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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)) .

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

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.

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?

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

Question Number 17328 Answers: 0 Comments: 3

Question Number 17247 Answers: 0 Comments: 0

A carrier based on its anual records notes that its trucks cover 50000 km with a normal distribution with a detour of 12000 km. How many miles can be traveled at least 80% of trucks ?

$${A}\:{carrier}\:{based}\:{on}\:{its}\:{anual}\:{records}\:{notes}\:{that}\:{its}\:{trucks}\:{cover}\:\mathrm{50000} \\ $$$${km}\:{with}\:{a}\:{normal}\:{distribution}\:{with}\:{a}\:{detour}\:{of}\:\mathrm{12000}\:{km}. \\ $$$${How}\:{many}\:{miles}\:{can}\:{be}\:{traveled}\:{at}\:{least}\:\mathrm{80\%}\:{of}\:{trucks}\:? \\ $$

Question Number 17220 Answers: 1 Comments: 0

Show that ∫_a ^( b) f(kx)dx=(1/k)∫_(ka) ^( kb) f(x)dx

$$\mathrm{Show}\:\mathrm{that}\:\int_{\mathrm{a}} ^{\:\mathrm{b}} {f}\left(\mathrm{kx}\right)\mathrm{dx}=\frac{\mathrm{1}}{\mathrm{k}}\int_{\mathrm{ka}} ^{\:\mathrm{kb}} {f}\left(\mathrm{x}\right)\mathrm{dx} \\ $$

Question Number 17219 Answers: 1 Comments: 1

∫_0 ^( 2a) xy dx=? where x^2 −y^2 =a^2 and y≥0

$$\int_{\mathrm{0}} ^{\:\mathrm{2a}} \mathrm{xy}\:\mathrm{dx}=?\:\:\mathrm{where}\:\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} =\mathrm{a}^{\mathrm{2}} \:\mathrm{and}\:\mathrm{y}\geqslant\mathrm{0} \\ $$

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