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Vinil7 [7]
3 years ago
6

Which is the proportional relationship for this graph?

Mathematics
1 answer:
elixir [45]3 years ago
3 0

Answer:

For every the canoe is rented, the total cost goes up by $12.

Step-by-step explanation:

To find the proportional relationship, Take two points from the graph, for example (2, 24) and (4, 48), and put them into the slope formula: \frac{y2-y1}{x2-x1}

\frac{48-24}{4-2}

Solve:

48 - 24 = 24

4 - 2 = 2

24/2 = 12

The proportional relationship between the hours the canoe is rented and the total cost is $12.

Hope this helps :)

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Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of
Tomtit [17]

Apparently my answer was unclear the first time?

The flux of <em>F</em> across <em>S</em> is given by the surface integral,

\displaystyle\iint_S\mathbf F\cdot\mathrm d\mathbf S

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\mathbf r(u,v)=7\cos u\sin v\,\mathbf i+7\sin u\sin v\,\mathbf j+7\cos v\,\mathbf k

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d<em>S</em> = <em>n</em> • d<em>S</em>

where <em>n</em> is the normal vector to the surface. Take it to be

\mathbf n=\dfrac{\frac{\partial\mathbf r}{\partial v}\times\frac{\partial\mathbf r}{\partial u}}{\left\|\frac{\partial\mathbf r}{\partial v}\times\frac{\partial\mathbf r}{\partial u}\right\|}

The surface element reduces to

\mathrm d\mathbf S=\mathbf n\,\mathrm dS=\mathbf n\left\|\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}\right\|\,\mathrm du\,\mathrm dv

\implies\mathbf n\,\mathrm dS=-49(\cos u\sin^2v\,\mathbf i+\sin u\sin^2v\,\mathbf j+\cos v\sin v\,\mathbf k)\,\mathrm du\,\mathrm dv

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\displaystyle\iint_S\mathbf F\cdot\mathrm d\mathbf S=\int_0^{\pi/2}\int_0^{\pi/2}\mathbf F(x(u,v),y(u,v),z(u,v))\cdot\mathbf n\,\mathrm dS

=\displaystyle-49\int_0^{\pi/2}\int_0^{\pi/2}(7\cos u\sin v\,\mathbf i-7\cos v\,\mathbf j+7\sin u\sin v\,\mathbf )\cdot\mathbf n\,\mathrm dS

=-343\displaystyle\int_0^{\pi/2}\int_0^{\pi/2}\cos^2u\sin^3v\,\mathrm du\,\mathrm dv=\boxed{-\frac{343\pi}6}

4 0
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suppose 5 men and 7 women are on a crowded elevator. at the next floor, four people get off the elevator. find the probability t
lubasha [3.4K]
The total number of arrangements for all of them to be women is:
C(7, 4) because the order does not matter; we'd still have the same arrangements.

Now, we can simplify this:
C(7, 4) = \frac{7!}{4!(7 - 4)!}
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Now, the total number of arrangements, without restriction, is simply: C(12, 4) because we don't care who we pick.

\text{P(4 women): } \frac{35}{495} = \frac{7}{99}
3 0
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