Question Number 41921 by Tawa1 last updated on 15/Aug/18 $$\mathrm{Find}\:\mathrm{x}\::\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{625}^{\mathrm{x}\:−\:\mathrm{5}} \:=\:\mathrm{200}\left(\sqrt{\mathrm{x}}\right)^{\mathrm{3}} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 15/Aug/18 $$\left(\mathrm{5}^{\mathrm{4}} \right)^{{x}−\mathrm{5}} =\mathrm{5}^{\mathrm{2}} ×\mathrm{2}^{\mathrm{3}} ×{x}^{\frac{\mathrm{3}}{\mathrm{2}}}…
Question Number 107454 by Rio Michael last updated on 10/Aug/20 $$\mathrm{Given}\:\mathrm{the}\:\mathrm{function}\:{f}\left({x}\right)\:=\:\frac{{x}\:+\:\mathrm{3}}{{x}−\mathrm{2}}\:\mathrm{and}\:\mathrm{g}\left({x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}}{xe}^{{x}} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{centre}\:\mathrm{of}\:\mathrm{symmetry}\:\mathrm{of}\:{f}. \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Define}\:\mathrm{the}\:\mathrm{monotony}\:\mathrm{of}\:\mathrm{g}\:\mathrm{and}\:\mathrm{if}\:\mathrm{possible}\:\mathrm{draw}\:\mathrm{a}\:\mathrm{variation} \\ $$$$\mathrm{table}\:\mathrm{for}\:\mathrm{g}\left({x}\right). \\ $$$$\left(\mathrm{3}\right)\:\mathrm{Sketch}\:\mathrm{the}\:\mathrm{function}\:\mathrm{g}\left({x}\right) \\ $$$$\left(\mathrm{4}\right)\:\mathrm{determine}\:\mathrm{if}\:{f}\:\mathrm{and}\:\mathrm{g}\:\mathrm{intersect}. \\ $$ Answered by…
Question Number 172984 by dragan91 last updated on 04/Jul/22 Answered by Mathspace last updated on 04/Jul/22 $$\Upsilon_{\mathrm{1}} +\Upsilon_{\mathrm{2}} =\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\sqrt{{x}}+\sqrt{{x}+\mathrm{1}}\right)\left(\sqrt{{x}}−\sqrt{{x}+\mathrm{1}}\right){dx} \\ $$$$=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({x}−{x}−\mathrm{1}\right){dx}…
Question Number 41912 by pieroo last updated on 15/Aug/18 $$\mathrm{The}\:\mathrm{estimated}\:\mathrm{time}\:\mathrm{for}\:\mathrm{Abu}\:\mathrm{and}\:\mathrm{Ali}\:\mathrm{to}\:\mathrm{repair}\:\mathrm{a} \\ $$$$\mathrm{faulty}\:\mathrm{car}\:\mathrm{is}\:\mathrm{six}\:\mathrm{hours}.\:\mathrm{If}\:\mathrm{Abu}\:\mathrm{used}\:\mathrm{10}\:\mathrm{hours}\:\mathrm{to} \\ $$$$\mathrm{repair}\:\mathrm{the}\:\mathrm{car},\:\mathrm{how}\:\mathrm{many}\:\mathrm{hours}\:\mathrm{will}\:\mathrm{Ali}\:\mathrm{use}\:\mathrm{to}\:\mathrm{repair} \\ $$$$\mathrm{the}\:\mathrm{car}? \\ $$ Answered by MJS last updated on 15/Aug/18…
Question Number 107438 by lalitchand last updated on 10/Aug/20 Answered by mr W last updated on 10/Aug/20 $${x}\left(\frac{\mathrm{1}}{{n}+{p}}+\frac{\mathrm{1}}{{p}+{m}}+\frac{\mathrm{1}}{{m}+{n}}\right)=\mathrm{3}+\frac{{m}}{{n}+{p}}+\frac{{n}}{{p}+{m}}+\frac{{p}}{{m}+{n}} \\ $$$$\Rightarrow{x}=\frac{\mathrm{3}+\frac{{m}}{{n}+{p}}+\frac{{n}}{{p}+{m}}+\frac{{p}}{{m}+{n}}}{\frac{\mathrm{1}}{{n}+{p}}+\frac{\mathrm{1}}{{p}+{m}}+\frac{\mathrm{1}}{{m}+{n}}} \\ $$ Terms of Service…
Question Number 172956 by dragan91 last updated on 03/Jul/22 Commented by Shrinava last updated on 04/Jul/22 $$\mathrm{say}:\:\mathrm{m}=\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{2} \\ $$$$\mathrm{ab}+\mathrm{ac}+\mathrm{bc}=\frac{\mathrm{4}−\mathrm{n}^{\mathrm{2}} }{\mathrm{3}}\geqslant\mathrm{0} \\ $$$$\mathrm{k}=\mathrm{abc} \\ $$$$…\Leftrightarrow\mathrm{k}\leqslant\frac{\mathrm{2}\left(\mathrm{n}−\mathrm{2}\right)\left(\mathrm{n}+\mathrm{2}\right)}{\mathrm{25}+\mathrm{2n}^{\mathrm{2}} }…
Question Number 172948 by Mikenice last updated on 03/Jul/22 Commented by Rasheed.Sindhi last updated on 03/Jul/22 $$\left.{x}+{y}=\mathrm{5}\:\:\:\:\::\right) \\ $$ Commented by Shrinava last updated on…
Question Number 41879 by Tawa1 last updated on 14/Aug/18 $$\mathrm{If}\:\mathrm{a}\:\mathrm{fraction}\:\mathrm{is}\:\mathrm{added}\:\mathrm{to}\:\mathrm{its}\:\mathrm{denominator}\:,\:\:\mathrm{it}\:\mathrm{reduces}\:\mathrm{to}\:\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{and}\: \\ $$$$\mathrm{when}\:\mathrm{the}\:\mathrm{same}\:\mathrm{fraction}\:\mathrm{added}\:\mathrm{to}\:\mathrm{numerator},\:\mathrm{it}\:\mathrm{also}\:\mathrm{reduces}\:\mathrm{to}\:\frac{\mathrm{2}}{\mathrm{3}} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{fraction} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{square}\:\mathrm{root}\:\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{result}\:\mathrm{of}\:\mathrm{the}\:\mathrm{fraction}\:\mathrm{is}\:\mathrm{less} \\ $$$$\mathrm{than}\:\mathrm{1} \\ $$$$ \\ $$ Answered by tanmay.chaudhury50@gmail.com…
Question Number 41877 by Tawa1 last updated on 14/Aug/18 $$\mathrm{The}\:\mathrm{tens}\:\mathrm{digit}\:\mathrm{of}\:\mathrm{a}\:\mathrm{two}\:\mathrm{digit}\:\mathrm{number}\:\mathrm{is}\:\mathrm{3}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{the}\:\mathrm{units}\:\mathrm{digit}. \\ $$$$\mathrm{When}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{are}\:\mathrm{reversed},\:\mathrm{the}\:\mathrm{number}\:\mathrm{is}\:\mathrm{reduced}\:\mathrm{by}\:\mathrm{27}. \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{number}\:? \\ $$ Answered by MrW3 last updated on 14/Aug/18 $${let}'{s}\:{say}\:{the}\:{number}\:{is}\:{ab} \\…
Question Number 172947 by Mikenice last updated on 03/Jul/22 Answered by Rasheed.Sindhi last updated on 03/Jul/22 $$\mathrm{5}^{{x}−\mathrm{2}} =\frac{\mathrm{125}^{{x}−\mathrm{1}} }{\mathrm{5}^{{x}+\mathrm{2}} } \\ $$$$\mathrm{5}^{{x}−\mathrm{2}} \centerdot\mathrm{5}^{{x}+\mathrm{2}} =\left(\mathrm{5}^{\mathrm{3}} \right)^{{x}−\mathrm{1}}…