Question Number 210858 by hardmath last updated on 20/Aug/24 $$\mathrm{Solve}\:\mathrm{The}\:\mathrm{Equation}: \\ $$$$\left(\mathrm{7x}+\mathrm{1}\right)\left(\mathrm{9x}+\mathrm{1}\right)\left(\mathrm{21x}+\mathrm{1}\right)\left(\mathrm{63x}+\mathrm{1}\right)=\:\frac{\mathrm{160}}{\mathrm{189}} \\ $$ Answered by mm1342 last updated on 20/Aug/24 $$\left(\mathrm{63}{x}+\mathrm{9}\right)\left(\mathrm{63}{x}+\mathrm{7}\right)\left(\mathrm{63}{x}+\mathrm{3}\right)\left(\mathrm{63}{x}+\mathrm{1}\right)=\mathrm{160} \\ $$$$\mathrm{63}{x}+\mathrm{5}={u} \\…
Question Number 210851 by RojaTaniya last updated on 20/Aug/24 Commented by mr W last updated on 21/Aug/24 $${answer}\:=\mathrm{2024}? \\ $$ Answered by A5T last updated…
Question Number 210840 by hardmath last updated on 19/Aug/24 $$ \\ $$Prove that if x, y are rational numbers satisfying the equation x^5 + y^5…
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Question Number 210843 by peter frank last updated on 20/Aug/24 Answered by Spillover last updated on 20/Aug/24 $${let}\:{u},{v}\:{be}\:{a}\:{two}\:{unit}\:{vectors}\:{with}\:{direction} \\ $$$${cosine}\:\left({l}_{\mathrm{1}\:} ,{m}_{\mathrm{1}} ,{n}_{\mathrm{1}} \right)\:{and}\:\left({l}_{\mathrm{2}\:} ,{m}_{\mathrm{2}} ,{n}_{\mathrm{2}}…
Question Number 210842 by peter frank last updated on 20/Aug/24 Answered by mm1342 last updated on 20/Aug/24 $${AB}:{y}−\mathrm{2}{x}=\mathrm{1} \\ $$$${AC}:{y}−{x}=\mathrm{0} \\ $$$${BC}:−\mathrm{3}{y}+{x}=−\mathrm{4} \\ $$$$\Rightarrow{A}\left(−\mathrm{1},−\mathrm{1}\right)\:\&\:{B}\left(\frac{\mathrm{1}}{\mathrm{5}},\frac{\mathrm{7}}{\mathrm{5}}\right)\:\&\:{C}\left(\mathrm{2},\mathrm{2}\right)\Rightarrow{D}\left(\frac{\mathrm{11}}{\mathrm{10}},\frac{\mathrm{17}}{\mathrm{10}}\right) \\…
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Question Number 210789 by peter frank last updated on 19/Aug/24 Answered by mr W last updated on 19/Aug/24 $${Area}\:{of}\:{sector}\:{O}\overset{\frown} {{PQ}}: \\ $$$${A}_{\mathrm{1}} =\frac{\theta}{\mathrm{2}\pi}×\pi{r}^{\mathrm{2}} =\frac{{r}^{\mathrm{2}} \theta}{\mathrm{2}}…
Question Number 210737 by mathlove last updated on 18/Aug/24 $${f}\left({x}\right)=\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{2}} +\mathrm{1}}\:\:\:\:{then} \\ $$$${f}\left(\frac{\mathrm{1}}{\mathrm{1}}\right)+{f}\left(\frac{\mathrm{2}}{\mathrm{1}}\right)+…..+{f}\left(\frac{\mathrm{100}}{\mathrm{1}}\right)+{f}\left(\frac{\mathrm{1}}{\mathrm{2}}\right) \\ $$$$+{f}\left(\frac{\mathrm{2}}{\mathrm{2}}\right)+…+{f}\left(\frac{\mathrm{100}}{\mathrm{2}}\right)+{f}\left(\frac{\mathrm{1}}{\mathrm{100}}\right)+{f}\left(\frac{\mathrm{2}}{\mathrm{100}}\right) \\ $$$$+……+{f}\left(\frac{\mathrm{100}}{\mathrm{100}}\right)=? \\ $$ Answered by mr W last…
Question Number 210767 by lmcp1203 last updated on 18/Aug/24 Commented by Frix last updated on 19/Aug/24 $$\mathrm{35} \\ $$ Commented by lmcp1203 last updated on…