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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
$${is}\:{there}\:{any}\:{other}\:{maths}\:{forum}\:{apart}\:{from}\:{this}? \\ $$
Question Number 46546 Answers: 0 Comments: 7
Question Number 46542 Answers: 0 Comments: 5
$${pls}\:{help}\: \\ $$$$\:\boldsymbol{{Find}}\:\boldsymbol{{L}}\left({cos}^{\mathrm{2}} {t}\right) \\ $$
Question Number 46534 Answers: 1 Comments: 0
$$\mathrm{using}\:\mathrm{taylors}\:\mathrm{expansion} \\ $$$$\mathrm{find}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\left.\mathrm{a}\right)\mathrm{tan45}°\:\mathrm{1}'\: \\ $$$$\left.\mathrm{b}\right)\mathrm{sin30}°\:\mathrm{1}' \\ $$
Question Number 46527 Answers: 0 Comments: 5
$$\underset{\mathrm{n}=\:\mathrm{1}} {\overset{\infty} {\boldsymbol{\sum}}}\:\left(\frac{\mathrm{log}\:\mathrm{n}}{\mathrm{n}}\right)^{\mathrm{2}} \\ $$$$\mathrm{Does}\:\mathrm{the}\:\mathrm{series}\:\mathrm{converge}\:\mathrm{or}\:\mathrm{diverge},\:\:\mathrm{help}\:\mathrm{find}\:\mathrm{the}\:\mathrm{sum}\:... \\ $$
Question Number 46522 Answers: 0 Comments: 0
$$\int\:\mathrm{x}\:\mathrm{cot}^{−\mathrm{1}} \left(\mathrm{3x}^{\mathrm{2}} \right)\:\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{6x}^{\mathrm{2}} \right) \\ $$
Question Number 46502 Answers: 1 Comments: 1
$$\int_{\mathrm{0}} ^{\infty} \left(\frac{\mathrm{sin}\:\left(\boldsymbol{\mathrm{x}}\right)}{\boldsymbol{\mathrm{x}}}\right)\boldsymbol{\mathrm{dx}} \\ $$
Question Number 46503 Answers: 0 Comments: 0
$$\mathrm{true}\:\mathrm{or}\:\mathrm{false}\:? \\ $$$$\theta_{\mathrm{1}} +\theta_{\mathrm{2}} =\mathrm{90}^{°} \:\mathrm{and}\:\mathrm{m}_{\mathrm{1}} \neq\mathrm{m}_{\mathrm{2}} \\ $$$$\mathrm{in}\:\mathrm{elastic}\:\mathrm{collision} \\ $$
Question Number 46499 Answers: 2 Comments: 0
Question Number 46483 Answers: 1 Comments: 0
$$\mathrm{If}\:\:\mathrm{tan}^{\mathrm{2}} \alpha\:\mathrm{tan}^{\mathrm{2}} \beta+\mathrm{tan}^{\mathrm{2}} \beta\:\mathrm{tan}^{\mathrm{2}} \gamma+\mathrm{tan}^{\mathrm{2}} \gamma\:\mathrm{tan}^{\mathrm{2}} \alpha \\ $$$$+\mathrm{2tan}^{\mathrm{2}} \alpha\:\mathrm{tan}^{\mathrm{2}} \beta\:\mathrm{tan}^{\mathrm{2}} \gamma=\mathrm{1},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{sin}^{\mathrm{2}} \alpha+\mathrm{sin}^{\mathrm{2}} \beta+\mathrm{sin}^{\mathrm{2}} \gamma\:\mathrm{is} \\ $$
Question Number 46482 Answers: 1 Comments: 1
Question Number 46481 Answers: 0 Comments: 3
$${Four}\:{spheres}\:{with}\:{radii}\:{a},{b},{c}\:{and}\:{d} \\ $$$${touch}\:{each}\:{other}.\:{Find}\:{the}\:{radii}\:{of} \\ $$$${their}\:{circumscribed}\:{sphere}\:\left({R}\right)\:{and} \\ $$$${their}\:{inscribed}\:{sphere}\:\left({r}\right)\:{in}\:{terms}\:{of}\: \\ $$$${a},{b},{c}\:{and}\:{d}. \\ $$
Question Number 46478 Answers: 1 Comments: 1
$${If}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{xy}=\mathrm{1}.\:{Find}\:{range}\:{of}\: \\ $$$${E}\:=\:{x}^{\mathrm{3}} {y}+{xy}^{\mathrm{3}} +\mathrm{4}\:. \\ $$
Question Number 46475 Answers: 1 Comments: 2
Question Number 46474 Answers: 2 Comments: 2
$$\left.\mathrm{a}\right)\left[\mathrm{If}\:\mathrm{tan}^{−\mathrm{1}} \mathrm{a}+\mathrm{tan}^{−\mathrm{1}} \mathrm{b}+\mathrm{tan}^{−\mathrm{1}} \mathrm{c}=\pi\:\:\mathrm{show}\:\mathrm{that}\:\frac{\mathrm{a}+\mathrm{b}+\mathrm{c}}{\mathrm{abc}}=\mathrm{1}\right. \\ $$$$\left.\mathrm{b}\right)\left[\:\:\mathrm{If}\:\:\mathrm{tanx}=\frac{\mathrm{nsinycosy}}{\mathrm{1}−\mathrm{nsin}^{\mathrm{2}} \mathrm{y}}\right. \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{tan}\left(\mathrm{y}−\mathrm{x}\right)=\left(\mathrm{1}−\mathrm{n}\right)\mathrm{tany} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$
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