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Question Number 218560 Answers: 0 Comments: 1

Question Number 218557 Answers: 1 Comments: 1

Question Number 218547 Answers: 1 Comments: 1

Question Number 218543 Answers: 1 Comments: 1

Question Number 218539 Answers: 1 Comments: 0

Solve (∂^2 w/∂t^2 )=c^2 (∂^2 w/∂x^2 ) w(0,t)=f(t) ,lim_(x→∞) w(x,t)=0 (Boundary Condition) w(x,0)=0 , w_t (x,0)=0 (Initial Condition) f(t) { ((sin(t) , t∈[0,2π))),((0 , otherwise)) :}

$S olve$ $\frac{\partial^{2} w}{\partial t^{2}} = c^{2} \frac{\partial^{2} w}{\partial x^{2}}$ $w (0, t) = f (t), \lim_{x \to \infty} w (x, t) = 0 (Boundary Condition)$ $w (x, 0) = 0, w_{t} (x, 0) = 0 (Initial Condition)$ $f (t) {\begin{cases} \sin (t), t \in [0, 2 π) \\ 0, otherwise \end{cases}$

Question Number 218532 Answers: 0 Comments: 0

Question Number 218534 Answers: 0 Comments: 0

I Find Fun integral problem! ∫ x^dx −1 =?? note) I already know that integral Solution Try integral problem! (# Product Integral , #Integral)

$I Find Fun integral problem!$ $\int x^{d x} - 1 = ? ?$ $note) I already know that integral Solution$ $Try integral problem!$ $You can't use 'macro parameter character #' in math mode$

Question Number 218528 Answers: 3 Comments: 0

Question Number 218527 Answers: 1 Comments: 0

Question Number 218526 Answers: 2 Comments: 2

Question Number 218525 Answers: 1 Comments: 0

Question Number 218515 Answers: 0 Comments: 0

Question Number 218504 Answers: 1 Comments: 0

Let a>1 fixed Solve for real numbers the system { ((a^x + 2^x = ay + 2)),((a^y + 2^y = az + 2)),((a^z + 2^z = ax + 2)) :}

$Let a > 1 fixed$ $Solve for real numbers the system$ ${\begin{cases} a^{x} + 2^{x} = ay + 2 \\ a^{y} + 2^{y} = az + 2 \\ a^{z} + 2^{z} = ax + 2 \end{cases}$

Question Number 218494 Answers: 4 Comments: 0

Question Number 218493 Answers: 2 Comments: 0

Question Number 218491 Answers: 5 Comments: 1

Question Number 218485 Answers: 1 Comments: 0

solve the equation 1) X^6 −1=0 2) X^4 +X^2 +1=0

$s o l v e t h e e q u a t i o n$ $1) X^{6} - 1 = 0$ $2) X^{4} + X^{2} + 1 = 0$

Question Number 218482 Answers: 0 Comments: 1

solve for real x; _( 3(√(((x^5 −5x^4 +10x^3 −10x^2 +5x)/(x^2 −2x+1))+(√(x^4 +4x^2 +4))))=(√(3 )) )

$s o l v e f o r r e a l x;$ $\underset{3 \sqrt{\frac{x^{5} - 5 x^{4} + 10 x^{3} - 10 x^{2} + 5 x}{x^{2} - 2 x + 1} + \sqrt{x^{4} + 4 x^{2} + 4}} = \sqrt{3}}{}$

Question Number 218476 Answers: 1 Comments: 0

Question Number 218475 Answers: 5 Comments: 0

Question Number 218474 Answers: 1 Comments: 0

solve for real x (√(x+(√(x^2 +1)))) = (√2)

$s o l v e f o r r e a l x$ $\sqrt{x + \sqrt{x^{2} + 1}} = \sqrt{2}$

Question Number 218473 Answers: 2 Comments: 0

Solve the following equation for the real x value; x^4 −4x^3 +6x^2 −4x+2 = (√(2x^4 −8x^3 +12x^2 −8x+5))

$S o l v e t h e f o l l o w i n g e q u a t i o n f o r t h e r e a l x v a l u e;$ $x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 2 = \sqrt{2 x^{4} - 8 x^{3} + 12 x^{2} - 8 x + 5}$

Question Number 218462 Answers: 2 Comments: 0

∫(dx/( (√(2x−x^2 +3))))

$\int \frac{d x}{\sqrt{2 x - x^{2} + 3}}$

Question Number 218459 Answers: 0 Comments: 2

F^→ (x,y)=−(1/2)ye_1 ^→ +(1/2)xe_2 ^→ ▽^→ ×F^→ (x,y)= determinant ((( e_1 ^→ ),e_2 ^→ ,e_3 ^→ ),(( ∂_x ),( ∂_y ),∂_z ),((−(1/2)y),((1/2)x),0))=0e_1 ^→ −0e_2 ^→ +((1/2)−(−(1/2)))e_3 ^→ ∮_( C) F^→ ∙dl=∮_( C) −(1/2)ydx+(1/2)xdx=∫∫_( R^2 ) e_3 ^→ ∙n^→ dS ∴∮_( C) −(1/2)ydx+(1/2)xdx=∫∫_( R^2 ) dS.....is right...??

$\vec{F} (x, y) = - \frac{1}{2} y {\vec{e}}_{1} + \frac{1}{2} x {\vec{e}}_{2}$ $\vec{▽} \times \vec{F} (x, y) = | \begin{matrix} {\vec{e}}_{1} & {\vec{e}}_{2} & {\vec{e}}_{3} \\ \partial_{x} & \partial_{y} & \partial_{z} \\ - \frac{1}{2} y & \frac{1}{2} x & 0 \end{matrix} | = 0 {\vec{e}}_{1} - 0 {\vec{e}}_{2} + (\frac{1}{2} - (- \frac{1}{2})) {\vec{e}}_{3}$ $\oint_{C} \vec{F} \cdot d l = \oint_{C} - \frac{1}{2} y d x + \frac{1}{2} x d x = \int \int_{R^{2}} {\vec{e}}_{3} \cdot \vec{n} dS$ $∴ \oint_{C} - \frac{1}{2} y d x + \frac{1}{2} x d x = \int \int_{R^{2}} dS . . . . . is right . . . ? ?$

Question Number 218456 Answers: 5 Comments: 0

Question Number 218445 Answers: 3 Comments: 0

there are 100 students in a school. it is found out that each student should select at least 4 courses, so that no two students have the same selection. how many different courses does the school offer?

$t h e r e a r e 100 s t u d e n t s i n a s c h o o l .$ $i t i s f o u n d o u t t h a t e a c h s t u d e n t$ $s h o u l d s e l e c t a t l e a s t 4 c o u r s e s, s o$ $t h a t n o t w o s t u d e n t s h a v e t h e s a m e$ $s e l e c t i o n .$ $h o w m a n y d i f f e r e n t c o u r s e s d o e s$ $t h e s c h o o l o f f e r ?$

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