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Category: Logic

If-is-a-root-of-the-equation-4x-2-2x-1-0-How-do-you-prove-the-other-root-is-4-3-3-

Question Number 113211 by bemath last updated on 11/Sep/20 $$\mathrm{If}\:\alpha\:\mathrm{is}\:\mathrm{a}\:\mathrm{root}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{4x}^{\mathrm{2}} +\mathrm{2x}−\mathrm{1}=\mathrm{0}\:.\:\mathrm{How}\:\mathrm{do}\:\mathrm{you} \\ $$$$\mathrm{prove}\:\mathrm{the}\:\mathrm{other}\:\mathrm{root}\:\mathrm{is} \\ $$$$\mathrm{4}\alpha^{\mathrm{3}} −\mathrm{3}\alpha\:?\: \\ $$ Answered by 1549442205PVT last updated…

Question-112507

Question Number 112507 by bemath last updated on 08/Sep/20 Answered by mr W last updated on 09/Sep/20 $$\frac{\mathrm{1}}{{A}}+\frac{\mathrm{1}}{{B}}=\frac{\mathrm{1}}{\mathrm{35}} \\ $$$$\frac{\mathrm{5}}{\mathrm{7}}{A}+\frac{\mathrm{2}}{\mathrm{7}}{B}=\mathrm{90} \\ $$$$\mathrm{5}{A}^{\mathrm{2}} −\mathrm{735}{A}+\mathrm{630}×\mathrm{35}=\mathrm{0} \\ $$$${A}=\frac{\mathrm{735}\pm\mathrm{315}}{\mathrm{10}}=\mathrm{105}\:{or}\:\mathrm{42}…

Given-a-transformation-T-C-C-z-Show-that-if-z-i-z-1-then-z-i-1-Hence-the-image-of-the-line-z-i-z-2-under-the-transformation-T-the-plane-is-a-circle-w

Question Number 110504 by Rio Michael last updated on 29/Aug/20 $$\mathrm{Given}\:\mathrm{a}\:\mathrm{transformation}\:,\:\mathcal{T}:\:\mathbb{C}\:\rightarrow\:\mathbb{C}\:;\:{z}\:\rightarrow\:\omega \\ $$$$\:\mathrm{Show}\:\mathrm{that}\:\mathrm{if}\:\omega\:=\:\frac{{z}−{i}}{{z}\:+\mathrm{1}}\:\mathrm{then}\:{z}\:=\:\frac{\omega\:+\:{i}}{\mathrm{1}−\omega}.\:\mathrm{Hence} \\ $$$$\mathrm{the}\:\mathrm{image}\:\mathrm{of}\:\mathrm{the}\:\mathrm{line}\:\mid{z}−{i}\mid\:=\:\mid{z}\:+\:\mathrm{2}\mid\:\mathrm{under}\:\mathrm{the}\:\mathrm{transformation} \\ $$$$\mathcal{T}\:\:\:\:\mathrm{the}\:\omega−\mathrm{plane}\:\mathrm{is}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{with}\:\mathrm{center}\:\left(−\mathrm{2},−{i}\right)\:\mathrm{and}\:\mathrm{radius}\:\sqrt{\mathrm{10}}\:.\: \\ $$ Terms of Service Privacy Policy Contact:…

what-are-the-differences-among-if-only-if-and-if-and-only-if-

Question Number 175923 by CrispyXYZ last updated on 09/Sep/22 $$\mathrm{what}\:\mathrm{are}\:\mathrm{the}\:\mathrm{differences}\:\mathrm{among}\:“\:{if}\:'',\:“\:{only}\:\:{if}\:''\:\mathrm{and}\:“\:{if}\:\:{and}\:\:{only}\:\:{if}\:''? \\ $$ Answered by Vynho last updated on 09/Sep/22 $${if}={necessary}\:{condition} \\ $$$${only}\:{if}\:=\:{sufficient}\:{condition} \\ $$$${if}\:{and}\:{only}\:{if}={necessary}\:{and}\:{sufficient}\:{condition} \\…

Question-175017

Question Number 175017 by oustmuchiya@gmail.com last updated on 16/Aug/22 Commented by TheHoneyCat last updated on 16/Aug/22 $$\mathrm{Not}\:\mathrm{sure}\:\mathrm{I}\:\mathrm{get}\:\mathrm{the}\:\mathrm{question}… \\ $$$$\mathrm{what}\:\mathrm{is}\:“\mathrm{A}\alpha''? \\ $$$$\mathrm{Is}\:\mathrm{A}\:\mathrm{a}\:\mathrm{function}? \\ $$$$\mathrm{Or}\:\mathrm{a}\:\mathrm{set}\:\left(\mathrm{then}\:\mathrm{is}\:\mathrm{it}\:\mathrm{the}\:\mathrm{product}\:\mathrm{with}\:\alpha\:\mathrm{and}\:\mathrm{if}\right. \\ $$$$\left.\mathrm{so}\:\mathrm{wath}\:\mathrm{product}…\:\mathrm{is}\:\Omega\subset\mathbb{C}?\right)…