Question Number 213650 by MathematicalUser2357 last updated on 12/Nov/24 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{pythagorean}\:\mathrm{theorem}\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} ={c}^{\mathrm{2}} \:\mathrm{exist}. \\ $$ Answered by MathematicalUser2357 last updated on 12/Nov/24 $$ \\ $$$$…
Question Number 213636 by hardmath last updated on 11/Nov/24 $$\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{x}\:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$$$\mathrm{find}:\:\:\:\mathrm{x}^{\mathrm{10}} \:=\:? \\ $$ Answered by A5T last updated on 11/Nov/24 $${x}^{\mathrm{2}} ={x}−\mathrm{1}\Rightarrow{x}^{\mathrm{3}}…
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Question Number 213624 by hardmath last updated on 10/Nov/24 $$\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{5x}\:−\:\mathrm{42}\:=\:\left(\mathrm{x}\:−\:\mathrm{3}\right)\centerdot\mathrm{P}\left(\mathrm{x}\right) \\ $$$$\mathrm{Find}:\:\:\:\mathrm{P}\left(\mathrm{3}\right)\:=\:? \\ $$ Answered by A5T last updated on 10/Nov/24 $$\left({x}−\mathrm{3}\right)\left({x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{14}\right)−\left({x}−\mathrm{3}\right){P}\left({x}\right)=\mathrm{0} \\…
Question Number 213626 by Tawa11 last updated on 10/Nov/24 Commented by Tawa11 last updated on 10/Nov/24 The area of ABCD is 40.5 square units .…
Question Number 213621 by hardmath last updated on 10/Nov/24 $$\mathrm{a},\mathrm{b}>\mathrm{0} \\ $$$$\frac{\mathrm{1}}{\mathrm{a}}\:+\:\frac{\mathrm{1}}{\mathrm{b}}\:=\:\mathrm{2}\:\:\:\mathrm{and}\:\:\:\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:=\:\mathrm{12} \\ $$$$\mathrm{a}\:+\:\mathrm{b}\:=\:? \\ $$ Answered by Ghisom last updated on 10/Nov/24…
Question Number 213613 by Spillover last updated on 10/Nov/24 Answered by Frix last updated on 10/Nov/24 $$\mathrm{The}\:\mathrm{universe}\:\mathrm{is}\:\mathrm{all}\:\mathrm{that}\:\mathrm{there}\:\mathrm{is},\:\mathrm{it}'\mathrm{s}\:\mathrm{simply} \\ $$$$\mathrm{expanding}\:\mathrm{into}\:\mathrm{itself}. \\ $$$$\mathrm{We}\:\mathrm{cannot}\:\mathrm{find}\:\mathrm{analogies}\:\mathrm{to}\:\mathrm{this},\:\mathrm{the}\:\mathrm{picture} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{balloon}\:\mathrm{isn}'\mathrm{t}\:\mathrm{accurate}. \\ $$…
Question Number 213614 by Spillover last updated on 10/Nov/24 Commented by Frix last updated on 10/Nov/24 $$\mathrm{A}\:\mathrm{photon}\:\mathrm{is}\:\mathrm{a}\:\mathrm{quantum}\:\mathrm{particle}. \\ $$$$\mathrm{We}\:\mathrm{cannot}\:\mathrm{measure}\:\mathrm{its}\:\mathrm{location}\:\mathrm{because} \\ $$$$\mathrm{we}\:\mathrm{exactly}\:\mathrm{know}\:\left(\mathrm{measured}\right)\:\mathrm{its}\:\mathrm{speed}. \\ $$$$\mathrm{Its}\:\mathrm{speed}\:\mathrm{is}\:\mathrm{the}\:\mathrm{same}\:\mathrm{in}\:\mathrm{every}\:\mathrm{reference} \\ $$$$\mathrm{frame}.\:\mathrm{You}\:\mathrm{cannot}\:\mathrm{stop}\:\mathrm{it}\:\mathrm{and}\:\mathrm{say}\:“\mathrm{here}…
Question Number 213615 by Spillover last updated on 10/Nov/24 Answered by Frix last updated on 10/Nov/24 $$\mathrm{The}\:\mathrm{photon}. \\ $$$$\mathrm{The}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{light}\:\mathrm{is}\:\mathrm{the}\:\mathrm{same}\:\mathrm{in}\:\mathrm{every} \\ $$$$\mathrm{reference}\:\mathrm{frame}.\:\mathrm{This}\:\mathrm{means}\:\mathrm{no}\:\mathrm{matter}\:\mathrm{how} \\ $$$$\mathrm{fast}\:\mathrm{the}\:\mathrm{observer}\:\mathrm{moves},\:\mathrm{the}\:\mathrm{photons}\:\mathrm{are} \\ $$$$\mathrm{always}\:\mathrm{moving}\:\mathrm{away}\:\mathrm{from}\:\mathrm{him}\:\mathrm{with}\:\mathrm{about}…