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Category: Algebra

If-x-2sec-3t-and-y-4tan-3t-Show-that-y-4-x-2-4-

Question Number 25536 by tawa tawa last updated on 11/Dec/17 $$\mathrm{If}\:\:\:\mathrm{x}\:=\:\mathrm{2sec}\left(\mathrm{3t}\right)\:\:\mathrm{and}\:\:\mathrm{y}\:=\:\mathrm{4tan}\left(\mathrm{3t}\right),\:\:\:\mathrm{Show}\:\mathrm{that}\:\:\:\:\mathrm{y}\:=\:\mathrm{4}\left(\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{4}\right) \\ $$ Answered by prakash jain last updated on 11/Dec/17 $${x}=\mathrm{2sec}\:\mathrm{3}{t}\Rightarrow\frac{{x}}{\mathrm{2}}=\mathrm{sec}\:\mathrm{3}{t} \\ $$$${y}=\mathrm{4tan}\:\mathrm{3}{t}\Rightarrow\frac{{y}}{\mathrm{4}}=\mathrm{tan}\:\mathrm{3}{t}…

Three-sets-of-beans-l-m-and-n-are-sold-for5-for-5-00-15-00-and-17-50-respectively-per-kg-If-they-are-mixed-in-the-ratio-of-1-3-2-what-is-the-cost-per-kg-of-the-mixture-

Question Number 25533 by pieroo last updated on 11/Dec/17 $${Three}\:{sets}\:{of}\:{beans}\:{l},\:{m},\:{and}\:{n}\:{are}\:{sold}\:{for}\mathrm{5} \\ $$$${for}\:\$\mathrm{5}.\mathrm{00},\:\$\mathrm{15}.\mathrm{00}\:{and}\:\$\mathrm{17}.\mathrm{50}\:{respectively} \\ $$$${per}\:{kg}.\:{If}\:{they}\:{are}\:{mixed}\:{in}\:{the}\:{ratio}\:{of} \\ $$$$\mathrm{1}:\mathrm{3}:\mathrm{2},\:{what}\:{is}\:{the}\:{cost}\:{per}\:{kg}\:{of}\:{the}\:{mixture}?× \\ $$ Answered by mrW1 last updated on 11/Dec/17…

Find-all-the-triplets-a-b-c-of-pozitif-integers-such-that-a-3-b-3-c-3-abc-2-

Question Number 156591 by amin96 last updated on 12/Oct/21 $${Find}\:{all}\:{the}\:{triplets}\:\left({a},\:{b},\:{c}\right)\:{of}\:{pozitif}\:{integers} \\ $$$${such}\:{that} \\ $$$$\boldsymbol{\mathrm{a}}^{\mathrm{3}} +\boldsymbol{\mathrm{b}}^{\mathrm{3}} +\boldsymbol{\mathrm{c}}^{\mathrm{3}} =\left(\boldsymbol{\mathrm{abc}}\right)^{\mathrm{2}} \\ $$$$ \\ $$$$ \\ $$$$?????? \\ $$…

if-a-b-c-d-gt-1-then-cyc-log-a-b-3-c-3-d-3-b-2-c-2-d-2-4-

Question Number 156573 by MathSh last updated on 12/Oct/21 $$\mathrm{if}\:\:\:\mathrm{a};\mathrm{b};\mathrm{c};\mathrm{d}>\mathrm{1}\:\:\:\mathrm{then}: \\ $$$$\underset{\boldsymbol{\mathrm{cyc}}} {\sum}\:\mathrm{log}_{\boldsymbol{\mathrm{a}}} \:\left(\frac{\mathrm{b}^{\mathrm{3}} \:+\:\mathrm{c}^{\mathrm{3}} \:+\:\mathrm{d}^{\mathrm{3}} }{\mathrm{b}^{\mathrm{2}} \:+\:\mathrm{c}^{\mathrm{2}} \:+\:\mathrm{d}^{\mathrm{2}} }\right)\:\geqslant\:\mathrm{4} \\ $$ Terms of Service…

Find-the-value-of-x-by-using-Cardon-s-Method-1-x-2-x-1-3-x-2-1-

Question Number 156579 by Mr.D.N. last updated on 12/Oct/21 $$\:\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{by}}\:\boldsymbol{\mathrm{using}}\:\boldsymbol{\mathrm{Cardon}}'\boldsymbol{\mathrm{s}}\:\boldsymbol{\mathrm{Method}}. \\ $$$$\:\:\:\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}}\:+\:\frac{\mathrm{2}}{\boldsymbol{\mathrm{x}}+\mathrm{1}}+\:\frac{\mathrm{3}}{\boldsymbol{\mathrm{x}}+\mathrm{2}}\:=\:\mathrm{1} \\ $$ Answered by mr W last updated on 13/Oct/21 $$\frac{\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)+\mathrm{2}{x}\left({x}+\mathrm{2}\right)+\mathrm{3}{x}\left({x}+\mathrm{1}\right)}{{x}\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)}=\mathrm{1} \\ $$$${x}^{\mathrm{2}}…