Question Number 213944 by Spillover last updated on 22/Nov/24 Answered by Spillover last updated on 23/Nov/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 213945 by Spillover last updated on 22/Nov/24 Answered by mathmax last updated on 23/Nov/24 $${I}=\int_{\mathrm{0}} ^{\infty} \:{e}^{−\left[{x}\right]\left(\mathrm{1}+{x}−\left[{x}\right]\right)} {dx} \\ $$$$=\mathrm{1}+\sum_{{n}=\mathrm{1}} ^{\infty} \int_{{n}} ^{{n}+\mathrm{1}}…
Question Number 213962 by depressiveshrek last updated on 22/Nov/24 $$\int\frac{{x}^{\mathrm{4}} −\mathrm{1}}{{x}\left({x}^{\mathrm{4}} −\mathrm{5}\right)\left({x}^{\mathrm{5}} −\mathrm{5}{x}+\mathrm{1}\right)}{dx} \\ $$ Answered by Frix last updated on 23/Nov/24 $$\int\frac{{x}^{\mathrm{4}} −\mathrm{1}}{{x}\left({x}^{\mathrm{4}} −\mathrm{5}\right)\left({x}^{\mathrm{5}}…
Question Number 213956 by Ari last updated on 22/Nov/24 Answered by A5T last updated on 22/Nov/24 $${Let}\:{the}\:{numbers}\:{be}:\:\left({x}−\mathrm{2},{x}−\mathrm{1},{x},{x}+\mathrm{1},{x}+\mathrm{2}\right) \\ $$$${x}=\mathrm{5}{a}+\mathrm{2}=\mathrm{7}{b}+\mathrm{1}=\mathrm{9}{c}=\mathrm{11}{d}−\mathrm{1}=\mathrm{13}{e}−\mathrm{2} \\ $$$$\mathrm{7}{b}+\mathrm{1}\equiv\mathrm{2}\left({mod}\:\mathrm{5}\right)\Rightarrow{b}\equiv\mathrm{3}\left({mod}\:\mathrm{5}\right)\Rightarrow{b}=\mathrm{5}{f}+\mathrm{3} \\ $$$$\Rightarrow\mathrm{7}\left(\mathrm{5}{f}+\mathrm{3}\right)+\mathrm{1}\equiv\mathrm{0}\left({mod}\:\mathrm{9}\right)\Rightarrow{f}\equiv\mathrm{4}\left({mod}\:\mathrm{9}\right)\Rightarrow{f}=\mathrm{9}{g}+\mathrm{4} \\ $$$$\Rightarrow\mathrm{7}{g}\equiv\mathrm{2}\left({mod}\:\mathrm{11}\right)\Rightarrow{g}\equiv\mathrm{5}\left({mod}\:\mathrm{11}\right)\Rightarrow{g}=\mathrm{11}{h}+\mathrm{5}…
Question Number 213953 by efronzo1 last updated on 22/Nov/24 Answered by mehdee7396 last updated on 22/Nov/24 $${let}\:\:\:{f}\left({x}\right)=\frac{{ax}+{b}}{{cx}+{d}}\Rightarrow{f}\left({f}\left({x}\right)\right)=\frac{{a}\frac{{ax}+{b}}{{cx}+{d}}+{b}}{{c}\frac{{ax}+{b}}{{cx}+{d}}+{d}} \\ $$$$=\frac{\frac{{a}^{\mathrm{2}} {x}+{ab}}{{cx}+{d}}+{b}}{\frac{{acx}+{bc}}{{cx}+{d}}+{d}}=\frac{\left({a}^{\mathrm{2}} +{bc}\right){x}+{ab}+{bd}}{\left({ac}+{cd}\right)+{bc}+{d}^{\mathrm{2}} } \\ $$$$\Rightarrow{a}^{\mathrm{2}} +{bc}=\mathrm{1}\:\:\&\:\:{ac}+{cd}=\mathrm{1}\:\&\:\:{ab}+{bd}=\mathrm{1}\:\:\&\:\:{bc}+{d}^{\mathrm{2}}…
Question Number 213939 by polymathAntunes last updated on 22/Nov/24 Commented by Frix last updated on 22/Nov/24 $$\mathrm{1}.\:\mathrm{All}\:{x}\:\mathrm{on}\:\mathrm{one}\:\mathrm{side}, \\ $$$$\:\:\:\:\:\mathrm{constants}\:\mathrm{to}\:\mathrm{the}\:\mathrm{other}\:\mathrm{side} \\ $$$$\:\:\:\:\:\frac{{x}}{\mathrm{4}}+\mathrm{20}=\frac{{x}}{\mathrm{3}}\:\:\:\:\:\mid−\frac{{x}}{\mathrm{3}}−\mathrm{20} \\ $$$$\:\:\:\:\:\frac{{x}}{\mathrm{4}}−\frac{{x}}{\mathrm{3}}=−\mathrm{20} \\ $$$$\mathrm{2}.\:\mathrm{Common}\:\mathrm{denominator}\:\mathrm{and}\:\mathrm{add}…
Question Number 213934 by ajfour last updated on 22/Nov/24 $$\int_{−\pi/\mathrm{2}} ^{\:\pi/\mathrm{2}} \int_{\mathrm{0}} ^{\:{R}} \frac{\left({d}\theta\right)\left({dr}\right)\left({a}+{r}\mathrm{cos}\:\theta\right)}{\left({r}^{\mathrm{2}} +{a}^{\mathrm{2}} +\mathrm{2}{ar}\mathrm{cos}\:\theta\right)^{\mathrm{3}/\mathrm{2}} }\:={f}\left({a},{R}\right) \\ $$$${Find}\:{f}\left({a},\:{R}\right). \\ $$ Commented by ajfour last…
Question Number 213893 by issac last updated on 21/Nov/24 $$\int_{\:−\pi} ^{\:\:\pi} \:\:\frac{\mathrm{d}{z}}{\mathrm{1}+\mathrm{3cos}^{\mathrm{2}} \left({z}\right)}=¿¿\:\:\: \\ $$ Commented by BHOOPENDRA last updated on 21/Nov/24 $$\pi??? \\ $$…
Question Number 213894 by Spillover last updated on 21/Nov/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 213920 by ajfour last updated on 21/Nov/24 Commented by ajfour last updated on 21/Nov/24 $${Can}\:{we}\:{find}\:{at}\:{what}\:{speed}\:{does}\:{point} \\ $$$${P}\:{approach}\:{the}\:{ground}\:{just}\:{before} \\ $$$${hitting}\:{the}\:{ground}\:{if}\:{released}\:{at}\:{say} \\ $$$${the}\:{lower}\:{edge}\:{at}\:\mathrm{45}°\:{to}\:{horizontal}. \\ $$$${The}\:{radius}\:{of}\:{semi}-{disc}\:{is}\:{r},\:{mass}\:{m}.…