Question Number 140260 by EnterUsername last updated on 05/May/21 $$\mathrm{Passage}:\:\mathrm{If}\:{z}_{\mathrm{1}} ,\:{z}_{\mathrm{2}} \:\mathrm{and}\:{z}_{\mathrm{3}} \:\mathrm{are}\:\mathrm{three}\:\mathrm{complex}\:\mathrm{numbers} \\ $$$$\mathrm{representing}\:\mathrm{the}\:\mathrm{points}\:{A},\:{B}\:\mathrm{and}\:{C},\:\mathrm{respectively},\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{Argands}\:\mathrm{plane}\:\mathrm{and}\:\angle{BAC}=\alpha,\:\mathrm{then} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{z}_{\mathrm{3}} −{z}_{\mathrm{1}} }{{z}_{\mathrm{2}} −{z}_{\mathrm{1}} }=\left(\frac{{AC}}{{AB}}\right)\left(\mathrm{cos}\alpha+{i}\mathrm{sin}\alpha\right) \\ $$$$\left({i}\right)\:\mathrm{If}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation}…
Question Number 74716 by chess1 last updated on 29/Nov/19 Answered by Tanmay chaudhury last updated on 29/Nov/19 $${x}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}}\right)×{x}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }\right)×…{x}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{25}} }\right)=\mathrm{1} \\ $$$${x}^{\mathrm{25}} ×{A}=\mathrm{1} \\ $$$${x}=\left(\frac{\mathrm{1}}{{A}}\right)^{\frac{\mathrm{1}}{\mathrm{25}}}…
Question Number 74712 by aliesam last updated on 29/Nov/19 Commented by MJS last updated on 29/Nov/19 $$\mathrm{easy}\:\mathrm{solutions} \\ $$$${x}={y}=\mathrm{1} \\ $$$${x}={y}=−\mathrm{2} \\ $$$$\mathrm{no}\:\mathrm{other}\:\mathrm{real}\:\mathrm{solutions} \\ $$$$\left(\mathrm{1}\right)−\left(\mathrm{2}\right)\:\mathrm{and}\:\mathrm{dividing}\:\mathrm{by}\:{x}^{\mathrm{2}}…
Question Number 140248 by EnterUsername last updated on 05/May/21 $$\mathrm{Let}\:{p}\:\mathrm{and}\:{q}\:\mathrm{be}\:\mathrm{positive}\:\mathrm{integers}\:\mathrm{having}\:\mathrm{no}\:\mathrm{positive} \\ $$$$\mathrm{common}\:\mathrm{divisors}\:\mathrm{except}\:\mathrm{unity}.\:\mathrm{Let}\:{z}_{\mathrm{1}} ,\:{z}_{\mathrm{2}} ,…,\:{z}_{{q}} \:\mathrm{be}\:\mathrm{the} \\ $$$${q}\:\mathrm{values}\:\mathrm{of}\:{z}^{{p}/{q}} ,\:\mathrm{where}\:{z}\:\mathrm{is}\:\mathrm{a}\:\mathrm{fixed}\:\mathrm{complex}\:\mathrm{number}.\:\mathrm{Then} \\ $$$$\mathrm{the}\:\mathrm{product}\:{z}_{\mathrm{1}} {z}_{\mathrm{2}} …{z}_{{q}} \:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\left(\mathrm{A}\right)\:{z}^{{p}}…
Question Number 140241 by mathdanisur last updated on 05/May/21 $$\int\left(\mathrm{4}{ctg}^{\mathrm{3}} {x}−\mathrm{5}{ctg}^{\mathrm{2}} {x}+\mathrm{7}{ctgx}\right){e}^{{x}} {dx}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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Question Number 140225 by mondli last updated on 05/May/21 $${x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{3}=\mathrm{0}\:\: \\ $$ Answered by MJS_new last updated on 05/May/21 $${x}^{\mathrm{2}} +{px}+{q}=\mathrm{0}\:\Rightarrow\:{x}=−\frac{{p}}{\mathrm{2}}\pm\sqrt{\frac{{p}^{\mathrm{2}} }{\mathrm{4}}−{q}} \\ $$…
Question Number 9141 by tawakalitu last updated on 20/Nov/16 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}\:\mathrm{if} \\ $$$$\left(\sqrt{\mathrm{2}\:+\:\sqrt{\mathrm{3}}}\right)^{\mathrm{x}} \:+\:\left(\sqrt{\mathrm{2}\:−\:\sqrt{\mathrm{3}}}\right)^{\mathrm{x}} \:=\:\mathrm{4} \\ $$ Commented by tawakalitu last updated on 20/Nov/16 $$\mathrm{please}\:\mathrm{help}. \\…
Question Number 140205 by EnterUsername last updated on 05/May/21 $${ABCD}\:\mathrm{is}\:\mathrm{a}\:\mathrm{rhombus}.\:\mathrm{Its}\:\mathrm{diagonals}\:{AC}\:\mathrm{and}\:{BD}\:\mathrm{inter}- \\ $$$$\mathrm{sect}\:\mathrm{at}\:{M}\:\mathrm{and}\:\mathrm{satisfy}\:{BD}=\mathrm{2}{AC}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{points}\:{D}\:\mathrm{and} \\ $$$${M}\:\mathrm{are}\:\mathrm{represented}\:\mathrm{by}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{numbers}\:\mathrm{1}+{i}\:\mathrm{and} \\ $$$$\mathrm{2}−{i},\:\mathrm{respectively},\:\mathrm{then}\:{A}\:\mathrm{is}\:\mathrm{represented}\:\mathrm{by} \\ $$$$\left(\mathrm{A}\right)\:\mathrm{3}−{i}/\mathrm{2}\:\:\:\:\:\:\:\:\:\left(\mathrm{B}\right)\:\mathrm{3}+{i}/\mathrm{2}\:\:\:\:\:\:\:\:\:\left(\mathrm{C}\right)\:\mathrm{1}+\mathrm{3}{i}/\mathrm{2}\:\:\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:\mathrm{1}−\mathrm{3}{i}/\mathrm{2} \\ $$ Answered by mr W last…
Question Number 140196 by mathdanisur last updated on 05/May/21 $${Calculate}:\:\sqrt{\mathrm{3}}\:{cosec}\:\mathrm{20}°−{sec}\:\mathrm{20}° \\ $$ Answered by liberty last updated on 05/May/21 $$\:\frac{\sqrt{\mathrm{3}}}{\mathrm{sin}\:\mathrm{20}°}−\frac{\mathrm{1}}{\mathrm{cos}\:\mathrm{20}°}\:=\: \\ $$$$\frac{\mathrm{2}\left(\sqrt{\mathrm{3}}\:\mathrm{cos}\:\mathrm{20}°−\mathrm{sin}\:\mathrm{20}°\right)}{\mathrm{sin}\:\mathrm{40}°}\:= \\ $$$$\frac{\mathrm{4}\left(\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\:\mathrm{cos}\:\mathrm{20}°−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}\:\mathrm{20}°\right)}{\mathrm{sin}\:\mathrm{40}°}\:= \\…