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2 years ago

Jim

Mathematics

2 answers:

umka2103 [35]2 years ago

8 0

Answer:

i dont agree because a negative integer divided by a negative integer is always gonna be positive.

Step-by-step explanation:

stealth61 [152]2 years ago

6 0

yes i agree because if all the integers are positive, the answer stays positive which means if you know your integer rules: a positive divide by a positive it stays positive. its the same thing for all the other operations. hope this helps.

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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

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

From this we need to subtract the contribution of

$\displaystyle\iint_D\vec F(x,y,z)\cdot\mathrm d\vec S$

that is, the integral of $\vec F$ over the disk, oriented downward. Since $z=0$ in $D$ , we have

$\vec F(x,y,0)=\dfrac{y^3}3\,\vec\jmath+y^2\,\vec k$

Parameterize $D$ by

$\vec r(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath$

where $0\le u\le 3$ and $0\le v\le2\pi$ . Take the normal vector to be

$\dfrac{\partial\vec r}{\partial v}\times\dfrac{\partial\vec r}{\partial u}=-u\,\vec k$

Then taking the dot product of $\vec F$ with the normal vector gives

$\vec F(x(u,v),y(u,v),0)\cdot(-u\,\vec k)=-y(u,v)^2u=-u^3\sin^2v$

So the contribution of integrating $\vec F$ over $D$ is

$\displaystyle\int_0^{2\pi}\int_0^3-u^3\sin^2v\,\mathrm du\,\mathrm dv=-\frac{81\pi}4$

and the value of the integral we want is

(integral of divergence of F) - (integral over D) = integral over S

==> 486π/5 - (-81π/4) = 2349π/20

5 0

3 years ago

Suppose that you and two friends go to a restaurant, which last month filled approximately 91.7 % of the orders correctly. comp

MrMuchimi

77.1% chance that all 3 orders are correct.
For three independent events to find the probability of each one occurring we multiply the probabilities together. .917*.917*.917 = .77109 or 77.1 percent chance of all three outcomes being favorable.

5 0

2 years ago

Evaluate the function f(x) = 2x3 - 6x + 1 for f(-2).

erma4kov [3.2K]

Answer:

- 3

Step-by-step explanation:

$f(x) = 2 {x}^{3} - 6x + 1 \\ plugging \: x = - 2 \\ f( - 2) = 2( { - 2})^{3} - 6( - 2)+ 1 \\ = 2 \times ( - 8) + 12 + 1 \\ = - 16 + 13 \\ = - 3 \\ f( - 2) = - 3$

7 0

3 years ago

Create a 5th degree trinomial that has a constant term of 3.

erastovalidia [21]

Answer:

$4x^5\:+\:9x^2\:+\:3$ is a trinomial having three terms, with degree 5 and the constant term '3'.

Step-by-step explanation:

Considering the trinomial

$4x^5\:+\:9x^2\:+\:3$

As the polynomial contains 3 terms, so it is a trinomial.

As the highest power of the variable 'x' is 5, so the degree of this polynomial is 5.

Any term with no variable is called a constant term. so, 3 is a term with no variable. Therefore, the constant term is 3.

Therefore, $4x^5\:+\:9x^2\:+\:3$ is a trinomial having three terms, with degree 5 and the constant term '3'.

8 0

2 years ago

Which weights more 2.48 or 2.5

Mazyrski [523]

2.5 weighs more. It’s a greater number than 2.48

6 0

2 years ago