Question Number 4633 by sanusihammed last updated on 16/Feb/16 $${The}\:{volume}\:{V}\:\left({in}\:{liters}\right)\:\:{of}\:{petrol}\:{in}\:{a}\:{car}\:{tank}\:{is}\:{decreasing}\: \\ $$$${at}\:{the}\:{rate}\:{of}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\frac{\mathrm{1}}{\mathrm{5}}\:−\:\frac{{m}}{\mathrm{2000}}\right)\:{liters}/{km} \\ $$$$ \\ $$$${After}\:{travelling}\:{m}\:{kilometers}.\:{Assuming}\:{that}\:{V}\:=\:\mathrm{40} \\ $$$${when}\:{m}\:=\:\mathrm{0}.\:{Find}\:{an}\:{expression}\:{for}\:{V}\:\:{in}\:{terms}\:{of}\:{m}. \\ $$$$ \\ $$ Answered…
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Question Number 4624 by sanusihammed last updated on 14/Feb/16 Answered by Yozzii last updated on 15/Feb/16 $$\left(\mathrm{12}\right)\:{The}\:{equation}\:{of}\:{motion}\:{of}\:{the}\:{particle} \\ $$$${is}\:{given}\:{as} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\frac{{d}}{{ds}}\left(\frac{{v}^{\mathrm{2}} }{\mathrm{2}}\right)=−{g}−{kv}^{\mathrm{2}} . \\ $$$${v}\:{is}\:{a}\:{function}\:{of}\:{s}\:{as}\:{s}\:{and}\:{v}\:{are}\:…
Question Number 70132 by RAKESH MANDA last updated on 01/Oct/19 $$\underset{{n}=\mathrm{1}} {\overset{\mathrm{3050}} {\sum}}\:{i}^{{n}} \\ $$ Commented by mathmax by abdo last updated on 01/Oct/19 $${S}\:=\sum_{{n}=\mathrm{0}}…
Question Number 135653 by I want to learn more last updated on 14/Mar/21 Commented by mr W last updated on 14/Mar/21 $${question}\:{is}\:{wrong}.\:{just}\:{check}\:{again}. \\ $$ Commented…
Question Number 4584 by MrGreg last updated on 08/Feb/16 $$ \\ $$ Answered by FilupSmith last updated on 09/Feb/16 $$\:\:\:\:{S}=\mathrm{1}−\mathrm{2}+\mathrm{4}−\mathrm{8}+\mathrm{16}−\mathrm{32}+\mathrm{64}−… \\ $$$$+{S}=\mathrm{0}+\mathrm{1}−\mathrm{2}+\mathrm{4}−\mathrm{8}+\mathrm{16}−\mathrm{32}+\mathrm{64}−… \\ $$$$\mathrm{2}{S}=\mathrm{1}+\left(−\mathrm{1}+\mathrm{2}−\mathrm{4}+\mathrm{8}−\mathrm{16}+…\right) \\…
Question Number 135638 by Dwaipayan Shikari last updated on 14/Mar/21 $$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(\sqrt{\mathrm{5}}−\mathrm{2}\right)^{\mathrm{2}{n}+\mathrm{1}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} }=\frac{\pi^{\mathrm{2}} }{\mathrm{24}}−\frac{\mathrm{1}}{\mathrm{12}}{log}^{\mathrm{2}} \left(\mathrm{2}+\sqrt{\mathrm{5}}\right) \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 70069 by tw000001 last updated on 01/Oct/19 $$\underset{{n}=\mathrm{1}} {\overset{\mathrm{5}} {\prod}}\frac{\left(\mathrm{12}{n}−\mathrm{2}\right)^{\mathrm{4}} +\mathrm{18}^{\mathrm{2}} }{\left(\mathrm{12}{n}−\mathrm{8}\right)^{\mathrm{4}} +\mathrm{18}^{\mathrm{2}} } \\ $$$$=\frac{\left(\mathrm{10}^{\mathrm{4}} +\mathrm{324}\right)\left(\mathrm{22}^{\mathrm{4}} +\mathrm{324}\right)\left(\mathrm{34}^{\mathrm{4}} +\mathrm{324}\right)\left(\mathrm{46}^{\mathrm{4}} +\mathrm{324}\right)\left(\mathrm{58}^{\mathrm{4}} +\mathrm{324}\right)}{\left(\mathrm{4}^{\mathrm{4}} +\mathrm{324}\right)\left(\mathrm{16}^{\mathrm{4}} +\mathrm{324}\right)\left(\mathrm{28}^{\mathrm{4}}…
Question Number 70051 by Aditya789 last updated on 30/Sep/19 $$\frac{{a}+{b}}{{c}}=\frac{{cos}\left(\frac{{a}−{b}}{\mathrm{2}}\right)}{{cos}\frac{{c}}{\mathrm{2}}} \\ $$ Answered by $@ty@m123 last updated on 01/Oct/19 $${LHS}=\frac{{a}+{b}}{{c}}=\frac{\mathrm{sin}\:{A}+\mathrm{sin}\:{B}}{\mathrm{sin}\:{C}} \\ $$$$=\frac{\mathrm{2sin}\:\frac{{A}+{B}}{\mathrm{2}}\mathrm{cos}\:\frac{{A}−{B}}{\mathrm{2}}}{\mathrm{2sin}\:\frac{{C}}{\mathrm{2}}\mathrm{cos}\:\frac{{C}}{\mathrm{2}}} \\ $$$$=\frac{\mathrm{sin}\:\frac{\pi−{C}}{\mathrm{2}}\mathrm{cos}\:\frac{{A}−{B}}{\mathrm{2}}}{\mathrm{sin}\:\frac{{C}}{\mathrm{2}}\mathrm{cos}\:\frac{{C}}{\mathrm{2}}} \\…