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Question-177665

Question Number 177665 by Ahmed777hamouda last updated on 07/Oct/22 Answered by Ar Brandon last updated on 07/Oct/22 $$\int_{−\infty} ^{\infty} \mathrm{sin}{x}^{\mathrm{2}} {dx}=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{sin}{t}}{\:\sqrt{{t}}}{dt}=\frac{\pi}{\mathrm{2}\Gamma\left(\frac{\mathrm{1}}{\mathrm{2}}\right)\mathrm{sin}\left(\frac{\pi}{\mathrm{2}}\centerdot\frac{\mathrm{1}}{\mathrm{2}}\right)}=\sqrt{\frac{\pi}{\mathrm{2}}} \\ $$…

Question-112133

Question Number 112133 by shwebotetun last updated on 06/Sep/20 Answered by som(math1967) last updated on 06/Sep/20 $$\left(−\mathrm{2b}\right)^{\mathrm{2}} +\mathrm{20b}+\mathrm{14}=\left(−\mathrm{2c}\right)^{\mathrm{2}} +\mathrm{20c}+\mathrm{14} \\ $$$$\mathrm{4b}^{\mathrm{2}} −\mathrm{4c}^{\mathrm{2}} +\mathrm{20}\left(\mathrm{b}−\mathrm{c}\right)=\mathrm{0} \\ $$$$\mathrm{4}\left\{\left(\mathrm{b}−\mathrm{c}\right)\left(\mathrm{b}+\mathrm{c}\right)+\mathrm{5}\left(\mathrm{b}−\mathrm{c}\right)\right\}=\mathrm{0}…

Solve-x-R-x-x-x-2-1-35-12-

Question Number 46586 by naka3546 last updated on 28/Oct/18 $${Solve}\:\:{x}\:\:\in\:\mathbb{R} \\ $$$$\:\:\:\:\:\:\:\:\:{x}\:+\:\:\frac{{x}}{\:\sqrt{{x}^{\mathrm{2}} \:+\:\mathrm{1}}}\:\:=\:\:\frac{\mathrm{35}}{\mathrm{12}} \\ $$ Answered by Kunal12588 last updated on 29/Oct/18 $$\Rightarrow\frac{{x}\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}+{x}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}=\frac{\mathrm{35}}{\mathrm{12}}…

A-certain-personal-identity-number-pin-is-a-sequence-of-four-digits-where-each-digit-is-selected-from-the-digits-0-to-9-How-many-such-pins-have-at-least-two-diffrent-digits-and-are-palindromes-Pa

Question Number 177633 by aurpeyz last updated on 07/Oct/22 $$\mathrm{A}\:\mathrm{certain}\:\mathrm{personal}\:\mathrm{identity}\:\mathrm{number}\:\left(\mathrm{pin}\right) \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{sequence}\:\mathrm{of}\:\mathrm{four}\:\mathrm{digits}\:\mathrm{where}\:\mathrm{each}\:\mathrm{digit} \\ $$$$\mathrm{is}\:\mathrm{selected}\:\mathrm{from}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{0}\:\mathrm{to}\:\mathrm{9}.\:\mathrm{How}\:\mathrm{many} \\ $$$$\mathrm{such}\:\mathrm{pins}\:\mathrm{have}\:\mathrm{at}\:\mathrm{least}\:\mathrm{two}\:\mathrm{diffrent}\:\mathrm{digits} \\ $$$$\mathrm{and}\:\mathrm{are}\:\mathrm{palindromes}.\:\left(\mathrm{Palindrome}\:\mathrm{is}\:\mathrm{a}\:\mathrm{cha}−\right. \\ $$$$\mathrm{racter}\:\mathrm{that}\:\mathrm{reads}\:\mathrm{the}\:\mathrm{same}\:\mathrm{forward}\:\mathrm{and}\: \\ $$$$\left.\mathrm{backward}\:\mathrm{e}.\mathrm{g}\:\mathrm{1221}\right) \\ $$ Commented…

Question-177634

Question Number 177634 by aurpeyz last updated on 07/Oct/22 Answered by HeferH last updated on 07/Oct/22 $$\: \\ $$$$\:\frac{{CD}}{{AD}}\:=\:\frac{\mathrm{1}}{\mathrm{3}}\: \\ $$$$\:\frac{{A}_{\mathrm{1}} }{{A}_{{t}} }\:\:=\:\frac{\mathrm{1}}{\mathrm{9}}\Rightarrow\:\frac{\mathrm{42}}{{A}_{{t}} }\:=\:\frac{\mathrm{1}}{\mathrm{9}} \\…

Question-112096

Question Number 112096 by mathdave last updated on 06/Sep/20 Answered by mr W last updated on 06/Sep/20 $${say}\:{ab}={k}^{\mathrm{2}} \\ $$$$\frac{{a}+{b}}{\mathrm{2}}−{k}=\mathrm{1} \\ $$$$\Rightarrow{a}+{b}=\mathrm{2}\left({k}+\mathrm{1}\right) \\ $$$${a},\:{b}\:{are}\:{roots}\:{of} \\…

Can-someone-please-explain-me-how-to-solve-a-quadratic-equation-without-the-common-formulas-but-with-the-sums-and-products-method-please-Thank-

Question Number 46553 by hassentimol last updated on 28/Oct/18 $$\mathrm{Can}\:\mathrm{someone}\:\mathrm{please}\:\mathrm{explain}\:\mathrm{me}\:\mathrm{how}\:\mathrm{to} \\ $$$$\mathrm{solve}\:\mathrm{a}\:\mathrm{quadratic}\:\mathrm{equation}\:\mathrm{without}\:\mathrm{the}\: \\ $$$$\mathrm{common}\:\mathrm{formulas}\:\mathrm{but}\:\mathrm{with}\:\mathrm{the}\:\mathrm{sums}\:\mathrm{and} \\ $$$$\mathrm{products}\:\mathrm{method}\:\mathrm{please}\:? \\ $$$$\mathrm{Thank} \\ $$ Answered by ajfour last updated…