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Question Number 17444    Answers: 1   Comments: 0

Evaluate: ∫_0 ^(π/4) (dx/(cos^3 x (√(2 sin 2x))))

$$\mathrm{Evaluate}:\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{4}}} {\int}}\frac{{dx}}{\mathrm{cos}^{\mathrm{3}} \:{x}\:\sqrt{\mathrm{2}\:\mathrm{sin}\:\mathrm{2}{x}}} \\ $$

Question Number 17440    Answers: 1   Comments: 0

3x−4y=0,4y−5z=0,5z−3x=0 then x,y,z is AP,GP,HP,AGP??????

$$\mathrm{3}{x}−\mathrm{4}{y}=\mathrm{0},\mathrm{4}{y}−\mathrm{5}{z}=\mathrm{0},\mathrm{5}{z}−\mathrm{3}{x}=\mathrm{0} \\ $$$${then}\:{x},{y},{z}\:{is}\:{AP},{GP},{HP},{AGP}?????? \\ $$

Question Number 17645    Answers: 2   Comments: 1

Suppose that the point M lying in the interior of the parallelogram ABCD, two parallels to AB and AD are drawn, intersecting the sides of ABCD at the points P, Q, R, S (See Figure). Prove that M lies on the diagonal AC if and only if [MRDS] = [MPBQ].

$$\mathrm{Suppose}\:\mathrm{that}\:\mathrm{the}\:\mathrm{point}\:{M}\:\mathrm{lying}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{interior}\:\mathrm{of}\:\mathrm{the}\:\mathrm{parallelogram}\:{ABCD}, \\ $$$$\mathrm{two}\:\mathrm{parallels}\:\mathrm{to}\:{AB}\:\mathrm{and}\:{AD}\:\mathrm{are}\:\mathrm{drawn}, \\ $$$$\mathrm{intersecting}\:\mathrm{the}\:\mathrm{sides}\:\mathrm{of}\:{ABCD}\:\mathrm{at}\:\mathrm{the} \\ $$$$\mathrm{points}\:{P},\:{Q},\:{R},\:{S}\:\left(\mathrm{See}\:\mathrm{Figure}\right).\:\mathrm{Prove} \\ $$$$\mathrm{that}\:{M}\:\mathrm{lies}\:\mathrm{on}\:\mathrm{the}\:\mathrm{diagonal}\:{AC}\:\mathrm{if}\:\mathrm{and} \\ $$$$\mathrm{only}\:\mathrm{if}\:\left[{MRDS}\right]\:=\:\left[{MPBQ}\right]. \\ $$

Question Number 17438    Answers: 0   Comments: 0

find the mean value and root mean square of i=25sin100Πt ranging from 0 to 10

$$\mathrm{find}\:\mathrm{the}\:\mathrm{mean}\:\mathrm{value}\:\mathrm{and}\:\mathrm{root}\:\mathrm{mean}\:\mathrm{square}\:\mathrm{of}\: \\ $$$$\mathrm{i}=\mathrm{25sin100}\Pi\mathrm{t}\:\:\:\:\:\mathrm{ranging}\:\mathrm{from}\:\mathrm{0}\:\mathrm{to}\:\mathrm{10} \\ $$

Question Number 17435    Answers: 1   Comments: 0

Find the value of 4 sin (π/(24)) cos (π/(12)) cos(π/6).

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{4}\:\mathrm{sin}\:\frac{\pi}{\mathrm{24}}\:\:\mathrm{cos}\:\frac{\pi}{\mathrm{12}}\:\:\mathrm{cos}\frac{\pi}{\mathrm{6}}. \\ $$

Question Number 17421    Answers: 1   Comments: 0

The number of solutions of the equation 2^(∣x∣) = 1 + 2∣cos x∣ is

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solutions}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{2}^{\mid{x}\mid} \:=\:\mathrm{1}\:+\:\mathrm{2}\mid\mathrm{cos}\:{x}\mid\:\mathrm{is} \\ $$

Question Number 17420    Answers: 1   Comments: 0

tan^6 (π/9)−33tan^4 (π/9)+27tan^2 (π/9)=?

$$\mathrm{tan}^{\mathrm{6}} \frac{\pi}{\mathrm{9}}−\mathrm{33tan}^{\mathrm{4}} \frac{\pi}{\mathrm{9}}+\mathrm{27tan}^{\mathrm{2}} \frac{\pi}{\mathrm{9}}=? \\ $$

Question Number 17454    Answers: 1   Comments: 0

Find all integers n such that (n^2 − n − 1)^(n + 2) = 1

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{integers}\:{n}\:\mathrm{such}\:\mathrm{that} \\ $$$$\left({n}^{\mathrm{2}} \:−\:{n}\:−\:\mathrm{1}\right)^{{n}\:+\:\mathrm{2}} \:=\:\mathrm{1} \\ $$

Question Number 17401    Answers: 0   Comments: 4

Find the sum of 4-digit greatest number and the 5-digit smallest number, each number having three different digits.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{4}-\mathrm{digit}\:\mathrm{greatest} \\ $$$$\mathrm{number}\:\mathrm{and}\:\mathrm{the}\:\mathrm{5}-\mathrm{digit}\:\mathrm{smallest} \\ $$$$\mathrm{number},\:\mathrm{each}\:\mathrm{number}\:\mathrm{having}\:\mathrm{three} \\ $$$$\mathrm{different}\:\mathrm{digits}. \\ $$

Question Number 17397    Answers: 1   Comments: 0

Question Number 17393    Answers: 1   Comments: 0

Find the modulus of z = 6 + 8i

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{modulus}\:\mathrm{of}\:\:\mathrm{z}\:=\:\mathrm{6}\:+\:\mathrm{8i} \\ $$

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)) .

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

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