Question Number 178415 by Spillover last updated on 16/Oct/22 $$\mathrm{If}\:\mathrm{acosh}\:\mathrm{x}+\mathrm{bsinh}\:\mathrm{x}=\mathrm{c}\: \\ $$$$\mathrm{show}\:\mathrm{that}. \\ $$$$\mathrm{x}=\mathrm{ln}\:\left[\frac{\mathrm{c}\pm\sqrt{\mathrm{c}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} −\mathrm{a}^{\mathrm{2}} }}{\mathrm{a}+\mathrm{b}}\right] \\ $$ Answered by haladu last updated on…
Question Number 47331 by MJS last updated on 08/Nov/18 $$\mathrm{this}\:\mathrm{remained}\:\mathrm{unsolved}… \\ $$$$\mid{x}−\frac{\mathrm{3}}{\mathrm{4}}\mid×\mid{x}+\frac{\mathrm{5}}{\mathrm{4}}\mid=\mathrm{3};\:{x}\in\mathbb{C} \\ $$ Commented by MJS last updated on 08/Nov/18 $$\mid{a}−\frac{\mathrm{3}}{\mathrm{4}}+{b}\mathrm{i}\mid×\mid{a}+\frac{\mathrm{5}}{\mathrm{4}}+{b}\mathrm{i}\mid=\mathrm{3}\:\mathrm{with}\:{a},\:{b}\:\in\mathbb{R} \\ $$$$\sqrt{\left({a}−\frac{\mathrm{3}}{\mathrm{4}}\right)^{\mathrm{2}} +{b}^{\mathrm{2}}…
Question Number 178400 by infinityaction last updated on 16/Oct/22 $$\:\:\mathrm{evaluate}\:\:\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{k}\:\mathrm{e}^{\mathrm{kx}} \\ $$ Answered by mr W last updated on 16/Oct/22 $${S}=\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{ke}^{{kx}}…
Question Number 178389 by cortano1 last updated on 16/Oct/22 $$\:\:\:\:\:\:\:\:\:\:\:\mathrm{show}\:\mathrm{that}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{p}\Rightarrow\left(\left(\mathrm{p}\Rightarrow\mathrm{q}\right)\Rightarrow\mathrm{q}\right)\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{is}\:\mathrm{tautology}\: \\ $$ Answered by Spillover last updated on 16/Oct/22 Terms of…
Question Number 178374 by depressiveshrek last updated on 16/Oct/22 $${Let}\:{the}\:{points}\:{ABC}\:{form}\:{a}\:{triangle}\:{on}\:{the} \\ $$$${cartesian}\:{plane},\:{whose}\:{area}\:{is}\:\mathrm{20}.\:{Let}\:{the}\:{coordinates} \\ $$$${of}\:{said}\:{points}\:{be}\:{A}\left(\mathrm{8},\:\mathrm{6}\right)\:{B}\left(\mathrm{2},\:\mathrm{4}\right)\:{and}\:{C}\left({x},\:{y}\right) \\ $$$${If}\:\mid{AC}\mid=\mid{BC}\mid,\:{find}\:{the}\:{coordinates}\:{of}\:{point}\:{C}. \\ $$ Answered by Ar Brandon last updated on…
Question Number 47291 by MJS last updated on 07/Nov/18 $$\mathrm{solve}\:\mathrm{for}\:{x}\in\mathbb{C}: \\ $$$$\mid{x}−\frac{\mathrm{3}}{\mathrm{4}}\mid×\mid{x}+\frac{\mathrm{5}}{\mathrm{4}}\mid=\mathrm{3} \\ $$ Answered by MrW3 last updated on 08/Nov/18 $${let}\:{x}+\frac{\mathrm{1}}{\mathrm{4}}={a}+{bi} \\ $$$$\mid{x}−\frac{\mathrm{3}}{\mathrm{4}}\mid×\mid{x}+\frac{\mathrm{5}}{\mathrm{4}}\mid=\mathrm{3} \\…
Question Number 178358 by Spillover last updated on 15/Oct/22 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{when}\:\mathrm{x}\:\mathrm{is}\:\mathrm{small}\: \\ $$$$\mathrm{ln}\:\left(\mathrm{cosh}\:\mathrm{x}\right)\approx\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}}−\frac{\mathrm{x}^{\mathrm{4}} }{\mathrm{12}}+…\:\mathrm{and} \\ $$$$\mathrm{that}\:\mathrm{when}\:\mathrm{x}\:\mathrm{is}\:\mathrm{large}\:\mathrm{ln}\:\left(\mathrm{cosh}\:\mathrm{x}\right)\approx\mathrm{x}−\mathrm{ln}\:\mathrm{2} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 178356 by Spillover last updated on 15/Oct/22 $$\mathrm{Solve}\:\mathrm{simultaneous} \\ $$$$\mathrm{sinh}\:\mathrm{x}+\mathrm{cosh}\:\mathrm{y}=\mathrm{5} \\ $$$$\mathrm{sinh}\:^{\mathrm{2}} \mathrm{x}+\mathrm{cosh}\:^{\mathrm{2}} \mathrm{y}=\mathrm{13} \\ $$ Answered by Ar Brandon last updated on…
Question Number 178357 by Spillover last updated on 15/Oct/22 $$\mathrm{Given}\:\mathrm{that}\:\mathrm{sinh}\:^{−\mathrm{1}} \mathrm{x}=\mathrm{sech}\:^{−\mathrm{1}} \mathrm{x}\:\:\: \\ $$$$\mathrm{show} \\ $$$$\mathrm{x}=\sqrt{\frac{\sqrt{\mathrm{5}}−\mathrm{1}}{\mathrm{2}}\:} \\ $$ Answered by Ar Brandon last updated on…
Question Number 178355 by Spillover last updated on 15/Oct/22 $$\mathrm{Show}\:\mathrm{that}\: \\ $$$$\mathrm{cosh}\:\mathrm{x}>\mathrm{sinh}\:\mathrm{x} \\ $$ Answered by Ar Brandon last updated on 16/Oct/22 $$\mathrm{cosh}{x}−\mathrm{sinh}{x}=\frac{\mathrm{1}}{\mathrm{2}}\left(\left({e}^{{x}} +{e}^{−{x}} \right)−\left({e}^{{x}}…