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AllQuestion and Answers: Page 212

Question Number 194809 Answers: 2 Comments: 0

If f(x)=ax^2 −5x+3 and g(x)=3x−3 intersection at points (1,h) and (3,t). Find

$I f f (x) = {a x}^{2} - 5 x + 3 a n d$ $g (x) = 3 x - 3 i n t e r s e c t i o n a t$ $p o i n t s (1, h) a n d (3, t) .$ $F i n d \underset{―}{}$

Question Number 194808 Answers: 0 Comments: 4

suppose a,b,c are positive real numbers prove the inequality (((a+b)/2))(((b+c)/2))(((c+a)/2))≥(((a+b+c)/3))(((abc)^2 ))^(1/3)

$s u p p o s e a, b, c a r e p o s i t i v e r e a l n u m b e r s$ $p r o v e t h e i n e q u a l i t y$ $(\frac{a + b}{2}) (\frac{b + c}{2}) (\frac{c + a}{2}) ⩾ (\frac{a + b + c}{3}) \sqrt[3]{{(a b c)}^{2}}$

Question Number 194796 Answers: 1 Comments: 0

A 1m^2 rectangle which length is less than 1 is a square. Why?

$A 1 m^{2} r e c t a n g l e w h i c h l e n g t h i s$ $l e s s t h a n 1 i s a s q u a r e . W h y ?$

Question Number 194791 Answers: 1 Comments: 0

$\underset{―}{\underset{⏟}{x}}$

Question Number 194790 Answers: 1 Comments: 0

Question Number 194786 Answers: 1 Comments: 0

x^n +y^n =¿ (n∈N^∗ )

$x^{n} + y^{n} = ¿ (n \in N^{*})$

Question Number 194785 Answers: 0 Comments: 0

∫∫ x^2 +y^2 dxdy (D=x^4 +y^4 ≤1)

$\int \int x^{2} + y^{2} d x d y (D = x^{4} + y^{4} ⩽ 1)$

Question Number 194781 Answers: 0 Comments: 0

f_(n ) the general sentence is seqiencee fibonacci. prove that : f_(2n−1) =f_n ^2 +f_(n−1) ^2

$f_{n} t h e g e n e r a l s e n t e n c e i s s e q i e n c e e$ $f i b o n a c c i .$ $p r o v e t h a t : f_{2 n - 1} = f_{n}^{2} + f_{n - 1}^{2}$

Question Number 194779 Answers: 1 Comments: 4

If a divided by b gives q remaining r Then (a/b) = q,rrr... in base b+1

$I f a d i v i d e d b y b g i v e s q r e m a i n i n g r$ $T h e n \frac{a}{b} = q, r r r . . . i n b a s e b + 1$

Question Number 194767 Answers: 2 Comments: 0

tan θ = 2 ((8sin θ+5cos θ)/(sin^3 θ+cos^3 θ+cos θ)) =?

$\tan θ = 2$ $\frac{8 \sin θ + 5 \cos θ}{\sin^{3} θ + \cos^{3} θ + \cos θ} = ?$

Question Number 194766 Answers: 2 Comments: 0

1+2cot 2x cot x = 3 x=?

$1 + 2 \cot 2 x \cot x = 3$ $x = ?$

Question Number 194759 Answers: 1 Comments: 1

∫_0 ^( 1) ∫_0 ^( 1) (((1+x^2 )/(1+x^2 +y^2 ))) dxdy

$\int_{0}^{1} \int_{0}^{1} (\frac{1 + x^{2}}{1 + x^{2} + y^{2}}) dxdy$

Question Number 194756 Answers: 3 Comments: 0

$\underset{⏟}{b}$

Question Number 194736 Answers: 0 Comments: 2

{: }

Question Number 194735 Answers: 1 Comments: 0

Question Number 194732 Answers: 2 Comments: 1

Question Number 194715 Answers: 0 Comments: 0

Question Number 194713 Answers: 0 Comments: 2

Question Number 194709 Answers: 1 Comments: 0

Show that in fibonacci sequence f_(3n) =f_n ^3 +f_(n+1) ^3 −f_(n−1) ^3

$S h o w t h a t i n f i b o n a c c i s e q u e n c e$ $f_{3 n} = f_{n}^{3} + f_{n + 1}^{3} - f_{n - 1}^{3}$

Question Number 194710 Answers: 0 Comments: 21

let p be a prime number & let a_1 ,a_2 ,a_3 ,...,a_(p ) be integers show that , there exists an integer k such that the numbers a_1 +k, a_2 +k,a_3 +k,....,a_p +k produce at least (1/2)p distinct remainders when divided by p.

$l e t p b e a p r i m e n u m b e r$ $& l e t a_{1}, a_{2}, a_{3}, . . ., a_{p} b e i n t e g e r s$ $s h o w t h a t, t h e r e e x i s t s a n i n t e g e r k s u c h t h a t t h e n u m b e r s$ $a_{1} + k, a_{2} + k, a_{3} + k, . . . ., a_{p} + k$ $p r o d u c e a t l e a s t \frac{1}{2} p d i s t i n c t r e m a i n d e r s$ $w h e n d i v i d e d b y p .$

Question Number 194700 Answers: 0 Comments: 2

Question Number 194697 Answers: 2 Comments: 0

$\underset{⏟}{}$

Question Number 194695 Answers: 1 Comments: 0

⇃

$⇃ \underset{―}{}$

Question Number 194693 Answers: 1 Comments: 0

if f_n =f_(n−1) +f_(n−2) ; f_1 =f_2 =1 then prove that 5∣f_(5n)

$i f f_{n} = f_{n - 1} + f_{n - 2}; f_{1} = f_{2} = 1$ $t h e n p r o v e t h a t 5 ∣ f_{5 n}$

Question Number 194685 Answers: 1 Comments: 0

Question Number 194662 Answers: 0 Comments: 2

∫_0 ^(Π/2) (√(4sin^2 t+cos^2 t)) dt

$\int_{0}^{\frac{Π}{2}} \sqrt{4 {s i n}^{2} t + {c o s}^{2} t} d t$

Question Number 194654 Answers: 1 Comments: 0

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