Question and Answers Forum

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.

$In a quadrilateral A B C D, it is given$ $that A B is parallel to C D and the$ $diagonals A C and B D are perpendicular$ $to each other .$ $Show that$ $(a) A D . B C ⩾ A B . C D;$ $(b) A D + B C ⩾ A B + C D .$

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

${\begin{cases} x + y^{2} + z^{3} = 3 \\ y + z^{2} + x^{3} = 3 \\ z + x^{2} + z^{3} = 3 \end{cases}$ $t r o u v e r l e s s o l u t i o n s p o s i t i v e s$

Question Number 22361 Answers: 0 Comments: 0

Question Number 23106 Answers: 0 Comments: 0

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

$I s 2 (x + 1) h a d a x = 3$

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.

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

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.)

$Let A B C be a triangle and h_{a} the$ $altitude through A . Prove that$ ${(b + c)}^{2} ⩾ a^{2} + 4 h_{a}^{2} .$ $(As usual a, b, c denote the sides B C,$ $C A, A B respectively .)$

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),())

$i f | \begin{matrix} z - \frac{z}{4} \end{matrix} | = 2 t h e n v a l u e o f | \begin{matrix} z \end{matrix} |$

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

$Δ A B C with sides a, b, c \in Z and ∠ A = 3 ∠ B$ $If its circumference is minimum, then$ $find a, b, c$

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

$Δ A B C with sides a, b, c \in Z and ∠ A = 3 ∠ B$ $If its circumference is minimum, then find a, b, c$

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

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

Question Number 21825 Answers: 0 Comments: 2

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

$Find the simplest form of$ $\underset{k = 1}{\sum^{n}} 2^{k} [\sin^{2} (\frac{2 k π}{3}) + \frac{1}{4}]$

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?

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

Question Number 21782 Answers: 0 Comments: 0

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

$a_{1} = 1, a_{n + 1} = \frac{a_{n}}{\sqrt{a_{n} + n + 1}}$ $\underset{n = 1}{\sum^{\infty}} a_{n} = ?$

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)

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

Question Number 21655 Answers: 1 Comments: 0

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

$(\begin{matrix} 2017 \\ 0 \end{matrix}) + (\begin{matrix} 2017 \\ 2 \end{matrix}) + (\begin{matrix} 2017 \\ 4 \end{matrix}) + (\begin{matrix} 2017 \\ 6 \end{matrix}) + . . . + (\begin{matrix} 2017 \\ 2016 \end{matrix})$ $is equal to . . .$

Question Number 21611 Answers: 1 Comments: 0

Sin5° =?

$Sin 5 ° = ?$

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.

$The cyclic octagon A B C D E F G H has$ $sides a, a, a, a, b, b, b, b respectively .$ $Find the radius of the circle that$ $circumscribes A B C D E F G H in terms$ $of a and b .$

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).

$A B C D is a cyclic quadrilateral; x, y, z$ $are the distances of A from the lines$ $B D, B C, C D respectively . Prove that$ $\frac{B D}{x} = \frac{B C}{y} + \frac{C D}{z} .$

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.

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

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