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Question Number 49220 Answers: 0 Comments: 2

(1+x−2x^2 )^8 =?

$$\left(\mathrm{1}+\mathrm{x}−\mathrm{2x}^{\mathrm{2}} \:\right)^{\mathrm{8}} =? \\ $$

Question Number 49210 Answers: 0 Comments: 1

Question Number 49202 Answers: 2 Comments: 4

1) If ω is an imaginary fifth root of unity, then find value of log _2 ∣1+ω+ω^2 +ω^3 −(1/ω)∣ ? 2) Find value of : (i+(√3))^(100) +(i−(√3))^(100) +2^(100) ?

$$\left.\mathrm{1}\right)\:{If}\:\omega\:{is}\:{an}\:{imaginary}\:{fifth}\:{root}\:{of} \\ $$$${unity},\:{then}\:{find}\:{value}\:{of}\: \\ $$$$\mathrm{log}\:_{\mathrm{2}} \:\mid\mathrm{1}+\omega+\omega^{\mathrm{2}} +\omega^{\mathrm{3}} −\frac{\mathrm{1}}{\omega}\mid\:? \\ $$$$\left.\mathrm{2}\right)\:{Find}\:{value}\:{of}\:: \\ $$$$\left({i}+\sqrt{\mathrm{3}}\right)^{\mathrm{100}} +\left({i}−\sqrt{\mathrm{3}}\right)^{\mathrm{100}} +\mathrm{2}^{\mathrm{100}} \:? \\ $$

Question Number 49200 Answers: 2 Comments: 1

1)Find the area of the triangle formed by roots of cubic equation (z+αb)^3 =α^3_ (α≠0). 2) Find product of all possible values of ((1/2)+(((√3)i)/2))^(3/4) .

$$\left.\mathrm{1}\right){Find}\:{the}\:{area}\:{of}\:{the}\:{triangle}\:{formed} \\ $$$${by}\:{roots}\:{of}\:{cubic}\:{equation} \\ $$$$\left({z}+\alpha{b}\right)^{\mathrm{3}} =\alpha^{\mathrm{3}_{} } \:\:\left(\alpha\neq\mathrm{0}\right). \\ $$$$ \\ $$$$\left.\mathrm{2}\right)\:{Find}\:{product}\:{of}\:{all}\:{possible}\:{values} \\ $$$${of}\:\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\sqrt{\mathrm{3}}{i}}{\mathrm{2}}\right)^{\frac{\mathrm{3}}{\mathrm{4}}} \:. \\ $$

Question Number 49197 Answers: 0 Comments: 1

A bus travelling along a straight road at 100 km/hr and the bus conductor walks at 6 km/hr on the floor of the bus and in the same direction as the bus. Find the speed of the conductor relative to the road, and relative to the bus. If the bus conductor now walks at the same rate but in opposite direction as the bus, find his new speed relative to the road. Answers 106 km/hr , 64 km/hr , 94 km/hr

Question Number 49188 Answers: 1 Comments: 1

solve for x,y,z∈R. x^2 +yz=1 y^2 +xz=2 z^2 +xy=3

$${solve}\:{for}\:{x},{y},{z}\in{R}. \\ $$$$\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{yz}}=\mathrm{1} \\ $$$$\boldsymbol{\mathrm{y}}^{\mathrm{2}} +\boldsymbol{\mathrm{xz}}=\mathrm{2} \\ $$$$\boldsymbol{\mathrm{z}}^{\mathrm{2}} +\boldsymbol{\mathrm{xy}}=\mathrm{3} \\ $$

Question Number 49187 Answers: 2 Comments: 0

∫((sinx)/(sin4x))dx

$$\int\frac{{sinx}}{{sin}\mathrm{4}{x}}{dx} \\ $$$$ \\ $$

Question Number 49186 Answers: 1 Comments: 4

please help... There is : 21x^2 − 21p x + 49p − 7 = 0 whose roots u and v. If u and v are not ∈Z , and u,v ≥ 1. find the value of u + v !

$$\boldsymbol{\mathrm{please}}\:\boldsymbol{\mathrm{help}}... \\ $$$$ \\ $$$$\mathrm{There}\:\mathrm{is}\::\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{21}\boldsymbol{{x}}^{\mathrm{2}} \:−\:\mathrm{21}\boldsymbol{{p}}\:\boldsymbol{{x}}\:+\:\mathrm{49}\boldsymbol{{p}}\:−\:\mathrm{7}\:=\:\mathrm{0} \\ $$$$\mathrm{whose}\:\mathrm{roots}\:\boldsymbol{{u}}\:\mathrm{and}\:\boldsymbol{{v}}.\:\mathrm{If}\:\boldsymbol{{u}}\:\mathrm{and}\:\boldsymbol{{v}}\:\mathrm{are}\:\mathrm{not}\:\in\mathbb{Z}\:,\: \\ $$$$\mathrm{and}\:\boldsymbol{{u}},\boldsymbol{{v}}\:\geqslant\:\mathrm{1}. \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\boldsymbol{{u}}\:+\:\boldsymbol{{v}}\:! \\ $$$$ \\ $$

Question Number 49183 Answers: 1 Comments: 3