Question Number 75203 by jagannath.02 last updated on 08/Dec/19 Answered by Rio Michael last updated on 08/Dec/19 $$\:{if}\:{we}\:{increase}\:{the}\:{temperature}\:{of}\: \\ $$$${a}\:{diatomic}\:{gas},\:{the}\:{molecules}\:{gain}\:{energy} \\ $$$${and}\:{move}\:{randomly}\:{applying}\:{more}\:{pressure}. \\ $$$${from}\:{the}\:{graph}\:{ab}\:{shows}\:{how}\:{temperature}\:{increases}. \\…
Question Number 140738 by BHOOPENDRA last updated on 12/May/21 Commented by BHOOPENDRA last updated on 12/May/21 $${mr}.{W}\:{sir}? \\ $$ Commented by mr W last updated…
Question Number 9662 by Joel575 last updated on 23/Dec/16 $$\mathrm{I}\:\mathrm{have}\:\mathrm{2}\:\mathrm{buckets}.\:\mathrm{Each}\:\mathrm{bucket}\:\mathrm{contains}\:\mathrm{green}\:\mathrm{and}\:\mathrm{blue}\:\mathrm{balls} \\ $$$$\mathrm{The}\:\mathrm{first}\:\mathrm{bucket}\:\mathrm{contains}\:\mathrm{3}\:\mathrm{green}\:\mathrm{balls}\:\mathrm{and}\:\mathrm{7}\:\mathrm{blue}\:\mathrm{balls}. \\ $$$$\mathrm{Second}\:\mathrm{bucket}\:\mathrm{contains}\:\mathrm{7}\:\mathrm{green}\:\mathrm{balls}\:\mathrm{and}\:\mathrm{8}\:\mathrm{blue}\:\mathrm{balls}. \\ $$$$\mathrm{I}\:\mathrm{want}\:\mathrm{to}\:\mathrm{take}\:\mathrm{those}\:\mathrm{balls}\:\mathrm{with}\:\mathrm{coin}\:\mathrm{toss}. \\ $$$$\mathrm{If}\:\mathrm{head},\:\mathrm{I}\:\mathrm{will}\:\mathrm{take}\:\mathrm{1}\:\mathrm{ball}\:\mathrm{from}\:\mathrm{each}\:\mathrm{bucket}. \\ $$$$\mathrm{But}\:\mathrm{if}\:\mathrm{tail},\:\mathrm{I}\:\mathrm{will}\:\mathrm{take}\:\mathrm{2}\:\mathrm{balls}\:\mathrm{from}\:\mathrm{each}\:\mathrm{bucket}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{propability}\:\mathrm{if}\:\mathrm{all}\:\mathrm{the}\:\mathrm{balls}\:\mathrm{that}\:\mathrm{have}\:\mathrm{been}\:\mathrm{taken} \\ $$$$\mathrm{have}\:\mathrm{the}\:\mathrm{same}\:\mathrm{color}? \\…
Question Number 140735 by ZiYangLee last updated on 12/May/21 $$\mathrm{Using}\:\mathrm{vector}\:\mathrm{method},\:\mathrm{prove}\:\mathrm{that}\:\mathrm{three} \\ $$$$\mathrm{median}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{are}\:\mathrm{concurrent}. \\ $$ Answered by MJS_new last updated on 12/May/21 $$\mathrm{let}\:{A}=\begin{pmatrix}{\mathrm{0}}\\{\mathrm{0}}\end{pmatrix}\:\wedge{B}=\begin{pmatrix}{{c}}\\{\mathrm{0}}\end{pmatrix}\:\wedge{C}=\begin{pmatrix}{{p}}\\{{h}}\end{pmatrix} \\ $$$${M}_{{a}} =\frac{{B}+{C}}{\mathrm{2}}=\begin{pmatrix}{\frac{{c}+{p}}{\mathrm{2}}}\\{\frac{{h}}{\mathrm{2}}}\end{pmatrix}\:\:\:\:\:{M}_{{b}}…
Question Number 9661 by geovane10math last updated on 23/Dec/16 $$\left.{a}\right)\:\mathrm{2}^{{i}} \:=\: \\ $$$$ \\ $$$$\left.{b}\right)\:\left({a}_{\mathrm{1}} \:+\:{b}_{\mathrm{1}} {i}\right)^{{a}_{\mathrm{2}} \:+\:{b}_{\mathrm{2}} {i}} \:=\: \\ $$$${Powers}\:{of}\:{complex}\:{numbers}\:??? \\ $$ Commented…
Question Number 140734 by liberty last updated on 12/May/21 $$\mathrm{Let}\:\mathrm{m},\mathrm{n}\:\mathrm{be}\:\mathrm{given}\:\mathrm{positive}\:\mathrm{integers}. \\ $$$$\mathrm{If}\:\mathrm{x}\:\&\:\mathrm{y}\:\mathrm{are}\:\mathrm{positive}\:\mathrm{numbers}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{x}+\mathrm{y}=\:\mathrm{S}\:,\:\mathrm{S}\:\mathrm{is}\:\mathrm{a}\:\mathrm{constant},\:\mathrm{find} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{that}\:\mathrm{maximize} \\ $$$$\mathrm{Q}=\mathrm{x}^{\mathrm{m}} \mathrm{y}^{\mathrm{n}} \:. \\ $$ Commented by mr…
Question Number 9658 by tawakalitu last updated on 23/Dec/16 $$\mathrm{Experiment}\:\mathrm{shows}\:\mathrm{that}\:\mathrm{the}\:\mathrm{viscous}\:\mathrm{force},\:\mathrm{F} \\ $$$$\mathrm{on}\:\mathrm{a}\:\mathrm{spherical}\:\mathrm{body}\:\mathrm{of}\:\mathrm{radius},\:\mathrm{r}\:\mathrm{moving}\:\mathrm{with} \\ $$$$\mathrm{angular}\:\mathrm{velocity},\:\mathrm{n}\:\mathrm{is},\:\mathrm{F}\:=\:\mathrm{Kr}^{\mathrm{a}} \mathrm{n}^{\mathrm{b}} \omega^{\mathrm{c}} . \\ $$$$\mathrm{Where}\:\mathrm{K}\:\mathrm{is}\:\mathrm{a}\:\mathrm{dimentionless}\:\mathrm{constant}. \\ $$$$\mathrm{using}\:\mathrm{the}\:\mathrm{method}\:\mathrm{of}\:\mathrm{dimentional}\:\mathrm{analysis}, \\ $$$$\mathrm{determine}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\mathrm{a},\:\mathrm{b}\:\mathrm{and}\:\mathrm{c} \\ $$…
Question Number 140730 by liberty last updated on 12/May/21 $$\mathrm{If}\:\mathrm{equation}\:\mathrm{2log}\:\left(\mathrm{x}+\mathrm{3}\right)=\mathrm{log}\:\mathrm{ax} \\ $$$$\mathrm{has}\:\mathrm{only}\:\mathrm{one}\:\mathrm{solution}.\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{a}. \\ $$ Answered by mr W last updated on 12/May/21 $${a}\neq\mathrm{0}…
Question Number 75193 by mathocean1 last updated on 08/Dec/19 $${it}\:{is}\:{given}\:{that}\:{cos}\frac{\pi}{\mathrm{5}}=\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{4}} \\ $$$${calculate}\:{the}\:{exact}\:{val}\mathrm{ue}\:{of}\: \\ $$$${cos}\frac{\mathrm{2}\pi}{\mathrm{5}}\:\:\:{and}\:\:{cos}\frac{\mathrm{3}\pi}{\mathrm{5}} \\ $$ Answered by $@ty@m123 last updated on 08/Dec/19 Commented by…
Question Number 9654 by ridwan balatif last updated on 22/Dec/16 $$\underset{{x}\rightarrow\mathrm{4}} {\mathrm{lim}}\frac{\mathrm{ax}+\mathrm{b}−\sqrt{\mathrm{x}}}{\mathrm{x}−\mathrm{4}}=\frac{\mathrm{3}}{\mathrm{4}},\:\:\mathrm{a}+\mathrm{b}=…? \\ $$ Answered by prakash jain last updated on 22/Dec/16 $$\underset{{x}\rightarrow\mathrm{4}} {\mathrm{lim}}\frac{\mathrm{ax}+\mathrm{b}−\sqrt{\mathrm{x}}}{\mathrm{x}−\mathrm{4}}=\frac{\mathrm{3}}{\mathrm{4}},\:\:\mathrm{a}+\mathrm{b}=…? \\…