Question Number 203564 by mnjuly1970 last updated on 22/Jan/24 $$ \\ $$$$\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}^{\:\mathrm{3}} \left({x}\right)}{{x}^{\:\mathrm{2}} }\:{dx}=\:?\:\:\:\:\: \\ $$ Answered by Mathspace last updated on 23/Jan/24…
Question Number 203565 by Mastermind last updated on 22/Jan/24 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{following}\:\mathrm{equation}\:\mathrm{simultaneously} \\ $$$$\mathrm{and}\:\mathrm{find}\:\mathrm{the}\:\mathrm{stationary}\:\mathrm{points}: \\ $$$$\mathrm{2xy}^{\mathrm{2}} \mathrm{c}^{\mathrm{2}} \:−\:\mathrm{4x}^{\mathrm{3}} \mathrm{y}^{\mathrm{2}} \:−\:\mathrm{2xy}^{\mathrm{4}} \:=\:\mathrm{0}\:—–\left(\mathrm{1}\right) \\ $$$$\mathrm{2x}^{\mathrm{2}} \mathrm{yc}^{\mathrm{2}} \:−\:\mathrm{2x}^{\mathrm{4}} \mathrm{y}\:−\:\mathrm{4x}^{\mathrm{2}} \mathrm{y}^{\mathrm{3}}…
Question Number 203566 by BaliramKumar last updated on 22/Jan/24 $$'\mathrm{P}'\:\mathrm{is}\:\mathrm{a}\:\mathrm{prime}\:\mathrm{number}\:\left(\mathrm{P}>\mathrm{1000}\right).\: \\ $$$$\mathrm{If}\:\:\:\mathrm{P}\:\equiv\:\mathrm{r}\:\left(\mathrm{mod}\:\mathrm{1000}\right).\:\mathrm{how}\:\mathrm{many}\:\mathrm{value}\:\mathrm{of}\:'\mathrm{r}'. \\ $$ Answered by MM42 last updated on 22/Jan/24 $${p}=\mathrm{1000}{k}+{r}\:\:\&\:\:\mathrm{0}<{r}<\mathrm{1000}\: \\ $$$$\Rightarrow“{p}''\:{is}\:{prime}\:{number}\: \\…
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Question Number 203561 by nomanmahmud last updated on 22/Jan/24 $$\sqrt{\mathrm{2}{x}−\mathrm{5}+\mathrm{3}=?} \\ $$ Commented by Rasheed.Sindhi last updated on 22/Jan/24 $$\sqrt{\mathrm{2}{x}−\mathrm{2}}\:=\sqrt{\mathrm{2}\left({x}−\mathrm{1}\right)}\:=\sqrt{\mathrm{2}}\:\sqrt{{x}−\mathrm{1}}\: \\ $$ Terms of Service…
Question Number 203544 by laxmanb2111 last updated on 21/Jan/24 $$\int_{\mathrm{0}} ^{\mathrm{1}_{} } \frac{{dx}}{\left(\mathrm{1}−{x}^{\mathrm{6}} \right)^{\frac{\mathrm{1}}{\mathrm{6}}} }\:=\frac{\pi}{\mathrm{3}} \\ $$ Answered by DwaipayanShikari last updated on 23/Jan/24 $$\int_{\mathrm{0}}…
Question Number 203545 by Mastermind last updated on 21/Jan/24 $$\mathrm{If}\:\mathrm{A},\mathrm{B},\mathrm{C}\:\mathrm{are}\:\mathrm{finite}\:\mathrm{sets}\:\mathrm{whose}\:\mathrm{elements}\:\mathrm{are}\: \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{same}\:\mathrm{universal}\:\mathrm{set}\:\mathrm{U}\:\mathrm{and}\:\mathrm{n}\left(\mathrm{A}\right)\: \\ $$$$\mathrm{denotes}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{element}\:\mathrm{in}\:\mathrm{the}\:\mathrm{set}\:\mathrm{A} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Show}\:\mathrm{by}\:\mathrm{means}\:\mathrm{of}\:\mathrm{venn}\:\mathrm{diagram}\:\mathrm{that} \\ $$$$\mathrm{n}\left(\mathrm{A}\:\cup\:\mathrm{B}\right)\:=\:\mathrm{n}\left(\mathrm{A}\right)\:+\:\mathrm{n}\left(\mathrm{B}\right)\:−\:\mathrm{n}\left(\mathrm{A}\:\cap\:\mathrm{B}\right) \\ $$$$\left(\mathrm{b}\right)\:\mathrm{Using}\:\mathrm{the}\:\mathrm{fact}\:\mathrm{that}\:\left(\mathrm{A}\:\cup\:\mathrm{B}\:\cup\:\mathrm{C}\right)\:=\:\left(\mathrm{A}\cup\mathrm{B}\right)\cup\mathrm{C} \\ $$$$=\mathrm{A}\cup\left(\mathrm{B}\cup\mathrm{C}\right)\:\mathrm{deduce}\:\mathrm{an}\:\mathrm{expression}\:\mathrm{for} \\ $$$$\left(\mathrm{A}\cup\mathrm{B}\cup\mathrm{C}\right) \\…
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Question Number 203533 by Mastermind last updated on 21/Jan/24 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}\:: \\ $$$$\mathrm{3}^{\mathrm{x}+\mathrm{2}} =\mathrm{15}^{\mathrm{x}−\mathrm{1}} \\ $$ Answered by Rasheed.Sindhi last updated on 21/Jan/24 $$\mathrm{3}^{{x}+\mathrm{2}} =\mathrm{3}^{{x}−\mathrm{1}} \centerdot\mathrm{5}^{{x}−\mathrm{1}}…
Question Number 203560 by professorleiciano last updated on 21/Jan/24 Commented by esmaeil last updated on 22/Jan/24 $${Dear}\:{professor}\:{pleas}\:{ask}\:{in}\:{english}! \\ $$ Terms of Service Privacy Policy Contact:…