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3 years ago

PLEASE HELP ASAP 25 POINTS

Mathematics

2 answers:

Lena [83]3 years ago

4 0

The answer to the question is a)

Nookie1986 [14]3 years ago

4 0

Answer is A .

How?

See the horizontal line parallel to x-axis.Now with the help of graph,I can write some points on that horizontal line which are:(0,3),(2,3),(-2,3),etc.Just analyze these points.In these points you can see that y-coordinate is constant and is equal to 3.So the equation of this horizontal line is:

y=3 which is analogous to y<=3(Why not y>=3 because the line limits the value to 3 )

The slanted line can be represented by y>2x-1

Also see this image to know why this slanted line bounds the region y>2x-1

You might be interested in

Use the Divergence Theorem to evaluate S F · dS, where F(x, y, z) = z2xi + y3 3 + sin z j + (x2z + y2)k and S is the top half of

kifflom [539]

Looks like we have

$\vec F(x,y,z)=z^2x\,\vec\imath+\left(\dfrac{y^3}3+\sin z\right)\,\vec\jmath+(x^2z+y^2)\,\vec k$

which has divergence

$\nabla\cdot\vec F(x,y,z)=\dfrac{\partial(z^2x)}{\partial x}+\dfrac{\partial\left(\frac{y^3}3+\sin z\right)}{\partial y}+\dfrac{\partial(x^2z+y^2)}{\partial z}=z^2+y^2+x^2$

By the divergence theorem, the integral of $\vec F$ across $S$ is equal to the integral of $\nabla\cdot\vec F$ over $R$ , where $R$ is the region enclosed by $S$ . Of course, $S$ is not a closed surface, but we can make it so by closing off the hemisphere $S$ by attaching it to the disk $x^2+y^2\le1$ (call it $D$ ) so that $R$ has boundary $S\cup D$ .

Then by the divergence theorem,

$\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iiint_R(x^2+y^2+z^2)\,\mathrm dV$

Compute the integral in spherical coordinates, setting

$\begin{cases}x=\rho\cos\theta\sin\varphi\\y=\rho\sin\theta\sin\varphi\\z=\rho\cos\varphi\end{cases}\implies\mathrm dV=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi$

so that the integral is

$\displaystyle\iiint_R(x^2+y^2+z^2)\,\mathrm dV=\int_0^{\pi/2}\int_0^{2\pi}\int_0^1\rho^4\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\frac{2\pi}5$

The integral of $\vec F$ across $S\cup D$ is equal to the integral of $\vec F$ across $S$ plus the integral across $D$ (without outward orientation, so that

$\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\frac{2\pi}5-\iint_D\vec F\cdot\mathrm d\vec S$

Parameterize $D$ by

$\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath$

with $0\le u\le1$ and $0\le v\le2\pi$ . Take the normal vector to $D$ to be

$\dfrac{\partial\vec s}{\partial v}\times\dfrac{\partial\vec s}{\partial u}=-u\,\vec k$

Then we have

$\displaystyle\iint_D\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^1\left(\frac{u^3}3\sin^3v\,\vec\jmath+u^2\sin^2v\,\vec k\right)\times(-u\,\vec k)\,\mathrm du\,\mathrm dv$

$=\displaystyle-\int_0^{2\pi}\int_0^1u^3\sin^2v\,\mathrm du\,\mathrm dv=-\frac\pi4$

Finally,

$\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\frac{2\pi}5-\left(-\frac\pi4\right)=\boxed{\frac{13\pi}{20}}$

6 0

4 years ago

Pls help this is due in a little bit I don't wanna failllll

Fittoniya [83]

The answer is 8 3/4. Hope this helps

6 0

3 years ago

Which function is linear?

gulaghasi [49]

Answer:

Step-by-step explanation:

5-1=4

4 0

3 years ago

What does -7x - 5x + 8 = -16 equal?

elena55 [62]

Answer:

x=2

Step-by-step explanation:

combine like terms= -7x -5x = -12x

-12x + 8 = -16

subtract 8 from both sides

-12x = -24

divide both sides by -12

x = 2

3 0

3 years ago

In a study of the relationship for senior citizens between physical activity and frequency of colds, participants were asked to

masha68 [24]

Answer:

Difference between Observational and Experimental Data

The data collected in the study is observational data.

Step-by-step explanation:

In an experimental study, the data collected is divided into two groups. One group is the control group. The other group is the treatment group (also known as the experimental group). Data is gathered about the groups in order to compare their different outcomes and to draw conclusions if there is any causality based on the two variables. With observational data, the researcher is interested in observing the variables to determine if there is any correlation.

8 0

3 years ago