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0-r-1-R-2-r-2-dr-

Question Number 182771 by liuxinnan last updated on 14/Dec/22 $$\int\:_{\mathrm{0}} ^{{r}} \:\frac{\mathrm{1}}{{R}^{\mathrm{2}} −{r}^{\mathrm{2}} }{dr}=? \\ $$ Commented by Frix last updated on 14/Dec/22 $$\mathrm{Error}:\:\mathrm{dependent}\:\mathrm{borders}\:\mathrm{are}\:\mathrm{not}\:\mathrm{allowed}. \\…

v2-220-Forum-viewing-improvement-After-update-you-will-see-options-to-zoom-out-of-post-with-longer-lines-to-view-whole-posts-without-scrolling-Similar-option-are-added-while-editing-in-Cursor-amp

Question Number 117215 by Tinku Tara last updated on 10/Oct/20 $$\mathrm{v2}.\mathrm{220}:\:\mathrm{Forum}\:\mathrm{viewing}\:\mathrm{improvement} \\ $$$$\bullet\:\mathrm{After}\:\mathrm{update}\:\mathrm{you}\:\mathrm{will}\:\mathrm{see}\:\mathrm{options} \\ $$$$\mathrm{to}\:\mathrm{zoom}\:\mathrm{out}\:\mathrm{of}\:\mathrm{post}\:\mathrm{with}\:\mathrm{longer}\:\mathrm{lines} \\ $$$$\mathrm{to}\:\mathrm{view}\:\mathrm{whole}\:\mathrm{posts}\:\mathrm{without}\:\mathrm{scrolling}. \\ $$$$\mathrm{Similar}\:\mathrm{option}\:\mathrm{are}\:\mathrm{added}\:\mathrm{while} \\ $$$$\mathrm{editing}\:\mathrm{in}\:'\mathrm{Cursor\&Page}'\:\mathrm{menu} \\ $$ Commented by…

0-1-t-1-t-1-t-dt-

Question Number 182726 by SANOGO last updated on 13/Dec/22 $$\int_{\mathrm{0}} ^{\mathrm{1}} \:{t}\sqrt{\frac{\mathrm{1}−{t}}{\mathrm{1}+{t}}}{dt}=? \\ $$ Commented by CElcedricjunior last updated on 13/Dec/22 $$\int_{\mathrm{0}} ^{\mathrm{1}} \boldsymbol{{t}}\sqrt{\frac{\mathrm{1}−\boldsymbol{{t}}}{\mathrm{1}+\boldsymbol{{t}}}}\boldsymbol{{dt}}=\boldsymbol{{k}} \\…

Question-182716

Question Number 182716 by sciencestudent last updated on 13/Dec/22 Answered by ARUNG_Brandon_MBU last updated on 13/Dec/22 $$\mathrm{In}\:\mathrm{a}\:\mathrm{space}\:\mathrm{of}\:\mathrm{20}\:\mathrm{seconds}\:\mathrm{the}\:\mathrm{school}\:\mathrm{bus}\:\mathrm{covered}\:\mathrm{a}\:\mathrm{distance} \\ $$$$\mathrm{of}\:{d}\:\mathrm{and}\:\mathrm{the}\:\mathrm{ambulance}\:\mathrm{covered}\:\mathrm{a}\:\mathrm{distance}\:\mathrm{of}\:\mathrm{40}+{d}+\mathrm{60}=\mathrm{100}+{d}. \\ $$$$ \\ $$$$\mathrm{Meanwhile}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{ambulance}=\frac{\mathrm{100}+{d}}{\mathrm{20}}=\mathrm{30}×\frac{\mathrm{5}}{\mathrm{18}}\:\left(\mathrm{in}\:{ms}^{−\mathrm{1}} \right) \\…

Question-182676

Question Number 182676 by yaslm last updated on 12/Dec/22 Answered by Acem last updated on 12/Dec/22 $${If}\:{we}\:{consider}\:{that}\:{the}\:{sequare}\:{isn}'{t}\:{a}\:{special} \\ $$$$\:{case}\:{of}\:{the}\:{rectangle},\:{then}\:{the}\:{required}\:{rectangles} \\ $$$$\left.\:{are}:\:\underset{\ell} {\underbrace{\right]\mathrm{0},\:\mathrm{1}\left[\:\cup\:\right]\mathrm{1},\:+\infty\left[}}\:×\:\underset{{w}} {\underbrace{\mathrm{1}}}\:\:\:\:\Leftrightarrow\:\:\:\:\underset{\ell} {\underbrace{\mathbb{R}^{+\bigstar,\:+\mathrm{1}} }}\:×\:\underset{{w}}…

Question-117140

Question Number 117140 by aurpeyz last updated on 09/Oct/20 Answered by bemath last updated on 10/Oct/20 $$=\mathrm{2}\left[\:\mathrm{1}−\mathrm{log}\:_{\mathrm{7}} \left(\mathrm{3}\right)−\mathrm{log}\:_{\mathrm{7}} \left(\mathrm{5}\right)\right]+\: \\ $$$$\mathrm{7}\:\left[\mathrm{2}\:\mathrm{log}\:_{\mathrm{7}} \left(\mathrm{5}\right)−\mathrm{log}\:_{\mathrm{7}} \left(\mathrm{3}\right)−\mathrm{2log}\:_{\mathrm{7}} \left(\mathrm{2}\right)\right]− \\…

Question-117143

Question Number 117143 by aurpeyz last updated on 09/Oct/20 Answered by prakash jain last updated on 13/Oct/20 $$\frac{\mathrm{2}{x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{3}} +\mathrm{4}{x}^{\mathrm{2}} −\mathrm{2}{x}}{\left({x}−\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{1}\right)} \\ $$$$={Ax}+{B}+\frac{{C}}{{x}−\mathrm{1}}+\frac{{Dx}+{E}}{{x}^{\mathrm{2}} +\mathrm{1}}…