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3 years ago

The the seats in the van are in pairs there are 16 seats How many pairs of seats are there

Mathematics

2 answers:

Papessa [141]3 years ago

5 0

Answer: There are 8 pairs of seats in the van.

Step-by-step explanation:

Given : The seats in the van are in pairs .

There are 16 seats in the van.

Since a pair contains two identical objects.

Therefore, to find the number of pairs we need to divide the total number of seats by 2 .

The number of pairs of seats = $16\div2=8$

Therefore, the number of pairs of seats =2

miskamm [114]3 years ago

4 0

Eight, I am pretty sure. Eight times two is 16.

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3 years ago

Find the area of the surface. the part of the plane 4x + 4y + z = 16 that lies inside the cylinder x2 + y2 = 9

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As a first step, convert to cylindrical coordinates. The equation $x^2+y^2=9=3^2$ is a clue to set

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So we parameterize the part of the plane within the cylinder with the vector-valued function

$\mathbf s(r,\theta)=(3r\cos\theta,3r\sin\theta,15-12r\cos\theta-12r\sin\theta)$

The surface integral giving the area of the surface is

$\displaystyle\iint_{\mathcal S}\mathrm dS$

where $\mathcal S$ denotes the surface in question, and the surface element $\mathrm dS$ is

$\mathrm dS=\left\|\dfrac{\partial\mathbf s}{\partial r}\times\dfrac{\partial\mathbf s}{\partial\theta}\right\|\,\mathrm dr\,\mathrm d\theta$

We have

$\dfrac{\partial\mathbf s}{\partial r}=(3\cos\theta,3\sin\theta,-12(\cos\theta+\sin\theta))$

$\dfrac{\partial\mathbf s}{\partial\theta}=(-3r\sin\theta,3r\cos\theta,12r(\sin\theta-\cos\theta))$

$\implies\mathrm dS=\|(36r,36r,9r\|\,\mathrm dr\,\mathrm d\theta=9\sqrt{33}r\,\mathrm dr\,\mathrm d\theta$

So the area is

$\displaystyle\iint_{\mathcal S}\mathrm dS=9\sqrt{33}\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}r\,\mathrm dr\,\mathrm d\theta=18\sqrt{33}\,\pi$

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3 years ago