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Author: Tinku Tara

If-a-seller-could-purchase-goods-at-an-8-lower-price-by-keeping-the-selling-price-fixed-his-profit-over-the-cost-price-would-increase-from-the-current-x-to-x-10-So-what-is-the-value-of-x-

Question Number 71439 by Mr. K last updated on 15/Oct/19 $${If}\:{a}\:{seller}\:{could}\:{purchase}\:{goods}\:{at}\:{an} \\ $$$$\mathrm{8\%}\:{lower}\:{price}\:{by}\:{keeping}\:{the}\:{selling} \\ $$$${price}\:{fixed},\:{his}\:{profit}\:{over}\:{the}\:{cost} \\ $$$${price}\:{would}\:{increase}\:{from}\:{the}\: \\ $$$${current}\:{x\%}\:{to}\:\left({x}+\mathrm{10}\right)\%.\:{So},\:{what}\:{is} \\ $$$${the}\:{value}\:{of}\:{x}? \\ $$ Commented by…

Prove-that-log-n-gt-3n-10-1-2-1-3-1-4-1-n-1-

Question Number 5900 by 314159 last updated on 04/Jun/16 $${Prove}\:{that} \\ $$$${log}\:{n}!\:>\frac{\mathrm{3}{n}}{\mathrm{10}}\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}+…+\frac{\mathrm{1}}{{n}}−\mathrm{1}\right). \\ $$ Answered by Yozzii last updated on 05/Jun/16 $${Let}\:{for}\:{n}\in\mathbb{N},{n}\geqslant\mathrm{2},\: \\ $$$${P}\left({n}\right):\:{logn}!>\frac{\mathrm{3}{n}}{\mathrm{10}}\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}+…+\frac{\mathrm{1}}{{n}}−\mathrm{1}\right). \\…

0-pi-2-1-sec-2-t-sec-t-1-sec-t-2-2-dt-

Question Number 136969 by liberty last updated on 28/Mar/21 $$\int_{\mathrm{0}} ^{\:\pi/\mathrm{2}} \frac{\left(\mathrm{1}+\mathrm{sec}\:^{\mathrm{2}} \mathrm{t}\right)\:\sqrt{\mathrm{sec}\:\mathrm{t}}}{\left(\mathrm{1}+\mathrm{sec}\:\mathrm{t}\right)^{\mathrm{2}} −\mathrm{2}}\:\mathrm{dt}\:=?\: \\ $$ Answered by EDWIN88 last updated on 28/Mar/21 $$\:\mathrm{E}\:=\:\int_{\mathrm{0}} ^{\:\pi/\mathrm{2}}…

1-8-x-2-4-x-2-dx-2-x-6-2x-2-5x-3-

Question Number 136968 by Eric002 last updated on 28/Mar/21 $$\left.\mathrm{1}\right)\int\frac{\mathrm{8}}{{x}^{\mathrm{2}} \sqrt{\mathrm{4}−{x}^{\mathrm{2}} }}{dx} \\ $$$$\left.\mathrm{2}\right)\int\frac{{x}−\mathrm{6}\:}{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{3}} \\ $$ Answered by EDWIN88 last updated on 28/Mar/21 $$\left(\mathrm{1}\right)\int\:\frac{\mathrm{8}}{\mathrm{x}^{\mathrm{3}}…

csc-4-x-cot-2-x-dx-

Question Number 136971 by Eric002 last updated on 28/Mar/21 $$\int{csc}^{\mathrm{4}} \left({x}\right)\:{cot}^{\mathrm{2}} \left({x}\right)\:{dx} \\ $$ Answered by Ñï= last updated on 28/Mar/21 $$\int{csc}\:^{\mathrm{4}} {x}\mathrm{cot}\:^{\mathrm{2}} {xdx}=−\int\left(\mathrm{1}+\mathrm{cot}\:^{\mathrm{2}} {x}\right)\mathrm{cot}\:^{\mathrm{2}}…

If-four-people-all-said-HELLO-to-each-other-once-how-many-times-would-the-word-HELLO-be-spoken-

Question Number 5897 by sanusihammed last updated on 04/Jun/16 $${If}\:{four}\:{people}\:{all}\:{said}\:\:{HELLO}\:{to}\:{each}\:{other}\:{once}.\:{how}\:{many}\: \\ $$$${times}\:{would}\:{the}\:{word}\:\:{HELLO}\:\:{be}\:{spoken}\:? \\ $$ Answered by FilupSmith last updated on 04/Jun/16 $${person}\:\mathrm{1}\:{talks}\:{to}\:\mathrm{3}\:{people} \\ $$$${person}\:\mathrm{2}\:{talks}\:{to}\:\mathrm{2}\:{people} \\…