Question Number 162253 by ZiYangLee last updated on 28/Dec/21 $$\mathrm{The}\:\mathrm{tangent}\:\mathrm{of}\:\mathrm{a}\:\mathrm{parabola}\:{y}^{\mathrm{2}} =\mathrm{4}{ax}\:\mathrm{at}\:\mathrm{the}\:\mathrm{point} \\ $$$${P}\:\left({ap}^{\mathrm{2}} ,\:\mathrm{2}{ap}\right)\:\mathrm{intersects}\:\mathrm{the}\:\mathrm{line}\:{x}+{a}=\mathrm{0}\:\mathrm{at}\:{T}\:. \\ $$$$\left(\mathrm{i}\right)\:\mathrm{If}\:{M}\:\mathrm{is}\:\mathrm{the}\:\mathrm{midpoint}\:\mathrm{of}\:{PT}\:,\:\mathrm{find}\:\mathrm{the}\: \\ $$$$\:\:\:\:\:\:\mathrm{coordinates}\:\mathrm{of}\:{M}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:{a}\:\mathrm{and}\:{p}. \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{locus}\:\mathrm{of}\:{M}\:\mathrm{is} \\ $$$$\:\:\:\:\:\:\:\:{y}^{\mathrm{2}} \left(\mathrm{2}{x}+{a}\right)={a}\left(\mathrm{3}{x}+{a}\right)^{\mathrm{2}} \\ $$…
Question Number 162240 by Gbenga last updated on 27/Dec/21 $$\int\frac{\mathrm{2}\boldsymbol{{x}}−\mathrm{5}}{\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{4}\boldsymbol{{x}}+\mathrm{5}}\boldsymbol{{dx}} \\ $$ Answered by Ar Brandon last updated on 27/Dec/21 $$\mathrm{2}{x}−\mathrm{5}=\alpha\left(\mathrm{2}{x}+\mathrm{4}\right)+\beta=\mathrm{2}\alpha{x}+\left(\mathrm{4}\alpha+\beta\right) \\ $$$$\Rightarrow\alpha=\mathrm{1},\:\mathrm{4}+\beta=−\mathrm{5},\:\beta=−\mathrm{9} \\…
Question Number 162234 by EvaNelle00 last updated on 27/Dec/21 $$ \\ $$$$\:\:\:\:\:\:\underset{{p}=\mathrm{0}} {\overset{{n}} {\sum}}\left(−\mathrm{1}\right)^{{p}} {C}_{{p}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \left(−\mathrm{1}\right)^{{n}−{p}} {C}_{{n}−{p}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \:=\:\:\:???? \\ $$$$\:\:\:\:\:\:\:{Please}\:{Help}\:{me}\left({Aidez}\:{moi}\right) \\ $$$$ \\…
Question Number 162231 by SANOGO last updated on 27/Dec/21 $${nature}\:{et}\:{calcul} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{lnx}}{\:\sqrt{\mathrm{1}−{x}}}{dx} \\ $$ Answered by amin96 last updated on 27/Dec/21 $$\mathrm{1}−{x}={t}\:\:\:{dx}=−{dt} \\…
Question Number 96682 by liki last updated on 03/Jun/20 Commented by liki last updated on 03/Jun/20 $$…\mathrm{am}\:\mathrm{i}\:\mathrm{right}\:\mathrm{if}\:\mathrm{use}\:\mathrm{concept}\:\mathrm{of}\:\mathrm{arthmetic}\:\mathrm{progression}?,\mathrm{please}\:\mathrm{if}\:\mathrm{i}\:\mathrm{do}\:\mathrm{mistake}\:\mathrm{need}\:\mathrm{correcton}! \\ $$ Commented by Rio Michael last updated…
Question Number 162189 by SANOGO last updated on 27/Dec/21 $${show}\:{the}\:{converge}^{} {nce}\:{and}\:{calculate} \\ $$$$\int_{−\mathrm{1}} ^{\mathrm{1}} \sqrt{\frac{\mathrm{1}−{t}}{\mathrm{1}+{t}}}\:{dt} \\ $$ Commented by Ar Brandon last updated on 27/Dec/21…
Question Number 162190 by naka3546 last updated on 27/Dec/21 $$\lfloor\:\frac{\mathrm{3}^{\mathrm{2}} +\mathrm{1}}{\mathrm{3}^{\mathrm{2}} −\mathrm{1}}\:+\:\frac{\mathrm{3}^{\mathrm{3}} +\mathrm{1}}{\mathrm{3}^{\mathrm{3}} −\mathrm{1}}\:+\:\frac{\mathrm{3}^{\mathrm{4}} +\mathrm{1}}{\mathrm{3}^{\mathrm{4}} −\mathrm{1}}\:+\:\ldots+\:\frac{\mathrm{3}^{\mathrm{2017}} +\mathrm{1}}{\mathrm{3}^{\mathrm{2017}} −\mathrm{1}}\:\rfloor\:=\:\:? \\ $$ Answered by mr W last…
Question Number 31109 by naka3546 last updated on 02/Mar/18 $$\boldsymbol{{a}}^{\mathrm{4}} \:+\:\boldsymbol{{b}}^{\mathrm{4}} \:+\:\mathrm{13}\:\:\:{is}\:\:{a}\:\:{possible}\:\:{largest}\:\:{prime}\:\:{number}\:. \\ $$$$\boldsymbol{{a}}\:\:{and}\:\:\boldsymbol{{b}}\:\:{are}\:\:{prime}\:\:{numbers}\:. \\ $$$${Find}\:\:\boldsymbol{{a}}\:\:{and}\:\:\boldsymbol{{b}}\:. \\ $$ Commented by rahul 19 last updated on…
Question Number 96616 by mathocean1 last updated on 03/Jun/20 Answered by Rio Michael last updated on 03/Jun/20 $${A}\:=\:\begin{pmatrix}{{a}}&{{b}}\\{{b}}&{{c}}\end{pmatrix}\:\mathrm{and}\:{B}\:=\:\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix} \\ $$$${AB}\:=\:\begin{pmatrix}{{a}}&{{b}}\\{{b}}&{{c}}\end{pmatrix}\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix}\:=\:\begin{pmatrix}{{ax}\:+\:{by}}\\{{bx}\:+\:{cy}}\end{pmatrix} \\ $$$${BA}\:=\:\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix}\begin{pmatrix}{{a}}&{{b}}\\{{b}}&{{c}}\end{pmatrix}\:\mathrm{impossible}\:\mathrm{since}\: \\ $$$$\mathrm{order}\:\left(\mathrm{A}\right)\:=\:\mathrm{2}\:×\mathrm{2}\:\:\mathrm{and}\:\mathrm{order}\:\left(\mathrm{B}\right)\:=\:\mathrm{2}×\:\mathrm{1} \\…
Question Number 96617 by mathocean1 last updated on 03/Jun/20 $${Given}\:{matrix}\:{A}\begin{bmatrix}{{a}\:\:\:\:\:{c}}\\{{b}\:\:\:\:\:{d}}\end{bmatrix}{and}\:{B}\begin{pmatrix}{{x}}\\{{y}_{} }\end{pmatrix}. \\ $$$${Determinate}\:{A}×{B}\:{and}\:{B}×{A}. \\ $$ Commented by bobhans last updated on 03/Jun/20 $$\mathrm{B}×\mathrm{A}\:\mathrm{undefine} \\ $$…