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4 years ago

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Leo owns a hostel and counted the number of guests staying in each room. he then created both a histogram and a dot plot to disp

lay the same data (both diagrams are shown below). which display can be used to find the maximum number of guests in a room?

2 answers:

Helga [31]4 years ago

6 0

Only the box plot will show the maximum number of guests in a room. Histograms will only give us an interval that may or may not include the numbers at the beginning and the end of the interval. A box plot is created using the upper and lower extremes at both ends, so this value will be represented.

vovangra [49]4 years ago

4 0

Answer:

its dotplot for both the q's

Step-by-step explanation:

ur welcome

kaaan academy

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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

kifflom [539]

Looks like we have

$\vec F(x,y,z)=z^2x\,\vec\imath+\left(\dfrac{y^3}3+\sin z\right)\,\vec\jmath+(x^2z+y^2)\,\vec k$

which has divergence

$\nabla\cdot\vec F(x,y,z)=\dfrac{\partial(z^2x)}{\partial x}+\dfrac{\partial\left(\frac{y^3}3+\sin z\right)}{\partial y}+\dfrac{\partial(x^2z+y^2)}{\partial z}=z^2+y^2+x^2$

By the divergence theorem, the integral of $\vec F$ across $S$ is equal to the integral of $\nabla\cdot\vec F$ over $R$ , where $R$ is the region enclosed by $S$ . Of course, $S$ is not a closed surface, but we can make it so by closing off the hemisphere $S$ by attaching it to the disk $x^2+y^2\le1$ (call it $D$ ) so that $R$ has boundary $S\cup D$ .

Then by the divergence theorem,

$\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iiint_R(x^2+y^2+z^2)\,\mathrm dV$

Compute the integral in spherical coordinates, setting

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

so that the integral is

$\displaystyle\iiint_R(x^2+y^2+z^2)\,\mathrm dV=\int_0^{\pi/2}\int_0^{2\pi}\int_0^1\rho^4\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\frac{2\pi}5$

The integral of $\vec F$ across $S\cup D$ is equal to the integral of $\vec F$ across $S$ plus the integral across $D$ (without outward orientation, so that

$\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\frac{2\pi}5-\iint_D\vec F\cdot\mathrm d\vec S$

Parameterize $D$ by

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

with $0\le u\le1$ and $0\le v\le2\pi$ . Take the normal vector to $D$ to be

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

Then we have

$\displaystyle\iint_D\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^1\left(\frac{u^3}3\sin^3v\,\vec\jmath+u^2\sin^2v\,\vec k\right)\times(-u\,\vec k)\,\mathrm du\,\mathrm dv$

$=\displaystyle-\int_0^{2\pi}\int_0^1u^3\sin^2v\,\mathrm du\,\mathrm dv=-\frac\pi4$

Finally,

$\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\frac{2\pi}5-\left(-\frac\pi4\right)=\boxed{\frac{13\pi}{20}}$

6 0

4 years ago

One light-year is equal to 9,460,600,000,000 kilometers. What is this distance represented in scientific notation

Vsevolod [243]

Answer:

9.4606 × 10^12

Step-by-step explanation:

7 0

3 years ago

Find the sum of 100 + 222 + 333

klasskru [66]

Answer:

655

Step-by-step explanation:

this feels like elementary school maths

7 0

3 years ago

Read 2 more answers

Can someone help me ASAP

lianna [129]

Answer:

D. 1/5^15

Step-by-step explanation:

When an exponent is negative you need to get the reciprocal to make it positive.

3 0

3 years ago

Read 2 more answers

How to find the limit of that question

jeka94

Factor the numerator using difference of cubes:
$a^3 - b^3 = (a-b)(a^2 +ab+b^2)$
a = x
b = 2

$\frac{x^3 - 8}{x-2} = \frac{(x-2)(x^2 +2x+4)}{x-2} = x^2 +2x+4$

Now you can evaluate limit as x=2.
$\lim_{x \to 2} (x^2 +2x+4) = 2^2 +2(2)+4 = 12$

5 0

4 years ago