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Question Number 46631 Answers: 0 Comments: 1
Question Number 46629 Answers: 1 Comments: 0
$${An}\:{object}\:{is}\:{projected}\:{from}\:{a} \\ $$$${height}\:{of}\:\mathrm{80}{m}\:{above}\:{the}\:{ground} \\ $$$${with}\:{a}\:{velocity}\:{of}\:\mathrm{40}{m}/{s}\:{at}\:{an} \\ $$$${angle}\:{of}\:\mathrm{30}\:{degree}\:{to}\:{the} \\ $$$${horizontal}.{What}\:{is}\:{the}\:{tume}\:{of} \\ $$$${flight}? \\ $$
Question Number 46624 Answers: 1 Comments: 4
$${The}\:{value}\:{of}\:{k}\:{which}\:{minimizes} \\ $$$${F}\left({k}\right)=\:\int_{\mathrm{0}} ^{\mathrm{4}} \mid{x}\left(\mathrm{4}−{x}\right)−{k}\mid{dx}\:=\:? \\ $$
Question Number 46617 Answers: 1 Comments: 1
$${calculate}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{1}}{{n}\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)\left({n}+\mathrm{3}\right)\left({n}+\mathrm{4}\right)\left({n}+\mathrm{5}\right)} \\ $$
Question Number 46612 Answers: 1 Comments: 4
$$\left.\mathrm{1}\right)\:{calculate}\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:{x}^{{n}} \:{e}^{\left(\mathrm{1}−{i}\right){x}} {dx}\:{with}\:{n}\:{integr}\:{natural}\:{and}\:{i}^{\mathrm{2}} =−\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\int_{\mathrm{0}} ^{\infty} \:{x}^{\mathrm{4}{k}+\mathrm{3}} \:{xsinx}\:{dx}\:. \\ $$
Question Number 46611 Answers: 2 Comments: 1
Question Number 46610 Answers: 0 Comments: 2
$${let}\:{f}_{{n}} \left({x}\right)={e}^{−{nx}} −\mathrm{2}{e}^{−\mathrm{2}{nx}} \:\:{with}\:{x}\:{from}\left[\mathrm{0},+\infty\left[\right.\right. \\ $$$$\left.\mathrm{1}\right){calculate}\:\int_{\mathrm{0}} ^{\infty} \:{f}_{{n}} \left({x}\right){dx}\:\:{and}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\left(\int_{\mathrm{0}} ^{\infty} \:{f}_{{n}} \left({x}\right){dx}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{S}\left({x}\right)=\sum_{{n}=\mathrm{0}} ^{\infty} \:{f}_{{n}} \left({x}\right)\:\:{and}\:\int_{\mathrm{0}} ^{\infty} \:{S}\left({x}\right){dx} \\ $$
Question Number 46609 Answers: 0 Comments: 1
$${solve}\:\:\:\:{x}\:{y}^{''} \:−{e}^{−{x}} {y}^{'} \:\:\:={x}\:{sinx} \\ $$
Question Number 46608 Answers: 0 Comments: 0
$${let}\:{the}\:{d}.{e}\:\:{xy}^{''} \:+\left({x}^{\mathrm{2}} −{x}\right){y}^{'} \:+\mathrm{2}{y}\:=\mathrm{0} \\ $$$${find}\:{a}\:{solution}\:{developpable}\:{at}\:{integr}\:{serie}. \\ $$$$ \\ $$
Question Number 46607 Answers: 0 Comments: 1
$${calculate}\:\sum_{\left({i},{j}\right)\in\:{N}^{\mathrm{2}} } \:\:\:\:\:\frac{{i}+{j}}{\mathrm{3}^{{i}+{j}} } \\ $$
Question Number 46604 Answers: 0 Comments: 1
$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{x}\mathrm{cos}\:{x}−\mathrm{sin}\:{x}}{{x}^{\mathrm{2}} +\mathrm{sin}\:{x}}\:{dx}\:=\:? \\ $$
Question Number 46598 Answers: 1 Comments: 1
$${calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{arctan}\left(\frac{\mathrm{1}}{{n}^{\mathrm{2}} \:+{n}+\mathrm{1}}\right) \\ $$
Question Number 46594 Answers: 1 Comments: 0
$${find}\:\int\:\left(\sqrt{{x}+\sqrt{{x}}}−\sqrt{{x}−\sqrt{{x}}}\right){dx} \\ $$
Question Number 46592 Answers: 2 Comments: 1
$$\mathrm{Find}\:\mathrm{a}\:\mathrm{solution}\:\mathrm{to}:\:\:\:\mathrm{7x}\:+\:\mathrm{5y}\:+\:\mathrm{15z}\:+\:\mathrm{12w}\:=\:\mathrm{149} \\ $$
Question Number 46586 Answers: 2 Comments: 0
$${Solve}\:\:{x}\:\:\in\:\mathbb{R} \\ $$$$\:\:\:\:\:\:\:\:\:{x}\:+\:\:\frac{{x}}{\sqrt{{x}^{\mathrm{2}} \:+\:\mathrm{1}}}\:\:=\:\:\frac{\mathrm{35}}{\mathrm{12}} \\ $$
Question Number 46576 Answers: 0 Comments: 2
$$\mathrm{Please}\:\mathrm{any}\:\mathrm{note}\:\mathrm{on}\:\mathrm{how}\:\mathrm{to}\:\mathrm{find}\:\mathrm{the}\:\mathrm{first}\:\mathrm{digit},\:\mathrm{first}\:\mathrm{two}\:\mathrm{digit}\:\mathrm{and}\:\mathrm{first}\:\mathrm{three}\:\mathrm{digits} \\ $$$$\mathrm{of}\:\mathrm{any}\:\mathrm{power} \\ $$
Question Number 46573 Answers: 1 Comments: 4
$${Show}\:{that}\: \\ $$$${sin}\mathrm{2}{x}\:\equiv\frac{\mathrm{2}{tanx}}{\mathrm{1}+{tan}^{\mathrm{2}} {x}} \\ $$
Question Number 46570 Answers: 1 Comments: 0
$${If}\:{in}\:{triangle}\:{ABC}\:\:\:\frac{{cosB}}{{b}}\:=\frac{{cosC}}{{c}},\:{show}\:{that}\:{the} \\ $$$${triangle}\:{is}\:{isosceles} \\ $$
Question Number 46569 Answers: 1 Comments: 0
$${show}\:{that}\:\:{If}\:{a}^{\mathrm{2}} ,{b}^{\mathrm{2}} ,{c}^{\mathrm{2}\:} \:{are}\:{in}\:{A}.{P}\:\:{the}\:{cotA},{cotB},{cotC}\:{are} \\ $$$${also}\:{in}\:{A}.{P} \\ $$
Question Number 46568 Answers: 0 Comments: 0
$${show}\:{that}\:{if}\:{the}\:{side}\:{of}\:{a}\:{triangle}\:{are}\:{in}\:{A}.{P}, \\ $$$${then}\:{the}\:{cotangent}\:{also}\:{in}\:{A}.{P} \\ $$
Question Number 46567 Answers: 0 Comments: 0
$$\mathrm{Solve}:\:\:\:\:\:\:\underset{\mathrm{n}\:=\:\mathrm{1}} {\overset{\infty} {\boldsymbol{\sum}}}\:\:\left(\frac{\mathrm{log}\:\boldsymbol{\mathrm{n}}}{\boldsymbol{\mathrm{n}}}\right)^{\mathrm{2}} \\ $$
Question Number 46563 Answers: 1 Comments: 0
$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{{a}^{{x}} +{b}^{{x}} +{c}^{{x}} }{\mathrm{3}}\right)^{\mathrm{1}/{x}} \\ $$
Question Number 46558 Answers: 1 Comments: 0
$${calculate}\:{the}\:{uncertainty}\:{in}\:{velocity}\:{of}\:{an}\:{electron}\:{which}\:{is}\:{confined}\:{in}\:{a}\:\mathrm{10}^{−\mathrm{10}\:} {meter} \\ $$
Question Number 46553 Answers: 1 Comments: 0
$$\mathrm{Can}\:\mathrm{someone}\:\mathrm{please}\:\mathrm{explain}\:\mathrm{me}\:\mathrm{how}\:\mathrm{to} \\ $$$$\mathrm{solve}\:\mathrm{a}\:\mathrm{quadratic}\:\mathrm{equation}\:\mathrm{without}\:\mathrm{the}\: \\ $$$$\mathrm{common}\:\mathrm{formulas}\:\mathrm{but}\:\mathrm{with}\:\mathrm{the}\:\mathrm{sums}\:\mathrm{and} \\ $$$$\mathrm{products}\:\mathrm{method}\:\mathrm{please}\:? \\ $$$$\mathrm{Thank} \\ $$
Question Number 46552 Answers: 1 Comments: 2
Question Number 46549 Answers: 0 Comments: 3
$${is}\:{there}\:{any}\:{other}\:{maths}\:{forum}\:{apart}\:{from}\:{this}? \\ $$
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