Question Number 206609 by universe last updated on 20/Apr/24 $$\:\:\:\mathrm{let}\:\mathrm{matrix}\:\:\mathrm{A}_{\mathrm{n}×\mathrm{n}} \:\mathrm{and}\:\mathrm{B}_{\mathrm{n}×\mathrm{n}} \:\mathrm{satisfying} \\ $$$$\:\:\:\mathrm{A}^{\mathrm{2}} =\:\mathrm{A}\:\:\&\:\:\mathrm{B}^{\mathrm{2}} =\:\mathrm{B}\:\:\mathrm{then}\:\mathrm{prove} \\ $$$$\:\:\:\rho\left(\mathrm{A}−\mathrm{B}\right)\:=\:\rho\left(\mathrm{A}−\mathrm{AB}\right)+\:\:\rho\left(\mathrm{B}−\mathrm{AB}\right) \\ $$$$\:\:\:\mathrm{here}\:\rho\:=\:\mathrm{rank} \\ $$ Terms of Service…
Question Number 206532 by necx122 last updated on 17/Apr/24 $${Find}\:{the}\:{nth}\:{term}\:{of}\:{the}\:{sequence} \\ $$$$\mathrm{0},\mathrm{3},\mathrm{8},\mathrm{15},\mathrm{24},…… \\ $$ Answered by Berbere last updated on 17/Apr/24 $${Impossibl} \\ $$$${there}\:{are}\left[{infinity}\:{way}\:\right. \\…
Question Number 206501 by hardmath last updated on 16/Apr/24 $$\mathrm{If} \\ $$$$\mathrm{x}^{\boldsymbol{\mathrm{log}}_{\mathrm{3}} \:\boldsymbol{\mathrm{x}}\:−\:\mathrm{1}} \:\:=\:\:\mathrm{log}_{\mathrm{3}} \:\mathrm{x}\:+\:\mathrm{3} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{log}_{\mathrm{3}} \:\mathrm{x}_{\mathrm{1}} \:+\:\mathrm{log}_{\mathrm{3}} \:\mathrm{x}_{\mathrm{2}} \:=\:? \\ $$ Commented by…
Question Number 206477 by hardmath last updated on 15/Apr/24 $$\mathrm{If}\:\:\:\mathrm{a}>\mathrm{b}>\mathrm{0}\:\:\:\mathrm{and}\:\:\:\mathrm{4a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:=\:\mathrm{4ab} \\ $$$$\mathrm{Find}:\:\:\:\frac{\mathrm{a}\:−\:\mathrm{b}}{\mathrm{a}\:+\:\mathrm{b}}\:=\:? \\ $$ Answered by MATHEMATICSAM last updated on 16/Apr/24 $$\mathrm{4}{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}}…
Question Number 206458 by mathlove last updated on 15/Apr/24 $${if}\:{f}\left({x}\right)=\sqrt{{x}−{x}^{\mathrm{2}} }\:\:\:\:\:{then}\:\:{f}^{−\mathrm{1}} \left({x}\right)=? \\ $$ Answered by Skabetix last updated on 15/Apr/24 $${f}^{−\mathrm{1}} \left({x}\right)=\frac{\mathrm{1}\pm\sqrt{−\mathrm{4}{x}^{\mathrm{2}} +\mathrm{1}}}{\mathrm{2}} \\…
Question Number 206473 by hardmath last updated on 15/Apr/24 $$\mathrm{If}\:\:\:\mathrm{4}^{\boldsymbol{\mathrm{p}}} \:=\:\mathrm{5} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{2}^{\mathrm{3}\boldsymbol{\mathrm{p}}} \:=\:? \\ $$ Answered by A5T last updated on 15/Apr/24 $$\mathrm{2}^{\mathrm{2}{p}} =\mathrm{5}\Rightarrow\mathrm{2}^{\mathrm{3}{p}}…
Question Number 206475 by hardmath last updated on 15/Apr/24 $$\mathrm{If}\:\:\:\frac{\mathrm{a}^{\mathrm{2}} }{\mathrm{12}}\:−\:\mathrm{5b}^{\mathrm{3}} \:=\:−\mathrm{30} \\ $$$$\mathrm{Find}:\:\:\:\frac{\mathrm{2}}{\mathrm{45}}\:\mathrm{a}^{\mathrm{2}} \:−\:\frac{\mathrm{8}}{\mathrm{3}}\:\mathrm{b}^{\mathrm{3}} \:=\:? \\ $$ Answered by A5T last updated on 15/Apr/24…
Question Number 206443 by Safojon last updated on 14/Apr/24 Commented by necx122 last updated on 15/Apr/24 getting a more detailed solution will be excellent for us. I still tried going through the solution already done but I couldn't understand the approaches readily. Please, whoever can expound would be a help. Thanks. Commented by A5T last updated on 15/Apr/24 $${Let}\:\boldsymbol{{u}}=\left({a},{b},{c}\right);\boldsymbol{{v}}=\left({x},{y},{z}\right)…
Question Number 206425 by hardmath last updated on 13/Apr/24 $$\mathrm{If}\:\:\:\mathrm{cos}\boldsymbol{\alpha}\:=\:\frac{\mathrm{3}}{\mathrm{5}}\:\:\:\left(\mathrm{0}<\boldsymbol{\alpha}<\frac{\boldsymbol{\pi}}{\mathrm{2}}\right) \\ $$$$\mathrm{Find}:\:\:\:\frac{\mathrm{tan}^{\mathrm{2}} \:\left(\mathrm{45}°\:+\:\frac{\boldsymbol{\alpha}}{\mathrm{2}}\right)}{\mathrm{3}}\:=\:? \\ $$ Answered by MM42 last updated on 13/Apr/24 $${tan}^{\mathrm{2}} {a}=\frac{\mathrm{1}−{cos}\mathrm{2}{a}}{\mathrm{1}+{cos}\mathrm{2}{a}} \\…
Question Number 206391 by hardmath last updated on 13/Apr/24 $$\mathrm{Find}: \\ $$$$\int_{−\mathrm{3}} ^{\:−\mathrm{2}} \:\left(\mid\mathrm{x}\mid\:+\:\mid\mathrm{x}\:−\:\mathrm{4}\mid\right)\:\mathrm{dx}\:=\:? \\ $$ Answered by MM42 last updated on 13/Apr/24 $${I}=\int_{−\mathrm{3}} ^{−\mathrm{2}}…