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Category: Algebra

There-are-128-players-in-the-first-round-of-a-knockout-competition-Half-of-the-players-were-knocked-out-in-each-round-How-many-players-took-part-in-the-fourth-round-How-many-rounds-were-there-in-th

Question Number 57513 by pete last updated on 06/Apr/19 $$\mathrm{There}\:\mathrm{are}\:\mathrm{128}\:\mathrm{players}\:\mathrm{in}\:\mathrm{the}\:\mathrm{first}\:\mathrm{round} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{knockout}\:\mathrm{competition}.\:\mathrm{Half}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{players}\:\mathrm{were}\:\mathrm{knocked}\:\mathrm{out}\:\mathrm{in}\:\mathrm{each}\:\mathrm{round}. \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{players}\:\mathrm{took}\:\mathrm{part}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{fourth}\:\mathrm{round}?\:\mathrm{How}\:\mathrm{many}\:\mathrm{rounds}\:\mathrm{were}\:\mathrm{there} \\ $$$$\mathrm{in}\:\mathrm{this}\:\mathrm{competion}? \\ $$ Commented by mr…

Question-123024

Question Number 123024 by aupo14 last updated on 21/Nov/20 Answered by Olaf last updated on 21/Nov/20 $$\mathrm{We}\:\mathrm{can}\:\mathrm{easily}\:\mathrm{find}\:\mathrm{the}\:\mathrm{solution}\:{x}\:=\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\mathrm{and}\:\mathrm{by}\:\mathrm{plotting}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{we}\:\mathrm{verify} \\ $$$$\mathrm{there}\:\mathrm{are}\:\mathrm{no}\:\mathrm{more}\:\mathrm{solutions}. \\ $$ Terms of…

Question-123025

Question Number 123025 by ajfour last updated on 21/Nov/20 Commented by ajfour last updated on 22/Nov/20 $${If}\:\alpha,\:\beta,\:\gamma\:{are}\:{roots}\:{of}\:{cubic}\:{eq}. \\ $$$${x}^{\mathrm{3}} −{x}−{c}\:=\mathrm{0}\:\:\:\left(\mathrm{0}<{c}<\frac{\mathrm{2}}{\mathrm{3}\sqrt{\mathrm{3}}}\right)\:;\:{wirh}\:{the} \\ $$$${help}\:{of}\:{suitable}\:{p}\:,\:{find}\:\alpha. \\ $$ Commented…

if-F-x-y-F-y-x-and-x-y-c-constant-prove-that-F-max-or-min-F-c-2-c-2-

Question Number 57480 by mr W last updated on 05/Apr/19 $${if}\:{F}\left({x},{y}\right)={F}\left({y},{x}\right)\:{and}\:{x}+{y}={c}\:\left({constant}\right) \\ $$$${prove}\:{that}\:{F}_{{max}\:{or}\:{min}} ={F}\left(\frac{{c}}{\mathrm{2}},\frac{{c}}{\mathrm{2}}\right). \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 07/Apr/19 $${what}\:{is}\:{the}\:{difference}\:{between}\:{F}\left({x},{y}\right)\:{and}\:{F}\left({y},{x}\right) \\…

solve-the-equation-x-y-z-5-z-yx-7-z-1-x-x-y-z-

Question Number 188536 by normans last updated on 03/Mar/23 $$ \\ $$$$\:\:\:\:\boldsymbol{{solve}}\:\boldsymbol{{the}}\:\boldsymbol{{equation}}; \\ $$$$\:\:\:\:\:\:\:\left.\begin{matrix}{\boldsymbol{{x}}\:+\:\boldsymbol{{y}}\:−\:\boldsymbol{{z}}\:=\mathrm{5}}\\{\boldsymbol{{z}}\:−\:\boldsymbol{{yx}}\:=\:\mathrm{7}}\\{\boldsymbol{{z}}\:=\:\mathrm{1}\:+\:\boldsymbol{{x}}}\end{matrix}\right\}\:\:\boldsymbol{{x}};\boldsymbol{{y}};\boldsymbol{{z}}\:=??\:\:\:\:\:\: \\ $$$$ \\ $$ Answered by Rasheed.Sindhi last updated on 03/Mar/23…

Question-188535

Question Number 188535 by Rupesh123 last updated on 03/Mar/23 Answered by mr W last updated on 03/Mar/23 $${due}\:{to}\:{symmetry} \\ $$$${at}\:{extremum} \\ $$$${a}={b}={c}={x}>\mathrm{0} \\ $$$${S}=\frac{\mathrm{3}\left({x}+\mathrm{1}\right)^{\mathrm{3}} }{{x}}=\frac{\mathrm{3}\left({x}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}\right)}{{x}}…

in-AB-C-a-3-b-6-c-7-find-the-value-of-E-a-b-cos-C-b-c-cos-A-a-c-cos-B-

Question Number 188515 by mnjuly1970 last updated on 02/Mar/23 $$ \\ $$$$\:\:\:\:\:{in}\:\:{A}\overset{\Delta} {{B}C}\:\::\:\:\:{a}=\mathrm{3}\:\:,\:\:{b}=\mathrm{6}\:\:,\:\:{c}=\mathrm{7} \\ $$$$\:\:\: \\ $$$$\: \\ $$$$\:\:\:\:{find}\:\:{the}\:{value}\:\:{of}\:: \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:\:{E}\:=\:\left({a}+{b}\:\right){cos}\left({C}\right)\:+\:\left({b}+{c}\right){cos}\left({A}\right)+\:\left({a}+{c}\:\right){cos}\left({B}\right)=?\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:…