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Question Number 42291 by Joel578 last updated on 22/Aug/18 $${y}\:=\:\frac{\mathrm{1080}\:−\:\mathrm{19}{x}}{\mathrm{49}}\:\:\:\:\:\:\:\:\left({x},{y}\:\in\:\mathbb{Z}\right) \\ $$$$\mathrm{Find}\:\left({x},{y}\right) \\ $$ Answered by ajfour last updated on 22/Aug/18 $$\mathrm{19}{x}+\mathrm{49}{y}=\mathrm{1080} \\ $$$$\mathrm{19}\left({x}+{y}\right)+\mathrm{30}{y}=\mathrm{30}×\mathrm{36} \\…
Question Number 41754 by Tawa1 last updated on 12/Aug/18 Answered by candre last updated on 12/Aug/18 $$\mathrm{we}\:\mathrm{have}\:\mathrm{from}\:\mathrm{1}\:\mathrm{to}\:\mathrm{1000}\:\mathrm{number}\:\mathrm{that}\:\mathrm{can}\:\mathrm{have}\:\mathrm{3} \\ $$$$\mathrm{3}×× \\ $$$$×\mathrm{3}× \\ $$$$××\mathrm{3} \\ $$$$\mathrm{separating}\:\mathrm{cases}…
Question Number 172210 by Rasheed.Sindhi last updated on 24/Jun/22 $$\boldsymbol{\mathrm{Solve}}\:\boldsymbol{\mathrm{in}}\:\mathbb{N}: \\ $$$$\mathrm{6}^{\boldsymbol{\mathrm{x}}} +\mathrm{6}^{\boldsymbol{\mathrm{y}}} =\mathrm{222} \\ $$ Commented by infinityaction last updated on 24/Jun/22 $$\left(\mathrm{1},\mathrm{3}\right)\:{and}\:\left(\mathrm{3},\mathrm{1}\right) \\…
Question Number 40974 by Penguin last updated on 30/Jul/18 $${X}\:=\:\left({x}_{\mathrm{1}} ,\:{x}_{\mathrm{2}} ,\:…,\:{x}_{{n}} \right),\:\:\:\:{X}\in\mathbb{P}^{{n}} \\ $$$$\: \\ $$$$\mathrm{Does}\:\mathrm{there}\:\mathrm{exist}\:\mathrm{a}\:\mathrm{point}\:\mathrm{in}\:\mathrm{N}-\mathrm{dimensions}, \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{points}\:\mathrm{and}\:\mathrm{line}\:\mathrm{length}\:\left(\mathrm{from}\:\mathrm{origin}\right) \\ $$$$\mathrm{are}\:\mathrm{prime}? \\ $$$$\: \\ $$$$\mathrm{That}\:\mathrm{is},…
Question Number 106409 by bemath last updated on 05/Aug/20 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{number}\:\mathrm{positive}\:\mathrm{integral}\:\mathrm{solutions} \\ $$$$\mathrm{for}\:\mathrm{xy}\:=\:\mathrm{72}\left(\mathrm{x}+\mathrm{y}\right)\:? \\ $$ Answered by 1549442205PVT last updated on 05/Aug/20 $$\mathrm{We}\:\mathrm{have}\: \\ $$$$\mathrm{xy}=\mathrm{72}\left(\mathrm{x}+\mathrm{y}\right)\Leftrightarrow\left(\mathrm{x}−\mathrm{72}\right)\left(\mathrm{y}−\mathrm{72}\right)=\mathrm{72}^{\mathrm{2}} \:\left(\ast\right)…
Question Number 106222 by Rasheed.Sindhi last updated on 03/Aug/20 $$\mathcal{D}{etermine}\:{x}\:\&\:{y}\:{such}\:{that}: \\ $$$$\mathrm{lcm}\left({x},{y}\right)−\mathrm{gcd}\left({x},{y}\right)={x}+{y}. \\ $$ Commented by Rasheed.Sindhi last updated on 03/Aug/20 Thanks sir 〽️�� �� Commented by Rasheed.Sindhi…
Question Number 106017 by Rasheed.Sindhi last updated on 02/Aug/20 $$\mathcal{D}{etermine}\:{x}\:\&\:{y},\:{such}\:{that}: \\ $$$$\mathrm{lcm}\left({x},{y}\right)−\mathrm{gcd}\left({x},{y}\right)={x}+{y}. \\ $$ Answered by Rasheed.Sindhi last updated on 03/Aug/20 $${Let}\:\mathrm{gcd}\left({x},{y}\right)={k}\:{and} \\ $$$$\:\:\:\:{x}={pk}\:,\:{y}={qk}\:\:{with}\:\mathrm{gcd}\left({p},{q}\right)=\mathrm{1} \\…
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Question Number 171359 by Mr.D.N. last updated on 13/Jun/22 $$\mathrm{A}\:\mathrm{heavenly}\:\mathrm{body}\:\mathrm{has}\:\mathrm{mass}\:\mathrm{one}\:\mathrm{third}\:\mathrm{of}\:\mathrm{the}\:\mathrm{earth}\:\mathrm{and}\:\mathrm{its} \\ $$$$\:\mathrm{radius}\:\mathrm{is}\:\mathrm{half}\:\mathrm{as}\:\mathrm{that}\:\mathrm{of}\:\mathrm{the}\:\mathrm{earth}.\:\mathrm{if}\:\mathrm{a}\:\mathrm{stone}\:\mathrm{weights}\:\mathrm{200N}\:\mathrm{on} \\ $$$$\mathrm{the}\:\mathrm{earth}'\mathrm{s}\:\mathrm{surface},\:\mathrm{find}\:\mathrm{its}\:\mathrm{weight}\:\mathrm{on}\:\mathrm{that}\:\mathrm{heavenly}\:\mathrm{body}. \\ $$ Answered by aleks041103 last updated on 13/Jun/22 $${W}=\frac{{GM}_{{pl}} {m}}{{R}^{\mathrm{2}}…