Question Number 133903 by shaker last updated on 25/Feb/21 Commented by mr W last updated on 25/Feb/21 $${what}\:{do}\:{mean}\:{with}\:{argth}\left({x}\right)?\:{is}\:{it} \\ $$$${the}\:{same}\:{as}\:{arctanh}\left({x}\right)\:{in}\:{your} \\ $$$${country}? \\ $$ Commented…
Question Number 133885 by bemath last updated on 25/Feb/21 $$\:\mathrm{Consider}\:\mathrm{the}\:\mathrm{equations}\:\mathrm{of}\:\mathrm{two} \\ $$$$\mathrm{intersecting}\:\mathrm{straight}\:\mathrm{lines} \\ $$$$\begin{cases}{{ax}+{by}+{c}=\mathrm{0}}\\{{a}_{\mathrm{1}} {x}+{b}_{\mathrm{1}} {y}+{c}_{\mathrm{1}} =\mathrm{0}}\end{cases} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{straight}\:\mathrm{line} \\ $$$$\mathrm{passing}\:\mathrm{through}\:\mathrm{a}\:\mathrm{given}\:\mathrm{point} \\ $$$$\left(\mathrm{x}_{\mathrm{0}} ,\mathrm{y}_{\mathrm{0}} \right)\:\mathrm{and}\:\mathrm{the}\:\mathrm{intersection}\:\mathrm{point}…
Question Number 2796 by Rasheed Soomro last updated on 27/Nov/15 $${Prove}\:{that} \\ $$$$\left({i}\right)\:\zeta\left(\mathrm{2}\right)=\frac{\pi^{\mathrm{2}} }{\mathrm{6}}\:\:\:\:\:\:\:\:\:\:\:\:\:\left({ii}\right)\:\:\zeta\left(\mathrm{4}\right)=\frac{\pi^{\mathrm{4}} }{\mathrm{90}} \\ $$ Answered by prakash jain last updated on 28/Nov/15…
Question Number 68336 by pete last updated on 09/Sep/19 $$\mathrm{A}\:\mathrm{man}\:\mathrm{gave}\:\$\mathrm{5},\mathrm{720}.\mathrm{00}\:\mathrm{to}\:\mathrm{be}\:\mathrm{shared}\:\mathrm{among} \\ $$$$\mathrm{his}\:\mathrm{son}\:\mathrm{and}\:\mathrm{three}\:\mathrm{daughters}.\:\mathrm{If}\:\mathrm{each}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{daughter}'\mathrm{s}\:\mathrm{share}\:\mathrm{is}\:\frac{\mathrm{3}}{\mathrm{4}}\:\mathrm{of}\:\mathrm{the}\:\mathrm{son}'\mathrm{s}\:\mathrm{share}, \\ $$$$\mathrm{how}\:\mathrm{much}\:\mathrm{did}\:\mathrm{the}\:\mathrm{son}\:\mathrm{receive}? \\ $$ Commented by Rasheed.Sindhi last updated on 09/Sep/19…
Question Number 2762 by Rasheed Soomro last updated on 26/Nov/15 $${Without}\:{using}\:\underset{−} {{induction}}\:{o}\underset{−} {{r}\:\:{arithmatic}\:{series}−{concept}\:\:\:} \\ $$$$\:{prove}\:{the}\:{following}: \\ $$$$\mathrm{1}+\mathrm{2}+\mathrm{3}+…+{n}=\frac{{n}\left({n}+\mathrm{1}\right)}{\mathrm{2}} \\ $$ Answered by prakash jain last updated…
Question Number 2759 by RasheedAhmad last updated on 26/Nov/15 $${Without}\:{using}\:{arithmatic}\:{Series} \\ $$$${concept}\:{or}\:{formula}\:{prove}\:{the}\:{following}: \\ $$$$\mathrm{1}+\mathrm{2}+\mathrm{3}+…+{n}=\frac{{n}\left({n}+\mathrm{1}\right)}{\mathrm{2}} \\ $$ Answered by 123456 last updated on 26/Nov/15 $$\mathrm{induction} \\…
Prove-that-i-2-n-gt-n-2-for-all-integral-values-of-n-5-ii-n-gt-3-n-1-for-all-integral-values-of-n-5-
Question Number 2750 by RasheedAhmad last updated on 26/Nov/15 $${Prove}\:{that}: \\ $$$$\left({i}\right)\:\:\mathrm{2}^{{n}} >{n}^{\mathrm{2}} \:\:{for}\:{all}\:{integral}\:{values} \\ $$$${of}\:\:{n}\geqslant\mathrm{5} \\ $$$$\left({ii}\right)\:{n}!>\mathrm{3}^{{n}−\mathrm{1}} ,{for}\:{all}\:{integral}\:{values} \\ $$$${of}\:{n}\geqslant\mathrm{5} \\ $$ Answered by…
Question Number 2748 by Rasheed Soomro last updated on 26/Nov/15 $${Show}\:{that}\:\frac{\mathrm{3}^{\mathrm{2}{n}+\mathrm{1}} +\mathrm{5}^{\mathrm{2}{n}+\mathrm{1}} }{\mathrm{8}}\:{is}\:{an}\:{integer}\:{for}\:{n}\in\mathbb{Z}^{+} \:. \\ $$ Answered by prakash jain last updated on 26/Nov/15 $${f}\left({n}\right)=\mathrm{3}^{\mathrm{2}{n}+\mathrm{1}}…
Question Number 68285 by mezihloic last updated on 08/Sep/19 $${two}\:{students}\:{ngum}\:{ebon}\:{gave}\:{their}\:{ages}\:{as}\:\mathrm{124}_{\mathrm{4}} {and}\:\mathrm{33}_{{x}} {respectively}.{if}\:{both}\:{of}\:{them}\:{are}\:{of}\:{thesame}\:{ages}\:.{find}\:{in}\:{what}\:{base}\:{ebon}\:{gave}\:{her}\:{age} \\ $$ Commented by Rasheed.Sindhi last updated on 08/Sep/19 $$\mathrm{124}_{\mathrm{4}} ? \\ $$$$\mathrm{A}\:\mathrm{number}\:\mathrm{written}\:\mathrm{in}\:\mathrm{the}\:\mathrm{base}\:\mathrm{of}\:\mathrm{4}…
Question Number 68280 by mezihloic last updated on 08/Sep/19 $${given}\:{that}\:\mathrm{432}_{{n}} −\mathrm{413}_{{n}} =\mathrm{11}_{\mathrm{10}} .{find}\:{the}\:{value}\:{of}\:{n} \\ $$ Commented by TawaTawa last updated on 08/Sep/19 $$\mathrm{4}\:×\:\mathrm{n}^{\mathrm{2}} \:+\:\mathrm{3}\:×\:\mathrm{n}^{\mathrm{1}} \:+\:\mathrm{2}\:×\:\mathrm{n}^{\mathrm{0}}…