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Question Number 47216 Answers: 0 Comments: 1

Question Number 47199 Answers: 0 Comments: 0

S_n = [4 − (1/(n^2 )) , 6 + (1/n) ], find ∩_(n = 1) ^∞ S_n and ∪_(n = 1) ^∞ S_n

$$\mathrm{S}_{\mathrm{n}} \:\:=\:\:\left[\mathrm{4}\:−\:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} \:}\:,\:\:\:\:\:\:\:\:\mathrm{6}\:+\:\frac{\mathrm{1}}{\mathrm{n}}\:\right],\:\:\:\mathrm{find}\:\:\:\:\:\:\:\:\:\:\:\cap_{\mathrm{n}\:=\:\mathrm{1}} ^{\infty} \:\mathrm{S}_{\mathrm{n}} \:\:\:\:\:\:\mathrm{and}\:\:\:\:\cup_{\mathrm{n}\:=\:\mathrm{1}} ^{\infty} \:\:\mathrm{S}_{\mathrm{n}} \\ $$

Question Number 47195 Answers: 1 Comments: 0

Find the volume of the pyramid which is folded from a trangular paper with sides a, b and c.

$${Find}\:{the}\:{volume}\:{of}\:{the}\:{pyramid}\:{which} \\ $$$${is}\:{folded}\:{from}\:{a}\:{trangular}\:{paper}\:{with} \\ $$$${sides}\:\boldsymbol{{a}},\:\boldsymbol{{b}}\:{and}\:\boldsymbol{{c}}. \\ $$

Question Number 47194 Answers: 1 Comments: 4

The velocity of a ship Q relqtive to a ship P is 10km/h in a direction N45^. E.If the velocity of P is 20km/h in a direction N60^. W.Find the actual velocity of Q in magnitude and direction.

$${The}\:{velocity}\:{of}\:{a}\:{ship}\:{Q}\:{relqtive}\:{to} \\ $$$${a}\:{ship}\:{P}\:\:{is}\:\mathrm{10}{km}/{h}\:{in}\:{a}\:{direction} \\ $$$${N}\mathrm{45}^{.} {E}.{If}\:{the}\:{velocity}\:{of}\:{P}\:\:{is}\:\mathrm{20}{km}/{h} \\ $$$${in}\:{a}\:{direction}\:{N}\mathrm{60}^{.} {W}.{Find}\:{the} \\ $$$${actual}\:{velocity}\:{of}\:{Q}\:{in}\:{magnitude} \\ $$$${and}\:{direction}. \\ $$

Question Number 47190 Answers: 1 Comments: 0

find the angel between the surface x^2 +y^2 +z^2 and 3x^2 −y^2 +2z=1 at (1,−2,1)

$${find}\:{the}\:{angel}\:{between}\:{the}\:{surface}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \:\:{and}\:\mathrm{3}{x}^{\mathrm{2}} −{y}^{\mathrm{2}} +\mathrm{2}{z}=\mathrm{1}\:{at}\:\left(\mathrm{1},−\mathrm{2},\mathrm{1}\right) \\ $$

Question Number 47189 Answers: 1 Comments: 2

show that ▽^2 (log r)=1/r

$$\:{show}\:{that}\:\bigtriangledown^{\mathrm{2}} \left({log}\:{r}\right)=\mathrm{1}/{r} \\ $$

Question Number 47188 Answers: 1 Comments: 0

verify stoke theorem for f=y^2 j+x^3 j where “s” is the sircular disc x^2 +y^2 ≤1,z=0

$${verify}\:{stoke}\:{theorem}\:{for}\:{f}={y}^{\mathrm{2}} {j}+{x}^{\mathrm{3}} {j}\:{where}\:``{s}''\:{is}\:{the}\:{sircular}\:{disc}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \leqslant\mathrm{1},{z}=\mathrm{0} \\ $$

Question Number 47186 Answers: 1 Comments: 0

how to know sum of digits : 3^(313) + 3^(354) ?

$${how}\:\:{to}\:\:{know}\:\:{sum}\:\:{of}\:\:{digits}\:\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{3}^{\mathrm{313}} \:+\:\mathrm{3}^{\mathrm{354}} \:\:\:\:? \\ $$

Question Number 47185 Answers: 0 Comments: 1

Question Number 47174 Answers: 1 Comments: 0

y=log_2 (log_2 ^x )then (dy/dx)=

$$\mathrm{y}=\mathrm{log}_{\mathrm{2}} \left(\mathrm{log}_{\mathrm{2}} ^{\mathrm{x}} \right)\mathrm{then}\:\:\frac{\mathrm{dy}}{\mathrm{dx}}= \\ $$

Question Number 47150 Answers: 1 Comments: 2

Question Number 47139 Answers: 1 Comments: 0

Solve for n: 4^n + 2^n − 6 = (2^n − 4)^3 + (4^n − 2)^3 ....

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{n}:\:\:\:\:\:\:\mathrm{4}^{\mathrm{n}} \:+\:\mathrm{2}^{\mathrm{n}} \:−\:\mathrm{6}\:=\:\left(\mathrm{2}^{\mathrm{n}} \:−\:\mathrm{4}\right)^{\mathrm{3}} \:+\:\left(\mathrm{4}^{\mathrm{n}} \:−\:\mathrm{2}\right)^{\mathrm{3}} \:.... \\ $$

Question Number 47138 Answers: 0 Comments: 0

Question Number 47135 Answers: 1 Comments: 3

Question Number 47120 Answers: 0 Comments: 0

calculate ∫_0 ^∞ e^(−t) ln(1+2t^2 )dt

$${calculate}\:\int_{\mathrm{0}} ^{\infty} {e}^{−{t}} {ln}\left(\mathrm{1}+\mathrm{2}{t}^{\mathrm{2}} \right){dt} \\ $$

Question Number 47119 Answers: 0 Comments: 1

let u_n =∫_(−∞) ^∞ e^(−nx^2 +x) dx 1)calculate u_n 2)find Σ_n u_n

$${let}\:{u}_{{n}} =\int_{−\infty} ^{\infty} \:{e}^{−{nx}^{\mathrm{2}} +{x}} {dx} \\ $$$$\left.\mathrm{1}\right){calculate}\:{u}_{{n}} \\ $$$$\left.\mathrm{2}\right){find}\:\sum_{{n}} \:{u}_{{n}} \\ $$

Question Number 47114 Answers: 0 Comments: 1

calculate ∫_0 ^1 (((x^2 −1)ln(x))/((x^2 +2x−1)(x^2 −2x−1)))dx

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\left({x}^{\mathrm{2}} −\mathrm{1}\right){ln}\left({x}\right)}{\left({x}^{\mathrm{2}} \:+\mathrm{2}{x}−\mathrm{1}\right)\left({x}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{1}\right)}{dx} \\ $$

Question Number 47113 Answers: 0 Comments: 4

Question Number 47112 Answers: 1 Comments: 3

calculate ∫_0 ^(π/2) ln(cosx+sinx)ex

$${calculate}\:\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left({cosx}+{sinx}\right){ex} \\ $$

Question Number 47111 Answers: 0 Comments: 4

Question Number 47145 Answers: 1 Comments: 1

Question Number 47101 Answers: 1 Comments: 1

Question Number 47090 Answers: 0 Comments: 0

Avery large field of charge has density of 5μC/m^2 . Determine the electric field intensity at a distance of 25cm.Taking medium as vacuum

$$\mathrm{Avery}\:\mathrm{large}\:\mathrm{field}\:\mathrm{of}\:\mathrm{charge}\:\mathrm{has}\:\mathrm{density} \\ $$$$\mathrm{of}\:\mathrm{5}\mu\mathrm{C}/\mathrm{m}^{\mathrm{2}} .\:\mathrm{Determine}\:\mathrm{the}\:\mathrm{electric}\:\mathrm{field} \\ $$$$\mathrm{intensity}\:\mathrm{at}\:\mathrm{a}\:\mathrm{distance}\:\mathrm{of}\:\mathrm{25cm}.\mathrm{Taking} \\ $$$$\mathrm{medium}\:\mathrm{as}\:\mathrm{vacuum} \\ $$

Question Number 47088 Answers: 1 Comments: 0

Question Number 47087 Answers: 0 Comments: 0

A charge of 1500μC is distributed over a very large sheet having surface area of 300m^2 . calculate the electric field intensity at a distance of 25cm. please help

$$\mathrm{A}\:\mathrm{charge}\:\mathrm{of}\:\mathrm{1500}\mu\mathrm{C}\:\mathrm{is}\:\mathrm{distributed} \\ $$$$\mathrm{over}\:\mathrm{a}\:\mathrm{very}\:\mathrm{large}\:\mathrm{sheet}\:\mathrm{having}\:\mathrm{surface} \\ $$$$\mathrm{area}\:\mathrm{of}\:\mathrm{300m}^{\mathrm{2}} . \\ $$$$\mathrm{calculate}\:\mathrm{the}\:\mathrm{electric}\:\mathrm{field}\:\mathrm{intensity} \\ $$$$\mathrm{at}\:\mathrm{a}\:\mathrm{distance}\:\mathrm{of}\:\mathrm{25cm}. \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help} \\ $$

Question Number 47071 Answers: 0 Comments: 0

prove that union of two subgroups of a group is a subgroup iff one is contained in other

$${prove}\:{that}\:{union}\:{of}\:{two}\:{subgroups}\:{of}\:{a}\:{group}\:{is}\:{a}\:{subgroup}\:{iff}\:{one}\:{is}\:{contained}\:{in}\:{other} \\ $$

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