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Category: Algebra

find-such-a-polynomial-if-is-divided-by-x-2-then-the-remainder-is-5-if-it-isdivided-by-x-3-the-remainder-is-9-if-it-is-divided-by-x-4-the-remainder-is-13-if-divide-by-x-10-and-the-remaid

Question Number 94818 by student work last updated on 21/May/20 $$\:\mathrm{find}\:\mathrm{such}\:\mathrm{a}\:\mathrm{polynomial}\:\mathrm{if}\:\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\left(\mathrm{x}−\mathrm{2}\right)\:\mathrm{then}\:\mathrm{the}\: \\ $$$$\mathrm{remainder}\:\mathrm{is}\:\mathrm{5},\:\mathrm{if}\:\mathrm{it}\:\mathrm{isdivided}\:\mathrm{by}\:\left(\mathrm{x}−\mathrm{3}\right)\:\mathrm{the}\:\mathrm{remainder} \\ $$$$\mathrm{is}\:\mathrm{9},\:\mathrm{if}\:\mathrm{it}\:\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\left(\mathrm{x}−\mathrm{4}\right)\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{is}\:\mathrm{13},\:\mathrm{if}\: \\ $$$$\mathrm{divide}\:\mathrm{by}\:\left(\mathrm{x}−\mathrm{10}\right)\:\mathrm{and}\:\mathrm{the}\:\mathrm{remaider}\:\mathrm{becomes}\:\mathrm{37}\:\mathrm{and} \\ $$$$\mathrm{if}\:\left(\mathrm{x}−\frac{\mathrm{3}}{\mathrm{4}}\right)\:\mathrm{divided}\:\mathrm{by}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{becomes}\:\mathrm{zero}? \\ $$ Commented by Rasheed.Sindhi last…

dx-x-x-2-3-

Question Number 94811 by Abdulrahman last updated on 21/May/20 $$\int\frac{\mathrm{dx}}{\mathrm{x}+\sqrt{\mathrm{x}}}\:\:\:\left(\mathrm{2},\mathrm{3}\right)=? \\ $$ Answered by ElOuafi last updated on 21/May/20 $$\int\frac{{dx}}{{x}+\sqrt{{x}}}=\int\frac{{dx}}{\:\sqrt{{x}}\left(\sqrt{{x}}+\mathrm{1}\right)}=\int\frac{\frac{\mathrm{2}}{\mathrm{2}\sqrt{{x}}}}{\:\sqrt{{x}}+\mathrm{1}}\:{dx}=\mathrm{2}\int\frac{{d}\left(\sqrt{{x}}+\mathrm{1}\right)}{\:\sqrt{{x}}+\mathrm{1}} \\ $$$${put}\:{u}=\sqrt{{x}}+\mathrm{1}\Rightarrow=\mathrm{2}\int\frac{{du}}{{u}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{2}{ln}\left(\sqrt{{x}}+\mathrm{1}\right)+{c} \\…

Question-160342

Question Number 160342 by alf123 last updated on 28/Nov/21 Answered by Rasheed.Sindhi last updated on 28/Nov/21 $$\mathrm{4}^{{x}} =\mathrm{6};\:\frac{\mathrm{8}^{{x}} +\mathrm{8}^{−{x}} }{\mathrm{4}^{{x}} +\mathrm{4}^{−{x}} }=? \\ $$$$\mathrm{8}=\mathrm{4}^{\frac{\mathrm{3}}{\mathrm{2}}} \\…

there-are-25-persons-in-a-conical-tent-every-person-needs-an-area-of-4-sq-m-on-the-ground-under-the-tent-if-height-if-the-tent-is-18m-find-the-volume-of-the-tent-

Question Number 29264 by bbbbbb last updated on 06/Feb/18 $$\mathrm{there}\:\mathrm{are}\:\mathrm{25}\:\mathrm{persons}\:\mathrm{in}\:\mathrm{a}\:\mathrm{conical}\:\mathrm{tent} \\ $$$$\mathrm{every}\:\mathrm{person}\:\mathrm{needs}\:\mathrm{an}\:\mathrm{area}\:\mathrm{of}\:\mathrm{4}\:\mathrm{sq}\:\mathrm{m}\: \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{ground}\:\mathrm{under}\:\mathrm{the}\:\mathrm{tent}.\:\mathrm{if} \\ $$$$\mathrm{height}\:\mathrm{if}\:\mathrm{the}\:\mathrm{tent}\:\mathrm{is}\:\mathrm{18m}.\mathrm{find}\:\mathrm{the}\:\mathrm{volume} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{tent}. \\ $$ Answered by Rasheed.Sindhi last updated…

x-y-N-0-1-x-y-find-z-N-with-z-x-y-

Question Number 94786 by MJS last updated on 21/May/20 $${x},\:{y}\:\in\mathbb{N}\backslash\left\{\mathrm{0},\:\mathrm{1}\right\}\:\wedge\:{x}\leqslant{y} \\ $$$$\mathrm{find}\:{z}\in\mathbb{N}\:\mathrm{with}\:{z}!={x}!{y}! \\ $$ Commented by hknkrc46 last updated on 21/May/20 $$\left(\mathrm{a}\right)\:\mathrm{x}!=\mathrm{y}+\mathrm{1}\:\Rightarrow\:\mathrm{z}!=\left(\mathrm{y}+\mathrm{1}\right)!\:\Rightarrow\:\mathrm{z}=\mathrm{y}+\mathrm{1}\: \\ $$$$\left(\mathrm{a}.\mathrm{1}\right)\:\mathrm{x}=\mathrm{3}\Rightarrow\mathrm{y}=\mathrm{5}\Rightarrow\mathrm{z}=\mathrm{6} \\…

x-x-4-12-2x-7-x-

Question Number 94780 by Abdulrahman last updated on 20/May/20 $$\mathrm{x}!\left(\mathrm{x}−\mathrm{4}\right)!=\mathrm{12}\left(\mathrm{2x}−\mathrm{7}\right)! \\ $$$$\mathrm{x}=? \\ $$ Commented by MJS last updated on 21/May/20 $${x}\geqslant\mathrm{4} \\ $$$$\mathrm{trying} \\…