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miv72 [106K]
3 years ago
9

En un censo realizado en escuelas de enseñanza media superior de un municipio, participaron 8 escuelas que indicaron la cantidad

de estudiantes graduados un año determinado. Los datos se muestran en la siguiente gráfica y de acuerdo a ésta, ¿Cuál fue el promedio de estudiantes graduados?
Mathematics
1 answer:
Harrizon [31]3 years ago
7 0

Answer:

In a census carried out in upper secondary schools in a municipality, 8 schools participated, indicating the number of students who graduated in a given year. The data is shown in the following graph and according to this, what was the average number of graduated students?

Step-by-step explanation:

This is what it says in english

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3 years ago
Use Stokes' Theorem to evaluate S curl F · dS. F(x, y, z) = x2 sin(z)i + y2j + xyk, S is the part of the paraboloid z = 9 − x2 −
Korolek [52]

The vector field

\vec F(x,y,z)=x^2\sin z\,\vec\imath+y^2\,\vec\jmath+xy\,\vec k

has curl

\nabla\times\vec F(x,y,z)=x\,\vec\imath+(x^2\cos z-y)\,\vec\jmath

Parameterize S by

\vec s(u,v)=x(u,v)\,\vec\imath+y(u,v)\,\vec\jmath+z(u,v)\,\vec k

where

\begin{cases}x(u,v)=u\cos v\\y(u,v)=u\sin v\\z(u,v)=(9-u^2)\end{cases}

with 0\le u\le3 and 0\le v\le2\pi.

Take the normal vector to S to be

\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial v}=2u^2\cos v\,\vec\imath+2u^2\sin v\,\vec\jmath+u\,\vec k

Then by Stokes' theorem we have

\displaystyle\int_{\partial S}\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S

=\displaystyle\int_0^{2\pi}\int_0^3(\nabla\times\vec F)(\vec s(u,v))\cdot\left(\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial v}\right)\,\mathrm du\,\mathrm dv

=\displaystyle\int_0^{2\pi}\int_0^3u^3(2u\cos^3v\sin(u^2-9)+\cos^3v\sin v+2u\sin^3v+\cos v\sin^3v)\,\mathrm du\,\mathrm dv

which has a value of 0, since each component integral is 0:

\displaystyle\int_0^{2\pi}\cos^3v\,\mathrm dv=0

\displaystyle\int_0^{2\pi}\sin v\cos^3v\,\mathrm dv=0

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3 years ago
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3 years ago
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