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Category: Algebra

6-6-6-6-6-2-6-6-6-3-6-6-6-1000-6-

Question Number 165309 by cortano1 last updated on 29/Jan/22 $$\:\frac{\mathrm{6}}{\mathrm{6}+\sqrt{\mathrm{6}}}\:+\:\frac{\mathrm{6}}{\mathrm{6}^{\mathrm{2}} +\sqrt{\mathrm{6}}}\:+\frac{\mathrm{6}}{\mathrm{6}^{\mathrm{3}} +\sqrt{\mathrm{6}}}\:+…+\frac{\mathrm{6}}{\mathrm{6}^{\mathrm{1000}} +\sqrt{\mathrm{6}}}\:=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question-165291

Question Number 165291 by HongKing last updated on 28/Jan/22 Answered by mahdipoor last updated on 29/Jan/22 $$\frac{{sin}\rho+{cos}\varphi}{{sin}\varphi+{cos}\rho}=\frac{{sin}\rho+{cos}\left(\mathrm{90}−\left(\theta+\rho\right)\right)}{{sin}\left(\mathrm{90}−\left(\theta+\rho\right)\right)+{cos}\rho}= \\ $$$$\frac{{sin}\rho+{sin}\left(\theta+\rho\right)}{{cos}\left(\theta+\rho\right)+{cos}\rho}=\frac{\mathrm{2}{sin}\left(\rho+\frac{\theta}{\mathrm{2}}\right){cos}\left(\frac{\theta}{\mathrm{2}}\right)}{\mathrm{2}{cos}\left(\rho+\frac{\theta}{\mathrm{2}}\right){cos}\left(\frac{\theta}{\mathrm{2}}\right)}= \\ $$$${tan}\left(\rho+\frac{\theta}{\mathrm{2}}\right)={k} \\ $$ Commented by…

A-wire-that-is-highly-insulated-has-a-radius-of-2-1-mm-and-a-current-of-6-Agoes-through-it-The-material-used-in-insulation-has-thickness-of-2-1-mm-with-a-thermal-conductivity-of-0-2-W-Km-the-materia

Question Number 99744 by Rio Michael last updated on 23/Jun/20 $$\mathrm{A}\:\mathrm{wire}\:\mathrm{that}\:\mathrm{is}\:\mathrm{highly}\:\mathrm{insulated}\:\mathrm{has}\:\mathrm{a}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{2}.\mathrm{1}\:\mathrm{mm}\:\mathrm{and}\:\mathrm{a}\:\mathrm{current} \\ $$$$\mathrm{of}\:\mathrm{6}\:\mathrm{Agoes}\:\mathrm{through}\:\mathrm{it}.\:\mathrm{The}\:\mathrm{material}\:\mathrm{used}\:\mathrm{in}\:\mathrm{insulation}\:\mathrm{has}\:\mathrm{thickness} \\ $$$$\mathrm{of}\:\mathrm{2}.\mathrm{1}\:\mathrm{mm}\:\mathrm{with}\:\mathrm{a}\:\mathrm{thermal}\:\mathrm{conductivity}\:\mathrm{of}\:\mathrm{0}.\mathrm{2}\:\mathrm{W}/\mathrm{Km}.\:\mathrm{the}\:\mathrm{material}\:\mathrm{used} \\ $$$$\mathrm{in}\:\mathrm{constructing}\:\mathrm{the}\:\mathrm{wire}\:\mathrm{has}\:\mathrm{a}\:\mathrm{resistivity}\:\mathrm{of}\:\mathrm{4}.\mathrm{2}\:×\:\mathrm{10}^{−\mathrm{7}} \Omega\mathrm{m}.\:\mathrm{assume}\:\mathrm{the}\: \\ $$$$\mathrm{the}\:\mathrm{materials}\:\mathrm{reach}\:\mathrm{steady}\:\mathrm{state}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{difference}\:\mathrm{in}\:\mathrm{temperature} \\ $$$$\mathrm{between}\:\mathrm{the}\:\mathrm{outer}\:\mathrm{suface}\:\mathrm{and}\:\mathrm{inner}\:\mathrm{surface}. \\ $$ Answered…

Find-the-value-of-x-5x-5x-5-5-5-5x-555x-55x-5-5-5-x-555555555555555-proof-z-a-

Question Number 165243 by Zaynal last updated on 28/Jan/22 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\lfloor\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{{x}}???\rfloor \\ $$$$\:\:\:\lfloor\mathrm{5}\boldsymbol{{x}}\:+\:\frac{\mathrm{5}\boldsymbol{{x}}}{\left(\mathrm{5}\:+\:\mathrm{5}\right)^{\mathrm{5}} }\:×\:\left(−\mathrm{5}\boldsymbol{{x}}\right)\:\boldsymbol{\div}\:\mathrm{555}\boldsymbol{{x}}\:−\mathrm{55}\boldsymbol{{x}}\:×\frac{\mathrm{5}\boldsymbol{\div}\mathrm{5}}{\mathrm{5}}\:\:+\:\boldsymbol{{x}}\:=\:\mathrm{555555555555555}\rfloor \\ $$$$\:^{\mathrm{proof}:\mathrm{z}.\mathrm{a}} \\ $$ Answered by alephzero last updated on 28/Jan/22 $$\mathrm{5}{x}+\frac{\mathrm{5}{x}}{\left(\mathrm{5}+\mathrm{5}\right)^{\mathrm{5}}…