Question Number 143728 by Dwaipayan Shikari last updated on 17/Jun/21 $$\int_{\mathrm{1}} ^{\infty} \frac{\left\{{x}\right\}}{{x}^{\mathrm{3}} }{dx}=\mathrm{1}−\frac{\pi^{\mathrm{2}} }{\mathrm{12}} \\ $$ Answered by mathmax by abdo last updated on…
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Question Number 12631 by 786786AM last updated on 27/Apr/17 $$\:\:\mathrm{Find}\:\mathrm{tbe}\:\mathrm{sloution}\:\mathrm{set}\:\mathrm{of}\:\frac{\mathrm{5}}{\left(\mathrm{x}−\mathrm{3}\right)\left(\mathrm{3}+\mathrm{x}\right)}\:>\:\mathrm{0}. \\ $$ Answered by mrW1 last updated on 27/Apr/17 $$\left({x}−\mathrm{3}\right)\left({x}+\mathrm{3}\right)>\mathrm{0} \\ $$$${x}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} >\mathrm{0} \\…
Question Number 78160 by Lontum Hans last updated on 14/Jan/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{term}\:\mathrm{independent}\:\mathrm{of}\:\mathrm{x}\:\mathrm{in} \\ $$$$\:\:\left[\:\:\frac{\mathrm{x}−\mathrm{1}}{\mathrm{x}}\right]^{\mathrm{9}} \\ $$ Commented by mathmax by abdo last updated on 14/Jan/20 $$\left(\frac{{x}−\mathrm{1}}{{x}}\right)^{\mathrm{9}}…
Question Number 78161 by TawaTawa last updated on 14/Jan/20 Answered by mr W last updated on 15/Jan/20 $${M}=\mathrm{5}\:{kg} \\ $$$${m}=\mathrm{2}\:{kg} \\ $$$${T}−\mu{mg}={ma} \\ $$$${F}−{T}−\mu{mg}−\mu\left({m}+{Mg}\right)={Ma} \\…
Question Number 143698 by Dwaipayan Shikari last updated on 17/Jun/21 $$\:{My}\:{first}\:{Contribution}\:{to}\:{this}\:{forum}.\: \\ $$$${One}\:{year}\:{later}\: \\ $$$${Q}\:\mathrm{98831} \\ $$ Commented by Dwaipayan Shikari last updated on 17/Jun/21…
Question Number 78156 by Rio Michael last updated on 14/Jan/20 $$\mathrm{Given}\:\mathrm{that}\:{u}_{{n}\:+\:\mathrm{1}} =\:\frac{{a}_{{n}} }{\mathrm{2}}\:+\:\mathrm{5}\:\:\: \\ $$$${evalatuate}\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{a}_{{n}} \\ $$$${deduce}\:{if}\:{a}_{{n}\:} \:{is}\:{convergent}\:{or}\:{divergent}. \\ $$ Commented by mathmax by…
Question Number 12612 by frank ntulah last updated on 26/Apr/17 $$\mathrm{Use}\:\mathrm{Newtown}\:\mathrm{Raphson}\:\mathrm{method}\:\mathrm{to}\:\mathrm{find}\:\mathrm{aproximate} \\ $$$$\mathrm{value}\:\mathrm{of}\:\:\boldsymbol{{X}}=\sqrt{\left(\frac{\mathrm{7}}{\boldsymbol{{x}}+\mathrm{1}}\right)}\:,\mathrm{starting}\:\mathrm{with}\:\boldsymbol{{x}}_{\mathrm{0}} =\mathrm{2}. \\ $$$$\boldsymbol{{perform}}\:\mathrm{4}\:\boldsymbol{{iteration}}\:\boldsymbol{{and}}\:\boldsymbol{{all}}\:\boldsymbol{{iteration}}\: \\ $$$$\boldsymbol{{should}}\:\boldsymbol{{be}}\:\boldsymbol{{presented}}\:\boldsymbol{{in}}\:\mathrm{4}\:\boldsymbol{{decimal}}\:\boldsymbol{{places}} \\ $$ Answered by mrW1 last updated…
Question Number 12611 by tawa last updated on 26/Apr/17 $$\mathrm{A}\:\mathrm{drum}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{100g}\:\mathrm{is}\:\mathrm{rolled}\:\mathrm{into}\:\mathrm{the}\:\mathrm{deck}\:\mathrm{of}\:\mathrm{a}\:\mathrm{lorry}\:\mathrm{1}.\mathrm{5m}\:\mathrm{above}\:\mathrm{a}\: \\ $$$$\mathrm{horizontal}\:\mathrm{floor}\:\mathrm{using}\:\mathrm{a}\:\mathrm{plank}\:\mathrm{4m}\:\mathrm{long}.\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{workdone}\:\mathrm{against} \\ $$$$\mathrm{gravity}\:\mathrm{during}\:\mathrm{the}\:\mathrm{process}.\:\left(\mathrm{g}\:=\:\mathrm{10m}/\mathrm{s}^{\mathrm{2}} \right). \\ $$ Answered by mrW1 last updated on 27/Apr/17 $${W}={mgh}=\mathrm{0}.\mathrm{1}×\mathrm{10}×\mathrm{1}.\mathrm{5}=\mathrm{1}.\mathrm{5}\:{J}…
Question Number 12610 by tawa last updated on 26/Apr/17 $$\mathrm{A}\:\mathrm{steam}\:\mathrm{engine}\:\mathrm{of}\:\mathrm{efficiency}\:\mathrm{50\%}\:\mathrm{burns}\:\mathrm{a}\:\mathrm{1g}\:\mathrm{of}\:\mathrm{coal}\:\mathrm{to}\:\mathrm{produce}\:\mathrm{10000J} \\ $$$$\mathrm{of}\:\mathrm{energy}.\:\mathrm{if}\:\mathrm{it}\:\mathrm{burns}\:\mathrm{20g}\:\mathrm{per}\:\mathrm{sec},\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{output}\:\mathrm{power}. \\ $$ Answered by mrW1 last updated on 27/Apr/17 $${P}=\mathrm{0}.\mathrm{5}×\mathrm{20}×\mathrm{10000}=\mathrm{100000}\:{Watt}=\mathrm{100}\:{kW} \\ $$ Commented…