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Hey guys can you answer this one question real quick

Umnica [9.8K]

Answer:

a. 1/5

b. (3, 3/5)

c. 1/5x = y

Step-by-step explanation:

Remember: (x, y)

0.5 = 1/2

(1/2, 1/10) = 1/10 ÷ 1/2 = 1/10 • 2 = 1/5, you can divide y/x = constant of proportionality. 1/10 ÷ 1/2.

1 2/5 = 7/5

(7, 7/5) = 7/5 ÷ 7 = 7/5 • 1/7 = 1/5, y/x = constant of proportionality. 7/5 ÷ 7.

a. 1/5 is the constant of proportionality
b. (3, 3/5) because 3/5 ÷ 3 or 3/5 • 1/3 = 1/5.
c. 1/5x = y

6 0

3 years ago

Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of

tresset_1 [31]

Because I've gone ahead with trying to parameterize $S$ directly and learned the hard way that the resulting integral is large and annoying to work with, I'll propose a less direct approach.

Rather than compute the surface integral over $S$ straight away, let's close off the hemisphere with the disk $D$ of radius 9 centered at the origin and coincident with the plane $y=0$ . Then by the divergence theorem, since the region $S\cup D$ is closed, we have

$\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iiint_R(\nabla\cdot\vec F)\,\mathrm dV$

where $R$ is the interior of $S\cup D$ . $\vec F$ has divergence

$\nabla\cdot\vec F(x,y,z)=\dfrac{\partial(xz)}{\partial x}+\dfrac{\partial(x)}{\partial y}+\dfrac{\partial(y)}{\partial z}=z$

so the flux over the closed region is

$\displaystyle\iiint_Rz\,\mathrm dV=\int_0^\pi\int_0^\pi\int_0^9\rho^3\cos\varphi\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=0$

The total flux over the closed surface is equal to the flux over its component surfaces, so we have

$\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iint_S\vec F\cdot\mathrm d\vec S+\iint_D\vec F\cdot\mathrm d\vec S=0$

$\implies\boxed{\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=-\iint_D\vec F\cdot\mathrm d\vec S}$

Parameterize $D$ by

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

with $0\le u\le9$ and $0\le v\le2\pi$ . Take the normal vector to $D$ to be

$\vec s_u\times\vec s_v=-u\,\vec\jmath$

Then the flux of $\vec F$ across $S$ is

$\displaystyle\iint_D\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^9\vec F(x(u,v),y(u,v),z(u,v))\cdot(\vec s_u\times\vec s_v)\,\mathrm du\,\mathrm dv$

$=\displaystyle\int_0^{2\pi}\int_0^9(u^2\cos v\sin v\,\vec\imath+u\cos v\,\vec\jmath)\cdot(-u\,\vec\jmath)\,\mathrm du\,\mathrm dv$

$=\displaystyle-\int_0^{2\pi}\int_0^9u^2\cos v\,\mathrm du\,\mathrm dv=0$

$\implies\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\boxed{0}$

8 0

4 years ago

Alan and Margot each drive from City A to City B, a distance of 147 miles. They take the same route and drive at constant speeds

Westkost [7]

Answer:

Margot gets from A to B faster

Step-by-step explanation:

Alan takes 2 hr and 35 min = 2. 58... hr

Margot takes 147/64 hr = 2.296.. hr

7 0

3 years ago

Harold wants to get at a grade of 70 to 75 in his math class. His grade will be the average

ratelena [41]

Answer:

132

cause you need to multiple by one thousand to get your ans2er

3 0

3 years ago

which of the following are among the five basic postulates of euclidean geometry? check all that apply

MAVERICK [17]

The five essential hypothesizes of Geometry, additionally alluded to as Euclid's proposes are the accompanying:
1.) A straight line section can be drawn joining any two focuses.
2.) Any straight line portion can be expanded uncertainly in a straight line.
3.) Given any straight line fragment, a circle can be drawn having the portion as a span and one endpoint as the inside.
4.) All correct points are harmonious.
5.) If two lines are drawn which meet a third such that the total of the internal points on one side is under two right edges (or 180 degrees), then the two lines unavoidably should converge each other on that side if reached out sufficiently far.

7 0

3 years ago