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3 years ago

Helpppppppppppppppppppppppp

Mathematics

1 answer:

m_a_m_a [10]3 years ago

4 0

12 should be y = -9 ( srry have to go to 20 words or more)

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Surface integrals using an explicit description. Evaluate the surface integral \iint_{S}^{}f(x,y,z)dS using an explicit represen

Jobisdone [24]

Parameterize $S$ by the vector function

$\vec r(x,y)=x\,\vec\imath+y\,\vec\jmath+f(x,y)\,\vec k$

so that the normal vector to $S$ is given by

$\dfrac{\partial\vec r}{\partial x}\times\dfrac{\partial\vec r}{\partial y}=\left(\vec\imath+\dfrac{\partial f}{\partial x}\,\vec k\right)\times\left(\vec\jmath+\dfrac{\partial f}{\partial y}\,\vec k\right)=-\dfrac{\partial f}{\partial x}\vec\imath-\dfrac{\partial f}{\partial y}\vec\jmath+\vec k$

with magnitude

$\left\|\dfrac{\partial\vec r}{\partial x}\times\dfrac{\partial\vec r}{\partial y}\right\|=\sqrt{\left(\dfrac{\partial f}{\partial x}\right)^2+\left(\dfrac{\partial f}{\partial y}\right)^2+1}$

In this case, the normal vector is

$\dfrac{\partial\vec r}{\partial x}\times\dfrac{\partial\vec r}{\partial y}=-\dfrac{\partial(8-x-2y)}{\partial x}\,\vec\imath-\dfrac{\partial(8-x-2y)}{\partial y}\,\vec\jmath+\vec k=\vec\imath+2\,\vec\jmath+\vec k$

with magnitude $\sqrt{1^2+2^2+1^2}=\sqrt6$ . The integral of $f(x,y,z)=e^z$ over $S$ is then

$\displaystyle\iint_Se^z\,\mathrm d\Sigma=\sqrt6\iint_Te^{8-x-2y}\,\mathrm dy\,\mathrm dx$

where $T$ is the region in the $x,y$ plane over which $S$ is defined. In this case, it's the triangle in the plane $z=0$ which we can capture with $0\le x\le8$ and $0\le y\le\frac{8-x}2$ , so that we have

$\displaystyle\sqrt6\iint_Te^{8-x-2y}\,\mathrm dx\,\mathrm dy=\sqrt6\int_0^8\int_0^{(8-x)/2}e^{8-x-2y}\,\mathrm dy\,\mathrm dx=\boxed{\sqrt{\frac32}(e^8-9)}$

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3 years ago

Classify tue following triangle

yuradex [85]

I think it's right and scalene
It's a right triangle because it has a right angle and it's a scalene triangle because it has three unequal sides.

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3 years ago

13. SOLVE FOR X 21) 18 21 x+ 13 A) 8 C) 7 28 B) 11 D) 6

timurjin [86]

Well first go to 'Add Attachments' when your asking a question.

Click whatever file/photo that you wanna show us, and click done.

See?

Ta da~

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3 years ago

If john had 500 bottles of water and sally took 60263 how much does john have

lukranit [14]

Answer:

John technically doesn't have anymore. Instead, sally owes John 59763 bottles of water. If you're asking for something mathematical, John now has -59763 bottles of water.

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2 years ago

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Please help please i really need it Click the attach image

vesna_86 [32]

second one is correct :))

(-2, 1, 0, 2)

6 0

2 years ago

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