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Category: Algebra

Question-6791

Question Number 6791 by Tawakalitu. last updated on 26/Jul/16 Commented by Yozzii last updated on 27/Jul/16 $$\frac{\mathrm{2}}{\mathrm{3}}{a}=\frac{\mathrm{3}}{\mathrm{4}}{b}=\frac{\mathrm{5}}{\mathrm{6}}{c}=\frac{\mathrm{6}}{\mathrm{5}}{d}\:\:\:\:\left({a},{b},{c},{d}\in\mathbb{N}\right) \\ $$$$\frac{{a}}{{b}}=\frac{\mathrm{9}}{\mathrm{8}},\:\frac{{b}}{{c}}=\frac{\mathrm{10}}{\mathrm{9}},\:\frac{{c}}{{d}}=\frac{\mathrm{36}}{\mathrm{25}} \\ $$$$\frac{{a}}{{c}}=\frac{{a}}{{b}}×\frac{{b}}{{c}}=\frac{\mathrm{9}}{\mathrm{8}}×\frac{\mathrm{10}}{\mathrm{9}}=\frac{\mathrm{5}}{\mathrm{4}}\Rightarrow{a}=\frac{\mathrm{5}}{\mathrm{4}}{c} \\ $$$${b}=\frac{\mathrm{10}}{\mathrm{9}}{c},\:{d}=\frac{\mathrm{25}}{\mathrm{36}}{c} \\ $$$$…

When-the-price-of-egg-was-raised-by-2-an-egg-the-number-of-eggs-which-can-be-bought-for-120-is-reduced-by-5-What-is-the-present-price-of-the-egg-

Question Number 6792 by Tawakalitu. last updated on 26/Jul/16 $${When}\:{the}\:{price}\:{of}\:{egg}\:\:{was}\:{raised}\:{by}\:#\mathrm{2}\:{an}\:{egg},\:\:{the}\:{number}\:{of}\:{eggs} \\ $$$${which}\:{can}\:{be}\:{bought}\:{for}\:#\mathrm{120}\:{is}\:{reduced}\:{by}\:#\mathrm{5}.\:{What}\:{is}\:{the} \\ $$$${present}\:{price}\:{of}\:{the}\:{egg}. \\ $$ Commented by Yozzii last updated on 27/Jul/16 $${Let}\:{price}\:{per}\:{egg}\:{be}\:{p}={p}_{\mathrm{0}} +\mathrm{2}\:\left({p}_{\mathrm{0}}…

What-is-the-smallest-even-number-greater-than-3-that-cannot-be-expressed-as-the-sum-of-two-prime-numbers-

Question Number 6772 by Tawakalitu. last updated on 24/Jul/16 $${What}\:{is}\:{the}\:{smallest}\:{even}\:{number}\:{greater}\:{than}\:\mathrm{3}\:{that}\:{cannot} \\ $$$${be}\:{expressed}\:{as}\:{the}\:{sum}\:{of}\:{two}\:{prime}\:{numbers}\:? \\ $$ Commented by Yozzii last updated on 24/Jul/16 $${Let}\:{S}\:{be}\:{a}\:{set}\:{of}\:{n}\:{elements},\:{so}\:{that}\:\mid{S}\mid={n}\geqslant\mathrm{4}. \\ $$$${Let}\:{P}\:{be}\:{a}\:{partition}\:{of}\:{S}\:{into}\:{two}\:{sets} \\…

Question-72291

Question Number 72291 by aliesam last updated on 27/Oct/19 Answered by mr W last updated on 27/Oct/19 $$\left(\mathrm{5}{m}\:\mathrm{sin}\:\left(\mathrm{3}{x}\right)\right)^{\mathrm{2}} =\left(\mathrm{4}\:\mathrm{sin}\:{x}\right)^{\mathrm{2}} \\ $$$$\mathrm{5}{m}\:\mathrm{sin}\:\left(\mathrm{3}{x}\right)=\pm\mathrm{4}\:\mathrm{sin}\:{x} \\ $$$$\mathrm{5}{m}\:\mathrm{sin}\:{x}\:\left(\mathrm{3}−\mathrm{4}\:\mathrm{sin}^{\mathrm{2}} \:{x}\right)=\pm\mathrm{4}\:\mathrm{sin}\:{x} \\…

Question-137772

Question Number 137772 by peter frank last updated on 06/Apr/21 Answered by bemath last updated on 06/Apr/21 $$\Leftrightarrow\:\frac{\left(\mathrm{2}^{{n}} \right)^{\mathrm{3}} +\left(\mathrm{3}^{{n}} \right)^{\mathrm{3}} }{\left(\mathrm{2}^{{n}} \right)^{\mathrm{2}} \left(\mathrm{3}\right)^{{n}} +\mathrm{2}^{{n}}…