Question Number 89726 by M±th+et£s last updated on 18/Apr/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{6}\sqrt{\frac{{x}}{{x}^{\mathrm{2}} +\mathrm{1}}}\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 155257 by mr W last updated on 27/Sep/21 Commented by mr W last updated on 28/Sep/21 $${the}\:{grid}\:{has}\:\boldsymbol{{m}}×\boldsymbol{{n}}\:{steps}. \\ $$$${find}\:{the}\:{number}\:{of}\:{routes}\:{with}\:\boldsymbol{{k}} \\ $$$${turns}. \\ $$…
Question Number 24186 by Tinkutara last updated on 14/Nov/17 $$\left({n}\:−\:\mathrm{1}\right)\:\mathrm{equal}\:\mathrm{point}\:\mathrm{masses}\:\mathrm{each}\:\mathrm{of}\:\mathrm{mass} \\ $$$${m}\:\mathrm{are}\:\mathrm{placed}\:\mathrm{at}\:\mathrm{the}\:\mathrm{vertices}\:\mathrm{of}\:\mathrm{a}\:\mathrm{regular} \\ $$$${n}-\mathrm{polygon}.\:\mathrm{The}\:\mathrm{vacant}\:\mathrm{vertex}\:\mathrm{has}\:\mathrm{a} \\ $$$$\mathrm{position}\:\mathrm{vector}\:{a}\:\mathrm{with}\:\mathrm{respect}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{centre}\:\mathrm{of}\:\mathrm{the}\:\mathrm{polygon}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{position} \\ $$$$\mathrm{vector}\:\mathrm{of}\:\mathrm{centre}\:\mathrm{of}\:\mathrm{mass}. \\ $$ Commented by mrW1…
Question Number 155259 by Fridunatjan08 last updated on 27/Sep/21 $${If}:\:{x}+\frac{\mathrm{1}}{{x}}=\mathrm{6}\:\:{then}\:\:{x}^{\mathrm{3}} +\frac{\mathrm{1}}{{x}^{\mathrm{3}} }=? \\ $$ Commented by puissant last updated on 27/Sep/21 $$\left({x}+\frac{\mathrm{1}}{{x}}\right)^{\mathrm{3}} =\:\mathrm{6}^{\mathrm{3}} \:=\:\mathrm{216} \\…
Question Number 24184 by FilupES last updated on 14/Nov/17 Commented by FilupES last updated on 14/Nov/17 $$\mathrm{I}\:\mathrm{will}\:\mathrm{upload}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{my}\:\mathrm{challange}\:\mathrm{later}, \\ $$$$\mathrm{or}\:\mathrm{if}\:\mathrm{requested}! \\ $$ Commented by FilupES last…
Question Number 89718 by abdomathmax last updated on 18/Apr/20 $${let}\:{f}\left({x}\right)=\sqrt{\mathrm{2}{x}+\mathrm{1}}−\sqrt{\mathrm{2}{x}−\mathrm{1}} \\ $$$${find}\:{f}^{\left({n}\right)} \:{by}\:{recurence} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 155252 by mnjuly1970 last updated on 27/Sep/21 $$ \\ $$$$\:\:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {x}.{sin}^{\:\mathrm{2}} \left({x}\right).{ln}\left({sin}\left({x}\right)\right){dx} \\ $$ Answered by phanphuoc last updated on 28/Sep/21 $${lnsinx}=−{ln}\mathrm{2}−\sum_{{k}=\mathrm{1}}…
Question Number 89719 by abdomathmax last updated on 18/Apr/20 $${find}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{{arctan}\left({ln}\left({x}\right)\right)}{\mathrm{4}+{x}^{\mathrm{2}} }{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 89716 by abdomathmax last updated on 18/Apr/20 $${calculate}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{n}\left[{x}\right]} \:{sin}\left(\frac{\left[{x}\right]}{{n}}\right){dx} \\ $$$${find}\:{nature}\:{of}\:\Sigma\:{n}^{\mathrm{2}} \:{A}_{{n}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 24181 by gopikrishnan005@gmail.com last updated on 14/Nov/17 $${if}\:{the}\:{points}\:{C}\left(−\mathrm{1},\mathrm{2}\right)\:{divides}\:{internally}\:{the}\:{line}\:{segment}\:{joining}\:{the}\:{points}\:{A}\left(\mathrm{2},\mathrm{5}\right)\:{and}\:{B}\left({x},{y}\right)\:{in}\:{the}\:{ratio}\:\mathrm{3}:\mathrm{4}\:{find}\:{the}\:{value}\:{of}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \\ $$ Answered by mrW1 last updated on 14/Nov/17 $$\frac{−\mathrm{1}−\mathrm{2}}{{x}−\mathrm{2}}=\frac{\mathrm{3}}{\mathrm{3}+\mathrm{4}}=\frac{\mathrm{3}}{\mathrm{7}} \\ $$$$\Rightarrow\mathrm{3}\left({x}−\mathrm{2}\right)=\mathrm{7}\left(−\mathrm{1}−\mathrm{2}\right) \\ $$$$\Rightarrow{x}=−\mathrm{5}…