Question Number 138613 by byaw last updated on 15/Apr/21 Answered by physicstutes last updated on 15/Apr/21 $$\mathrm{This}\:\mathrm{question}\:\mathrm{is}\:\mathrm{real}\:\mathrm{lol}! \\ $$$$\mathrm{2}.\:\left(\mathrm{a}\right)\:\mathrm{Total}\:\mathrm{length}\:=\:\frac{\mathrm{9}}{\mathrm{4}}\:\mathrm{m}\: \\ $$$$\Rightarrow\:\mathrm{lenght}\:\mathrm{used}\:\mathrm{for}\:\mathrm{a}\:\mathrm{job}\:=\:\frac{\mathrm{2}}{\mathrm{3}}×\frac{\mathrm{9}}{\mathrm{4}}\:=\:\frac{\mathrm{3}}{\mathrm{2}}\:\mathrm{m} \\ $$$$\mathrm{length}\:\mathrm{used}\:=\:\frac{\mathrm{9}}{\mathrm{4}}−\frac{\mathrm{3}}{\mathrm{2}}\:=\:\frac{\mathrm{3}}{\mathrm{4}}\mathrm{m} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{lenght}\:\mathrm{used}\:\mathrm{for}\:\mathrm{job}\:=\:\frac{\mathrm{1}}{\mathrm{8}}×\frac{\mathrm{3}}{\mathrm{4}}\:=\:\frac{\mathrm{3}}{\mathrm{32}}…
Question Number 138600 by Raxreedoroid last updated on 15/Apr/21 $$\mathrm{prove}\:\mathrm{or}\:\mathrm{disprove} \\ $$$$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{f}\left({k}\right)={f}\left(\mathrm{1}\right)+\underset{{k}=\mathrm{2}} {\overset{{n}} {\sum}}\left(\frac{\underset{{i}=\mathrm{1}} {\overset{{k}−\mathrm{1}} {\sum}}\left(−\mathrm{1}\right)^{{i}+\mathrm{1}} {f}\left({i}+\mathrm{1}\right){C}_{{i}−\mathrm{1}} ^{{k}−\mathrm{2}} }{\left({k}−\mathrm{1}\right)!}\:\underset{{i}=\mathrm{1}} {\overset{{k}−\mathrm{1}} {\prod}}\left({n}−{i}\right)\right) \\ $$…
Question Number 7519 by Tawakalitu. last updated on 01/Sep/16 $${A}\:\left(\mathrm{2}\:×\:\mathrm{3}\right)\:{rectangle}\:{and}\:{a}\:\left(\mathrm{3}\:×\:\mathrm{4}\right)\:{rectangle}\:{are}\:{contain}\:{within}\: \\ $$$${a}\:{square}\:{without}\:{over}\:{laping}\:{at}\:{any}\:{inferior}\:{point}\:,\:{and}\:{the}\: \\ $$$${sides}\:{of}\:{the}\:{square}\:{are}\:{parallel}\:{to}\:{the}\:{sides}\:{of}\:{the}\:{two}\:{given} \\ $$$${rectangles}.\:{what}\:{is}\:{the}\:{smallest}\:{possible}\:{area}\:{of}\:{the}\:{square}. \\ $$ Commented by Rasheed Soomro last updated on…
Question Number 138560 by Raxreedoroid last updated on 14/Apr/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}} \left(\mathrm{ln}\:\left({n}+\mathrm{1}\right)−\mathrm{ln}\:\left({n}\right)\right)=? \\ $$ Answered by Dwaipayan Shikari last updated on 14/Apr/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty}…
Question Number 7449 by Tawakalitu. last updated on 29/Aug/16 $${The}\:{sum}\:{of}\:{the}\:{first}\:\mathrm{3}\:{terms}\:{of}\:{an}\:{AP}\:{is}\:\mathrm{36}\:{and}\:{the} \\ $$$${product}\:{of}\:{the}\:{first}\:\mathrm{3}\:{terms}\:{of}\:{a}\:{GP}\:{is}\:\mathrm{1728}.\:{if}\:{the} \\ $$$${second}\:{term}\:{of}\:{the}\:{linear}\:{sequence}\:{is}\:\mathrm{12}\:{and}\:{such} \\ $$$${that}\:{the}\:{second}\:{term}\:{of}\:{the}\:{GP}\:{is}\:{equal}\:{to}\:{the}\:{second} \\ $$$${term}\:{of}\:{the}\:{AP}.\:{find} \\ $$$$\left(\mathrm{1}\right)\:{The}\:{AP} \\ $$$$\left(\mathrm{2}\right)\:{The}\:{GP} \\ $$ Answered…
Question Number 138513 by mathlove last updated on 14/Apr/21 Answered by MJS_new last updated on 14/Apr/21 $${AB}+\mathrm{9}=\mathrm{3}\left({BA}\right) \\ $$$$\mathrm{10}{A}+{B}+\mathrm{9}=\mathrm{30}{B}+\mathrm{3}{A} \\ $$$${A}=\frac{\mathrm{29}{B}−\mathrm{9}}{\mathrm{7}}\:\Rightarrow\:{B}=\mathrm{2}\wedge{A}=\mathrm{7} \\ $$$$\mathrm{72}+\mathrm{9}=\mathrm{3}×\mathrm{27} \\ $$$${A}+{B}=\mathrm{9}…
Question Number 7442 by lakshaysethi last updated on 29/Aug/16 $${is}\:\mathrm{0}×\mathrm{0}\:{not}\:{defined}\:{or}\:{equal}\:{to}\:\mathrm{0}? \\ $$$${if}\:{it}\:{is}\:{not}\:{defined}\:{then}\:{why}? \\ $$ Commented by Rasheed Soomro last updated on 29/Aug/16 $$\mathrm{0}×\mathrm{0}\:{is}\:{defined}\:{and}\:{it}\:{is}\:{equal}\:{to}\:\mathrm{0}. \\ $$…
Question Number 138511 by mathlove last updated on 14/Apr/21 Commented by MJS_new last updated on 14/Apr/21 $$\mathrm{005}\:\:\:\:\:\mathrm{014}\:\:\:\:\:\mathrm{023}\:\:\:\:\:\mathrm{113}\:\:\:\:\:\mathrm{122}\:\:\:\:\:… \\ $$$$\mathrm{050}\:\:\:\:\:\mathrm{140}\:\:\:\:\:\mathrm{230}\:\:\:\:\:\mathrm{131}\:\:\:\:\:\mathrm{221} \\ $$$$\mathrm{500}\:\:\:\:\:\mathrm{401}\:\:\:\:\:\mathrm{302}\:\:\:\:\:\mathrm{311}\:\:\:\:\:\mathrm{212} \\ $$$$==\:\:\:\:\:==\:\:\:\:\:==\:\:\:\:\:==\:\:\:\:\:== \\ $$$$\mathrm{555}\:\:\:\:\:\mathrm{555}\:\:\:\:\:\mathrm{555}\:\:\:\:\:\mathrm{555}\:\:\:\:\:\mathrm{555}…
Question Number 72965 by Raxreedoroid last updated on 05/Nov/19 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{this}\:\mathrm{equation}\:\mathrm{is}\:\mathrm{true}: \\ $$$$\underset{{x}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\prod}}\left(\mathrm{2}{x}+\mathrm{1}\right)=\frac{\left(\mathrm{2}{x}−\mathrm{1}\right)!}{\left(\mathrm{2}\right)^{{x}−\mathrm{1}} \left({x}−\mathrm{1}\right)!} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 7399 by Tawakalitu. last updated on 27/Aug/16 $${In}\:{an}\:{AP}\:,\:{if}\:{the}\:{m}^{{th}} \:{term}\:{is}\:{n}\:{and}\:{the}\:{n}^{{th}} \:{term} \\ $$$${is}\:{m}.\:{where}\:{m}\:{is}\:{not}\:{equal}\:{to}\:{n}.\:{find} \\ $$$$\left(\mathrm{1}\right)\:{The}\:{value}\:{of}\:\left({m}\:+\:{n}\right)^{{th}} \:{term} \\ $$$$\left(\mathrm{2}\right)\:{The}\:{p}^{{th}} \:{term}. \\ $$ Answered by Yozzia…