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3 years ago

What two numbers add to 10 and multiply to -192? How do you find it?

1 answer:

7 0

There is a way to do this algebraically using equations, but it is really messy so I am going to go over the way to do it. The way you do this is by finding whole numbers that multiply to make -192. Start with 1 and 192, 2 and 96, 3 and 64, etc and make the smaller number negative.
The reason why you make the smaller number negative is because we are looking for what numbers add together to make a positive number (10). If the bigger number was negative, then we would get a negative sum.
From what i could find, there aren't any whole numbers that satisfy this, and i doubt that the question would want you to find decimals for this.

The way to find this with equations (in short) is to have to variables, x and y, and make two equations. in this case x+y=10 and xy=-192. Solve one equation for a variable and then use substitution to plug that variable into the other equation. if you do this you get really long decimals.

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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

Can someone help me with this please?

GarryVolchara [31]

Answer:

16.49

Step-by-step explanation:

21^2 - 13^2 = 272

square root 272 = 16.49

7 0

2 years ago

What is the hypotenuse of a right triangle?

Alex73 [517]

The hypotenuse^2 = leg1^2 + leg2^2
The hypotenuse is always the LONGEST side of any right triangle.
It is also the side that is opposite the right angle

6 0

2 years ago

What kind of sequence is the pattern 1, 6, 7, 13, 20, ...?

AlexFokin [52]

Answer:

The given sequence 6, 7, 13, 20, ... is a recursive sequence

Step-by-step explanation:

As the given sequence is

$6, 7, 13, 20, ...$

It cannot be an arithmetic sequence as the common difference between two consecutive terms in not constant.

$d = 7-6=1$ , $d = 13-7=6$

As d is not same. Hence, it cannot be an arithmetic sequence.

It also cannot be a geometrical sequence and exponential sequence.

It cannot be geometric sequence as the common ratio between two consecutive terms in not constant.

$r = 7-6=1$ , $r = 13-7=6$

$r = \frac{7}{6}$ , $r = \frac{13}{7}$

As r is not same, Hence, it cannot be a geometric sequence or exponential sequence. As exponential sequence and geometric sequence are basically the same thing.

So, if we carefully observe, we can determine that:

The given sequence 6, 7, 13, 20, ... is a recursive sequence.

Please have a close look that each term is being created by adding the preceding two terms.

For example, the sequence is generated by starting from 1.

${\displaystyle F_{1}=1$

and

$F_{n}=F_{n-1}+F_{n-2}$

for n > 1.

Keywords: sequence, arithmetic sequence, geometric sequence, exponential sequence

Learn more about sequence from brainly.com/question/10986621

#learnwithBrainly

6 0

3 years ago

Find slope of the line -12x+13y=-6

Burka [1]

Answer: 2 x - 3 y = 6 i think but let let me know if i'm wrong

7 0

3 years ago