I need an answer to this, I dont get it, wouldnt it be impossible due to like terms? g3b=5x+2

Mathematics

1 answer:

Serjik [45]2 years ago

4 0

Answer:

Step-by-step explanation:

hiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii bot

$x^{2} x^{2} \geq x^{2} \neq \geq \geq$

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Consider the set S={1,2,3,4,5,6,7,8,9,12,13,14,15,16,17,18,19,23,24, .............. ,123456789}, which consists of all positive

jarptica [38.1K]

Answer:

12345

Step-by-step explanation:

The number of numbers with n digits is the same as the number of combinations of n things taken from 9. That means as many numbers have 5 or more digits as have 4 or fewer, with the exception that the number 123456789 is not matched by the number 0 (or a number with no digits). There are 256 numbers with 5 or more digits, but only 255 with 4 or fewer.

So, the median number is the first number with 5 digits:

12345

6 0

3 years ago

Use the Divergence Theorem to evaluate S F · dS, where F(x, y, z) = z2xi + y3 3 + sin z j + (x2z + y2)k and S is the top half of

GenaCL600 [577]

Close off the hemisphere $S$ by attaching to it the disk $D$ of radius 3 centered at the origin in the plane $z=0$ . By the divergence theorem, we have

$\displaystyle\iint_{S\cup D}\vec F(x,y,z)\cdot\mathrm d\vec S=\iiint_R\mathrm{div}\vec F(x,y,z)\,\mathrm dV$

where $R$ is the interior of the joined surfaces $S\cup D$ .

Compute the divergence of $\vec F$ :

$\mathrm{div}\vec F(x,y,z)=\dfrac{\partial(xz^2)}{\partial x}+\dfrac{\partial\left(\frac{y^3}3+\sin z\right)}{\partial y}+\dfrac{\partial(x^2z+y^2)}{\partial k}=z^2+y^2+x^2$

Compute the integral of the divergence over $R$ . Easily done by converting to cylindrical or spherical coordinates. I'll do the latter:

$\begin{cases}x(\rho,\theta,\varphi)=\rho\cos\theta\sin\varphi\\y(\rho,\theta,\varphi)=\rho\sin\theta\sin\varphi\\z(\rho,\theta,\varphi)=\rho\cos\varphi\end{cases}\implies\begin{cases}x^2+y^2+z^2=\rho^2\\\mathrm dV=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi\end{cases}$

So the volume integral is

$\displaystyle\iiint_Rx^2+y^2+z^2\,\mathrm dV=\int_0^{\pi/2}\int_0^{2\pi}\int_0^3\rho^4\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\frac{486\pi}5$