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3 years ago

Need help FAST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Mathematics

1 answer:

vova2212 [387]3 years ago

8 0

Answer:

Right angle 90 degrees is always going to be a right angle.

Step-by-step explanation:

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Gemiola [76]

The second one because Idk I’m just guessing lol it doesn’t look like it should be there though

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3 years ago

I graduated from high school and received $1500 in gifts from family

kvv77 [185]

Answer

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3 years ago

Read 2 more answers

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

What are the vertices of AA'B'C'if AABC is dilated by a scale factor of 2?

gulaghasi [49]

Answer:

Step-by-step explanation:

Multiply each point's x and y coordinates by 2.

3 0

3 years ago

Ellen drove 357.9 miles. Her car gets about 21 miles per gallon. Which is the best estimate of how many gallons of gas Ellen use

Bad White [126]

When you're trying to find an estimate, the best thing to do is to round them accordingly.
357.9 can be rounded to 360 (as it is over 5, therefore, it is rounded up)
21 can be rounded to 20 (as it is under 5, it is rounded down)

Then to find the miles per gallon, you need to divide the distance driven (360), by the amount of gas (20)
360/20= 18

As an estimate, Ellen gets 18 miles to the gallon.
(The actual answer is 357.9/21= 17.13 miles to the gallon)

Hope this helps :)

8 0

3 years ago