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Question Number 184738 Answers: 1 Comments: 0

α , β are roots of , x^( 2) −x−1=0 ( α > β ) and , t_( n) = ((α^( n) − β^( n) )/(α−β)) ( n ∈ N ), if , b_1 =1 , b_( n) = t_( n−1) +t_( n−2) ( n ≥2 ) find the value of S = Σ_(n=1) ^∞ (( b_( n) )/(10^( n) )) =?

$$ \\ $$$$\alpha\:\:,\:\beta\:\:{are}\:{roots}\:{of}\:\:,\:{x}^{\:\mathrm{2}} −{x}−\mathrm{1}=\mathrm{0} \\ $$$$\left(\:\:\alpha\:>\:\beta\:\right)\:{and}\:,\:\:{t}_{\:{n}} =\:\frac{\alpha^{\:{n}} −\:\beta^{\:{n}} }{\alpha−\beta} \\ $$$$\:\left(\:{n}\:\in\:\mathbb{N}\:\right),\:{if}\:,\:{b}_{\mathrm{1}} =\mathrm{1}\:,\:{b}_{\:{n}} =\:{t}_{\:{n}−\mathrm{1}} +{t}_{\:{n}−\mathrm{2}} \\ $$$$\:\:\:\left(\:{n}\:\geqslant\mathrm{2}\:\right)\:{find}\:{the}\:{value}\:{of} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{S}\:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:{b}_{\:{n}} }{\mathrm{10}^{\:{n}} }\:=? \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 184735 Answers: 0 Comments: 3

f(x,y)=((√(3xy^2 )))(((x^5 y^2 ))^(1/5) ) f^′ (x,y)=? f′′(x,y)=?

$$ \\ $$$${f}\left({x},{y}\right)=\left(\sqrt{\mathrm{3}{xy}^{\mathrm{2}} }\right)\left(\sqrt[{\mathrm{5}}]{{x}^{\mathrm{5}} {y}^{\mathrm{2}} }\right) \\ $$$${f}^{'} \left({x},{y}\right)=?\:\:\:\:\:{f}''\left({x},{y}\right)=? \\ $$$$ \\ $$

Question Number 184731 Answers: 1 Comments: 0

Express this function in both its Cartesian and polar form f(z) = ze^(iz) . Help!

$$\mathrm{Express}\:\mathrm{this}\:\mathrm{function}\:\mathrm{in}\:\mathrm{both}\:\mathrm{its} \\ $$$$\mathrm{Cartesian}\:\mathrm{and}\:\mathrm{polar}\:\mathrm{form} \\ $$$$\mathrm{f}\left(\mathrm{z}\right)\:=\:\mathrm{ze}^{\mathrm{iz}} . \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 184728 Answers: 5 Comments: 0

x^( 2) − 3x +1=0 α , β are roots : ( α^( 3) +(1/β) )^( 3) + ( β^^( 3) +(1/α) )^( 3) = ?

$$ \\ $$$$\:\:\:\:\:\:{x}^{\:\mathrm{2}} −\:\mathrm{3}{x}\:+\mathrm{1}=\mathrm{0} \\ $$$$\:\:\:\:\:\:\alpha\:,\:\beta\:{are}\:{roots}\:: \\ $$$$\:\:\:\left(\:\alpha^{\:\mathrm{3}} \:+\frac{\mathrm{1}}{\beta}\:\right)^{\:\mathrm{3}} \:+\:\left(\:\beta^{\:^{\:\mathrm{3}} } \:+\frac{\mathrm{1}}{\alpha}\:\right)^{\:\mathrm{3}} =\:? \\ $$$$ \\ $$

Question Number 184726 Answers: 1 Comments: 0

Question Number 184724 Answers: 0 Comments: 1

Question Number 184720 Answers: 1 Comments: 0

y=((√(3xy^2 )))(((x^5 y^2 ))^(1/5) ) y′=? y^(′′) =?

$$ \\ $$$${y}=\left(\sqrt{\mathrm{3}{xy}^{\mathrm{2}} }\right)\left(\sqrt[{\mathrm{5}}]{{x}^{\mathrm{5}} {y}^{\mathrm{2}} }\right) \\ $$$${y}'=?\:\:\:\:\:\:{y}^{''} =? \\ $$

Question Number 184719 Answers: 1 Comments: 0

Question Number 184718 Answers: 2 Comments: 0

Question Number 184706 Answers: 1 Comments: 0

deg[3p(x)+Q(x)]=6 deg[p(x)+x^4 ]=5 deg[(((x^4 +1)p(x^2 ))/(x^3 ∙Q(x)))]=? deg=degree

$$\mathrm{deg}\left[\mathrm{3p}\left(\mathrm{x}\right)+\mathrm{Q}\left(\mathrm{x}\right)\right]=\mathrm{6} \\ $$$$\mathrm{deg}\left[\mathrm{p}\left(\mathrm{x}\right)+\mathrm{x}^{\mathrm{4}} \right]=\mathrm{5} \\ $$$$\mathrm{deg}\left[\frac{\left(\mathrm{x}^{\mathrm{4}} +\mathrm{1}\right)\mathrm{p}\left(\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{x}^{\mathrm{3}} \centerdot\mathrm{Q}\left(\mathrm{x}\right)}\right]=? \\ $$$$\mathrm{deg}=\mathrm{degree}\: \\ $$

Question Number 184705 Answers: 0 Comments: 0

Question Number 184683 Answers: 1 Comments: 0

x′′ − (5/t) x′ + (8/t^2 ) x = ((2 ln t)/t^2 ) solve the differential eqn

$${x}''\:−\:\frac{\mathrm{5}}{{t}}\:{x}'\:+\:\frac{\mathrm{8}}{{t}^{\mathrm{2}} }\:{x}\:=\:\frac{\mathrm{2}\:{ln}\:{t}}{{t}^{\mathrm{2}} } \\ $$$${solve}\:{the}\:{differential}\:{eqn} \\ $$

Question Number 184669 Answers: 0 Comments: 3

Question Number 184668 Answers: 0 Comments: 0

Question Number 184656 Answers: 1 Comments: 0

prove that the area of a triangle whose two sides are A^− and B^− is given by (1/2)∣A×B∣. Also find the direction−cosine of normal to this area. Help!

$$\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle} \\ $$$$\mathrm{whose}\:\mathrm{two}\:\mathrm{sides}\:\mathrm{are}\:\overset{−} {\mathrm{A}}\:\mathrm{and}\:\overset{−} {\mathrm{B}}\:\mathrm{is} \\ $$$$\mathrm{given}\:\mathrm{by}\:\frac{\mathrm{1}}{\mathrm{2}}\mid\mathrm{A}×\mathrm{B}\mid. \\ $$$$\mathrm{Also}\:\mathrm{find}\:\mathrm{the}\:\mathrm{direction}−\mathrm{cosine} \\ $$$$\mathrm{of}\:\mathrm{normal}\:\mathrm{to}\:\mathrm{this}\:\mathrm{area}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 184655 Answers: 1 Comments: 0

prove that an angle inscribe in a semi−circle is a right angle. Help!

$$\mathrm{prove}\:\mathrm{that}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{inscribe}\:\mathrm{in}\:\mathrm{a}\: \\ $$$$\mathrm{semi}−\mathrm{circle}\:\mathrm{is}\:\mathrm{a}\:\mathrm{right}\:\mathrm{angle}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 184645 Answers: 1 Comments: 0