Question Number 153508 by mathdanisur last updated on 07/Sep/21 Answered by maged last updated on 08/Sep/21 $${x}=\mathrm{2},{y}=\mathrm{2},{z}=\mathrm{2}\Rightarrow\mathrm{2}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} =\mathrm{12} \\ $$$${S}_{{min}} =\mathrm{2}+\mathrm{2}+\mathrm{2}+\mathrm{8}+\frac{\mathrm{1}}{\mathrm{4}+\mathrm{4}+\mathrm{4}} \\ $$$${S}_{{min}}…
Question Number 153505 by mathdanisur last updated on 07/Sep/21 Commented by MJS_new last updated on 08/Sep/21 $$\sqrt[{\mathrm{3}}]{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{5}}−\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{5}}=\mathrm{5}\:\mathrm{has}\:\mathrm{no}\:\mathrm{solution}\:\in\mathbb{C} \\ $$ Answered by…
Question Number 153500 by Engr_Jidda last updated on 07/Sep/21 $${Evaluate}\:{the}\:{line}\:{integral}\:{space} \\ $$$${if}\:{f}\left({r}\right)={Zi}+{Xj}+{Yk}\:{and}\:{C}\:{is}\:{a}\:{helix} \\ $$$${given}\:{by}\:{C}:\:{r}\left({t}\right)=\left({cost},{sint},−\mathrm{3}{t}\right)\:\:\mathrm{0}\leqslant{t}\leqslant\mathrm{2}\pi \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 22423 by Tinkutara last updated on 17/Oct/17 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{no}\:\mathrm{three}\:\mathrm{consecutive} \\ $$$$\mathrm{binomial}\:\mathrm{coefficient}\:\mathrm{can}\:\mathrm{be}\:\mathrm{in}\:\mathrm{G}.\mathrm{P}.\:\mathrm{or}\:\mathrm{H}.\mathrm{P}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 22392 by Tinkutara last updated on 17/Oct/17 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{odd}\:\mathrm{coefficients} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{1}\:+\:\mathrm{2}{x}\:−\:\mathrm{3}{x}^{\mathrm{2}} \right)^{\mathrm{1025}} \\ $$$$\mathrm{is}\:\mathrm{an}\:\mathrm{even}\:\mathrm{integer}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 22394 by Tinkutara last updated on 17/Oct/17 $$\mathrm{Prove}\:\mathrm{that}\::\:\frac{\:^{{n}} {C}_{\mathrm{0}} }{{n}}−\frac{\:^{{n}} {C}_{\mathrm{1}} }{{n}+\mathrm{1}}+\frac{\:^{{n}} {C}_{\mathrm{2}} }{{n}+\mathrm{2}}−…+\left(−\mathrm{1}\right)^{{n}} .\frac{\:^{{n}} {C}_{{n}} }{\mathrm{2}{n}}=\frac{\mathrm{1}}{{n}.^{\mathrm{2}{n}} {C}_{{n}} } \\ $$ Terms of…
Question Number 22389 by Tinkutara last updated on 17/Oct/17 $${Simplify}: \\ $$$$\:^{{n}−\mathrm{1}} {C}_{\mathrm{2}} +\mathrm{2}\:^{{n}−\mathrm{2}} {C}_{\mathrm{2}} +\mathrm{3}\:^{{n}−\mathrm{3}} {C}_{\mathrm{2}} +…+\left({n}−\mathrm{2}\right)\:^{\mathrm{2}} {C}_{\mathrm{2}} \\ $$ Terms of Service Privacy…
Question Number 22379 by Tinkutara last updated on 16/Oct/17 $$\mathrm{For}\:\mathrm{each}\:\mathrm{positive}\:\mathrm{integer}\:{n},\:\mathrm{define}\:{a}_{{n}} \:= \\ $$$$\mathrm{20}\:+\:{n}^{\mathrm{2}} ,\:\mathrm{and}\:{d}_{{n}} \:=\:{gcd}\left({a}_{{n}} ,\:{a}_{{n}+\mathrm{1}} \right).\:\mathrm{Find} \\ $$$$\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{all}\:\mathrm{values}\:\mathrm{that}\:\mathrm{are}\:\mathrm{taken}\:\mathrm{by} \\ $$$${d}_{{n}} \:\mathrm{and}\:\mathrm{show}\:\mathrm{by}\:\mathrm{examples}\:\mathrm{that}\:\mathrm{each}\:\mathrm{of} \\ $$$$\mathrm{these}\:\mathrm{values}\:\mathrm{are}\:\mathrm{attained}. \\…
Question Number 153450 by liberty last updated on 07/Sep/21 $$\begin{cases}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} ={x}+{y}+\mathrm{2}}\\{\left({y}+\mathrm{1}\right)^{\mathrm{2}} ={y}+{z}+\mathrm{2}}\\{\left({z}+\mathrm{1}\right)^{\mathrm{2}} ={z}+{x}+\mathrm{2}}\end{cases} \\ $$ Answered by EDWIN88 last updated on 07/Sep/21 Commented by Tawa11…
Question Number 153446 by mathdanisur last updated on 07/Sep/21 $$\mathrm{L}^{−\mathrm{1}} \left\{\frac{\mathrm{s}}{\mathrm{s}^{\mathrm{2}} \:-\:\mathrm{12s}\:+\:\mathrm{40}}\right\}\:=\:? \\ $$ Commented by alisiao last updated on 07/Sep/21 $$=\:{L}^{−\mathrm{1}} \:\left\{\frac{\left({s}−\mathrm{6}\right)}{\left({s}−\mathrm{6}\right)^{\mathrm{2}} +\mathrm{4}}\:+\:\frac{\mathrm{6}}{\left({s}−\mathrm{6}\right)^{\mathrm{2}} +\mathrm{4}}\right\}…