Question Number 201888 by MrGHK last updated on 15/Dec/23 Answered by namphamduc last updated on 15/Dec/23 $${S}=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\psi\left({n}+\mathrm{2}\right)}{\left({n}+\mathrm{2}\right)^{\mathrm{2}} }=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\psi\left({n}+\mathrm{1}\right)}{\left({n}+\mathrm{1}\right)^{\mathrm{2}} }=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{H}_{{n}}…
Question Number 201890 by sonukgindia last updated on 15/Dec/23 Answered by mr W last updated on 15/Dec/23 $${B}'=\left(−\mathrm{2},\mathrm{1}\right) \\ $$$$\frac{{y}_{{P}} −\mathrm{1}}{\mathrm{0}−\left(−\mathrm{2}\right)}=\frac{\mathrm{5}−\mathrm{1}}{\mathrm{5}−\left(−\mathrm{2}\right)} \\ $$$$\Rightarrow{y}_{{P}} =\frac{\mathrm{15}}{\mathrm{7}}\:\Rightarrow{P}\left(\mathrm{0},\:\frac{\mathrm{15}}{\mathrm{7}}\right) \\…
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Question Number 201853 by sonukgindia last updated on 14/Dec/23 Answered by AST last updated on 14/Dec/23 $${Let}\:{green}\:{segment}={g};{orange}\:{segment}={r} \\ $$$${and}\:{blue}\:{segment}={b};{side}\:{of}\:{square}={s} \\ $$$$\frac{{b}}{{r}}=\frac{\mathrm{7}−\mathrm{5}}{\mathrm{7}−\mathrm{3}}\Rightarrow{r}=\mathrm{2}{b};\frac{{g}}{{g}+{s}}=\frac{\mathrm{2}}{\mathrm{4}}\Rightarrow{g}={s} \\ $$$$\frac{\mathrm{2}{b}}{\mathrm{2}{b}+{s}}=\frac{\mathrm{7}−\mathrm{3}}{\mathrm{13}−\mathrm{3}}=\frac{\mathrm{2}}{\mathrm{5}}\Rightarrow\mathrm{5}{r}=\mathrm{2}{r}+\mathrm{2}{s}\Rightarrow{r}=\frac{\mathrm{2}{s}}{\mathrm{3}} \\ $$$${r}^{\mathrm{2}}…
Question Number 201854 by cortano12 last updated on 14/Dec/23 Commented by cortano12 last updated on 14/Dec/23 $$\:\:\begin{cases}{\mathrm{x}^{\mathrm{2}} −\mathrm{3y}^{\mathrm{2}} =\frac{\mathrm{17}}{\mathrm{x}}}\\{\mathrm{3x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} =\frac{\mathrm{23}}{\mathrm{y}}}\end{cases} \\ $$$$\:\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\:\sqrt[{\mathrm{m}}]{\mathrm{n}}\:,\:\mathrm{m},\mathrm{n}\:\in\mathbb{Z}^{+}…
Question Number 201848 by cortano12 last updated on 14/Dec/23 Answered by dimentri last updated on 14/Dec/23 $$\:\:\mathrm{1820}\:=\:\mathrm{2}^{\mathrm{2}} ×\mathrm{5}×\mathrm{7}×\mathrm{13} \\ $$$$\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{positive}\:\mathrm{factors} \\ $$$$\:\mathrm{from}\:\mathrm{1820}\:=\:\underset{\mathrm{i}=\mathrm{0}} {\overset{\mathrm{5}} {\sum}}\begin{pmatrix}{\mathrm{5}}\\{\mathrm{i}}\end{pmatrix}\:=\:\mathrm{2}^{\mathrm{5}} =\:\mathrm{32}…
Question Number 201882 by hardmath last updated on 14/Dec/23 Commented by hardmath last updated on 14/Dec/23 $$ \\ $$If angleABC=45°, angleADC=60°,DC = 2BD, then find…
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Question Number 201846 by cortano12 last updated on 14/Dec/23 $$\:\:\: \\ $$ Commented by Frix last updated on 14/Dec/23 $$\mathrm{Seriously}??? \\ $$$$\mathrm{3184}:\mathrm{2}=\mathrm{1592} \\ $$$$\mathrm{1592}:\mathrm{2}=\mathrm{796} \\…