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Category: Algebra

Solve-the-equation-x-2-dy-dx-y-x-2-3-given-y-10-when-x-4-4-1-2026-

Question Number 227174 by Spillover last updated on 04/Jan/26 $${Solve}\:{the}\:{equation} \\ $$$$\left(\boldsymbol{{x}}−\mathrm{2}\right)\frac{\boldsymbol{{dy}}}{\boldsymbol{{dx}}}−\boldsymbol{{y}}=\left(\boldsymbol{{x}}−\mathrm{2}\right)^{\mathrm{3}} \\ $$$$\boldsymbol{{given}}\:\boldsymbol{{y}}=\mathrm{10}\:\:\boldsymbol{{when}}\:\boldsymbol{{x}}=\mathrm{4}. \\ $$$$\mathrm{4}/\mathrm{1}/\mathrm{2026} \\ $$ Answered by AgniMath last updated on 04/Jan/26…

prove-i-1-n-i-sin-1-i-gt-1-n-n-1-

Question Number 227115 by MrAjder last updated on 01/Jan/26 $$\mathrm{prove}:\underset{{i}=\mathrm{1}} {\overset{{n}} {\prod}}{i}\:\mathrm{sin}\frac{\mathrm{1}}{{i}}>\frac{\mathrm{1}}{{n}\left({n}+\mathrm{1}\right)} \\ $$ Answered by MrAjder last updated on 01/Jan/26 $$\forall{i}\in\mathbb{Z}^{+} ,\mathrm{0}<\frac{\mathrm{1}}{{i}}\leq\mathrm{1}\Rightarrow\mathrm{sin}\frac{\mathrm{1}}{{i}}>\frac{\mathrm{1}}{{i}}−\frac{\mathrm{1}}{\mathrm{6}{i}^{\mathrm{3}} }\Rightarrow{i}\:\mathrm{sin}\frac{\mathrm{1}}{{i}}>\mathrm{1}−\frac{\mathrm{1}}{\mathrm{6}{i}^{\mathrm{2}} }…

2025-2026-2027-2026-1-3-

Question Number 227124 by BaliramKumar last updated on 01/Jan/26 $$\sqrt[{\mathrm{3}}]{\mathrm{2025}×\mathrm{2026}×\mathrm{2027}\:+\:\mathrm{2026}}\:=\:?\:\:\:\:\:\:\: \\ $$ Answered by TonyCWX last updated on 01/Jan/26 $$\sqrt[{\mathrm{3}}]{\left({x}−\mathrm{1}\right)\left({x}\right)\left({x}+\mathrm{1}\right)+{x}} \\ $$$$=\:\sqrt[{\mathrm{3}}]{{x}^{\mathrm{3}} −{x}+{x}} \\ $$$$=\:\sqrt[{\mathrm{3}}]{{x}^{\mathrm{3}}…

Question-227085

Question Number 227085 by Rojarani last updated on 29/Dec/25 Commented by mr W last updated on 30/Dec/25 $${to}\:{wabi}\:{sir}: \\ $$$${please}\:{don}'{t}\:{put}\:{your}\:{new}\:{question} \\ $$$${as}\:{comment}\:{to}\:{an}\:{other}\:{question}! \\ $$$${please}\:{post}\:{it}\:{as}\:{new}\:{question}! \\…

Velocity-v-time-t-and-displacement-x-of-a-particle-are-in-the-relation-1-t-3-v-3t-2-x-4t-If-at-t-0-x-1-m-then-find-displacement-at-t-1-s-

Question Number 227034 by AgniMath last updated on 27/Dec/25 $$\mathrm{Velocity}\:\left({v}\right),\:\mathrm{time}\:\left({t}\right)\:\mathrm{and}\:\mathrm{displacement} \\ $$$$\left({x}\right)\:\mathrm{of}\:\mathrm{a}\:\mathrm{particle}\:\mathrm{are}\:\mathrm{in}\:\mathrm{the}\:\mathrm{relation} \\ $$$$\left(\mathrm{1}\:+\:{t}^{\mathrm{3}} \right){v}\:+\:\mathrm{3}{t}^{\mathrm{2}} {x}\:=\:\mathrm{4}{t}.\:\mathrm{If}\:\mathrm{at}\:{t}\:=\:\mathrm{0},\:{x}\:=\:\mathrm{1}\:\mathrm{m} \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{displacement}\:\mathrm{at}\:{t}\:=\:\mathrm{1}\:\mathrm{s}. \\ $$ Commented by fantastic2 last updated…