Question and Answers Forum

AllQuestion and Answers: Page 1895

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 .

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)) .

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

Pg 1890 Pg 1891 Pg 1892 Pg 1893 Pg 1894 Pg 1895 Pg 1896 Pg 1897 Pg 1898 Pg 1899

Contact: info@tinkutara.com