Question and Answers Forum

AllQuestion and Answers: Page 508

Question Number 167964 Answers: 1 Comments: 1

Question Number 167963 Answers: 0 Comments: 0

show that_β_(1 =( nΣxy−ΣxΣy)/(nΣx^2 −(Σx)^2 )=Σxy/Σ(xy)^(2 ) where x=(x−x^− ) and y=(y−y^− ) )

$$\:{show}\:{that}_{\beta_{\mathrm{1}\:=\left(\:{n}\Sigma{xy}−\Sigma{x}\Sigma{y}\right)/\left({n}\Sigma{x}^{\mathrm{2}} −\left(\Sigma{x}\right)^{\mathrm{2}} \right)=\Sigma{xy}/\Sigma\left({xy}\right)^{\mathrm{2}\:} \:\:\:\:\:\:\:{where}\:{x}=\left({x}−\overset{−} {{x}}\right)\:{and}\:{y}=\left({y}−\overset{−} {{y}}\right)\:\:} } \: \\ $$$$ \\ $$

Question Number 167956 Answers: 0 Comments: 0

Question Number 167955 Answers: 2 Comments: 0

Question Number 167943 Answers: 2 Comments: 3

lim_(x→3) ((e^x −e^3 )/(x−3))=? wiht out H,pital ruls

$$\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\frac{{e}^{{x}} −{e}^{\mathrm{3}} }{{x}−\mathrm{3}}=? \\ $$$${wiht}\:{out}\:{H},{pital}\:{ruls} \\ $$

Question Number 167942 Answers: 1 Comments: 0

(x−1)(x+4)(x−2)^2 =10x^2 x=???

$$\left({x}−\mathrm{1}\right)\left({x}+\mathrm{4}\right)\left({x}−\mathrm{2}\right)^{\mathrm{2}} =\mathrm{10}{x}^{\mathrm{2}} \\ $$$${x}=??? \\ $$

Question Number 167939 Answers: 0 Comments: 0

find the root of f(x)=x^3 −5^x +3 using newton raphson iteration method

$${find}\:{the}\:{root}\:{of}\: \\ $$$${f}\left({x}\right)={x}^{\mathrm{3}} −\mathrm{5}^{{x}} +\mathrm{3} \\ $$$${using}\:{newton}\:{raphson}\:{iteration}\:{method} \\ $$

Question Number 190928 Answers: 0 Comments: 6

Solve the equation : 2+x^2 (x^4 +1)=(((√2)x^3 (x^4 −1))/( (√(x^4 +1))))

$${Solve}\:{the}\:{equation}\:: \\ $$$$\mathrm{2}+{x}^{\mathrm{2}} \left({x}^{\mathrm{4}} +\mathrm{1}\right)=\frac{\sqrt{\mathrm{2}}{x}^{\mathrm{3}} \left({x}^{\mathrm{4}} −\mathrm{1}\right)}{\:\sqrt{{x}^{\mathrm{4}} +\mathrm{1}}} \\ $$$$ \\ $$

Question Number 167930 Answers: 1 Comments: 1

y^(′′) − y^′ − 6y = xe^x sinx

$$\boldsymbol{{y}}\:^{''} \:−\:\boldsymbol{{y}}^{'} \:−\:\mathrm{6}\boldsymbol{{y}}\:=\:\boldsymbol{{xe}}^{\boldsymbol{{x}}} \:\boldsymbol{{sinx}} \\ $$

Question Number 167929 Answers: 1 Comments: 0

prove: (((a^2 +b^2 )sinαcosα−ab)/((a^2 +b^2 )cos^2 α−b^2 ))=((asinα−bcosα)/(acosα+bsinα))

$${prove}:\: \\ $$$$\:\:\:\:\:\:\:\frac{\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} \right)\mathrm{sin}\alpha\mathrm{cos}\alpha−{ab}}{\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} \right)\mathrm{cos}^{\mathrm{2}} \alpha−{b}^{\mathrm{2}} }=\frac{{a}\mathrm{sin}\alpha−{b}\mathrm{cos}\alpha}{{a}\mathrm{cos}\alpha+{b}\mathrm{sin}\alpha} \\ $$

Question Number 167928 Answers: 1 Comments: 0

Show that ∣1−i∣^x =2^x has no nonzero integral solution

$${Show}\:{that}\:\mid\mathrm{1}−{i}\mid^{{x}} =\mathrm{2}^{{x}} \:{has}\:{no}\:{nonzero}\:{integral}\:{solution}\: \\ $$

Question Number 167925 Answers: 1 Comments: 0

Given f(x) = ax^5 + bx^4 + cx^3 + dx^2 + ex + f . f(1) = 1 , f(2) = (1/4) , f(3) = (1/9) , f(4) = (1/(16)) , f(5) = (1/(25)) , and f(6) = (1/(36)) . Value of f(8) = ?

$$\mathrm{Given}\:\:{f}\left({x}\right)\:=\:{ax}^{\mathrm{5}} \:+\:{bx}^{\mathrm{4}} \:+\:{cx}^{\mathrm{3}} \:+\:{dx}^{\mathrm{2}} \:+\:{ex}\:+\:{f}\:. \\ $$$${f}\left(\mathrm{1}\right)\:=\:\mathrm{1}\:,\:{f}\left(\mathrm{2}\right)\:=\:\frac{\mathrm{1}}{\mathrm{4}}\:\:,\:\:{f}\left(\mathrm{3}\right)\:=\:\frac{\mathrm{1}}{\mathrm{9}}\:\:,\:\:{f}\left(\mathrm{4}\right)\:=\:\frac{\mathrm{1}}{\mathrm{16}}\:\:, \\ $$$${f}\left(\mathrm{5}\right)\:=\:\frac{\mathrm{1}}{\mathrm{25}}\:\:,\:\:{and}\:\:{f}\left(\mathrm{6}\right)\:=\:\frac{\mathrm{1}}{\mathrm{36}}\:. \\ $$$${Value}\:\:{of}\:\:{f}\left(\mathrm{8}\right)\:=\:? \\ $$

Question Number 167922 Answers: 4 Comments: 2

Find the value of Q if ∫_0 ^Q (√(cosec θ−1)) dθ=ln (((3+2(√2))/2))

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{Q}\:\:\mathrm{if} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{Q}} \sqrt{\mathrm{cosec}\:\theta−\mathrm{1}}\:\mathrm{d}\theta=\mathrm{ln}\:\left(\frac{\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}}}{\mathrm{2}}\right) \\ $$$$ \\ $$

Question Number 167917 Answers: 0 Comments: 0

_ Two small charged spheresn Two small charged spheresn cotain charges + q1 and + q2r espectively. A charge da ism reoved from sphere carryingh carge q1 and is transferredtoh te other. Find charge on eachs phere for maximum electrico frce between1 them.Ans.(12(q +q2) Twor paticles each having a mass of5 g and charge 107 C stay inlimiting equilibrium on ar hoizontal table with ai separaton of 10 cm betweene thm. The coefficient ofn frictio between each particlen ad the table is the same. Findthe value of thisn cocfficiet. Ans. u 018 cotain charges + q1 and + q2r espectively. A charge da ism reoved from sphere carryingh carge q1 and is transferredtoh te other. Find charge on eachs phere for maximum electrico frce between1 them.Ans.(12(q +q2) Twor paticles each having a mass of5 g and charge 107 C stay inlimiting equilibrium on ar hoizontal table with ai separaton of 10 cm betweene thm. The coefficient ofn frictio between each particlen ad the table is the same. Findthe value of thisn cocfficiet. Ans. u 018z

$$\:_{} \: \\ $$$$\mathrm{Two}\:\mathrm{small}\:\mathrm{charged}\:\mathrm{spheresn} \\ $$$$\mathrm{Two}\:\mathrm{small}\:\mathrm{charged}\:\mathrm{spheresn} \\ $$$$\mathrm{cotain}\:\mathrm{charges}\:+\:\mathrm{q1}\:\mathrm{and}\:+\:\mathrm{q2r} \\ $$$$\mathrm{espectively}.\:\mathrm{A}\:\mathrm{charge}\:\mathrm{da}\:\mathrm{ism} \\ $$$$\mathrm{reoved}\:\mathrm{from}\:\mathrm{sphere}\:\mathrm{carryingh} \\ $$$$\mathrm{carge}\:\mathrm{q1}\:\mathrm{and}\:\mathrm{is}\:\mathrm{transferredtoh} \\ $$$$\mathrm{te}\:\mathrm{other}.\:\mathrm{Find}\:\mathrm{charge}\:\mathrm{on}\:\mathrm{eachs} \\ $$$$\mathrm{phere}\:\mathrm{for}\:\mathrm{maximum}\:\mathrm{electrico} \\ $$$$\mathrm{frce}\:\mathrm{between1} \\ $$$$\mathrm{them}.\mathrm{Ans}.\left(\mathrm{12}\left(\mathrm{q}\:+\mathrm{q2}\right)\:\mathrm{Twor}\right. \\ $$$$\mathrm{paticles}\:\mathrm{each}\:\mathrm{having}\:\mathrm{a}\:\mathrm{mass}\: \\ $$$$\mathrm{of5}\:\mathrm{g}\:\mathrm{and}\:\mathrm{charge}\:\mathrm{107}\:\mathrm{C}\:\mathrm{stay}\: \\ $$$$\mathrm{inlimiting}\:\mathrm{equilibrium}\:\mathrm{on}\:\mathrm{ar} \\ $$$$\mathrm{hoizontal}\:\mathrm{table}\:\mathrm{with}\:\mathrm{ai} \\ $$$$\mathrm{separaton}\:\mathrm{of}\:\mathrm{10}\:\mathrm{cm}\:\mathrm{betweene} \\ $$$$\mathrm{thm}.\:\mathrm{The}\:\mathrm{coefficient}\:\mathrm{ofn} \\ $$$$\mathrm{frictio}\:\mathrm{between}\:\mathrm{each}\:\mathrm{particlen} \\ $$$$\mathrm{ad}\:\mathrm{the}\:\mathrm{table}\:\mathrm{is}\:\mathrm{the}\:\mathrm{same}.\: \\ $$$$\mathrm{Findthe}\:\mathrm{value}\:\mathrm{of}\:\mathrm{thisn} \\ $$$$\mathrm{cocfficiet}.\:\mathrm{Ans}.\:\mathrm{u}\:\:\mathrm{018} \\ $$$$\mathrm{cotain}\:\mathrm{charges}\:+\:\mathrm{q1}\:\mathrm{and}\:+\:\mathrm{q2r} \\ $$$$\mathrm{espectively}.\:\mathrm{A}\:\mathrm{charge}\:\mathrm{da}\:\mathrm{ism} \\ $$$$\mathrm{reoved}\:\mathrm{from}\:\mathrm{sphere}\:\mathrm{carryingh} \\ $$$$\mathrm{carge}\:\mathrm{q1}\:\mathrm{and}\:\mathrm{is}\:\mathrm{transferredtoh} \\ $$$$\mathrm{te}\:\mathrm{other}.\:\mathrm{Find}\:\mathrm{charge}\:\mathrm{on}\:\mathrm{eachs} \\ $$$$\mathrm{phere}\:\mathrm{for}\:\mathrm{maximum}\:\mathrm{electrico} \\ $$$$\mathrm{frce}\:\mathrm{between1} \\ $$$$\mathrm{them}.\mathrm{Ans}.\left(\mathrm{12}\left(\mathrm{q}\:+\mathrm{q2}\right)\:\mathrm{Twor}\right. \\ $$$$\mathrm{paticles}\:\mathrm{each}\:\mathrm{having}\:\mathrm{a}\:\mathrm{mass}\: \\ $$$$\mathrm{of5}\:\mathrm{g}\:\mathrm{and}\:\mathrm{charge}\:\mathrm{107}\:\mathrm{C}\:\mathrm{stay}\: \\ $$$$\mathrm{inlimiting}\:\mathrm{equilibrium}\:\mathrm{on}\:\mathrm{ar} \\ $$$$\mathrm{hoizontal}\:\mathrm{table}\:\mathrm{with}\:\mathrm{ai} \\ $$$$\mathrm{separaton}\:\mathrm{of}\:\mathrm{10}\:\mathrm{cm}\:\mathrm{betweene} \\ $$$$\mathrm{thm}.\:\mathrm{The}\:\mathrm{coefficient}\:\mathrm{ofn} \\ $$$$\mathrm{frictio}\:\mathrm{between}\:\mathrm{each}\:\mathrm{particlen} \\ $$$$\mathrm{ad}\:\mathrm{the}\:\mathrm{table}\:\mathrm{is}\:\mathrm{the}\:\mathrm{same}.\: \\ $$$$\mathrm{Findthe}\:\mathrm{value}\:\mathrm{of}\:\mathrm{thisn} \\ $$$$\mathrm{cocfficiet}.\:\mathrm{Ans}.\:\mathrm{u}\:\:\mathrm{018z} \\ $$$$ \\ $$$$ \\ $$

Question Number 167916 Answers: 1 Comments: 1

give: z=cos(((2π)/(2015)))+isin(((2π)/(2015))) find S=1+z+z^2 +z^3 +...+z^(2014)

$${give}:\:{z}={cos}\left(\frac{\mathrm{2}\pi}{\mathrm{2015}}\right)+{isin}\left(\frac{\mathrm{2}\pi}{\mathrm{2015}}\right) \\ $$$${find}\:{S}=\mathrm{1}+{z}+{z}^{\mathrm{2}} +{z}^{\mathrm{3}} +...+{z}^{\mathrm{2014}} \\ $$

Question Number 167915 Answers: 0 Comments: 0