Question Number 126079 by amns last updated on 17/Dec/20 $$\boldsymbol{\mathrm{If}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{product}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{three}}\:\boldsymbol{\mathrm{consecutive}}\:\boldsymbol{\mathrm{prime}}\:\boldsymbol{\mathrm{numbers}}\:\boldsymbol{\mathrm{is}}\:\mathrm{7}\:\boldsymbol{\mathrm{times}} \\ $$$$\boldsymbol{\mathrm{their}}\:\boldsymbol{\mathrm{sum}},\:\boldsymbol{\mathrm{what}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{prime}}\:\boldsymbol{\mathrm{number}}\:\boldsymbol{\mathrm{three}}? \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\left[{Ans}.\:{will}\:{be}\:{commented}\:{by}\:{me}\:{after}\:{someone}\:{tried}\:{to}\:{ans}.\:{it}\right] \\ $$ Commented by som(math1967)…
Question Number 191615 by MATHEMATICSAM last updated on 27/Apr/23 $${a}\:+\:{b}\:+\:{c}\:=\:\mathrm{0}.\:\mathrm{Prove}\:\mathrm{that}, \\ $$$$\frac{{a}}{{a}^{\mathrm{2}} \:−\:{bc}}\:+\:\frac{{b}}{{b}^{\mathrm{2}} \:−\:{ca}}\:+\:\frac{{c}}{{c}^{\mathrm{2}} \:−\:{ab}}\:=\:\mathrm{0}. \\ $$ Answered by som(math1967) last updated on 27/Apr/23 $$\:{a}+{b}+{c}=\mathrm{0}…
Question Number 126076 by liberty last updated on 17/Dec/20 $$\:\:\:{y}\left(\mathrm{ln}\:\left(\frac{{y}}{{x}}\right)+\mathrm{1}\right){dx}−{xdy}\:=\:\mathrm{0} \\ $$ Answered by benjo_mathlover last updated on 17/Dec/20 Terms of Service Privacy Policy Contact:…
Question Number 191614 by vishal1234 last updated on 27/Apr/23 $$\frac{\alpha^{\mathrm{100}} +\beta^{\mathrm{100}} }{\alpha^{\mathrm{100}} −\beta^{\mathrm{100}} }\:=\: \\ $$$$\frac{\left(−{w}\right)^{\mathrm{100}} +\left(−{w}^{\mathrm{2}} \right)^{\mathrm{100}} }{\left(−{w}\right)^{\mathrm{100}} −\left(−{w}^{\mathrm{2}} \right)^{\mathrm{100}} } \\ $$$$=\:\frac{{w}^{\mathrm{100}} +{w}^{\mathrm{200}}…
Question Number 191611 by vishal1234 last updated on 27/Apr/23 $${if}\:{x}^{\mathrm{2}} −{x}+\mathrm{1}\:=\:\mathrm{0}\:{and}\:\alpha\:{and}\:\beta\:{are}\:{thd}\:{roots} \\ $$$${of}\:{this}\:{equation}\:{then}\:{evaluate}\:\frac{\alpha^{\mathrm{100}} +\beta^{\mathrm{100}} }{\alpha^{\mathrm{100}} −\beta^{\mathrm{100}} } \\ $$ Answered by mehdee42 last updated on…
Question Number 191610 by mehdee42 last updated on 27/Apr/23 $${Q}:\:{if}\:\:{x}+\frac{\mathrm{1}}{{x}}=\mathrm{2}{cos}\left(\theta\right)\:\:{prove}\:{it}\:\:{x}^{{n}} +\frac{\mathrm{1}}{{x}^{{n}} }=\mathrm{2}{cos}\left({n}\theta\right) \\ $$ Answered by Frix last updated on 27/Apr/23 $${z}+\frac{\mathrm{1}}{{z}}=\mathrm{2}{c}\:\Rightarrow\:{z}={c}\pm\sqrt{{c}^{\mathrm{2}} −\mathrm{1}}\:\Rightarrow \\ $$$${x}=\mathrm{cos}\:\theta\:\pm\mathrm{i}\:\mathrm{sin}\:\theta\:=\mathrm{e}^{\pm\mathrm{i}\theta}…
Question Number 126073 by benjo_mathlover last updated on 17/Dec/20 Commented by benjo_mathlover last updated on 17/Dec/20 $${The}\:{graph}\:{of}\:{the}\:{differentiable}\: \\ $$$${function}\:{g}\:{with}\:{domain}\:−\mathrm{6}\leqslant{x}\leqslant\mathrm{2}\:{is} \\ $$$${shown}\:{in}\:{the}\:{figure}\:{above}.\:{The}\:{areas} \\ $$$${of}\:{the}\:{regions}\:{bounded}\:{by}\:{the}\:{x}−{axis} \\ $$$${and}\:{the}\:{graph}\:{of}\:{g}\:{on}\:{the}\:{intervals}\:\left[−\mathrm{6},−\mathrm{5}\right]…
Question Number 60536 by hovea cw last updated on 21/May/19 $$\mathrm{cosx}=\mathrm{sin3x} \\ $$$$\mathrm{find}\:\mathrm{x}\:\mathrm{with}\:\mathrm{solution}\:\: \\ $$$$\mathrm{pllllllz} \\ $$ Answered by mr W last updated on 21/May/19…
Question Number 126070 by benjo_mathlover last updated on 17/Dec/20 Commented by liberty last updated on 17/Dec/20 $${h}\left({x}\right)=\int_{\mathrm{1}} ^{\:{x}} {f}\left({t}\right)\:{dt}\:\Leftrightarrow\:{h}'\left({x}\right)=\:{f}\left({x}\right) \\ $$$${h}'\left(\mathrm{4}\right)={f}\left(\mathrm{4}\right)=\:\mathrm{2} \\ $$$$ \\ $$…
Question Number 60534 by aliesam last updated on 21/May/19 Commented by maxmathsup by imad last updated on 22/May/19 $${we}\:{have}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{dx}}{\mathrm{1}+{e}^{{x}^{\mathrm{2}} } }\:=\mathrm{2}\:\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{e}^{−{x}^{\mathrm{2}}…