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 $$\mathrm{cosh}{x}−\mathrm{sinh}{x}=\frac{\mathrm{1}}{\mathrm{2}}\left(\left({e}^{{x}} +{e}^{−{x}} \right)−\left({e}^{{x}}…
Question Number 178354 by Spillover last updated on 15/Oct/22 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{sinh}\:\mathrm{x}+\mathrm{ncosh}\:\mathrm{x}\:\mathrm{is}\:\sqrt{\mathrm{n}^{\mathrm{2}} −\mathrm{1}} \\ $$$$\mathrm{and}\:\mathrm{this}\:\mathrm{occurs}\:\mathrm{x}=\mathrm{0}.\mathrm{5ln}\:\left(\frac{\mathrm{n}−\mathrm{1}}{\mathrm{n}+\mathrm{1}}\right) \\ $$ Answered by Ar Brandon last updated on 16/Oct/22…
Question Number 178347 by Acem last updated on 15/Oct/22 $${Let}\:{f}\left({x}\right)=\:\left({ax}+\mathrm{1}\right)^{\mathrm{5}} .\left(\mathrm{1}+{bx}\right)^{\mathrm{4}} \:;\:{a},{b}\:\in\:\mathbb{N} \\ $$$$\:{if}\:{times}\:{of}\:{x}\:{equal}\:\mathrm{62}\:{so}\:{what}\:{are}\:{possible}\:{values} \\ $$$$\:{of}\:{the}\:{sum}\:{a},\:{b}? \\ $$$$ \\ $$ Answered by Acem last updated…