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Category: Algebra

Question-125428

Question Number 125428 by ajfour last updated on 11/Dec/20 Commented by ajfour last updated on 11/Dec/20 $${Find}\:{equation}\:{of}\:{circle}\:{passing} \\ $$$${through}\:\left(\mathrm{1},\mathrm{1}\right)\:{and}\:{P}\:\left({p},{p}^{\mathrm{2}} \right)\:{with} \\ $$$${radius}\:{t}<\mathrm{1}/\mathrm{2}\:.\: \\ $$ Terms…

Question-190947

Question Number 190947 by Shrinava last updated on 15/Apr/23 Answered by mr W last updated on 15/Apr/23 $$\frac{{BD}}{{AB}}=\frac{\mathrm{sin}\:\beta}{\mathrm{sin}\:\mathrm{30}}\:\:\:…\left({i}\right) \\ $$$$\frac{{AB}}{{AC}}=\frac{\mathrm{sin}\:\left(\beta+\mathrm{45}\right)}{\mathrm{sin}\:\mathrm{45}}\:\:\:…\left({ii}\right) \\ $$$$\left({i}\right)×\left({ii}\right): \\ $$$$\mathrm{1}=\frac{\mathrm{sin}\:\beta\:\mathrm{sin}\:\left(\beta+\mathrm{45}\right)}{\mathrm{sin}\:\mathrm{30}\:\mathrm{sin}\:\mathrm{45}} \\…

Question-190938

Question Number 190938 by Shrinava last updated on 14/Apr/23 Answered by Frix last updated on 15/Apr/23 $$\mathrm{tan}\:\mathrm{3}{x}\:−\mathrm{tan}\:{x}\:\mathrm{tan}\:\mathrm{11}{x}\:\mathrm{tan}\:\mathrm{13}{x}\:=\mathrm{0} \\ $$$$\mathrm{We}\:\mathrm{can}\:\mathrm{transform}\:\mathrm{this}\:\mathrm{to} \\ $$$$\mathrm{sin}\:\mathrm{28}{x}\:−\mathrm{sin}\:\mathrm{20}{x}\:+\mathrm{sin}\:\mathrm{4}{x}\:=\mathrm{0} \\ $$$${y}=\mathrm{4}{x} \\ $$$$\mathrm{sin}\:\mathrm{7}{y}\:−\mathrm{sin}\:\mathrm{5}{y}\:+\mathrm{sin}\:{y}\:=\mathrm{0}…

Question-190916

Question Number 190916 by Abdullahrussell last updated on 14/Apr/23 Commented by Rasheed.Sindhi last updated on 14/Apr/23 $$\mathrm{6}{A}+\mathrm{12}{B}+\mathrm{24}{C}=\mathrm{100} \\ $$$$\mathrm{6}\:\mid\:\left(\mathrm{6}{A}+\mathrm{12}{B}+\mathrm{24}{C}\right)\:\wedge\:\mathrm{6}\:\nmid\:\mathrm{100} \\ $$$$\Rightarrow\nexists\:{integer}\:{solution}! \\ $$ Terms of…