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Author: Tinku Tara

Question-150968

Question Number 150968 by mathdanisur last updated on 17/Aug/21 Answered by dumitrel last updated on 17/Aug/21 $$\Sigma\frac{\left(\mathrm{2}{x}+{y}\right)\left(\mathrm{3}{x}^{\mathrm{2}} +{xy}+\mathrm{2}{y}^{\mathrm{2}} \right)}{\mathrm{2}{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\leqslant\Sigma\mathrm{3}\left({x}+{y}\right)=\mathrm{6}\left({x}+{y}+{z}\right) \\ $$ Commented by…

Simplify-i-log-x-i-x-i-

Question Number 19898 by Tinkutara last updated on 17/Aug/17 $$\mathrm{Simplify}\::\:{i}\:\mathrm{log}\:\left(\frac{{x}\:−\:{i}}{{x}\:+\:{i}}\right). \\ $$ Answered by ajfour last updated on 22/Aug/17 $${let}\:{t}={i}\mathrm{ln}\:\left(\frac{{x}−{i}}{{x}+{i}}\right) \\ $$$${and}\:{let}\:{z}=\frac{{x}−{i}}{{x}+{i}}\: \\ $$$$\Rightarrow\:\mid{z}\mid=\mathrm{1} \\…

Question-150965

Question Number 150965 by EDWIN88 last updated on 17/Aug/21 Answered by john_santu last updated on 17/Aug/21 $$\mathrm{R}=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{log}\:_{\mathrm{10}} \mathrm{x}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{P}^{\mathrm{2}} \\ $$$$\mathrm{S}=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{log}\:_{\mathrm{10}} \mathrm{y}=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{Q}^{\mathrm{2}} \\ $$$$\Leftrightarrow\mathrm{P}+\mathrm{Q}+\mathrm{R}+\mathrm{S}\:=\:\mathrm{24}\: \\ $$$$\Leftrightarrow\mathrm{P}+\mathrm{Q}+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{P}^{\mathrm{2}}…

E-x-2-x-x-3-1-x-x-3-8-2x-2-3-E-2-

Question Number 150967 by EDWIN88 last updated on 17/Aug/21 $${E}\left({x}+\frac{\mathrm{2}}{{x}}\right)=\frac{{x}^{\mathrm{3}} +\mathrm{1}}{{x}}\:+\frac{{x}^{\mathrm{3}} +\mathrm{8}}{\mathrm{2}{x}^{\mathrm{2}} }\:+\mathrm{3}\:, \\ $$$$\:{E}\left(\mathrm{2}\right)=? \\ $$ Answered by john_santu last updated on 17/Aug/21 $$\:\mathrm{E}\left(\mathrm{x}+\frac{\mathrm{2}}{\mathrm{x}}\right)=\frac{\mathrm{x}^{\mathrm{3}}…

if-a-b-N-then-determine-all-the-prime-numbers-p-which-satisfy-p-2-a-p-2-b-

Question Number 150966 by mathdanisur last updated on 17/Aug/21 $$\mathrm{if}\:\:\mathrm{a};\mathrm{b}\in\mathbb{N}^{+} \:\:\mathrm{then}\:\mathrm{determine}\:\mathrm{all}\:\mathrm{the} \\ $$$$\mathrm{prime}\:\mathrm{numbers}\:\boldsymbol{\mathrm{p}}\:\mathrm{which}\:\mathrm{satisfy} \\ $$$$\left(\mathrm{p}\:+\:\mathrm{2}\right)^{\boldsymbol{\mathrm{a}}} \:=\:\left(\mathrm{p}\:-\:\mathrm{2}\right)^{\boldsymbol{\mathrm{b}}} \\ $$ Commented by Rasheed.Sindhi last updated on 17/Aug/21…

pi-4-0-sin-x-cos-x-9-16sin-2x-dx-

Question Number 85426 by john santu last updated on 22/Mar/20 $$\int\:_{\frac{\pi}{\mathrm{4}}} ^{\mathrm{0}} \:\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{\mathrm{9}+\mathrm{16sin}\:\mathrm{2}{x}}\:{dx} \\ $$ Commented by som(math1967) last updated on 22/Mar/20 $$\int\frac{{sinx}+{cosx}}{\mathrm{25}−\mathrm{16}\left(\mathrm{1}−{sin}\mathrm{2}{x}\right)}{dx} \\ $$$$\frac{\mathrm{1}}{\mathrm{4}}\int\frac{\mathrm{4}\left({sinx}+{cosx}\right)}{\mathrm{5}^{\mathrm{2}}…

given-x-y-is-a-prime-number-with-x-lt-y-and-x-3-y-3-20l8-30y-2-300y-30l8-find-the-value-of-x-

Question Number 150960 by john_santu last updated on 17/Aug/21 $$\mathrm{given}\:\mathrm{x}\:,\mathrm{y}\:\mathrm{is}\:\mathrm{a}\:\mathrm{prime}\:\mathrm{number}\: \\ $$$$\mathrm{with}\:\mathrm{x}<\mathrm{y}\:\mathrm{and}\:\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} +\mathrm{20l8}\:=\mathrm{30y}^{\mathrm{2}} −\mathrm{300y}+\mathrm{30l8} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$ Commented by otchereabdullai@gmail.com last updated on…

A-man-on-top-of-a-tower-of-height-35m-throws-a-stone-vertically-upwards-with-a-speed-of-14m-s-Find-i-the-height-above-the-ground-reached-by-the-stone-ii-the-speed-of-the-stone-when-it-reaches-th

Question Number 19890 by NECC last updated on 17/Aug/17 $${A}\:{man}\:{on}\:{top}\:{of}\:{a}\:{tower}\:{of}\:{height} \\ $$$$\mathrm{35}{m}\:{throws}\:{a}\:{stone}\:{vertically} \\ $$$${upwards}\:{with}\:{a}\:{speed}\:{of}\:\mathrm{14}{m}/{s}. \\ $$$${Find}: \\ $$$$\left({i}\right){the}\:{height}\:{above}\:{the}\:{ground}, \\ $$$${reached}\:{by}\:{the}\:{stone}. \\ $$$$\left({ii}\right){the}\:{speed}\:{of}\:{the}\:{stone},{when} \\ $$$${it}\:{reaches}\:{the}\:{ground}. \\…