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Question Number 23034    Answers: 0   Comments: 1

Question Number 22896    Answers: 0   Comments: 1

how can demonstred 17^(4n+1) +3×9^(2n+1) ≡0[11]

$${how}\:{can}\:{demonstred} \\ $$$$\mathrm{17}^{\mathrm{4}{n}+\mathrm{1}} +\mathrm{3}×\mathrm{9}^{\mathrm{2}{n}+\mathrm{1}} \equiv\mathrm{0}\left[\mathrm{11}\right] \\ $$

Question Number 22787    Answers: 0   Comments: 2

sin^(−1) (sin 10)=10 or 3π−10 Ans is 3π−10 How

$$\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{sin}\:\mathrm{10}\right)=\mathrm{10}\:\mathrm{or}\:\mathrm{3}\pi−\mathrm{10} \\ $$$$\mathrm{Ans}\:\mathrm{is}\:\mathrm{3}\pi−\mathrm{10}\:\:\:\mathrm{How} \\ $$

Question Number 22661    Answers: 1   Comments: 1

Question Number 23796    Answers: 1   Comments: 0

∫((2sinx+3cosx)/(3sinx+4cosx)) dx

$$\int\frac{\mathrm{2sinx}+\mathrm{3cosx}}{\mathrm{3sinx}+\mathrm{4cosx}}\:\mathrm{dx} \\ $$

Question Number 22545    Answers: 2   Comments: 0

∫(x^(1/2) /(x^(1/2) −x^(1/3) ))dx=

$$\int\frac{\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{2}}} }{\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{2}}} −\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{3}}} }\mathrm{dx}= \\ $$$$ \\ $$

Question Number 22525    Answers: 0   Comments: 4

Question Number 22524    Answers: 0   Comments: 1

toutes lessolutions du systeme

$${toutes}\:{lessolutions}\:{du}\:{systeme} \\ $$

Question Number 22522    Answers: 0   Comments: 1

Happy Diwali Friends !! :)

$$\mathrm{H}{appy}\: \\ $$$${Diwali} \\ $$$$\left.{Friends}\:!!\::\right) \\ $$

Question Number 22516    Answers: 0   Comments: 1

toutes les solutions ?

$${toutes}\:{les}\:{solutions}\:? \\ $$

Question Number 22515    Answers: 0   Comments: 0

In a quadrilateral ABCD, it is given that AB is parallel to CD and the diagonals AC and BD are perpendicular to each other. Show that (a) AD.BC ≥ AB.CD; (b) AD + BC ≥ AB + CD.

$$\mathrm{In}\:\mathrm{a}\:\mathrm{quadrilateral}\:{ABCD},\:\mathrm{it}\:\mathrm{is}\:\mathrm{given} \\ $$$$\mathrm{that}\:{AB}\:\mathrm{is}\:\mathrm{parallel}\:\mathrm{to}\:{CD}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{diagonals}\:{AC}\:\mathrm{and}\:{BD}\:\mathrm{are}\:\mathrm{perpendicular} \\ $$$$\mathrm{to}\:\mathrm{each}\:\mathrm{other}. \\ $$$$\mathrm{Show}\:\mathrm{that} \\ $$$$\left(\mathrm{a}\right)\:{AD}.{BC}\:\geqslant\:{AB}.{CD}; \\ $$$$\left(\mathrm{b}\right)\:{AD}\:+\:{BC}\:\geqslant\:{AB}\:+\:{CD}. \\ $$

Question Number 22478    Answers: 0   Comments: 1

{ ((x+y^2 +z^3 =3)),((y+z^2 +x^3 =3)),((z+x^2 +z^3 =3)) :} trouver les solutions positives

$$\begin{cases}{{x}+{y}^{\mathrm{2}} +{z}^{\mathrm{3}} =\mathrm{3}}\\{{y}+{z}^{\mathrm{2}} +{x}^{\mathrm{3}} =\mathrm{3}}\\{{z}+{x}^{\mathrm{2}} +{z}^{\mathrm{3}} =\mathrm{3}}\end{cases} \\ $$$${trouver}\:{les}\:{solutions}\:{positives} \\ $$$$ \\ $$

Question Number 22361    Answers: 0   Comments: 0

Question Number 23106    Answers: 0   Comments: 0

Is 2(x+1) had a x=3

$${Is}\:\mathrm{2}\left({x}+\mathrm{1}\right)\:{had}\:{a}\:{x}=\mathrm{3} \\ $$

Question Number 22112    Answers: 1   Comments: 0

A boy ran around a circular part of radius 14m in 15s. Calculate the average velocity and the average speed.

$$\mathrm{A}\:\mathrm{boy}\:\mathrm{ran}\:\mathrm{around}\:\mathrm{a}\:\mathrm{circular}\:\mathrm{part}\:\mathrm{of}\:\mathrm{radius}\:\mathrm{14m}\:\mathrm{in}\:\mathrm{15s}.\:\mathrm{Calculate}\:\mathrm{the}\: \\ $$$$\mathrm{average}\:\mathrm{velocity}\:\mathrm{and}\:\mathrm{the}\:\mathrm{average}\:\mathrm{speed}. \\ $$

Question Number 22079    Answers: 0   Comments: 1

Let ABC be a triangle and h_a the altitude through A. Prove that (b + c)^2 ≥ a^2 + 4h_a ^2 . (As usual a, b, c denote the sides BC, CA, AB respectively.)

$$\mathrm{Let}\:{ABC}\:\mathrm{be}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{and}\:{h}_{{a}} \:\mathrm{the} \\ $$$$\mathrm{altitude}\:\mathrm{through}\:{A}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\left({b}\:+\:{c}\right)^{\mathrm{2}} \:\geqslant\:{a}^{\mathrm{2}} \:+\:\mathrm{4}{h}_{{a}} ^{\mathrm{2}} . \\ $$$$\left(\mathrm{As}\:\mathrm{usual}\:{a},\:{b},\:{c}\:\mathrm{denote}\:\mathrm{the}\:\mathrm{sides}\:{BC},\right. \\ $$$$\left.{CA},\:{AB}\:\mathrm{respectively}.\right) \\ $$

Question Number 22055    Answers: 0   Comments: 1

Question Number 22001    Answers: 1   Comments: 0

if determinant (((z−(z/4))),())=2 then value of determinant ((z),())

$${if}\:\begin{vmatrix}{{z}−\frac{{z}}{\mathrm{4}}}\\{}\end{vmatrix}=\mathrm{2}\:{then}\:{value}\:{of}\:\begin{vmatrix}{{z}}\\{}\end{vmatrix} \\ $$

Question Number 21973    Answers: 1   Comments: 1

ΔABC with sides a, b, c ∈ Z and ∠A = 3∠B If its circumference is minimum, then find a, b, c

$$\Delta{ABC}\:\mathrm{with}\:\mathrm{sides}\:{a},\:{b},\:{c}\:\in\:\mathbb{Z}\:\mathrm{and}\:\angle{A}\:=\:\mathrm{3}\angle{B} \\ $$$$\mathrm{If}\:\mathrm{its}\:\mathrm{circumference}\:\mathrm{is}\:\mathrm{minimum},\:\mathrm{then} \\ $$$$\mathrm{find}\:{a},\:{b},\:{c} \\ $$

Question Number 21903    Answers: 0   Comments: 0

ΔABC with sides a, b, c ∈ Z and ∠A = 3∠B If its circumference is minimum, then find a, b, c

$$\Delta{ABC}\:\mathrm{with}\:\mathrm{sides}\:{a},\:{b},\:{c}\:\in\:\mathbb{Z}\:\mathrm{and}\:\angle{A}\:=\:\mathrm{3}\angle{B} \\ $$$$\mathrm{If}\:\mathrm{its}\:\mathrm{circumference}\:\mathrm{is}\:\mathrm{minimum},\:\mathrm{then}\:\mathrm{find}\:{a},\:{b},\:{c} \\ $$

Question Number 21840    Answers: 1   Comments: 0

A cone is placed inside a sphere. If volume of the cone is maximum, find the ratio of radius from the cone and sphere

$$\mathrm{A}\:\mathrm{cone}\:\mathrm{is}\:\mathrm{placed}\:\mathrm{inside}\:\mathrm{a}\:\mathrm{sphere}. \\ $$$$\mathrm{If}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cone}\:\mathrm{is}\:\mathrm{maximum}, \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{radius}\:\mathrm{from}\:\mathrm{the}\:\mathrm{cone}\:\mathrm{and}\:\mathrm{sphere} \\ $$

Question Number 21825    Answers: 0   Comments: 2

Find the simplest form of Σ_(k = 1) ^n 2^k [sin^2 (((2kπ)/3)) + (1/4)]

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{simplest}\:\mathrm{form}\:\mathrm{of} \\ $$$$\underset{{k}\:=\:\mathrm{1}} {\overset{{n}} {\sum}}\mathrm{2}^{{k}} \left[\mathrm{sin}^{\mathrm{2}} \:\left(\frac{\mathrm{2}{k}\pi}{\mathrm{3}}\right)\:+\:\frac{\mathrm{1}}{\mathrm{4}}\right] \\ $$

Question Number 21754    Answers: 1   Comments: 0

Q. In 2014, country X had 783 miles of paved roads. Starting in 2015, the country has been building 8 miles of new paved roads each year. At this rate, how many miles of paved roads will country X have in 2030?

$$\mathrm{Q}.\:\mathrm{In}\:\mathrm{2014},\:\mathrm{country}\:\mathrm{X}\:\mathrm{had}\:\mathrm{783}\:\mathrm{miles}\:\mathrm{of}\:\mathrm{paved}\:\mathrm{roads}.\:\mathrm{Starting}\:\mathrm{in}\: \\ $$$$\:\:\:\:\:\:\:\mathrm{2015},\:\mathrm{the}\:\mathrm{country}\:\mathrm{has}\:\:\mathrm{been}\:\mathrm{building}\:\:\mathrm{8}\:\:\mathrm{miles}\:\mathrm{of}\:\mathrm{new}\:\mathrm{paved} \\ $$$$\:\:\:\:\:\:\mathrm{roads}\:\mathrm{each}\:\mathrm{year}.\:\mathrm{At}\:\mathrm{this}\:\mathrm{rate},\:\:\mathrm{how}\:\:\mathrm{many}\:\mathrm{miles}\:\mathrm{of}\:\mathrm{paved}\:\mathrm{roads} \\ $$$$\:\:\:\:\:\:\mathrm{will}\:\mathrm{country}\:\mathrm{X}\:\mathrm{have}\:\mathrm{in}\:\mathrm{2030}? \\ $$

Question Number 21782    Answers: 0   Comments: 0

a_1 =1, a_(n+1) =(a_n /(√(a_n +n+1))) Σ_(n=1) ^∞ a_n =?

$${a}_{\mathrm{1}} =\mathrm{1},\:{a}_{{n}+\mathrm{1}} =\frac{{a}_{{n}} }{\sqrt{{a}_{{n}} +{n}+\mathrm{1}}} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{a}_{{n}} =? \\ $$

Question Number 21656    Answers: 0   Comments: 4

Let A(x) is a cubic polynomial and B(x) = (x −1)(x − 2)(x − 3) Find how many C(x) so that B(C(x)) = B(x) . A(x)

$$\mathrm{Let}\:{A}\left({x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{cubic}\:\mathrm{polynomial}\:\mathrm{and}\:{B}\left({x}\right)\:=\:\left({x}\:−\mathrm{1}\right)\left({x}\:−\:\mathrm{2}\right)\left({x}\:−\:\mathrm{3}\right) \\ $$$$\mathrm{Find}\:\mathrm{how}\:\mathrm{many}\:{C}\left({x}\right)\:\mathrm{so}\:\mathrm{that} \\ $$$${B}\left({C}\left({x}\right)\right)\:=\:{B}\left({x}\right)\:.\:{A}\left({x}\right) \\ $$

Question Number 21655    Answers: 1   Comments: 0

(((2017)),(( 0)) ) + (((2017)),(( 2)) ) + (((2017)),(( 4)) ) + (((2017)),(( 6)) ) + ... + (((2017)),((2016)) ) is equal to ...

$$\begin{pmatrix}{\mathrm{2017}}\\{\:\:\:\:\mathrm{0}}\end{pmatrix}\:+\:\begin{pmatrix}{\mathrm{2017}}\\{\:\:\:\:\mathrm{2}}\end{pmatrix}\:+\:\begin{pmatrix}{\mathrm{2017}}\\{\:\:\:\:\mathrm{4}}\end{pmatrix}\:+\:\begin{pmatrix}{\mathrm{2017}}\\{\:\:\:\:\mathrm{6}}\end{pmatrix}\:+\:...\:+\:\begin{pmatrix}{\mathrm{2017}}\\{\mathrm{2016}}\end{pmatrix} \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:... \\ $$

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