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VMariaS [17]
2 years ago
8

Solve the system of equations y=5x-1 y=9x-9

Mathematics
1 answer:
Leto [7]2 years ago
7 0

Answer:

Look at the equations:

y

=

−

9

x

−

21

and

y

=

5

x

+

7

Because both equations equal (y), they both equal the same.

If an equations says "

y

=

−

9

x

−

21

" , that means we can replace (y) with

−

9

x

−

21

.

Therefore when i take the equation:

y

=

5

x

+

7

, we can replace (y) to get:

−

9

x

−

21

=

5

x

+

7

Now isolate (x):

−

9

x

−

21

=

5

x

+

7

⇔

−

21

=

14

x

+

7

⇔

−

28

=

14

x

⇔

x

=

−

2

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Find the area of the surface. the part of the plane 4x + 4y + z = 16 that lies inside the cylinder x2 + y2 = 9
MAVERICK [17]
As a first step, convert to cylindrical coordinates. The equation x^2+y^2=9=3^2 is a clue to set

x=3r\cos\theta

y=3r\sin\theta

then have 0\le r\le1 and 0\le\theta\le2\pi. Meanwhile, the plane equation tells you to use

4x+4y+z=16\implies z=16-12r\cos\theta-12r\sin\theta

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
Can someone help me with this?
Lorico [155]
X^2=19^2+7^2=361+49=410
Therefore x=20.25
8 0
3 years ago
Read 2 more answers
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