Question Number 216769 by ArshadS last updated on 19/Feb/25 $${Solve}\:{for}\:{integer}\:{k},{m}\:{and}\:{n}: \\ $$$${k}^{\mathrm{2}} {m}−{n}^{\mathrm{2}} =\mathrm{8} \\ $$ Answered by mehdee7396 last updated on 20/Feb/25 $$“\:{m}\:''\:{must}\:{be}\:\:{positive} \\…
Question Number 216755 by Mingma last updated on 18/Feb/25 Answered by mr W last updated on 18/Feb/25 $$\boldsymbol{{w}}={a}\boldsymbol{{u}}+{b}\boldsymbol{{v}} \\ $$$$\begin{bmatrix}{\mathrm{1}}\\{\mathrm{2}}\\{{r}}\\{{s}}\end{bmatrix}={a}\begin{bmatrix}{\mathrm{1}}\\{\mathrm{0}}\\{\mathrm{5}}\\{−\mathrm{1}}\end{bmatrix}+{b}\begin{bmatrix}{\mathrm{1}}\\{\mathrm{1}}\\{\mathrm{3}}\\{\mathrm{1}}\end{bmatrix} \\ $$$$\mathrm{1}={a}×\mathrm{1}+{b}×\mathrm{1} \\ $$$$\mathrm{2}={a}×\mathrm{0}+{b}×\mathrm{1}\: \\…
Question Number 216733 by josemanuelrios last updated on 17/Feb/25 $$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Comparto}\:\mathrm{otro}\:\mathrm{reto}\:\mathrm{de}\:\mathrm{matematicas}\:\mathrm{que}\: \\ $$$$\mathrm{dice}\:\mathrm{literalmente}: \\…
Question Number 216734 by mnjuly1970 last updated on 17/Feb/25 Answered by sniper237 last updated on 18/Feb/25 $${Let}\:{E}=\left\{{f}:{A}\rightarrow{B}\right\}\:\:,\:\mid{E}\mid=\mathrm{3}^{{m}} \: \\ $$$${E}\backslash{S}=\left\{{f}\in{E},\:\:\mid{f}\left({A}\right)\mid=\mathrm{1}\:{or}\:\mathrm{2}\right\} \\ $$$$\mid{E}\backslash{S}\mid=\:{C}_{\mathrm{3}} ^{\mathrm{1}} .\mathrm{1}^{{m}} +{C}_{\mathrm{3}}…
Question Number 216726 by BaliramKumar last updated on 17/Feb/25 Commented by BaliramKumar last updated on 17/Feb/25 $${Q}.\:{not}\:{in}\:{real}\:{world} \\ $$$${Let}\:\:\:\:\:\:{second}\rightarrow{minutes} \\ $$ Commented by mr W…
Question Number 216754 by Tawa11 last updated on 17/Feb/25 $$\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{x}\:\mathrm{ln}^{\mathrm{2}} \left(\mathrm{x}\right)}{\mathrm{1}\:+\:\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx} \\ $$ Answered by issac last updated on 18/Feb/25 $$\int_{\:\mathrm{0}} ^{\:\mathrm{1}}…
Question Number 216722 by issac last updated on 17/Feb/25 $$\:\:\:\:\:\:\: \\ $$ Answered by MrGaster last updated on 17/Feb/25 $$\int_{\mathrm{0}} ^{\infty} \left(\frac{\mathrm{1}}{\ell}−\frac{\mathrm{1}}{{p}}\right){d}\ell=\int_{\mathrm{0}} ^{\infty} \left(\frac{{p}−\ell}{\ell{p}}\right){d}\ell \\…
Question Number 216748 by sniper237 last updated on 17/Feb/25 $${Find}\:\:\int_{−\mathrm{1}} ^{\mathrm{1}} {ln}\mid\Gamma\left(\frac{\mathrm{1}}{\mathrm{2}}+{it}\right)\mid{dt} \\ $$ Answered by issac last updated on 18/Feb/25 $$\mathrm{can}'\mathrm{t}\:\mathrm{simplify} \\ $$$$\mathrm{function}\:\mathrm{ln}\left(\mid\Gamma\left(\boldsymbol{{i}}{t}+\frac{\mathrm{1}}{\mathrm{2}}\right)\mid\right) \\…
Question Number 216749 by sniper237 last updated on 17/Feb/25 $${Find}\:\:\int_{\mathrm{0}} ^{\infty} \frac{\left(−\mathrm{1}\right)^{{E}\left({x}\right)} }{{E}\left(−{x}\right)}{dx} \\ $$ Answered by mehdee7396 last updated on 18/Feb/25 $$\int_{\mathrm{0}} ^{\infty} \frac{\left(−\mathrm{1}\right)^{{E}\left({x}\right)}…
Question Number 216750 by sniper237 last updated on 17/Feb/25 $${If}\:\:{a}−{b}=\sqrt{{ab}}\:\:\:{find}\:\:\:{the}\:{value}\:{of}\:\frac{{a}−{b}}{{a}+{b}} \\ $$ Answered by mr W last updated on 17/Feb/25 $$\left({a}+{b}\right)^{\mathrm{2}} =\left({a}−{b}\right)^{\mathrm{2}} +\mathrm{4}{ab}={ab}+\mathrm{4}{ab}=\mathrm{5}{ab} \\ $$$$\Rightarrow{a}+{b}=\pm\sqrt{\mathrm{5}{ab}}…