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Question Number 47259 Answers: 0 Comments: 0

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

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{tan}}^{−\mathrm{1}} \left(\frac{\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{x}}+\mathrm{1}}\right)}{\boldsymbol{\mathrm{tan}}^{−\mathrm{1}} \left(\frac{\mathrm{1}−\mathrm{2}\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{2}\boldsymbol{\mathrm{x}}}{\mathrm{2}}\right)}\boldsymbol{\mathrm{dx}} \\ $$

Question Number 47289 Answers: 0 Comments: 4

Pls can Q47194 be solved by using the cosine rule?If possible please show me with the required diagram. Thanks in advance.

$${Pls}\:{can}\:{Q}\mathrm{47194}\:{be}\:{solved}\:{by}\:{using} \\ $$$${the}\:{cosine}\:{rule}?{If}\:{possible}\:{please} \\ $$$${show}\:{me}\:{with}\:{the}\:{required}\:{diagram}. \\ $$$${Thanks}\:{in}\:{advance}. \\ $$

Question Number 47250 Answers: 1 Comments: 0

Question Number 47248 Answers: 0 Comments: 1

calculate ∫_(−1) ^1 ((ln(x+2))/((x+4)^2 −1))dx

$${calculate}\:\:\int_{−\mathrm{1}} ^{\mathrm{1}} \:\:\frac{{ln}\left({x}+\mathrm{2}\right)}{\left({x}+\mathrm{4}\right)^{\mathrm{2}} −\mathrm{1}}{dx} \\ $$

Question Number 47243 Answers: 1 Comments: 0

Question Number 47239 Answers: 1 Comments: 1

((1.8×10^6 )/(tan(89.9999°))) ∼ π (upto 9 decimal places) can i have some explanations how it is worked out ? Thank you!

$$\frac{\mathrm{1}.\mathrm{8}×\mathrm{10}^{\mathrm{6}} }{{tan}\left(\mathrm{89}.\mathrm{9999}°\right)}\:\sim\:\pi\:\left({upto}\:\mathrm{9}\:{decimal}\:{places}\right) \\ $$$${can}\:{i}\:{have}\:{some}\:{explanations}\:{how}\:{it}\:{is}\:{worked}\:{out}\:? \\ $$$${Thank}\:{you}! \\ $$

Question Number 47266 Answers: 1 Comments: 1

Question Number 47235 Answers: 0 Comments: 0

the force acting on a particle P of mass 2kg is (2ti +4j)N. P is initially at rest at point with position vector (i+2j). Find the velocity of P when t=2 and the position vector when t=2.

$${the}\:{force}\:{acting}\:{on}\:{a}\:{particle}\:{P}\:{of}\:{mass}\:\:\mathrm{2}{kg}\:{is}\:\left(\mathrm{2}{ti}\:+\mathrm{4}{j}\right){N}. \\ $$$${P}\:{is}\:{initially}\:{at}\:{rest}\:{at}\:{point}\:{with}\:{position}\:{vector}\:\left({i}+\mathrm{2}{j}\right). \\ $$$${Find}\:{the}\:{velocity}\:{of}\:{P}\:{when}\:{t}=\mathrm{2}\:{and}\:{the}\:{position}\:{vector}\: \\ $$$${when}\:{t}=\mathrm{2}. \\ $$

Question Number 47234 Answers: 0 Comments: 0

the force acting on a particle P of mass 2kg is (2ti +4j)N. P is initially at rest at point with position vector (i+2j). Find the velocity of P when t=2 and the position vector when t=2.

Question Number 47233 Answers: 0 Comments: 0

the force acting on a particle P of mass 2kg is (2ti +4j)N. P is initially at rest at point with position vector (i+2j). Find the velocity of P when t=2 and the position vector when t=2.

Question Number 47224 Answers: 3 Comments: 3

Could you please help me for this question : Solve for x : ∣ 3x + 2 ∣ + ∣ 7x − 5 ∣ = 20 Thank you

$$\mathrm{Could}\:\mathrm{you}\:\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{for}\:\mathrm{this}\:\mathrm{question}\:: \\ $$$$ \\ $$$$\boldsymbol{\mathrm{Solve}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{{x}}\:: \\ $$$$ \\ $$$$\:\mid\:\mathrm{3}{x}\:+\:\mathrm{2}\:\mid\:\:+\:\:\mid\:\mathrm{7}{x}\:−\:\mathrm{5}\:\mid\:\:=\:\:\mathrm{20} \\ $$$$ \\ $$$$\mathrm{Thank}\:\mathrm{you} \\ $$$$ \\ $$

Question Number 47217 Answers: 0 Comments: 1

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) ?