Question and Answers Forum

A (2 × 3) rectangle and a (3 × 4) rectangle are contain within a square without over laping at any inferior point , and the sides of the square are parallel to the sides of the two given rectangles. what is the smallest possible area of the square.

$A (2 \times 3) r e c t a n g l e a n d a (3 \times 4) r e c t a n g l e a r e c o n t a i n w i t h i n$ $a s q u a r e w i t h o u t o v e r l a p i n g a t a n y i n f e r i o r p o i n t, a n d t h e$ $s i d e s o f t h e s q u a r e a r e p a r a l l e l t o t h e s i d e s o f t h e t w o g i v e n$ $r e c t a n g l e s . w h a t i s t h e s m a l l e s t p o s s i b l e a r e a o f t h e s q u a r e .$

Question Number 7514 Answers: 1 Comments: 0

Question Number 7511 Answers: 1 Comments: 0

Factorise the expression 9x^4 + (1/x^4 ) +2.

$Factorise the expression 9 x^{4} + \frac{1}{x^{4}} + 2 .$

Question Number 7510 Answers: 0 Comments: 0

Factorise the expression 9x^4 + (1/x^4 ) +2.

$Factorise the expression 9 x^{4} + \frac{1}{x^{4}} + 2 .$

Question Number 7507 Answers: 0 Comments: 0

Given r, t, j >0 and n≥1; Prove that (([Σ_(p_1 =1) ^n (p_1 ^r +r)+Σ_(p_2 =1) ^n (p_2 ^t +t)]^2 )/(n^2 [(n!)^((r+t)/n) +r(n!)^(t/n) +t(n!)^(r/n) +rt])) +(([Σ_(p_2 =1) ^n (p_2 ^t +t)+Σ_(p_3 =1) ^n (p_3 ^j +j)]^2 )/(n^2 [(n!)^((t+j)/n) +t(n!)^(j/n) +j(n!)^(t/n) +tj])) ≥ 8 By: Mr. Chheang Chantria

$G i v e n r, t, j > 0 a n d n ⩾ 1; P r o v e t h a t$ $\frac{{[\underset{p_{1} = 1}{\sum^{n}} (p_{1}^{r} + r) + \underset{p_{2} = 1}{\sum^{n}} (p_{2}^{t} + t)]}^{2}}{n^{2} [{(n!)}^{\frac{r + t}{n}} + r {(n!)}^{\frac{t}{n}} + t {(n!)}^{\frac{r}{n}} + r t]} + \frac{{[\underset{p_{2} = 1}{\sum^{n}} (p_{2}^{t} + t) + \underset{p_{3} = 1}{\sum^{n}} (p_{3}^{j} + j)]}^{2}}{n^{2} [{(n!)}^{\frac{t + j}{n}} + t {(n!)}^{\frac{j}{n}} + j {(n!)}^{\frac{t}{n}} + t j]} ⩾ 8$ $B y : M r . C h h e a n g C h a n t r i a$

Question Number 7506 Answers: 1 Comments: 0

∫{((1−(√x))/(1+(√x)))}^(1/2) (dx/x)=?

$\int {\frac{1 - \sqrt{x}}{1 + \sqrt{x}}}^{\frac{1}{2}} \frac{d x}{x} = ?$

Question Number 7501 Answers: 1 Comments: 0

Compute lim_(A→+∞) {(1/A)∫_1 ^A A^(1/x) dx}. (IMC 2015)

$C o m p u t e \lim_{A \to + \infty} {\frac{1}{A} \int_{1}^{A} A^{\frac{1}{x}} d x} .$ $(I M C 2015)$

Question Number 7499 Answers: 0 Comments: 0

Let E be a banach space , Y is normed space and suppose that {Ta : a∈A} ⊆ B (E, Y) If {Tax : a∈A} ⊆ Y is bounded , for all x∈E, then {∥Ta∥ : a∈A} is bounded.

$L e t E b e a b a n a c h s p a c e, Y i s n o r m e d s p a c e a n d$ $s u p p o s e t h a t {T a : a \in A} \subseteq B (E, Y) I f {T a x : a \in A}$ $\subseteq Y i s b o u n d e d, f o r a l l x \in E, t h e n {∥ T a ∥ : a \in A} i s$ $b o u n d e d .$

Question Number 7500 Answers: 1 Comments: 0

5^(√(x )) − 5^(x − 7) = 100 Find the value of x. x = 9 please workings.

$5^{\sqrt{x}} - 5^{x - 7} = 100$ $F i n d t h e v a l u e o f x .$ $x = 9 p l e a s e w o r k i n g s .$

Question Number 7489 Answers: 1 Comments: 0

A pen with a cylindrical barrel of diameter 2 cm and height 10.5 cm, filled with ink, can write 3300 words. How many words can be written with that pen using 100 ml of ink. (Take 1cc = 1 ml)

$A pen with a cylindrical barrel of$ $diameter 2 cm and height 10.5 cm,$ $filled with ink, can write 3300 words .$ $How many words can be written with$ $that pen using 100 ml of ink .$ $(Take 1 cc = 1 ml)$

Question Number 7488 Answers: 1 Comments: 0

If A= [(1,2,3),(6,5,4) ] , then A^T =____.

$If A = [\begin{matrix} 1 & 2 & 3 \\ 6 & 5 & 4 \end{matrix}], then A^{T} =____.$

Pg 1940 Pg 1941 Pg 1942 Pg 1943 Pg 1944 Pg 1945 Pg 1946 Pg 1947 Pg 1948 Pg 1949

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