Question Number 203414 by professorleiciano last updated on 18/Jan/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 203378 by Calculusboy last updated on 18/Jan/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 203379 by York12 last updated on 18/Jan/24 $$\mathrm{If}\:{a},{b},{c}\:\in\mathbb{R}^{+} \:\mathrm{with}\:{a}+{b}+{c}=\mathrm{3}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{{a}^{\mathrm{6}} +{b}^{\mathrm{6}} +\mathrm{3}{c}^{\mathrm{3}} +\mathrm{4}}+\frac{\mathrm{1}}{{b}^{\mathrm{6}} +{c}^{\mathrm{6}} +\mathrm{3}{a}^{\mathrm{3}} +\mathrm{4}}+\frac{\mathrm{1}}{{c}^{\mathrm{6}} +{a}^{\mathrm{6}} +\mathrm{3}{b}^{\mathrm{3}} +\mathrm{4}}\leqslant\frac{\mathrm{3}}{\mathrm{3}+\mathrm{2}\left(\sqrt{{ab}}+\sqrt{{bc}}+\sqrt{{ac}}\right)} \\ $$ Terms…
Question Number 203401 by cherokeesay last updated on 18/Jan/24 Answered by MM42 last updated on 18/Jan/24 $$<{B}=\mathrm{30}^{{o}} \\ $$$${AB}=\mathrm{2}\sqrt{\mathrm{3}}×{cos}\mathrm{30}=\mathrm{3} \\ $$$${R}=\sqrt{\mathrm{21}} \\ $$$${EC}=\mathrm{2}\sqrt{\mathrm{3}}×{cos}\mathrm{60}=\sqrt{\mathrm{3}} \\ $$$${r}=\sqrt{\mathrm{3}}×{tan}\mathrm{30}\Rightarrow{r}=\mathrm{1}…
Question Number 203396 by Harkoriola last updated on 19/Jan/24 $$\mathrm{State}\:\mathrm{the}\:\mathrm{completness}\:\mathrm{axioms}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{real}\:\mathrm{number} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 203424 by Calculusboy last updated on 18/Jan/24 Answered by Rasheed.Sindhi last updated on 19/Jan/24 $${x}+{y}=\mathrm{2}^{{x}−{y}} \:…\left({i}\right) \\ $$$$\left({x}+{y}\right)^{{x}−{y}} =\mathrm{2}…\left({ii}\right) \\ $$$$\left({ii}\right)/\left({i}\right):\:\left({x}+{y}\right)^{{x}−{y}−\mathrm{1}} =\mathrm{2}^{\mathrm{1}−{x}+{y}} \\…
Question Number 203392 by professorleiciano last updated on 18/Jan/24 Commented by a.lgnaoui last updated on 19/Jan/24 Commented by a.lgnaoui last updated on 20/Jan/24 $$\bigtriangleup\boldsymbol{\mathrm{OAB}}\:\:\:\boldsymbol{\mathrm{a}}^{\mathrm{2}} =\mathrm{41}−\mathrm{40cos}\:\boldsymbol{\mathrm{x}}…
Question Number 203393 by professorleiciano last updated on 18/Jan/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 203394 by professorleiciano last updated on 18/Jan/24 Answered by som(math1967) last updated on 18/Jan/24 $$\frac{\bigtriangleup{BPQ}}{\bigtriangleup{ABC}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\Rightarrow\frac{{BQ}}{{BC}}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}} \\ $$$$\Rightarrow\frac{{BQ}}{\mathrm{2}}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\Rightarrow{BQ}=\frac{\mathrm{2}}{\:\sqrt{\mathrm{2}}}=\sqrt{\mathrm{2}}\:{cm} \\ $$ Terms of…
Question Number 203357 by Calculusboy last updated on 17/Jan/24 $$\boldsymbol{{For}}\:\boldsymbol{{the}}\:\boldsymbol{{series}}\:\mathrm{5}−\frac{\mathrm{5}}{\mathrm{2}}+\frac{\mathrm{5}}{\mathrm{4}}−\frac{\mathrm{5}}{\mathrm{8}}+\centerdot\centerdot\centerdot+\frac{\left(−\mathrm{1}\right)^{\boldsymbol{{n}}−\mathrm{1}} \mathrm{5}}{\mathrm{2}^{\boldsymbol{{n}}−\mathrm{1}} } \\ $$$$\boldsymbol{{find}}\:\boldsymbol{{an}}\:\boldsymbol{{expression}}\:\boldsymbol{{for}}\:\boldsymbol{{the}}\:\boldsymbol{{sum}}\:\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{first}} \\ $$$$\boldsymbol{{n}}\:\boldsymbol{{terms}}.\:\boldsymbol{{Also}}\:\boldsymbol{{if}}\:\boldsymbol{{the}}\:\boldsymbol{{series}}\:\boldsymbol{{converges}}, \\ $$$$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{sum}}\:\boldsymbol{{to}}\:\infty. \\ $$$$ \\ $$$$ \\ $$ Answered…