Question Number 201897 by mnjuly1970 last updated on 15/Dec/23 $$ \\ $$$$\:\:\:\:\:\mathrm{Q}{uestion}:\:\:{The}\:{congruence} \\ $$$$\:\:\:\:\:\:\:{equation}\:\:\:''\:\:\:\:\left(\:\mathrm{5}{a}\:+\mathrm{3}\:\right){x}\:\:\overset{\mathrm{3}{a}\:+\:\mathrm{4}} {\equiv}\:\mathrm{19}\:\:\:''\:\:{is}\:{given}. \\ $$$$\:\:\:\:\:\:\:{Find}\:{the}\:{sum}\:{of}\:{digits}\:{of}\:\: \\ $$$$\:\:\:\:\:\:\:{the}\:{smallest}\:\:{three}\:−{digit}\:{natural}\:{number}\:\:''\:{a}\:''\: \\ $$$$\:\:\:\:\:\:\:{such}\:{that}\:{the}\:{assumed}\:{equation}\:{has}\: \\ $$$$\:\:\:\:\:\:\:\:\:{no}\:\:{solution}\:\:{in}\:\:\:''\:\:\:\mathbb{Z}\:\:''. \\ $$$$…
Question Number 201898 by sonukgindia last updated on 15/Dec/23 Answered by Frix last updated on 15/Dec/23 $${I}=\mathrm{4}\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\frac{{dx}}{\mathrm{1}+\mathrm{3sin}^{\mathrm{2}} \:{x}}\:\overset{{t}=\mathrm{tan}\:{x}} {=}\:\mathrm{4}\underset{\mathrm{0}} {\overset{\infty} {\int}}\frac{{dt}}{\mathrm{4}{t}^{\mathrm{2}} +\mathrm{1}}= \\…
Question Number 201931 by hardmath last updated on 15/Dec/23 $$\mathrm{if}\:\:\:\left(\mathrm{a}−\mathrm{2}\right)^{\mathrm{2}} \:=\:\mathrm{4a} \\ $$$$\mathrm{find}:\:\:\:\mathrm{5a}\:+\:\mathrm{4}\:+\:\frac{\mathrm{16}}{\mathrm{5a}\:+\:\mathrm{4}}\:=\:? \\ $$ Answered by mr W last updated on 16/Dec/23 $${a}^{\mathrm{2}} −\mathrm{4}{a}+\mathrm{4}=\mathrm{4}{a}…
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Question Number 201892 by Abdullahrussell last updated on 15/Dec/23 Answered by NANIGOPAL last updated on 15/Dec/23 $$\mathrm{a}=\mathrm{36},\mathrm{b}=\mathrm{9},\mathrm{c}=\mathrm{24} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 201925 by Calculusboy last updated on 15/Dec/23 Commented by Calculusboy last updated on 17/Dec/23 $$\boldsymbol{{thanks}}\:\boldsymbol{{sir}} \\ $$ Commented by Frix last updated on…
Question Number 201888 by MrGHK last updated on 15/Dec/23 Answered by namphamduc last updated on 15/Dec/23 $${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}}…