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Question Number 17392    Answers: 2   Comments: 0

Find the cube root of z = − 1

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{cube}\:\mathrm{root}\:\mathrm{of}\:\:\mathrm{z}\:=\:−\:\mathrm{1} \\ $$

Question Number 17391    Answers: 1   Comments: 0

write z = (2 + 2(√3) i)^3 in polar form.

$$\mathrm{write}\:\:\:\mathrm{z}\:=\:\left(\mathrm{2}\:+\:\mathrm{2}\sqrt{\mathrm{3}}\:\mathrm{i}\right)^{\mathrm{3}} \:\:\mathrm{in}\:\mathrm{polar}\:\mathrm{form}. \\ $$

Question Number 17377    Answers: 1   Comments: 0

∫ ((cos(x))/(2 − cos(x))) dx

$$\int\:\:\frac{\mathrm{cos}\left(\mathrm{x}\right)}{\mathrm{2}\:−\:\mathrm{cos}\left(\mathrm{x}\right)}\:\mathrm{dx} \\ $$

Question Number 17374    Answers: 1   Comments: 1

Question Number 17373    Answers: 2   Comments: 0

Find the point in interior of a convex quadrilateral such that the sum of its distances to the 4 vertices is minimal. Find the point in interior of a convex quadrilateral such that the sum of its distances to the 4 sides is minimal.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{point}\:\mathrm{in}\:\mathrm{interior}\:\mathrm{of}\:\mathrm{a}\:\mathrm{convex} \\ $$$$\mathrm{quadrilateral}\:\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{its} \\ $$$$\mathrm{distances}\:\mathrm{to}\:\mathrm{the}\:\mathrm{4}\:\mathrm{vertices}\:\mathrm{is}\:\mathrm{minimal}. \\ $$$$ \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{point}\:\mathrm{in}\:\mathrm{interior}\:\mathrm{of}\:\mathrm{a}\:\mathrm{convex} \\ $$$$\mathrm{quadrilateral}\:\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{its} \\ $$$$\mathrm{distances}\:\mathrm{to}\:\mathrm{the}\:\mathrm{4}\:\mathrm{sides}\:\mathrm{is}\:\mathrm{minimal}. \\ $$

Question Number 17386    Answers: 2   Comments: 0

Solve the equation: log _2 x log _3 x log _5 x=log _2 x log _3 x +log _3 x log _5 x +log _5 x log _2 x .

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\mathrm{log}\:_{\mathrm{2}} \mathrm{x}\:\mathrm{log}\:_{\mathrm{3}} \mathrm{x}\:\mathrm{log}\:_{\mathrm{5}} \mathrm{x}=\mathrm{log}\:_{\mathrm{2}} \mathrm{x}\:\mathrm{log}\:_{\mathrm{3}} \mathrm{x} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+\mathrm{log}\:_{\mathrm{3}} \mathrm{x}\:\mathrm{log}\:_{\mathrm{5}} \mathrm{x} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+\mathrm{log}\:_{\mathrm{5}} \mathrm{x}\:\mathrm{log}\:_{\mathrm{2}} \mathrm{x}\:. \\ $$

Question Number 17359    Answers: 0   Comments: 5

For what values of m, the equation (1+m)x^2 −2(1+3m)x+(1+8m)=0 ; m ∈ R , has both roots positive ?

$$\mathrm{For}\:\mathrm{what}\:\mathrm{values}\:\mathrm{of}\:\mathrm{m},\:\mathrm{the}\:\mathrm{equation} \\ $$$$\left(\mathrm{1}+\mathrm{m}\right)\mathrm{x}^{\mathrm{2}} −\mathrm{2}\left(\mathrm{1}+\mathrm{3m}\right)\mathrm{x}+\left(\mathrm{1}+\mathrm{8m}\right)=\mathrm{0}\:; \\ $$$$\:\:\:\mathrm{m}\:\in\:\mathrm{R}\:,\:\mathrm{has}\:\mathrm{both}\:\mathrm{roots}\:\mathrm{positive}\:? \\ $$

Question Number 17354    Answers: 0   Comments: 5

Solve for x : ∣x−1∣−∣x−2∣+∣x+1∣>∣x+2∣+∣x∣−3 .

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}\:: \\ $$$$\mid\mathrm{x}−\mathrm{1}\mid−\mid\mathrm{x}−\mathrm{2}\mid+\mid\mathrm{x}+\mathrm{1}\mid>\mid\mathrm{x}+\mathrm{2}\mid+\mid\mathrm{x}\mid−\mathrm{3}\:. \\ $$

Question Number 17348    Answers: 3   Comments: 0

The number of points in (−∞, ∞) for which x^2 − x sin x − cos x = 0 is (1) 6 (2) 4 (3) 2 (4) 0

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{points}\:\mathrm{in}\:\left(−\infty,\:\infty\right)\:\mathrm{for} \\ $$$$\mathrm{which}\:{x}^{\mathrm{2}} \:−\:{x}\:\mathrm{sin}\:{x}\:−\:\mathrm{cos}\:{x}\:=\:\mathrm{0}\:\mathrm{is} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{6} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{4} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{2} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{0} \\ $$

Question Number 17339    Answers: 0   Comments: 0

Question Number 17336    Answers: 1   Comments: 1

The last time Nkechi was at school was on Saturday.She was first absent for 4days before that. Today is Tuesday,27th of September.When was Nkechi first absent?Give the day and date.Select one: 1.Monday september 12 2.Tuesday September 13 3.Wednesday September 14 4.Thursday September 15

$$\mathrm{The}\:\mathrm{last}\:\mathrm{time}\:\mathrm{Nkechi}\:\mathrm{was}\:\mathrm{at}\:\mathrm{school} \\ $$$$\mathrm{was}\:\mathrm{on}\:\mathrm{Saturday}.\mathrm{She}\:\mathrm{was}\:\mathrm{first} \\ $$$$\mathrm{absent}\:\mathrm{for}\:\mathrm{4days}\:\mathrm{before}\:\mathrm{that}. \\ $$$$\mathrm{Today}\:\mathrm{is}\:\mathrm{Tuesday},\mathrm{27th}\:\mathrm{of}\: \\ $$$$\mathrm{September}.\mathrm{When}\:\mathrm{was}\:\mathrm{Nkechi} \\ $$$$\mathrm{first}\:\mathrm{absent}?\mathrm{Give}\:\mathrm{the}\:\mathrm{day}\:\mathrm{and} \\ $$$$\mathrm{date}.\mathrm{Select}\:\mathrm{one}: \\ $$$$\mathrm{1}.\mathrm{Monday}\:\mathrm{september}\:\mathrm{12} \\ $$$$\mathrm{2}.\mathrm{Tuesday}\:\mathrm{September}\:\mathrm{13} \\ $$$$\mathrm{3}.\mathrm{Wednesday}\:\mathrm{September}\:\mathrm{14} \\ $$$$\mathrm{4}.\mathrm{Thursday}\:\mathrm{September}\:\mathrm{15} \\ $$

Question Number 17317    Answers: 0   Comments: 1

∫1/(√(sin 3xsin (x−α)))

$$\int\mathrm{1}/\sqrt{\mathrm{sin}\:\mathrm{3}{x}\mathrm{sin}\:\left({x}−\alpha\right)} \\ $$

Question Number 17313    Answers: 0   Comments: 0

Why magnetic force(F^→ ) on a moving charge q having velocity v is q(v^→ ×B^→ ) ?

$$\mathrm{Why}\:\mathrm{magnetic}\:\mathrm{force}\left(\overset{\rightarrow} {\mathrm{F}}\right)\:\mathrm{on}\:\mathrm{a}\:\mathrm{moving}\:\mathrm{charge} \\ $$$$\:\mathrm{q}\:\:\mathrm{having}\:\mathrm{velocity}\:\mathrm{v}\:\mathrm{is}\:\:\:\mathrm{q}\left(\overset{\rightarrow} {\mathrm{v}}×\overset{\rightarrow} {\mathrm{B}}\right)\:? \\ $$

Question Number 17303    Answers: 0   Comments: 0

What are next three numbers in the following sequence: 4,6,12,18,30,42,60,...

$$\mathrm{What}\:\mathrm{are}\:\mathrm{next}\:\mathrm{three}\:\mathrm{numbers} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{following}\:\mathrm{sequence}: \\ $$$$\mathrm{4},\mathrm{6},\mathrm{12},\mathrm{18},\mathrm{30},\mathrm{42},\mathrm{60},... \\ $$

Question Number 17302    Answers: 1   Comments: 2

Find the length of ρ=a(1−cos θ) . ρ=(√(x^2 +y^2 )) , θ=tan^(−1) ((y/x)) .

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\: \\ $$$$\:\:\rho=\mathrm{a}\left(\mathrm{1}−\mathrm{cos}\:\theta\right)\:. \\ $$$$\:\rho=\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }\:\:,\:\:\theta=\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{y}}{\mathrm{x}}\right)\:. \\ $$

Question Number 17323    Answers: 2   Comments: 0

Solve: (dy/dx) = ((2cos(2x))/(3 − 2y)) with y(0) = −1 (i) for what value of x > 0 does the situation exist (ii) for what value of x is y(x) maximum

$$\mathrm{Solve}:\:\:\:\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{2cos}\left(\mathrm{2x}\right)}{\mathrm{3}\:−\:\mathrm{2y}}\:\:\:\:\:\:\:\:\:\:\:\mathrm{with}\:\:\:\:\mathrm{y}\left(\mathrm{0}\right)\:=\:−\mathrm{1} \\ $$$$\left(\mathrm{i}\right)\:\mathrm{for}\:\mathrm{what}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}\:>\:\mathrm{0}\:\mathrm{does}\:\mathrm{the}\:\mathrm{situation}\:\mathrm{exist} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{for}\:\mathrm{what}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}\:\mathrm{is}\:\mathrm{y}\left(\mathrm{x}\right)\:\mathrm{maximum} \\ $$

Question Number 17322    Answers: 1   Comments: 0

Solve: (dy/dx) + (1/2)y = (3/2) with y(0) = 4

$$\mathrm{Solve}:\:\:\:\frac{\mathrm{dy}}{\mathrm{dx}}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{y}\:=\:\frac{\mathrm{3}}{\mathrm{2}}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{with}\:\:\:\mathrm{y}\left(\mathrm{0}\right)\:=\:\mathrm{4} \\ $$

Question Number 17280    Answers: 0   Comments: 2

prove that: cosh(2x) = 2cosh^2 (x) − 1

$$\mathrm{prove}\:\mathrm{that}:\:\:\mathrm{cosh}\left(\mathrm{2x}\right)\:=\:\mathrm{2cosh}^{\mathrm{2}} \left(\mathrm{x}\right)\:−\:\mathrm{1} \\ $$

Question Number 17279    Answers: 0   Comments: 3

Is cosh^2 (3x) = (1/2)[1 + cos(6x)] ??????

$$\mathrm{Is}\:\:\mathrm{cosh}^{\mathrm{2}} \left(\mathrm{3x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}}\left[\mathrm{1}\:+\:\mathrm{cos}\left(\mathrm{6x}\right)\right]\:\:?????? \\ $$

Question Number 17273    Answers: 1   Comments: 2

The intersection of the ABC triangle median is at G point. The corner of the BGC is 90°. If the AG cut length is 12 cm, locate the BC side.

$$\boldsymbol{\mathrm{The}}\:\boldsymbol{\mathrm{intersection}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{ABC}}\:\boldsymbol{\mathrm{triangle}} \\ $$$$\boldsymbol{\mathrm{median}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{G}}\:\boldsymbol{\mathrm{point}}.\:\boldsymbol{\mathrm{The}}\:\boldsymbol{\mathrm{corner}} \\ $$$$\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{BGC}}\:\boldsymbol{\mathrm{is}}\:\mathrm{90}°.\:\boldsymbol{\mathrm{If}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{AG}}\:\boldsymbol{\mathrm{cut}}\: \\ $$$$\boldsymbol{\mathrm{length}}\:\boldsymbol{\mathrm{is}}\:\mathrm{12}\:\boldsymbol{\mathrm{cm}},\:\boldsymbol{\mathrm{locate}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{BC}}\:\boldsymbol{\mathrm{side}}. \\ $$

Question Number 17272    Answers: 0   Comments: 5

Determine two distinct primes p and q such that: (i) p+q+1,p+q−1,((p+q)/2) ∈ P (All primes)? (ii) p+q+1,p+q−1,((p+q)/2),((p−q)/2) ∈ P (All primes)?

$$\mathrm{Determine}\:\mathrm{two}\:\mathrm{distinct}\:\mathrm{primes}\:\:\:\mathrm{p}\:\:\:\mathrm{and}\:\:\:\mathrm{q}\: \\ $$$$\mathrm{such}\:\mathrm{that}: \\ $$$$\left(\mathrm{i}\right)\:\mathrm{p}+\mathrm{q}+\mathrm{1},\mathrm{p}+\mathrm{q}−\mathrm{1},\frac{\mathrm{p}+\mathrm{q}}{\mathrm{2}}\:\in\:\mathbb{P}\:\left(\mathrm{All}\:\mathrm{primes}\right)? \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{p}+\mathrm{q}+\mathrm{1},\mathrm{p}+\mathrm{q}−\mathrm{1},\frac{\mathrm{p}+\mathrm{q}}{\mathrm{2}},\frac{\mathrm{p}−\mathrm{q}}{\mathrm{2}}\:\in\:\mathbb{P}\:\left(\mathrm{All}\:\mathrm{primes}\right)? \\ $$

Question Number 17271    Answers: 1   Comments: 0

Solve the equation. (√(((15)/4^(1−x) )+4^(1−x) ))=32.

$$\boldsymbol{\mathrm{Solve}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{equation}}. \\ $$$$\sqrt{\frac{\mathrm{15}}{\mathrm{4}^{\mathrm{1}−\boldsymbol{\mathrm{x}}} }+\mathrm{4}^{\mathrm{1}−\boldsymbol{\mathrm{x}}} }=\mathrm{32}. \\ $$

Question Number 17270    Answers: 1   Comments: 2

If x=((1+(√(17)))/2). Find the value of ((x^3 −2x^2 +7x−1)/(x^2 −x+1)) decimal point.

$$\boldsymbol{\mathrm{If}}\:\boldsymbol{\mathrm{x}}=\frac{\mathrm{1}+\sqrt{\mathrm{17}}}{\mathrm{2}}.\:\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}} \\ $$$$\frac{\boldsymbol{\mathrm{x}}^{\mathrm{3}} −\mathrm{2}\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{7}\boldsymbol{\mathrm{x}}−\mathrm{1}}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\boldsymbol{\mathrm{x}}+\mathrm{1}}\:\:\boldsymbol{\mathrm{decimal}}\:\boldsymbol{\mathrm{point}}. \\ $$

Question Number 17260    Answers: 1   Comments: 1

for a,b,c>0 prove that (ab+bc+ca)^2 ≥3(a+b+c)abc

$${for}\:{a},{b},{c}>\mathrm{0}\:{prove}\:{that} \\ $$$$\left({ab}+{bc}+{ca}\right)^{\mathrm{2}} \geqslant\mathrm{3}\left({a}+{b}+{c}\right){abc} \\ $$

Question Number 17255    Answers: 1   Comments: 0

∫_0 ^( (Π/2)) ((d(sinx+cosx))/(sinx+cosx))

$$\int_{\mathrm{0}} ^{\:\frac{\Pi}{\mathrm{2}}} \:\frac{\mathrm{d}\left(\mathrm{sinx}+\mathrm{cosx}\right)}{\mathrm{sinx}+\mathrm{cosx}} \\ $$

Question Number 17252    Answers: 0   Comments: 2

The sum of the digits of the number 2^(2000) 5^(2004) is Will it be 13 or 14?

$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{of}\:\mathrm{the}\:\mathrm{number} \\ $$$$\mathrm{2}^{\mathrm{2000}} \mathrm{5}^{\mathrm{2004}} \:\mathrm{is} \\ $$$$\mathrm{Will}\:\mathrm{it}\:\mathrm{be}\:\mathrm{13}\:\mathrm{or}\:\mathrm{14}? \\ $$

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