Question Number 52867 by hassentimol last updated on 14/Jan/19 Answered by iv@0uja last updated on 19/Jan/19 $$\:\:\:\:\:\underset{{l}=\mathrm{0}} {\overset{{m}+\mathrm{1}} {\prod}}\left({n}+{l}\right)−\underset{{l}=\mathrm{0}} {\overset{{m}+\mathrm{1}} {\prod}}\left({n}+{l}−\mathrm{1}\right) \\ $$$$=\left({n}+{m}+\mathrm{1}\right)\underset{{l}=\mathrm{0}} {\overset{{m}} {\prod}}\left({n}+{l}\right)−\left({n}−\mathrm{1}\right)\underset{{l}=\mathrm{0}}…
Question Number 183935 by SulaymonNorboyev last updated on 31/Dec/22 $$\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}+\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}={A} \\ $$$$\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}−\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}=? \\ $$ Answered by Rasheed.Sindhi last updated on 31/Dec/22…
Question Number 118386 by mohammad17 last updated on 17/Oct/20 $${if}:{x}+\sqrt{{y}}={a}\:,\:\sqrt{{x}}+{y}={b}\:{find}\:{x},{y} \\ $$ Answered by benjo_mathlover last updated on 17/Oct/20 $${let}\:\sqrt{{y}}\:=\:{t}\:\wedge\:\sqrt{{x}}\:=\:{q} \\ $$$$\Rightarrow\begin{cases}{{q}^{\mathrm{2}} +{t}={a}\:…\left(×{b}\right)}\\{{q}+{t}^{\mathrm{2}} ={b}\:…\left(×{a}\right)}\end{cases}\: \\…
Question Number 118384 by mohammad17 last updated on 17/Oct/20 Answered by Dwaipayan Shikari last updated on 18/Oct/20 $$\int_{\mathrm{0}} ^{\pi} \frac{{x}}{\mathrm{1}+{esinx}}{dx}=\int_{\mathrm{0}} ^{\pi} \frac{\pi−{x}}{\mathrm{1}+{esinx}}{dx}={I} \\ $$$$\mathrm{2}{I}=\pi\int_{\mathrm{0}} ^{\pi}…
Question Number 118378 by Cristina last updated on 17/Oct/20 $$\mathrm{TIPOLOGIE}\:\mathrm{DI}\:\mathrm{SOLUZIONI}\:\mathrm{DELLE}\:\mathrm{DISEQUAZIONI}\:\mathrm{DI}\:\mathrm{PRIMO} \\ $$$$\mathrm{GRADO} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{intervalli}\:\mathrm{limitati}\:\mathrm{superiormente}\:\mathrm{e}\:\mathrm{inferiormente} \\ $$$$−\mathrm{1}\leqslant\mathrm{x}\leqslant\mathrm{5}\:\left(\mathrm{tutti}\:\mathrm{i}\:\mathrm{numeri}\:\mathrm{compresi}\:\mathrm{tra}\:−\mathrm{1}\:\mathrm{e}\:\mathrm{5};\:\mathrm{sono}\:\mathrm{compresi}\:\mathrm{anche}\:−\mathrm{1}\:\mathrm{e}\:\mathrm{5}\right) \\ $$$$\left[−\mathrm{1};\mathrm{5}\right] \\ $$$$−\mathrm{1}<\mathrm{x}<\mathrm{5}\:\left(\mathrm{tutti}\:\mathrm{i}\:\mathrm{numeri}\:\mathrm{compresi}\:\mathrm{tra}\:−\mathrm{1}\:\mathrm{e}\:\mathrm{5};\:\mathrm{sono}\:\mathrm{esclusi}\:\mathrm{anche}\:−\mathrm{1}\:\mathrm{e}\:\mathrm{5}\right) \\ $$$$\left.\right]−\mathrm{1};\mathrm{5}\left[\right. \\ $$$$\left.\mathrm{2}\right)\:\mathrm{intervalli}\:\mathrm{limitati}\:\mathrm{solo}\:\mathrm{superiormente} \\…
Question Number 118379 by Cristina last updated on 17/Oct/20 $$\mathrm{INTERPRETAZIONE}\:\mathrm{GRAFICA}\:\mathrm{DI}\:\mathrm{UNA}\:\mathrm{DISEQUAZIONE} \\ $$$$\mathrm{y}=\mathrm{2x}+\mathrm{3}\:\:\:\:\mathrm{y}=\mathrm{mx}+\mathrm{q} \\ $$$$\mathrm{Pongo}:\:\mathrm{2x}+\mathrm{3}>\mathrm{0}\:\:\:\:\:\mathrm{x}>−\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\mathrm{Disegno}\:\mathrm{la}\:\mathrm{retta}\:\mathrm{y}=\mathrm{2x}+\mathrm{3}\:\mathrm{sul}\:\mathrm{piano}\:\mathrm{cartesiano} \\ $$$$\mathrm{La}\:\mathrm{retta}\:\grave {\mathrm{e}}\:\mathrm{la}\:\mathrm{funzione}\:\mathrm{che}\:\mathrm{permette}\:\mathrm{di}\:\mathrm{rappresentare}\:\mathrm{graficamente}\:\left(\mathrm{su}\:\mathrm{un}\right. \\ $$$$\left.\mathrm{piano}\:\mathrm{cartesiano}\right)\:\mathrm{una}\:\mathrm{disequazione}\:\mathrm{di}\:\mathrm{primo}\:\mathrm{grado}. \\ $$$$\mathrm{Rappresentazione}\:\mathrm{sul}\:\mathrm{piano}\:\mathrm{della}\:\mathrm{retta}\:\mathrm{y}=\mathrm{2x}+\mathrm{3} \\ $$$$…
Question Number 118372 by Cristina last updated on 17/Oct/20 $$\mathrm{DISEQUAZIONI}\:\mathrm{DI}\:\mathrm{PRIMO}\:\mathrm{GRADO} \\ $$$$\grave {\mathrm{E}}\:\mathrm{una}\:\mathrm{diseguaglianza}\:\mathrm{tra}\:\mathrm{due}\:\mathrm{espressioni} \\ $$$$\mathrm{ax}\geqslant\mathrm{b}\:\left(\mathrm{a}\:\mathrm{maggiore}/\mathrm{uguale}\:\mathrm{di}\:\mathrm{b}\right)\:\:\:\:\:\:\mathrm{ax}>\mathrm{b}\:\left(\mathrm{a}\:\mathrm{maggiore}\:\mathrm{di}\:\mathrm{b}\right) \\ $$$$\mathrm{ax}\leqslant\mathrm{b}\:\:\left(\mathrm{a}\:\mathrm{minore}/\mathrm{uguale}\:\mathrm{di}\:\mathrm{b}\right)\:\:\:\:\:\:\:\:\:\mathrm{ax}<\mathrm{b}\:\left(\mathrm{a}\:\mathrm{minore}\:\mathrm{di}\:\mathrm{b}\right) \\ $$$$\mathrm{Principi}\:\mathrm{di}\:\mathrm{equivalenza} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{aggiungendo}\:\mathrm{o}\:\mathrm{sottraendo}\:\mathrm{un}\:\mathrm{numero}\:\mathrm{ad}\:\mathrm{entrambe}\:\mathrm{le}\:\mathrm{espressioni},\:\mathrm{ottengo} \\ $$$$\mathrm{una}\:\mathrm{diseguaglianza}\:\mathrm{equivalente} \\ $$$$\mathrm{5}+\mathrm{3x}−\mathrm{2}>\mathrm{3}+\mathrm{5}…
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