Question Number 223213 by mr W last updated on 18/Jul/25 Commented by mr W last updated on 18/Jul/25 $${find}\:{the}\:{area}\:{of}\:{rectangle}\:{ABCD}. \\ $$ Answered by gregori last…
Question Number 223230 by hardmath last updated on 18/Jul/25 $$\mathrm{Maksimum}\:\left(\frac{\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{4x}\:+\:\mathrm{1}}{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{1}}\right)\:=\:? \\ $$ Answered by fantastic last updated on 18/Jul/25 $${Let}\:{f}\left({x}\right)=\left(\frac{{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}\right) \\…
Question Number 223224 by wewji12 last updated on 18/Jul/25 $$\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{k}}=\infty \\ $$$$\underset{\mathrm{p}\:\mathrm{prime}} {\sum}\:\frac{\mathrm{1}}{{p}}=\infty \\ $$$$\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}….\right)−\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{5}}+…\right)=?? \\ $$ Commented by Ghisom last updated on…
Question Number 223216 by Ari last updated on 18/Jul/25 Answered by som(math1967) last updated on 18/Jul/25 $${let}\:{alcohol}=\mathrm{4}{xl},\:{water}=\mathrm{3}{xl} \\ $$$$\:\therefore\:\frac{\mathrm{4}{x}}{\mathrm{3}{x}+\mathrm{7}}=\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\Rightarrow\mathrm{16}{x}=\mathrm{9}{x}+\mathrm{21} \\ $$$$\Rightarrow\mathrm{7}{x}=\mathrm{21}\Rightarrow{x}=\mathrm{3} \\ $$$$\:{amount}\:{of}\:{alcohol}=\mathrm{4}×\mathrm{3}=\mathrm{12}{l}…
Question Number 223192 by Nicholas666 last updated on 17/Jul/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{Evaluate}}\:;\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\mathrm{1}−{q}^{\mathrm{24}{n}} \right)\:\mathrm{d}{q} \\ $$$$ \\ $$ Terms of Service Privacy…
Question Number 223193 by Tawa11 last updated on 17/Jul/25 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\:\:\:\:\:\:\:\int_{\:\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\mathrm{tan}^{−\:\mathrm{1}} \left(\mathrm{r}\:\mathrm{sin}\:\theta\right)\:\mathrm{d}\theta\:\:\:=\:\:\:\mathrm{2}\boldsymbol{\chi}_{\mathrm{2}} \left(\frac{\sqrt{\mathrm{1}\:\:+\:\:\mathrm{r}^{\mathrm{2}} }\:\:−\:\:\mathrm{1}}{\mathrm{r}}\right) \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 223210 by fantastic last updated on 17/Jul/25 $${I}\:{have}\:{a}\:{theory}.\:{this}\:{may}\:{not}\:{be}\:{true}\:{and} \\ $$$${I}\:{cannot}\:{prove}\:{it}\:.\:{I}\:{think} \\ $$$${If}\:{you}\:{want}\:{to}\:{draw} \\ $$$$\:{a}\:{closed}\:{shape}\:{in}\:{x}^{{th}} \:{dimention} \\ $$$${the}\:{minimum}\:{number}\:{of} \\ $$$$\:{vertex}\:{you}\:{will}\:{need}\:{is}\:{x}+\mathrm{1} \\ $$$$ \\ $$$$\:{like}\:{if}\:{you}\:{want}\:{to}\:{draw}\:{a}\:{closed}\:{shape}…
Question Number 223204 by Nadirhashim last updated on 17/Jul/25 $$\:\:\:\underset{\frac{\pi}{\mathrm{6}}} {\overset{\frac{\pi}{\mathrm{3}}} {\int}}\frac{\boldsymbol{{dx}}}{\mathrm{1}+\sqrt{\boldsymbol{{tanx}}}}\:=…? \\ $$ Answered by som(math1967) last updated on 17/Jul/25 $$\:\:\:{I}=\int_{\frac{\pi}{\mathrm{6}}\:} ^{\frac{\pi}{\mathrm{3}}} \frac{{dx}}{\mathrm{1}+\sqrt{{tan}\left(\frac{\pi}{\mathrm{3}}+\frac{\pi}{\mathrm{6}}−{x}\right)}} \\…
Question Number 223191 by Nicholas666 last updated on 17/Jul/25 $$ \\ $$$$\:\:\:\:\:\:\:\boldsymbol{\mathrm{Evaluate}}\:;\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\:\left(\mathrm{1}−{q}^{\mathrm{4}{n}} \right)^{\mathrm{6}} \:{dq} \\ $$$$ \\ $$ Terms of Service…
Question Number 223203 by ajfour last updated on 17/Jul/25 $${Find}\:{x}\:{and}\:{y} \\ $$$$\:\:\:\:{ix}+{y}={ix}^{\mathrm{3}} −{y}^{\mathrm{3}} \\ $$$$\:\:\:{and}\: \\ $$$$\:\:\:\:{xy}\left({y}−{ix}\right)={c} \\ $$ Answered by mr W last updated…