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3 years ago

Find the value of x Kinda confused

Mathematics

1 answer:

Nat2105 [25]3 years ago

5 0

Answer:

x = 374/7

Step-by-step explanation:

all of the angles should equal to 360 degrees since it's a quadrilateral.

So,

1+ (2x+10)+(3x-5)+(2x-20) = 360

1+ 2x+10 +3x-5+2x-20 = 360

7x -14 =360

7x = 360+14

7x = 374

x= 374/7

x= 53.428...

Hope this helps!

Please mark brainliest if you think I helped! Would really appreciate!

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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

Please help me on questions 19-21 using this diagram attached

Leona [35]

Vas happenin!!

19. TX
20. O and I can’t see the other bottom of the cube
21. WS
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Sorry if it’s wrong

6 0

3 years ago

I neeed help plz 30 points

Mice21 [21]

Answer:

Step-by-step explanation:

NA = √[(- 4 - 1 )² + (- 3 - 2)²] = 5√2

AT = √[(8 - 1 )² + (1 - 2)²] = 5√2

TS = √[(3 - 8 )² + (- 4 - 1)²] = 5√2

NS = √[(- 4 - 3 )² + (- 3 + 4)²] = 5√2

NA = AT = TS = NS = 5√2

$m_{NA}$ = (- 3 - 2) / (- 4 - 1) = 1 ........ (1)

$m_{TS}$ = (- 4 - 1) / (3 - 8 ) = 1 ......... (2)

From (1) and (2) ⇒ NA║TS

$m_{AT}$ = ( 1 - 2) / ( 8 - 1) = - 1 / 7 .......... (3)

$m_{NS}$ = ( - 4 + 3) / ( 3 + 4) = - 1 / 7 .... (4)

From (3) and (4) ⇒ AT║NS

Thus, NATS is rhombus.

4 0

3 years ago

X/3-4=-7 please help me solve

Vanyuwa [196]

In order to solve this we need to get x by itself on one side.

We need o start by adding across the 4 so that we get:

x/3 = -7 + 4 = -3

We then need to multiply both sides by 3 to get a singular x:

x = -3 * 3 = -9

5 0

3 years ago

Read 2 more answers

In order to ensure efficient usage of a server, it is necessary to estimate the mean number

juin [17]

Answer:

a. [36.19;39.21]

b. Reject the null hypothesis. The population mean of users that are connected at the same time is greater than 35.

Step-by-step explanation:

Hello!

Your study variable is,

X: "number of users of one server at a time"

The objective is to estimate the mean, for this, a sample of n=100 times was taken and the standard deviation S= 9.2 and the sample mean is X[bar]= 37.7 were calculated.

You need to study the population mean, for this you need your variable to have at least normal distribution. Since you don't have information about its distribution, but the sample is big enough (n≥30) you can apply the Central Limit Theorem and approximate the distribution of the sample mean X[bar] to normal:

X[bar]≈N(μ;σ²/n)

a. With this approximation, you can construct the 90% Confidence Interval using the approximate Z

[X[bar] ± $Z_{1-\alpha /2}$ * S/√n]

$Z_{1-\alpha /2}$ = $Z_{0.95}$ = 1.64

[37.7± 1.64* 9.2/√100]

[36.19;39.21]

b. You need to test if the population mean is greater than 35 with a level of significance of 1%.

The hypothesis is:

H₀: μ ≤ 35

H₁: μ > 35

α: 0.01

This is a one-tailed test so you have only one critical level (right tail):

$Z_{1\alpha } = Z_{0.99} = 2.33$

This means that if the value of the calculated statistic is equal or greater than 2.33 you will reject the null Hypothesis.

If the value is less than 2.33 you will support the null hypothesis.

The statistic is:

Z= X[bar] - μ = 37.7 - 35 = 2.93

S/√n 9.2/10

The value 2.93 > 2.33, so you reject the null hypothesis. This means that the population mean of users that are connected at the same time is greater than 35.

Note: To make the decision using the interval calculated on a), the hypothesis should have been two-tailed and the confidence and significance levels complementary.

I hope it helps!

7 0

3 years ago