Question Number 168399 by Mastermind last updated on 09/Apr/22 $${solve} \\ $$$${z}^{\frac{\mathrm{1}}{\mathrm{4}}} −{i}=\mathrm{0} \\ $$$$ \\ $$$${Mastermind} \\ $$ Answered by nurtani last updated on…
Question Number 102822 by Dwaipayan Shikari last updated on 11/Jul/20 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}!}{{n}^{{n}} } \\ $$ Commented by Dwaipayan Shikari last updated on 11/Jul/20 $${RATIO}\:{TEST}…
Question Number 37249 by Rio Mike last updated on 11/Jun/18 $${a}\:{triangle}\:{with}\:{vertices}\: \\ $$$$\:{A}\left(\mathrm{2},\mathrm{1}\right),{B}\left(\mathrm{6},\mathrm{1}\right)\:{and}\:\left(\mathrm{3},\mathrm{3}\right)\:{is}\:{transformed} \\ $$$${by}\:\begin{pmatrix}{\mathrm{2}\:\:\:\:\:\:\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\:\:\:\:\:\:\:\mathrm{2}}\end{pmatrix}\: \\ $$$$\left.{a}\right){find}\:{the}\:{image}\:{A}'{B}'{C}'\:{after}\: \\ $$$${this}\:{transformstion} \\ $$$$\left.{b}\right)\:{state}\:{the}\:{type}\:{of}\:{transformation} \\ $$ Terms of…
Question Number 37218 by Rio Mike last updated on 10/Jun/18 $$\:{Proove}\:{that} \\ $$$$\left.{a}\right)\:\:\frac{\mathrm{1}−{cosA}\:+\:{cos}\:{B}\:−\:{cos}\left({A}+{B}\right)}{\mathrm{1}+{cos}\:{A}\:−\:{cosB}−{cos}\left({A}+{B}\right)}=\:{tan}\frac{{A}}{\mathrm{2}}.{cot}\:\frac{{B}}{\mathrm{2}} \\ $$$$\left.{b}\right)\:{cos}\alpha\:{cos}\left(\mathrm{60}−\alpha\right){cos}\left(\mathrm{60}+\alpha\right)=\:\frac{\mathrm{1}}{\mathrm{4}}{cos}\mathrm{3}\alpha \\ $$$$ \\ $$ Answered by $@ty@m last updated on…
Question Number 168280 by Florian last updated on 07/Apr/22 $${Wath}\:{is}\:{your}\:{favourite}\:{formula}\:??? \\ $$ Answered by alephzero last updated on 07/Apr/22 $${e}^{{i}\tau} +{e}^{{i}\pi} =\mathrm{0} \\ $$ Terms…
Question Number 102745 by Dwaipayan Shikari last updated on 10/Jul/20 $$\mathrm{1}−\mathrm{1}+\mathrm{1}−\mathrm{1}+\mathrm{1}−\mathrm{1}+\mathrm{1}−\mathrm{1}+…..=\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\left\{{But}\:{it}\:{diverges}\right. \\ $$$$\mathrm{1}+\mathrm{1}+\mathrm{1}+\mathrm{1}+\mathrm{1}+\mathrm{1}+\mathrm{1}+……=−\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\:\:\left\{{But}\:{it}\:{diverges}\right. \\ $$$$\mathrm{1}+\mathrm{2}+\mathrm{4}+\mathrm{8}+\mathrm{16}+…..=−\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left\{{But}\:{it}\:{diverges}\right. \\ $$$$\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+\mathrm{5}+\mathrm{6}+\mathrm{7}=−\frac{\mathrm{1}}{\mathrm{12}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left\{{But}\:{it}\:{diverges}\right. \\ $$$$\mathrm{1}−\mathrm{2}+\mathrm{4}−\mathrm{8}+…..=\frac{\mathrm{1}}{\mathrm{3}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left\{{But}\:{it}\:{diverges}\right. \\ $$$$\mathrm{1}−\mathrm{2}+\mathrm{3}−\mathrm{4}+\mathrm{5}−\mathrm{6}+…..=\frac{\mathrm{1}}{\mathrm{4}}\:\:\:\:\:\:\:\left\{{Is}\:{it}\:{a}\:{divergent}?????\right. \\ $$ Commented by…
Question Number 168278 by Florian last updated on 07/Apr/22 $$\:\:\:\:\:\frac{{log}_{\mathrm{3}} \left(\mathrm{12}\right)}{{log}_{\mathrm{36}} \left(\mathrm{3}\right)}−\frac{{log}_{\mathrm{3}} \left(\mathrm{4}\right)}{{log}_{\mathrm{108}} \left(\mathrm{3}\right)}\:=\:{x} \\ $$$$\:\:\:\:\:{x}\:=\: \\ $$ Commented by benhamimed last updated on 07/Apr/22…
Question Number 168264 by Mastermind last updated on 07/Apr/22 Answered by som(math1967) last updated on 07/Apr/22 $${let}\:{speed}\:={xkm}/{hr} \\ $$$$\therefore\frac{\mathrm{240}}{{x}−\mathrm{4}}\:−\frac{\mathrm{240}}{{x}}=\mathrm{2} \\ $$$$\Rightarrow\mathrm{240}\left\{\frac{{x}−{x}+\mathrm{4}}{{x}\left({x}−\mathrm{4}\right)}\right\}=\mathrm{2} \\ $$$$\Rightarrow\frac{\mathrm{240}×\mathrm{4}}{{x}^{\mathrm{2}} −\mathrm{4}{x}}=\mathrm{2} \\…
Question Number 168274 by Mastermind last updated on 07/Apr/22 Answered by MikeH last updated on 07/Apr/22 $$\mathrm{width}\:=\:{x} \\ $$$$\mathrm{length}\:={x}\:+\:\mathrm{11} \\ $$$$\mathrm{area}\:=\:{x}\left({x}+\mathrm{11}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:=\:{x}^{\mathrm{2}} +\mathrm{11}{x} \\…
Question Number 168247 by Mastermind last updated on 07/Apr/22 $${Solve}\:{for}\:{x} \\ $$$$\frac{\mathrm{8}^{{x}} +\mathrm{27}^{{x}} }{\mathrm{12}^{{x}} +\mathrm{18}^{{x}} }=\frac{\mathrm{7}}{\mathrm{6}} \\ $$$$ \\ $$$${Mastermind} \\ $$ Answered by MJS_new…