Question and Answers Forum

AllQuestion and Answers: Page 1348

Question Number 75321 Answers: 0 Comments: 0

lim_(x→∞) ((𝚷_(k=0) ^n ((n),(k) )))^(1/(n(n+1)))

$$ \\ $$$$\: \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{l}\boldsymbol{\mathrm{im}}}\:\sqrt[{\boldsymbol{{n}}\left(\boldsymbol{{n}}+\mathrm{1}\right)}]{\underset{\boldsymbol{{k}}=\mathrm{0}} {\overset{\boldsymbol{{n}}} {\boldsymbol{\prod}}}\begin{pmatrix}{\boldsymbol{{n}}}\\{\boldsymbol{{k}}}\end{pmatrix}} \\ $$

Question Number 75319 Answers: 0 Comments: 0

Question Number 75318 Answers: 0 Comments: 6

Question Number 75317 Answers: 2 Comments: 1

Find the image of the line ((x−2)/(−1)) = ((y−3)/2) = ((z−4)/3) in the plane 2x+3y−4z +3=0.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{image}\:\mathrm{of}\:\mathrm{the}\:\mathrm{line}\: \\ $$$$\frac{{x}−\mathrm{2}}{−\mathrm{1}}\:=\:\frac{\mathrm{y}−\mathrm{3}}{\mathrm{2}}\:=\:\frac{\mathrm{z}−\mathrm{4}}{\mathrm{3}}\:\:\:\mathrm{in}\:\mathrm{the}\:\mathrm{plane}\: \\ $$$$\mathrm{2}{x}+\mathrm{3}{y}−\mathrm{4}{z}\:+\mathrm{3}=\mathrm{0}. \\ $$

Question Number 75306 Answers: 0 Comments: 3

Use Venn diagram to represent the set of natural numbers, integers, rational numbers, irrational numbers, real numbers, complex numbers

$${Use}\:{Venn}\:{diagram}\:{to} \\ $$$${represent}\:{the}\:{set}\:{of}\:{natural} \\ $$$${numbers},\:{integers},\:{rational} \\ $$$${numbers},\:{irrational} \\ $$$${numbers},\:{real}\:{numbers}, \\ $$$${complex}\:{numbers} \\ $$

Question Number 75303 Answers: 1 Comments: 0

If cosθ = ((cosα−cosβ)/(1−cosα cosβ)) , prove that one of the value of tan(θ/2) is tan(α/2) . tan(β/2) ??

$$\mathrm{If}\:{cos}\theta\:=\:\frac{{cos}\alpha−\mathrm{cos}\beta}{\mathrm{1}−{cos}\alpha\:{cos}\beta}\:,\:\mathrm{prove}\:\mathrm{that}\:\mathrm{one} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{tan}\frac{\theta}{\mathrm{2}}\:\mathrm{is}\:{tan}\frac{\alpha}{\mathrm{2}}\:.\:{tan}\frac{\beta}{\mathrm{2}}\:?? \\ $$

Question Number 75302 Answers: 1 Comments: 1

If θ is eleminated from the equation x = a cos(θ−α) and y = b cos(θ−β) then prove that (x^2 /a^2 ) + (y^2 /b^2 ) − ((2xy)/(ab)) cos(α−β) = sin^2 (α−β) ?

$$\mathrm{If}\:\theta\:\mathrm{is}\:\mathrm{eleminated}\:\mathrm{from}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{x}\:=\: \\ $$$${a}\:{cos}\left(\theta−\alpha\right)\:\mathrm{and}\:{y}\:=\:{b}\:{cos}\left(\theta−\beta\right)\:\mathrm{then} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }\:+\:\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }\:−\:\frac{\mathrm{2}{xy}}{{ab}}\:{cos}\left(\alpha−\beta\right)\:=\:{sin}^{\mathrm{2}} \left(\alpha−\beta\right)\:? \\ $$

Question Number 75301 Answers: 0 Comments: 4

Find S_n and S_∞ of the series : (1/(1.2.3.4)) + (1/(2.3.4.5)) + (1/(3.4.5.6)) + . . .

$$\mathrm{Find}\:\mathrm{S}_{\mathrm{n}} \:\mathrm{and}\:\mathrm{S}_{\infty} \:\mathrm{of}\:\mathrm{the}\:\mathrm{series}\::\:\frac{\mathrm{1}}{\mathrm{1}.\mathrm{2}.\mathrm{3}.\mathrm{4}}\:+\:\frac{\mathrm{1}}{\mathrm{2}.\mathrm{3}.\mathrm{4}.\mathrm{5}}\:+\:\frac{\mathrm{1}}{\mathrm{3}.\mathrm{4}.\mathrm{5}.\mathrm{6}}\:+\:.\:.\:. \\ $$

Question Number 75300 Answers: 1 Comments: 0

A line is such that its segment between the lines 5x−y+4 = 0 and 3x+4y−4 = 0 is bisected at the point (1,5). Obtain its equation ?

$$\mathrm{A}\:\mathrm{line}\:\mathrm{is}\:\mathrm{such}\:\mathrm{that}\:\mathrm{its}\:\mathrm{segment}\:\mathrm{between} \\ $$$$\mathrm{the}\:\mathrm{lines}\:\mathrm{5x}−\mathrm{y}+\mathrm{4}\:=\:\mathrm{0}\:\mathrm{and}\:\mathrm{3x}+\mathrm{4y}−\mathrm{4}\:=\:\mathrm{0} \\ $$$$\mathrm{is}\:\mathrm{bisected}\:\mathrm{at}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{1},\mathrm{5}\right).\:\mathrm{Obtain}\:\mathrm{its} \\ $$$$\mathrm{equation}\:? \\ $$

Question Number 75299 Answers: 0 Comments: 1

What is the value of this? lim_(x→∞) [ (1/(10^n )) ] a) 0.00...001 b) 0 c) uknown

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{this}? \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left[\:\frac{\mathrm{1}}{\mathrm{10}^{{n}} }\:\right] \\ $$$$\left.\mathrm{a}\right)\:\mathrm{0}.\mathrm{00}...\mathrm{001} \\ $$$$\left.\mathrm{b}\right)\:\mathrm{0} \\ $$$$\left.\mathrm{c}\right)\:\mathrm{uknown} \\ $$

Question Number 75296 Answers: 1 Comments: 2

Question Number 75291 Answers: 1 Comments: 0

Question Number 75280 Answers: 1 Comments: 0

A car travels at a constant speed and covers 240km in 8hours . How far does it travel at the same speed in 5hours

$$\mathrm{A}\:\mathrm{car}\:\mathrm{travels}\:\mathrm{at}\:\mathrm{a}\:\mathrm{constant}\:\mathrm{speed}\:\mathrm{and}\: \\ $$$$\mathrm{covers}\:\mathrm{240km}\:\mathrm{in}\:\mathrm{8hours}\:.\:\mathrm{How}\:\mathrm{far}\:\mathrm{does} \\ $$$$\mathrm{it}\:\mathrm{travel}\:\mathrm{at}\:\mathrm{the}\:\mathrm{same}\:\mathrm{speed}\:\mathrm{in}\:\mathrm{5hours} \\ $$$$ \\ $$

Question Number 75277 Answers: 1 Comments: 0

The scale of a map is 1:40,000 . Calculate the area in square centimeters on the map of forest reserved which covers 170km^2 . please help solve this question

$$\mathrm{The}\:\mathrm{scale}\:\mathrm{of}\:\mathrm{a}\:\mathrm{map}\:\mathrm{is}\:\mathrm{1}:\mathrm{40},\mathrm{000}\:.\:\mathrm{Calculate} \\ $$$$\mathrm{the}\:\mathrm{area}\:\mathrm{in}\:\mathrm{square}\:\mathrm{centimeters}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{map}\:\mathrm{of}\:\mathrm{forest}\:\mathrm{reserved}\:\mathrm{which}\:\mathrm{covers}\: \\ $$$$\mathrm{170km}^{\mathrm{2}} . \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{solve}\:\mathrm{this}\:\mathrm{question} \\ $$

Question Number 75276 Answers: 0 Comments: 2

Write the formula of a circle if coordinates of ends of diameter of the circle are given ?

$$\mathrm{Write}\:\mathrm{the}\:\mathrm{formula}\:\mathrm{of}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{if}\:\mathrm{coordinates} \\ $$$$\mathrm{of}\:\mathrm{ends}\:\mathrm{of}\:\mathrm{diameter}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{are}\:\mathrm{given}\:? \\ $$

Question Number 75272 Answers: 1 Comments: 0

a) If z=1+i(√3) prove that prove that z^(14) =2^(13) (−1+i(√3) ) b)prove that in triangle ABC a^2 −(b−c)^2 cos^2 (A/2)=(b+c)^2 sin^2 (A/2)

$$\left.{a}\right)\:{If}\:{z}=\mathrm{1}+{i}\sqrt{\mathrm{3}}\:{prove}\:{that} \\ $$$${prove}\:{that} \\ $$$${z}^{\mathrm{14}} =\mathrm{2}^{\mathrm{13}} \left(−\mathrm{1}+{i}\sqrt{\mathrm{3}}\:\right) \\ $$$$ \\ $$$$\left.{b}\right){prove}\:{that}\:{in}\:{triangle}\:{ABC} \\ $$$${a}^{\mathrm{2}} −\left({b}−{c}\right)^{\mathrm{2}} \mathrm{cos}\:^{\mathrm{2}} \frac{{A}}{\mathrm{2}}=\left({b}+{c}\right)^{\mathrm{2}} \mathrm{sin}\:^{\mathrm{2}} \frac{{A}}{\mathrm{2}} \\ $$

Question Number 75268 Answers: 0 Comments: 0