Question Number 152844 by bobhans last updated on 02/Sep/21 $$\:\:\:\:\:\:\:\:\:\:\:{simplify}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{3}^{{x}} \:+\:\mathrm{63}}{\mathrm{21}^{{x}−\mathrm{2}} \:+\:\mathrm{7}^{{x}−\mathrm{1}} }\: \\ $$ Answered by Rasheed.Sindhi last updated on 02/Sep/21 $$\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{3}^{{x}}…
Question Number 152840 by liberty last updated on 02/Sep/21 Answered by MJS_new last updated on 04/Sep/21 $$\mathrm{transforming}\:\Rightarrow \\ $$$${x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} +\left({y}^{\mathrm{2}} +\mathrm{3}\right){x}−{y}\left(\mathrm{3}{y}+\mathrm{1}\right)=\mathrm{0} \\ $$$${x}^{\mathrm{2}} −\frac{\mathrm{1}}{{y}}{x}+{y}^{\mathrm{2}}…
Question Number 87302 by M±th+et£s last updated on 03/Apr/20 $${for}\:\mid{z}−\mathrm{1}\mid=\mathrm{1}\:{show}\:{that} \\ $$$${tan}\left(\frac{{arg}\left({z}−\mathrm{1}\right)}{\mathrm{2}}\right)−\frac{\mathrm{2}{i}}{{z}}=−\mathrm{1} \\ $$ Commented by MJS last updated on 04/Apr/20 $$\mathrm{tan}\:\frac{\mathrm{arg}\:\left({z}−\mathrm{1}\right)}{\mathrm{2}}\:\in\mathbb{R} \\ $$$$−\frac{\mathrm{2i}}{{z}}\notin\mathbb{R}\:\forall\:{z}={a}+{b}\mathrm{i};\:{a}\neq\mathrm{0} \\…
Question Number 152834 by liberty last updated on 02/Sep/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 152828 by mathdanisur last updated on 01/Sep/21 $$\underset{\:\mathrm{1}} {\overset{\:\infty} {\int}}\:\frac{\sqrt{\mathrm{x}}\:\mathrm{ln}\:\mathrm{x}}{\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}}\:\mathrm{dx}\:=\:? \\ $$ Answered by Ar Brandon last updated on 01/Sep/21 $${f}\left(\kappa\right)=\int_{\mathrm{1}} ^{\infty}…
Question Number 152827 by mathdanisur last updated on 01/Sep/21 Answered by MJS_new last updated on 02/Sep/21 $${p}=\frac{{xy}}{{x}+{y}}\:\Leftrightarrow\:{y}=\frac{{px}}{{x}−{p}}\:\Leftrightarrow\:{x}=\frac{{py}}{{y}−{p}} \\ $$$$\Rightarrow\:{x}>{p}\wedge{y}>{p}\:\wedge\:\left({x}−{p}\right)\mid\left({px}\right)\:\wedge\:\left({y}−{p}\right)\mid\left({py}\right) \\ $$$$\Rightarrow \\ $$$$\left(\mathrm{1}\right)\:{y}={x}\:\Rightarrow\:{y}={x}=\mathrm{2}{p} \\ $$$$\left(\mathrm{2}\right)\:{y}={p}+\mathrm{1}\:\Rightarrow\:{x}={p}\left({p}+\mathrm{1}\right)…
Question Number 21733 by Joel577 last updated on 02/Oct/17 $$\mathrm{If}\:{p}\:\mathrm{is}\:\mathrm{one}\:\mathrm{of}\:\:\mathrm{roots}\:\mathrm{from}\:{x}^{\mathrm{2}} \:−\:\mathrm{2}{x}\:+\:\mathrm{6}\:=\:\mathrm{0} \\ $$$$\mathrm{then}\:{p}^{\mathrm{4}} \:+\:\mathrm{16}{p}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:… \\ $$ Answered by mrW1 last updated on 02/Oct/17 $$\mathrm{p}^{\mathrm{2}} −\mathrm{2p}+\mathrm{6}=\mathrm{0}…
Question Number 152791 by mathdanisur last updated on 01/Sep/21 Answered by MJS_new last updated on 02/Sep/21 $$\left({xy}−\mathrm{1}\right)^{\mathrm{2}} −\mathrm{16}\left({x}−\mathrm{1}\right)\left({y}−\mathrm{1}\right)\geqslant\mathrm{0} \\ $$$${x}^{\mathrm{2}} {y}^{\mathrm{2}} −\mathrm{18}{xy}+\mathrm{16}{x}+\mathrm{16}{y}−\mathrm{15}\geqslant\mathrm{0} \\ $$$${x}=\mathrm{3}+{p}\wedge{y}=\mathrm{3}+{q}\wedge{p}\geqslant\mathrm{0}\wedge{q}\geqslant\mathrm{0} \\…
Question Number 87253 by peter frank last updated on 03/Apr/20 $${Three}\:{pair}\:{of}\:{socks}\:{are} \\ $$$${placed}\:{in}\:{a}\:{box}.{If}\:{two} \\ $$$${socks}\:{are}\:{drawn}\:{at} \\ $$$${random}\:{from}\:{the}\:{box} \\ $$$${What}\:{is}\:{the}\:{probability} \\ $$$$\left({a}\right){of}\:{drawing}\:\:{a}\:{match} \\ $$$${pair} \\ $$$$\left({b}\right){of}\:{drawing}\:{a}\:{socks}…
Question Number 152790 by mathdanisur last updated on 01/Sep/21 Commented by MJS_new last updated on 01/Sep/21 $$\mathrm{you}\:\mathrm{can}\:\mathrm{do}\:\mathrm{it}\:\mathrm{yourself}. \\ $$$$\mathrm{simply}\:\mathrm{let}\:{x}=\frac{{t}}{{a}}\:\mathrm{and}\:\mathrm{solve}\:\mathrm{it}! \\ $$ Terms of Service Privacy…