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Question Number 75327 Answers: 1 Comments: 3

If T_(n + 1) = 1 + (1/2)T_n Find a formular for T_n in terms of n and find the sum of first n terms

$$\mathrm{If}\:\:\:\:\:\mathrm{T}_{\mathrm{n}\:+\:\mathrm{1}} \:\:\:=\:\:\:\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{T}_{\mathrm{n}} \\ $$$$\mathrm{Find}\:\mathrm{a}\:\mathrm{formular}\:\mathrm{for}\:\:\mathrm{T}_{\mathrm{n}} \:\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\:\mathrm{n} \\ $$$$\mathrm{and}\:\mathrm{find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{first}\:\mathrm{n}\:\mathrm{terms} \\ $$

Question Number 75325 Answers: 1 Comments: 0

Question Number 77131 Answers: 1 Comments: 0

Question Number 75338 Answers: 0 Comments: 3

The wall of mr nelsons bathroom is covered with 1200 square tiles eah of length 24cm. How many square tiles of sides length 24cm would be needed to cover the same wall.

$$\mathrm{The}\:\mathrm{wall}\:\mathrm{of}\:\mathrm{mr}\:\mathrm{nelsons}\:\mathrm{bathroom}\:\mathrm{is} \\ $$$$\mathrm{covered}\:\mathrm{with}\:\mathrm{1200}\:\mathrm{square}\:\mathrm{tiles}\:\mathrm{eah}\:\mathrm{of}\: \\ $$$$\mathrm{length}\:\mathrm{24cm}.\:\mathrm{How}\:\mathrm{many}\:\mathrm{square}\:\mathrm{tiles}\: \\ $$$$\mathrm{of}\:\mathrm{sides}\:\mathrm{length}\:\mathrm{24cm}\:\mathrm{would}\:\mathrm{be}\:\mathrm{needed}\:\mathrm{to}\: \\ $$$$\mathrm{cover}\:\mathrm{the}\:\mathrm{same}\:\mathrm{wall}. \\ $$

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