Question Number 206970 by MATHEMATICSAM last updated on 02/May/24 $$\mathrm{If}\:\mathrm{sin}\theta\:=\:\frac{{m}^{\mathrm{2}} \:+\:\mathrm{2}{mn}}{{m}^{\mathrm{2}} \:+\:\mathrm{2}{mn}\:+\:\mathrm{2}{n}^{\mathrm{2}} }\:\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{that}\:\mathrm{tan}\theta\:=\:\frac{{m}^{\mathrm{2}} \:+\:\mathrm{2}{mn}}{\mathrm{2}{mn}\:+\:\mathrm{2}{n}^{\mathrm{2}} }\:. \\ $$ Answered by Rasheed.Sindhi last updated on…
Question Number 206987 by hardmath last updated on 02/May/24 $$\frac{\mathrm{120}}{\mid\mathrm{x}−\mathrm{1}\mid\:+\:\mid\mathrm{x}−\mathrm{3}\mid\:+\:\mid\mathrm{x}−\mathrm{5}\mid}\:\:\:\Rightarrow\:\:\:\mathrm{max}\:=\:? \\ $$ Answered by Frix last updated on 02/May/24 $$\frac{\mathrm{120}}{{f}\left({x}\right)}\:\mathrm{is}\:\mathrm{max}\:\Rightarrow\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{min} \\ $$$$\mathrm{4}\leqslant\mid{x}−\mathrm{1}\mid+\mid{x}−\mathrm{3}\mid+\mid{x}−\mathrm{5}\mid \\ $$$$\Rightarrow\:\mathrm{Answer}\:\mathrm{is}\:\frac{\mathrm{120}}{\mathrm{4}}=\mathrm{30} \\…
Question Number 206971 by MATHEMATICSAM last updated on 02/May/24 $$\mathrm{Construct}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{whose}\:\mathrm{sine}\:\mathrm{is} \\ $$$$\frac{\mathrm{3}}{\mathrm{2}\:+\:\sqrt{\mathrm{5}}}\:. \\ $$ Answered by Rasheed.Sindhi last updated on 02/May/24 $$\mathrm{sin}\theta=\:\frac{\mathrm{3}}{\mathrm{2}\:+\:\sqrt{\mathrm{5}}} \\ $$$$\bullet\theta\:{is}\:{an}\:{angle}\:{of}\:{a}\:{right}\:{triangle} \\…
Question Number 206976 by mokys last updated on 02/May/24 $$\:{find}\:{the}\:{sum}\:{of}\::\:\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}\:{e}^{−\mathrm{2}\lambda_{{i}} \:{t}} \\ $$ Commented by mr W last updated on 02/May/24 $${what}\:{are}\:{the}\:\lambda_{{i}} \:?…
Question Number 206956 by mr W last updated on 01/May/24 Commented by mr W last updated on 01/May/24 $${find}\:{the}\:{radius}\:{of}\:{circle}. \\ $$ Answered by Frix last…
Question Number 206924 by mr W last updated on 01/May/24 Commented by mr W last updated on 01/May/24 $${x},\:{y},\:{z}\:\in\:\mathbb{N} \\ $$ Answered by MATHEMATICSAM last…
Question Number 206958 by hardmath last updated on 01/May/24 $$\mathrm{If}\:\:\:\frac{\mathrm{1}}{\mathrm{3}^{−\boldsymbol{\mathrm{x}}} }\:=\:\mathrm{5}\:\:\:\mathrm{find}:\:\:\mathrm{9}^{\boldsymbol{\mathrm{x}}+\mathrm{1}} \:=\:? \\ $$ Answered by Frix last updated on 01/May/24 $$\mathrm{3}^{{x}} =\mathrm{5} \\ $$$$\left(\mathrm{3}^{{x}}…
Question Number 206937 by efronzo1 last updated on 01/May/24 Answered by A5T last updated on 01/May/24 Commented by A5T last updated on 01/May/24 $$\mathrm{8}×\mathrm{14}={x}\left({x}+\mathrm{2}{r}\right)={x}^{\mathrm{2}} +\mathrm{2}{rx}=\mathrm{112}…
Question Number 206922 by mr W last updated on 01/May/24 $${solve}\:{for}\:{x},\:{y},\:{z}\:\in{R}^{+} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{2}{xy}\:\mathrm{cos}\:\gamma={c}^{\mathrm{2}} \\ $$$${y}^{\mathrm{2}} +{z}^{\mathrm{2}} −\mathrm{2}{yz}\:\mathrm{cos}\:\alpha={a}^{\mathrm{2}} \\ $$$${z}^{\mathrm{2}} +{x}^{\mathrm{2}} −\mathrm{2}{zx}\:\mathrm{cos}\:\beta={b}^{\mathrm{2}} \\ $$$${with}\:\alpha+\beta+\gamma=\mathrm{360}°…
Question Number 206939 by Tawa11 last updated on 01/May/24 In how many ways can the word KINECTIC be arranged so that no vowels can be…