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3 years ago

Find the midpoint of the line segment with the given endpoints. (-1,9)(-17,-29)

Mathematics

1 answer:

Ugo [173]3 years ago

6 0

Answer:

(-9,-10)

Step-by-step explanation:

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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

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

5 0

3 years ago

1+1+1+1+1 12312123 times

OverLord2011 [107]

Answer:

$12312123$

5 0

3 years ago

Read 2 more answers

Does anyone know how to solve this? I would really appreciate help.

Bess [88]

Answer:

Step-by-step explanation:

The intersection point (centroid) divides the medians in ratio 2:1. it does mean that the long segment value is the short segment value multiplied by two. let's call the centroid point G.

BG=DG*2=4*2=8

CG=EG*2=2*2=4

AG=FG*2 =>FG=AG/2=6/2=3

4 0

3 years ago

The Sanchez Family pays $1,975 per month to rent a four-bedroom house. They are planning to buy a house and make monthly payment

yuradex [85]

Determine the additional cost of housing for a month.

$2590-1975=615$

Determine the additional cost of housing for a year.

$12\cdot615=7380$

The moving charge is 545

3 0

1 year ago

Find the measure of the indicated arc in the circle

klasskru [66]

Answer:

80°

Step-by-step explanation:

The measure of arc AB is equal to the central angle ∠COB, that is

measure of arc AB = 80°

8 0

4 years ago