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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

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 ...

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

Question Number 21611 Answers: 1 Comments: 0

Sin5° =?

$$\mathrm{Sin5}°\:=? \\ $$

Question Number 21574 Answers: 1 Comments: 0

The cyclic octagon ABCDEFGH has sides a, a, a, a, b, b, b, b respectively. Find the radius of the circle that circumscribes ABCDEFGH in terms of a and b.

$$\mathrm{The}\:\mathrm{cyclic}\:\mathrm{octagon}\:{ABCDEFGH}\:\mathrm{has} \\ $$$$\mathrm{sides}\:{a},\:{a},\:{a},\:{a},\:{b},\:{b},\:{b},\:{b}\:\mathrm{respectively}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{that} \\ $$$$\mathrm{circumscribes}\:{ABCDEFGH}\:\mathrm{in}\:\mathrm{terms} \\ $$$$\mathrm{of}\:{a}\:\mathrm{and}\:{b}. \\ $$

Question Number 21571 Answers: 1 Comments: 0

ABCD is a cyclic quadrilateral; x, y, z are the distances of A from the lines BD, BC, CD respectively. Prove that ((BD)/x) = ((BC)/y) + ((CD)/z).

$${ABCD}\:\mathrm{is}\:\mathrm{a}\:\mathrm{cyclic}\:\mathrm{quadrilateral};\:{x},\:{y},\:{z} \\ $$$$\mathrm{are}\:\mathrm{the}\:\mathrm{distances}\:\mathrm{of}\:{A}\:\mathrm{from}\:\mathrm{the}\:\mathrm{lines} \\ $$$${BD},\:{BC},\:{CD}\:\mathrm{respectively}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\frac{{BD}}{{x}}\:=\:\frac{{BC}}{{y}}\:+\:\frac{{CD}}{{z}}. \\ $$

Question Number 21490 Answers: 1 Comments: 0

The kinetic energy of a body increases by 100%.Find the % increase in its momentum. please solve with explanations where necessary. Thanks.

$$\mathrm{The}\:\mathrm{kinetic}\:\mathrm{energy}\:\mathrm{of}\:\mathrm{a}\:\mathrm{body} \\ $$$$\mathrm{increases}\:\mathrm{by}\:\mathrm{100\%}.\mathrm{Find}\:\mathrm{the}\:\% \\ $$$$\mathrm{increase}\:\mathrm{in}\:\mathrm{its}\:\mathrm{momentum}. \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{solve}\:\mathrm{with}\:\mathrm{explanations} \\ $$$$\mathrm{where}\:\mathrm{necessary}.\:\mathrm{Thanks}. \\ $$

Question Number 21401 Answers: 0 Comments: 0

∫_0 ^∞ ((xdx)/(e^x +1))=?

$$\underset{\mathrm{0}} {\overset{\infty} {\int}}\frac{{xdx}}{{e}^{{x}} +\mathrm{1}}=? \\ $$

Question Number 21310 Answers: 1 Comments: 8

What do you guys think of creating a Telegram group to discuss theory and more descriptive questions?

$$\mathrm{What}\:\mathrm{do}\:\mathrm{you}\:\mathrm{guys}\:\mathrm{think}\:\mathrm{of} \\ $$$$\mathrm{creating}\:\mathrm{a}\:\mathrm{Telegram}\:\mathrm{group}\:\mathrm{to} \\ $$$$\mathrm{discuss}\:\mathrm{theory}\:\mathrm{and}\:\mathrm{more}\:\mathrm{descriptive} \\ $$$$\mathrm{questions}? \\ $$

Question Number 21231 Answers: 0 Comments: 0

Consider the areas of the four triangles obtained by drawing the diagonals AC and BD of a trapezium ABCD. The product of these areas, taken two at time, are computed. If among the six products so obtained, two products are 1296 and 576, determine the square root of the maximum possible area of the trapezium to the nearest integer.

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