If you’re good at statistics please help

Mathematics

1 answer:

erastova [34]3 years ago

7 0

Answer:

Step-by-step explanation:

probabilty distribution= interval of x/total area of the distribution

OR P(x)= frequency of x/total frequency(N)*the interval of x(w)

x f probabilty f/N*w

16 10 0.2

17 16 0.32

18 20 0.4

19 4 0.08

w is the width of the bar( interval) 17-16=1

N=10+16+20+4=50

( only need to draw histogram)

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Find the area of the surface. the part of the hyperbolic paraboloid z = y2 − x2 that lies between the cylinders x2 + y2 = 4 and

Nadusha1986 [10]

Call the surface $S$ ; then the area of $S$ is given by the surface integral

$\displaystyle\iint_S\mathrm d\mathbf S$

Parameterize the surface by

$\mathbf r(u,v)=\begin{cases}x(u,v)=u\cos v\\y(u,v)=u\sin v\\z(u,v)=u^2\cos^2v-u^2\sin^2v=u^2\cos2v\end{cases}$

with $2\le u\le4$ and $0\le v\le2\pi$ . The surface element is given by

$\mathrm d\mathbf S=\|\mathbf r_u\times\mathbf r_v\|\,\mathrm du\,\mathrm dv$
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So the area is

$\displaystyle\iint_S\mathrm d\mathbf S=\int_{v=0}^{v=2\pi}\int_{u=2}^{u=4}u\sqrt{1+4u^2}\,\mathrm du\,\mathrm dv$
$=\displaystyle2\pi\int_{w=17}^{w=65}\sqrt w\,\frac{\mathrm dw}8$

where $w=1+4u^2\implies\mathrm dw=8u\,\mathrm du$

$=\displaystyle\frac\pi4\frac23w^{3/2}\bigg|_{w=17}^{w=65}$
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8 0

3 years ago

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neonofarm [45]

Answer:

$one\\whole\\or\\\frac{4}{4}$