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Question-117140

Question Number 117140 by aurpeyz last updated on 09/Oct/20 Answered by bemath last updated on 10/Oct/20 $$=\mathrm{2}\left[\:\mathrm{1}−\mathrm{log}\:_{\mathrm{7}} \left(\mathrm{3}\right)−\mathrm{log}\:_{\mathrm{7}} \left(\mathrm{5}\right)\right]+\: \\ $$$$\mathrm{7}\:\left[\mathrm{2}\:\mathrm{log}\:_{\mathrm{7}} \left(\mathrm{5}\right)−\mathrm{log}\:_{\mathrm{7}} \left(\mathrm{3}\right)−\mathrm{2log}\:_{\mathrm{7}} \left(\mathrm{2}\right)\right]− \\…

Question-117143

Question Number 117143 by aurpeyz last updated on 09/Oct/20 Answered by prakash jain last updated on 13/Oct/20 $$\frac{\mathrm{2}{x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{3}} +\mathrm{4}{x}^{\mathrm{2}} −\mathrm{2}{x}}{\left({x}−\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{1}\right)} \\ $$$$={Ax}+{B}+\frac{{C}}{{x}−\mathrm{1}}+\frac{{Dx}+{E}}{{x}^{\mathrm{2}} +\mathrm{1}}…

as-we-can-know-for-Q-1-set-the-funvction-in-question-as-f-x-and-make-the-first-step-as-a-1-f-x-x-2-7x-3ln-x-df-x-2x-7-3-x-h-x-set-h-x-0-x-1-2-amp-x-3-so-the-monotonicity-of-f-x-is-f-n-l

Question Number 182657 by Strengthenchen last updated on 12/Dec/22 $${as}\:{we}\:{can}\:{know}\:{for}\:{Q}_{\mathrm{1}} ,\:{set}\:{the}\:{funvction}\:{in}\:{question}\:{as}\:{f}\left({x}\right) \\ $$$${and}\:{make}\:{the}\:{first}\:{step}\:{as}: \\ $$$${a}=\mathrm{1},{f}\left({x}\right)={x}^{\mathrm{2}} −\mathrm{7}{x}+\mathrm{3ln}\:{x} \\ $$$${df}\left({x}\right)=\mathrm{2}{x}−\mathrm{7}+\frac{\mathrm{3}}{{x}}={h}\left({x}\right) \\ $$$${set}\:{h}\left({x}\right)=\mathrm{0}\Rightarrow{x}=\frac{\mathrm{1}}{\mathrm{2}}\&{x}=\mathrm{3} \\ $$$${so},{the}\:{monotonicity}\:{of}\:{f}\left({x}\right)\:{is}\:{f}\left({n}\right)<{f}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)_{\mid{n}<\frac{\mathrm{1}}{\mathrm{2}}} ,{f}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)>{f}\left(\mathrm{2}\right),{f}\left(\mathrm{2}\right)<{f}\left({p}\underset{\mid{p}>\mathrm{2}.} {\right)} \\…

Question-117107

Question Number 117107 by Khalmohmmad last updated on 09/Oct/20 Answered by Dwaipayan Shikari last updated on 09/Oct/20 $$\mathrm{4}^{{x}} +\mathrm{6}^{{x}} =\mathrm{9}^{{x}} \\ $$$$\left(\frac{\mathrm{2}}{\mathrm{3}}\right)^{\mathrm{2}{x}} +\left(\frac{\mathrm{2}}{\mathrm{3}}\right)^{{x}} −\mathrm{1}=\mathrm{0} \\…

Question-117085

Question Number 117085 by mohammad17 last updated on 09/Oct/20 Answered by Dwaipayan Shikari last updated on 09/Oct/20 $$\int_{−\infty} ^{\infty} \frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$$$=\left[{tan}^{−\mathrm{1}} {x}\right]_{−\infty} ^{\infty}…

Question-182613

Question Number 182613 by sciencestudent last updated on 11/Dec/22 Answered by Acem last updated on 12/Dec/22 $$\:{Dis}.\:=\:{v}_{\mathrm{1}} \:\left({t}+\mathrm{4}\right)=\:{v}_{\mathrm{2}} \:\left({t}−\mathrm{2}\right) \\ $$$$\:\Rightarrow\:\frac{\mathrm{1}}{\mathrm{3}}\:\left({t}+\mathrm{4}\right)=\:\frac{\mathrm{5}}{\mathrm{12}}\:\left({t}−\mathrm{2}\right)\:,\:{t}=\:\mathrm{26}\:{min}\:_{\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{5}}{\mathrm{12}}\:\:{the}\:{same}} ^{{Exp}\:\frac{\mathrm{1}}{\mathrm{3}}=\:\frac{{v}_{\mathrm{1}} }{\mathrm{60}}\:{conv}.\:{to}\:{min}} \\ $$$$\:{Dis}=\:{v}_{\mathrm{1}}…

How-many-5-digits-positive-integers-x-1-x-2-x-3-x-4-x-5-are-there-such-that-x-1-x-2-x-3-x-4-x-5-

Question Number 117061 by ZiYangLee last updated on 09/Oct/20 $$\mathrm{How}\:\mathrm{many}\:\mathrm{5}-\mathrm{digits}\:\mathrm{positive}\:\mathrm{integers} \\ $$$${x}_{\mathrm{1}} {x}_{\mathrm{2}} {x}_{\mathrm{3}} {x}_{\mathrm{4}} {x}_{\mathrm{5}} \:\mathrm{are}\:\mathrm{there}\:\mathrm{such}\:\mathrm{that}\: \\ $$$${x}_{\mathrm{1}} \leqslant{x}_{\mathrm{2}} \leqslant{x}_{\mathrm{3}} \leqslant{x}_{\mathrm{4}} \leqslant{x}_{\mathrm{5}} ? \\…