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3 years ago

Zoe wants to make a driveway.

1 answer:

6 0

Well the volume of dirt she needs to remove is equal to length*width*height=6.2*4.9*0.225=6.8355

Now let's find how many bags she needs.

To solve for this, simply divide room in bags from total room.
6.8355/0.87=7.857

Thus Zoe has barely enough, but enough bags.

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A company's stock was selling at

Mandarinka [93]

Answer:

10%

Step-by-step explanation:

5 0

3 years ago

What is the value of i^n if the remainder of n/4 is 2?

nydimaria [60]

Answer:

C and D

Step-by-step explanation:

i=√-1

n/4=x.5

since 2 is the remainder

n=2x

then i^n=i^2x

when x is even, i^n =1

when x is odd, i^n=-1

7 0

3 years ago

Read 2 more answers

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

GenaCL600 [577]

Close off the hemisphere $S$ by attaching to it the disk $D$ of radius 3 centered at the origin in the plane $z=0$ . By the divergence theorem, we have

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

where $R$ is the interior of the joined surfaces $S\cup D$ .

Compute the divergence of $\vec F$ :

$\mathrm{div}\vec F(x,y,z)=\dfrac{\partial(xz^2)}{\partial x}+\dfrac{\partial\left(\frac{y^3}3+\sin z\right)}{\partial y}+\dfrac{\partial(x^2z+y^2)}{\partial k}=z^2+y^2+x^2$

Compute the integral of the divergence over $R$ . Easily done by converting to cylindrical or spherical coordinates. I'll do the latter:

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

So the volume integral is

$\displaystyle\iiint_Rx^2+y^2+z^2\,\mathrm dV=\int_0^{\pi/2}\int_0^{2\pi}\int_0^3\rho^4\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\frac{486\pi}5$

From this we need to subtract the contribution of

$\displaystyle\iint_D\vec F(x,y,z)\cdot\mathrm d\vec S$

that is, the integral of $\vec F$ over the disk, oriented downward. Since $z=0$ in $D$ , we have

$\vec F(x,y,0)=\dfrac{y^3}3\,\vec\jmath+y^2\,\vec k$

Parameterize $D$ by

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

where $0\le u\le 3$ and $0\le v\le2\pi$ . Take the normal vector to be

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

Then taking the dot product of $\vec F$ with the normal vector gives

$\vec F(x(u,v),y(u,v),0)\cdot(-u\,\vec k)=-y(u,v)^2u=-u^3\sin^2v$

So the contribution of integrating $\vec F$ over $D$ is

$\displaystyle\int_0^{2\pi}\int_0^3-u^3\sin^2v\,\mathrm du\,\mathrm dv=-\frac{81\pi}4$

and the value of the integral we want is

(integral of divergence of F) - (integral over D) = integral over S

==> 486π/5 - (-81π/4) = 2349π/20

5 0

3 years ago

4. The students in Mr. Michael’s art class are decorating a booth for Harvest Day. They have blue cloth that is 60 inches long,

MrRissso [65]

Length of blue cloth is 60 inches , length of gold cloth is 48 inches and length of white cloth is 72 inches.

a.

As, the length of all pieces are equal, so for getting the greatest possible length of the pieces, we need to find GCF(greatest common factor) of 60, 48 and 72.

First we will factor out all three numbers completely......

$60=2*2*3*5\\ \\ 48=2*2*2*2*3\\ \\ 72=2*2*2*3*3$

The common factors are: 2, 2 and 3

Thus the GCF $= 2*2*3=12$

So, the greatest possible length of the pieces without having any cloth left over will be 12 inches.

b.

For finding the number of pieces for each color cloth, we will just divide the length of each cloth by 12. So...

Number of pieces for blue cloth $=\frac{60}{12}=5$

Number of pieces for gold cloth $=\frac{48}{12}=4$ and

Number of pieces for white cloth $=\frac{72}{12}=6$

4 0

3 years ago

Easyy I need help guys...(easy fractions)

Ivanshal [37]

1a. 5/10 can be simplified to 1/2. (5 divided by 5 is one, 10 divided by 5 is 2.)

1b. 9/12 can be simplified to 3/4. (9 divided by 3 is 3, 12 divided by 3 is 4.)

1c. 12/18 can be simplified to 2/3. (12 divided by 6 is 2, 18 divided by 6 is 3.)

1d. 9/24 can be simplified to 3/8. (9 divided by 3 is 3, 24 divided by 3 is 8.)

1e. 27/90 can be simplified to 3/10. (27 divided by 9 is 3, 90 divided by 9 is 10.)

1f. 40/48 can be simplified to 5/6. (40 divided by 8 is 5, 48 divided by 8 is 6.)

8 0

3 years ago

Read 2 more answers