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AllQuestion and Answers: Page 1372

Question Number 68783 Answers: 1 Comments: 5

Question Number 68782 Answers: 0 Comments: 0

Let d_n be the determinant of the n×n matrix whose entries, from left to right and then from top to bottom, are cos 1, cos 2, ..., cos n^2 . (For example, d_3 = determinant (((cos 1 cos 2 cos 3)),((cos 4 cos 5 cos 6)),((cos 7 cos 8 cos 9))). The argument of cos is always in radians not degrees.) Evalue lim_(n→∞) d_(n.)

$Let d_{n} be the determinant of the n \times n$ $matrix whose entries, from left to right$ $and then from top to bottom, are$ $c o s 1, c o s 2, . . ., c o s n^{2} . (For example,$ $d_{3} = | \begin{matrix} c o s 1 c o s 2 c o s 3 \\ c o s 4 c o s 5 c o s 6 \\ c o s 7 c o s 8 c o s 9 \end{matrix} | .$ $The argument of c o s is always in radians$ $not degrees .)$ $Evalue \lim_{n \to \infty} d_{n .}$

Question Number 68775 Answers: 1 Comments: 0

Question Number 68774 Answers: 0 Comments: 0

Question Number 68773 Answers: 0 Comments: 0

Question Number 68768 Answers: 1 Comments: 1

((2x−1))^(1/3) +((x−1))^(1/3) = 1

$\sqrt[3]{2 x - 1} + \sqrt[3]{x - 1} = 1$

Question Number 68767 Answers: 0 Comments: 1

Question Number 68761 Answers: 1 Comments: 1

Two arcs having their centers on a circle are cutting each other at a single point inside the circle and thus dividing the circle in four regions. If the arcs cut each other in a:b & c:d ratios what is the ratio between four regions of the circle when the circle has radius R,the arc divided in a:b has radius r_1 and the arc divided in c:d has radius r_2 .

$Two arcs having their centers on a$ $circle are cutting each other at a$ $single point inside the circle and thus$ $dividing the circle in four regions .$ $If the arcs cut each other in a : b & c : d$ $ratios what is the ratio between four$ $regions of the circle when the circle$ $has radius R, the arc divided in a : b$ $has radius r_{1} and the arc divided in$ $c : d has radius r_{2} .$

Question Number 68740 Answers: 1 Comments: 1

Question Number 68721 Answers: 1 Comments: 1

Question Number 68732 Answers: 0 Comments: 0

Question Number 68714 Answers: 1 Comments: 0

Question Number 68712 Answers: 0 Comments: 3

given that x and y are two numbers other one. given that a>0 and b>0 and a^x = b^y = (ab)^(xy) show that x + y =0

$g i v e n t h a t x a n d y a r e t w o n u m b e r s o t h e r o n e .$ $g i v e n t h a t a > 0 a n d b > 0$ $a n d a^{x} = b^{y} = {(a b)}^{x y} s h o w t h a t x + y = 0$

Question Number 68710 Answers: 0 Comments: 3

Question Number 68703 Answers: 0 Comments: 5

(d/dx)(ln((√((x^2 −1)/(x^2 +1)))))=?

$\frac{d}{d x} (l n (\sqrt{\frac{x^{2} - 1}{x^{2} + 1}})) = ?$

Question Number 68699 Answers: 1 Comments: 2

∫ ln(x + 4) dx =

$\int l n (x + 4) d x =$

Question Number 68695 Answers: 1 Comments: 0

pour 1<k<n montrer que k(n+1−k)<(n+1/2)^2

$p o u r 1 < k < n m o n t r e r q u e$ $k (n + 1 - k) < {(n + 1 / 2)}^{2}$

Question Number 68693 Answers: 0 Comments: 2

Question Number 68788 Answers: 0 Comments: 1

∫1/(1+x^2 )^n dx

$\int 1 / {(1 + x^{2})}^{n} d x$

Question Number 68676 Answers: 0 Comments: 2

Solve the equation tanh^(−1) (((x−2)/(x+1))) = ln 2 show that the set {1,2,4,8} under ×_(15) ,multiplication mod 15 forms a group.

$S o l v e t h e e q u a t i o n$ ${t a n h}^{- 1} (\frac{x - 2}{x + 1}) = l n 2$ $s h o w t h a t t h e s e t {1, 2, 4, 8} u n d e r \times_{15}, m u l t i p l i c a t i o n m o d 15 f o r m s a g r o u p .$

Question Number 68675 Answers: 0 Comments: 3

Express in partial fraction f(x) ≡ ((2x^3 + x + 2)/((x^2 +1)(x+1)(x−2))) x ≠ −1,2 Hence or otherwise show that ∫_0 ^1 f(x) dx = −(1/(12))[ 13ln 2 + π]

$E x p r e s s i n p a r t i a l f r a c t i o n$ $f (x) \equiv \frac{2 x^{3} + x + 2}{(x^{2} + 1) (x + 1) (x - 2)} x \neq - 1, 2$ $H e n c e o r o t h e r w i s e s h o w t h a t$ $\int_{0}^{1} f (x) d x = - \frac{1}{12} [13 l n 2 + π]$

Question Number 68673 Answers: 0 Comments: 8

find sin 20°=?

$f i n d \sin 20 ° = ?$

Question Number 68664 Answers: 1 Comments: 0

In a equilateral triangle ABC whose side is a, the points M and N are taken on the side BC, such that the triangles ABM, AMN and ANC have the same perimeter. Calculate the distances from vertex A to points M and N. (solve in detail.)

$In a equilateral triangle A B C whose$ $side is a, the points M and N are taken$ $on the side B C, such that the triangles$ $A B M, A M N and A N C have the same$ $perimeter . Calculate the distances from$ $vertex A to points M and N .$ $(solve in detail .)$

Question Number 68660 Answers: 0 Comments: 2

∫e^(x+e^x ) dx

$\int e^{x + e^{x}} d x$

Question Number 68666 Answers: 1 Comments: 2

Question Number 68642 Answers: 0 Comments: 3

Young′s modulus of a material measures its resistance caused by external stresses. On a vertical wall is a solid mass of specific mass ρ and Young ε modulus in a straight parallelepiped shape, the dimensions of a which are shown in the figure. Based on the correlations between physical quantities, determine the the expression that best represents the deflection suffered by the solid by the action of its own weight.

${Young}^{'} s modulus of a material measures$ $its resistance caused by external stresses .$ $On a vertical wall is a solid mass of specific$ $mass ρ and Young ε modulus in a straight$ $parallelepiped shape, the dimensions$ $of a which are shown in the figure .$ $Based on the correlations between physical$ $quantities, determine the the expression that$ $best represents the deflection suffered$ $by the solid by the action of its own weight .$

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