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Author: Tinku Tara

Find-the-sum-of-3-2-and-5-4-

Question Number 53518 by 0955083339 last updated on 22/Jan/19 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\:\mathrm{3}.\overset{−} {\mathrm{2}}\:\:\mathrm{and}\:\:\mathrm{5}.\overset{−} {\mathrm{4}}\:\:. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 23/Jan/19 $$\mathrm{8}.\overset{−} {\mathrm{6}} \\ $$…

What-is-the-sum-of-ten-odd-numbers-and-eleven-even-numbers-

Question Number 53515 by 0955083339 last updated on 22/Jan/19 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{ten}\:\mathrm{odd}\:\mathrm{numbers} \\ $$$$\mathrm{and}\:\mathrm{eleven}\:\mathrm{even}\:\mathrm{numbers}? \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 23/Jan/19 $${S}_{{odd}} =\mathrm{1}+\mathrm{3}+\mathrm{5}+…+\left[\mathrm{1}+\left(\mathrm{10}−\mathrm{1}\right)\mathrm{2}\right] \\ $$$${S}_{{odd}}…

If-x-5-is-a-factor-of-2x-2-2px-2p-0-the-value-of-p-is-

Question Number 53502 by 0955083339 last updated on 22/Jan/19 $$\mathrm{If}\:\left({x}−\mathrm{5}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{factor}\:\mathrm{of}\:\:\mathrm{2}{x}^{\mathrm{2}} +\mathrm{2}{px}−\mathrm{2}{p}=\mathrm{0}, \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\:{p}\:\:\mathrm{is} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 22/Jan/19 $$\mathrm{2}×\mathrm{5}^{\mathrm{2}} +\mathrm{2}{p}×\mathrm{5}−\mathrm{2}{p}=\mathrm{0} \\…

The-value-of-the-integral-0-pi-x-dx-1-cos-sin-0-lt-lt-pi-is-

Question Number 53385 by gunawan last updated on 21/Jan/19 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{integral}\:\underset{\:\mathrm{0}} {\overset{\pi} {\int}}\:\frac{{x}\:{dx}}{\mathrm{1}+\mathrm{cos}\:\alpha\:\mathrm{sin}\:\alpha}\:, \\ $$$$\mathrm{0}<\:\alpha<\pi\:\:\:\mathrm{is} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 21/Jan/19 $$\frac{\mathrm{1}}{\mathrm{1}+{sin}\alpha{cos}\alpha}×\mid\frac{{x}^{\mathrm{2}} }{\mathrm{2}}\mid_{\mathrm{0}}…

If-1-sin-x-4-sin-x-1-dx-A-1-tan-x-2-1-B-tan-1-f-x-C-then-

Question Number 53383 by gunawan last updated on 21/Jan/19 $$\mathrm{If}\:\int\frac{\mathrm{1}}{\left(\mathrm{sin}\:{x}+\mathrm{4}\right)\left(\mathrm{sin}\:{x}−\mathrm{1}\right)}{dx} \\ $$$$\:\:\:\:\:\:\:\:\:=\:{A}\frac{\mathrm{1}}{\mathrm{tan}\:\frac{{x}}{\mathrm{2}}−\mathrm{1}}+{B}\:\mathrm{tan}^{−\mathrm{1}} \left({f}\left({x}\right)\right)+{C},\:\mathrm{then} \\ $$ Commented by maxmathsup by imad last updated on 21/Jan/19 $${let}\:{A}\:=\int\:\:\:\:\frac{{dx}}{\left({sinx}+\mathrm{4}\right)\left({sinx}−\mathrm{1}\right)}\:\Rightarrow{A}\:=_{{tan}\left(\frac{{x}}{\mathrm{2}}\right)={t}}…