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2 years ago

13

lipka reads a book of 1/34 hrs everyday she reads the entire book in 6 days how many hours in all were required by her to read t

he book

1 answer:

marshall27 [118]2 years ago

8 0

Answer: She needs 10 1/2 hours to read the book.

Step-by-step explanation:I day = 1 3/4 hours

6 days = 1 3/4 x 6

6 days = 7/4 x 6

6 days = 42/4

6 days = 10 1/2 hours

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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

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

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

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

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

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3 years ago

Is negative 12 a rational number or is it a integer

Dovator [93]

-12 is an integer because all fractions are rational numbers.

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3 years ago

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The cube has a volume of 27 in3. Find the volume of a scaled image with a scale factor of 2. in3 Cube with a side length of thre

WINSTONCH [101]

The new size of cube's side is 6. V new cube = 6*6*6 = 216

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4 years ago

The equation can be used to find the length of AB

dmitriy555 [2]

You can use
Sine25=9/c
Or
Sin25/9=sine 90/c

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3 years ago

VO) --<br>I not know how to do this

masha68 [24]

Answer:

Square root and the power of 2 cancel each other. The answer remain 4/7

The square of a number is the number times itself. For example the square of 3 is 3x3. The square of 4 is 4x4.

The square root is just the opposite of the square. You can think of it as the "root" of the square or the number that was used to make the square.

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3 years ago