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Question Number 75376    Answers: 1   Comments: 1

Question Number 75375    Answers: 0   Comments: 1

A rubber tube can be divided into 25 pieces each of length 56cm long. How many pieces each 35cm long can be out from the tube.

$$\mathrm{A}\:\mathrm{rubber}\:\mathrm{tube}\:\mathrm{can}\:\mathrm{be}\:\mathrm{divided}\:\mathrm{into} \\ $$$$\mathrm{25}\:\mathrm{pieces}\:\mathrm{each}\:\mathrm{of}\:\mathrm{length}\:\mathrm{56cm}\:\mathrm{long}.\: \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{pieces}\:\mathrm{each}\:\mathrm{35cm}\:\mathrm{long}\:\mathrm{can}\: \\ $$$$\mathrm{be}\:\mathrm{out}\:\mathrm{from}\:\mathrm{the}\:\mathrm{tube}. \\ $$

Question Number 75368    Answers: 2   Comments: 1

Find the interval for which the function f(x) = sinx + cosx, for x∈ [0, 2π] is strictly inceasing and srictly decreasing ?

$$ \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{interval}\:\mathrm{for}\:\mathrm{which}\:\mathrm{the}\:\mathrm{function} \\ $$$$\:{f}\left({x}\right)\:=\:{sinx}\:+\:{cosx},\:\mathrm{for}\:\:{x}\in\:\left[\mathrm{0},\:\mathrm{2}\pi\right] \\ $$$$\mathrm{is}\:\mathrm{strictly}\:\mathrm{inceasing}\:\mathrm{and}\:\mathrm{srictly}\:\mathrm{decreasing}\:? \\ $$

Question Number 75367    Answers: 1   Comments: 3

(6/(100))×10=?

$$\frac{\mathrm{6}}{\mathrm{100}}×\mathrm{10}=? \\ $$

Question Number 75366    Answers: 1   Comments: 0

i need the sol plz expansion the maclaurin series f(z)=(z/(z^4 + 9)) = (z/9) ×(1/(1+(z^4 /9)))

$${i}\:{need}\:{the}\:{sol}\:{plz} \\ $$$${expansion}\:{the}\:{maclaurin}\:{series} \\ $$$${f}\left({z}\right)=\frac{{z}}{{z}^{\mathrm{4}} \:+\:\mathrm{9}}\:=\:\frac{{z}}{\mathrm{9}}\:×\frac{\mathrm{1}}{\mathrm{1}+\frac{{z}^{\mathrm{4}} }{\mathrm{9}}}\: \\ $$

Question Number 75360    Answers: 0   Comments: 0

Question Number 75358    Answers: 0   Comments: 0

Question Number 75351    Answers: 1   Comments: 0

Question Number 75339    Answers: 0   Comments: 2

A water flows from a tap into an empty cylindrical jar at rate of 23211cm^3 per secons. At what time will the tap fill the cylinder with volume of 6011cm^3 .

$$\mathrm{A}\:\mathrm{water}\:\mathrm{flows}\:\mathrm{from}\:\mathrm{a}\:\mathrm{tap}\:\mathrm{into}\:\mathrm{an}\:\mathrm{empty} \\ $$$$\mathrm{cylindrical}\:\mathrm{jar}\:\mathrm{at}\:\mathrm{rate}\:\mathrm{of}\:\:\mathrm{23211cm}^{\mathrm{3}} \:\mathrm{per} \\ $$$$\mathrm{secons}.\:\mathrm{At}\:\mathrm{what}\:\mathrm{time}\:\mathrm{will}\:\mathrm{the}\:\mathrm{tap}\:\mathrm{fill}\: \\ $$$$\mathrm{the}\:\mathrm{cylinder}\:\mathrm{with}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{6011cm}^{\mathrm{3}} . \\ $$

Question Number 75330    Answers: 0   Comments: 3

Question Number 75329    Answers: 1   Comments: 0

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

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