\boldsymbol{{n}}=\mathrm{4} \\ $$$$\left(\mathrm{3}\right)\boldsymbol{{Simpson}}\:\mathrm{3}/\mathrm{8}\:−\boldsymbol{{rule}} \\ $$$$\boldsymbol{{then}}\:\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{truncation}}\:\boldsymbol{{error}}\:\boldsymbol{{in}}\:\boldsymbol{{each}}\:\boldsymbol{{case}}. \\ $$ Terms…
Question Number 224079 by OmoloyeMichael last updated on 18/Aug/25 $$\boldsymbol{{For}}\:\boldsymbol{{the}}\:\boldsymbol{{given}}\:\boldsymbol{{function}}\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right),\boldsymbol{{let}}\:\boldsymbol{{x}}_{\mathrm{0}} =\mathrm{0},\boldsymbol{{x}}_{\mathrm{1}} =\mathrm{0}.\mathrm{6} \\ $$$$\boldsymbol{{and}}\:\boldsymbol{{x}}_{\mathrm{2}} =\mathrm{0}.\mathrm{9}.\:\boldsymbol{{construct}}\:\boldsymbol{{the}}\:\boldsymbol{{lagrange}}\:\boldsymbol{{interpolating}} \\ $$$$\boldsymbol{{polynomials}}\:\boldsymbol{{of}}\:\boldsymbol{{degree}}.\:\left(\mathrm{1}\right)\:\boldsymbol{{at}}\:\boldsymbol{{most}}\:\mathrm{1}\:\left(\mathrm{2}\right)\boldsymbol{{at}}\:\boldsymbol{{most}}\:\mathrm{2} \\ $$$$\boldsymbol{{to}}\:\boldsymbol{{approximate}}\:\boldsymbol{{f}}\left(\mathrm{0}.\mathrm{45}\right)\:\boldsymbol{{if}}\: \\ $$$$\left(\boldsymbol{{a}}\right)\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)=\boldsymbol{{cosx}}\:\:\left(\boldsymbol{{b}}\right)\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)=\sqrt{\mathrm{1}+\boldsymbol{{x}}}\:\left(\boldsymbol{{c}}\right)\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)=\boldsymbol{{In}}\left(\mathrm{1}+\boldsymbol{{x}}\right) \\ $$$$\left(\boldsymbol{{d}}\right)\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)=\boldsymbol{{tanx}} \\ $$$$…
Question Number 224080 by OmoloyeMichael last updated on 18/Aug/25 $$\boldsymbol{{Use}}\:\boldsymbol{{choleski}}'\boldsymbol{{s}}\:\boldsymbol{{method}}\:\boldsymbol{{to}}\:\boldsymbol{{solve}}\:\boldsymbol{{the}}\:\boldsymbol{{following}}\:\boldsymbol{{system}} \\ $$$$\boldsymbol{{of}}\:\boldsymbol{{equation}} \\ $$$$\mathrm{4}\boldsymbol{{x}}_{\mathrm{1}} −\mathrm{2}\boldsymbol{{x}}_{\mathrm{2}} +\mathrm{2}\boldsymbol{{x}}_{\mathrm{3}} =\mathrm{6} \\ $$$$\mathrm{4}\boldsymbol{{x}}_{\mathrm{1}} −\mathrm{3}\boldsymbol{{x}}_{\mathrm{2}} −\mathrm{2}\boldsymbol{{x}}_{\mathrm{3}} =−\mathrm{8} \\ $$$$\mathrm{2}\boldsymbol{{x}}_{\mathrm{1}} +\mathrm{3}\boldsymbol{{x}}_{\mathrm{2}}…
Question Number 224069 by MirHasibulHossain last updated on 17/Aug/25 $$\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}}} \\ $$$${x}=\pm{e}^{\frac{\left(\mathrm{ln}\:\mathrm{2}\right){x}}{\mathrm{32}}}…
Question Number 224065 by MirHasibulHossain last updated on 17/Aug/25 $$\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.…