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Author: Tinku Tara

Show-that-a-b-R-a-b-1-3-b-a-1-3-2-a-b-1-a-1-b-1-3-

Question Number 3832 by Yozzii last updated on 21/Dec/15 $${Show}\:{that},\:\forall{a},{b}\in\mathbb{R}^{+} , \\ $$$$\:\left(\frac{{a}}{{b}}\right)^{\mathrm{1}/\mathrm{3}} +\left(\frac{{b}}{{a}}\right)^{\mathrm{1}/\mathrm{3}} \leqslant\left\{\mathrm{2}\left({a}+{b}\right)\left(\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}\right)\right\}^{\mathrm{1}/\mathrm{3}} . \\ $$$$ \\ $$ Commented by RasheedSindhi last updated…

Draw-a-rectangle-of-maximum-perimeter-by-ruler-and-compass-when-area-is-ab-AB-a-CD-b-are-given-

Question Number 3830 by Rasheed Soomro last updated on 21/Dec/15 $$\mathcal{D}{raw}\:{a}\:{rectangle}\:{of}\:{maximum}\:{perimeter}, \\ $$$${by}\:{ruler}\:{and}\:{compass},{when}\:{area}\:{is}\:\boldsymbol{\mathrm{ab}}.\: \\ $$$$\left(\boldsymbol{\mathrm{AB}}\:=\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{CD}}=\boldsymbol{\mathrm{b}}\:\boldsymbol{\mathrm{are}}\:\boldsymbol{\mathrm{given}}.\right) \\ $$ Commented by prakash jain last updated on 22/Dec/15…

Question-134902

Question Number 134902 by faysal last updated on 08/Mar/21 Commented by bobhans last updated on 08/Mar/21 $$\mathrm{use}\:\mathrm{that}\:\left(\mathrm{1}+\mathrm{sec}\:\mathrm{2x}\right)\mathrm{cot}\:\mathrm{2x}\:=\:\frac{\mathrm{1}+\mathrm{cos}\:\mathrm{2x}}{\mathrm{sin}\:\mathrm{2x}}\:=\mathrm{cot}\:\mathrm{x} \\ $$ Answered by bobhans last updated on…

Box-I-has-3-red-and-5-white-balls-while-Box-II-contains-4-red-and-2-white-balls-A-ball-is-chosen-at-random-from-the-first-box-and-placed-in-the-second-box-without-observing-its-colour-Then-a-ball-

Question Number 3824 by Yozzii last updated on 21/Dec/15 $${Box}\:{I}\:{has}\:\mathrm{3}\:{red}\:{and}\:\mathrm{5}\:{white}\:{balls}, \\ $$$${while}\:{Box}\:{II}\:{contains}\:\mathrm{4}\:{red}\:{and}\:\mathrm{2}\: \\ $$$${white}\:{balls}.\:{A}\:{ball}\:{is}\:{chosen}\:{at}\:{random} \\ $$$${from}\:{the}\:{first}\:{box}\:{and}\:{placed}\:{in}\:{the} \\ $$$${second}\:{box}\:{without}\:{observing}\:{its}\:{colour}. \\ $$$${Then}\:{a}\:{ball}\:{is}\:{drawn}\:{from}\:{the}\:{second} \\ $$$${box}.\:{Find}\:{the}\:{probability}\:{that}\:{it}\:{is}\:{white}. \\ $$ Commented…

Consider-a-triangle-ABC-Let-D-and-E-are-two-points-on-AB-and-AC-respectively-such-that-DE-BC-Now-there-are-two-parts-of-ABC-ADE-and-trapizoid-DBCE-If-these-two-regions-have-same-area-W

Question Number 3823 by Rasheed Soomro last updated on 21/Dec/15 $${Consider}\:{a}\:{triangle}\:\mathrm{ABC}.\:{Let}\:\mathrm{D}\:\:{and}\:\:\mathrm{E} \\ $$$${are}\:{two}\:{points}\:{on}\:\mathrm{AB}\:\:{and}\:\:\mathrm{AC}\:{respectively} \\ $$$${such}\:{that}\:\mathrm{DE}\:\parallel\:\mathrm{BC}.\:{Now}\:{there}\:{are}\:{two} \\ $$$${parts}\:{of}\:\bigtriangleup\mathrm{ABC}\::\:\bigtriangleup\mathrm{ADE}\:\:\:{and}\:\:{trapizoid} \\ $$$$\mathrm{DBCE}.\:{If}\:{these}\:{two}\:{regions}\:{have}\:{same}\:{area} \\ $$$${What}\:{will}\:{be}\:{the}\:{ratio}\:{of}\:{two}\:{distances}\:: \\ $$$$\left({i}\right)\:{distance}\:{of}\:\mathrm{DE}\:{from}\:{point}\:\mathrm{A}\:{and} \\ $$$$\left({ii}\right)\:{distance}\:{between}\:\mathrm{BC}\:{and}\:\mathrm{DE}\:\:?…