4 1/6 X 6 in simplest form. help fast pls

How many vertices (corners) does a cube have?

vladimir2022 [97]

Answer:

The answer is below

Step-by-step explanation:

a) A cube is a three dimensional solid with 6 square faces.

A cube has 8 vertices

b) A rectangular prism is a three dimensional solid with two parallel rectangular bases.

A rectangular prism has 6 faces.

c) A rectangular prism is a three dimensional solid with two parallel rectangular bases.

A rectangular prism has 12 edges.

d) A square-based pyramid is a pyramid with a square base.

A square-based pyramid has 8 edges

e) A triangular prism is a three dimensional solid with two parallel triangular bases.

A triangular prism has 5 faces.

f) A triangular prism is a three dimensional solid with two parallel triangular bases.

A triangular prism has 6 vertices.

4 0

3 years ago

What is 16,700,000,000,000,000 estimated as the product of a single digit and a power of 10?

True [87]

For short you call this scientific notation.
FIRST
Count how many time you need to move the decimal over to make your single digit more then 1 and less then 10. So we will erase the 0's as we go along.
167000,000,000,000
So in this case we want to make the single digit 1.67 so it can be greater then 1 and less then 10
So now we see how many times we need to move the decimal and when you cant see the decimal just imagine it at the very end of the problem
167000,000,000,000
(For the mods out there I copied and pasted the bold number so i didn't have to take a while to retype the whole number. Thanks.)
SO NOW I get 14 because that's how many spots the decimal moved over.
Now since we need to right it in SN we need to write out this
X*10^X
The exponent X stands for how many times we moved the decimal over. I got 14 so we have that exponent
X*10^14
NOW We need to fiqure out X.... X was just the number we made greater then one and less then 0.
So thats 1.67
So we get
1.67*10^14

Did this help? <3

4 0

3 years ago

F(x, y, z) = z tan−1(y2)i + z3 ln(x2 + 3)j + zk. find the flux of f across s, the part of the paraboloid x2 + y2 + z = 18 that l

Cerrena [4.2K]

$\mathbf F(x,y,z)=z\tan^{-1}(y^2)\,\mathbf i+z^3\ln(x^2+3)\,\mathbf j+z\,\mathbf k$
$\implies\mathrm{div}\mathbf F(x,y,z)=0+0+1=1$

By the divergence theorem, the flux of $\mathbf F$ across the *closed* surface $\mathcal S$ combined with the plane $z=2$ is given by a volume integral over the closed region:

$\displaystyle\iint_{\mathcal S}\mathbf F\cdot\mathrm d\mathbf S=\iiint_{\mathcal R}\nabla\cdot\mathbf F\,\mathrm dV$

So in fact, to find the flux over $\mathcal S$ alone, we'll need to subtract the flux of $\mathbf F$ over the planar portion, oriented outward. First, compute the volume integral by converting to cylindrical coordinates:

$x^2+y^2+z=18$
$z=2\implies x^2+y^2=16\implies r^2=16\implies r=4$

$\displaystyle\iiint_{\mathcal R}\mathrm dV=\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=4}\int_{z=2}^{z=18-r^2}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta=128\pi$

If the surface does actually contain $z=2$ , then you can stop here; otherwise, continue.

Now, parameterize the part of the *closed* surface in $z=2$ by

$\mathbf s(r,\theta)=r\cos\theta\,\mathbf i+r\sin\theta\,\mathbf j+2\,\mathbf k$

where $0\le r\le4$ and $0\le\theta\le2\pi$ . We get a surface element

$\mathrm d\mathbf S=(\mathbf s_r\times\mathbf s_\theta)\,\mathrm dr\,\mathrm d\theta=(r\,\mathbf k)\,\mathrm dr\,\mathrm d\theta$

We don't need to worry about the first two components of

and so the surface integral over this region is

$\displaystyle\iint_{z=2\,\land\,x^2+y^2\le16}\mathbf F\cdot\mathrm d\mathbf S=\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=4}2r\,\mathrm dr\,\mathrm d\theta=32\pi$

Then the total flux over $\mathcal S$ alone is $(128-32)\pi=96\pi$ .

4 0

3 years ago

What do exponential functions model in the real world? How does the

sineoko [7]

They model various situations where there is an increasing curve. An example is if you throw a baseball and it curves back down as gravity has more and more of a affect on it. This would be a different equation than if you threw a basketball as the basketball wouldn't go as high but would have about the same downwards acceleration due to gravity.

3 0

3 years ago

On the track and field team,

defon

Answer:

It could be anywhere from eight to 15 members.

Step-by-step explanation:

Answer:

A. Count the members on each team

Hurdles = ⅜ × 40 = 3 × 5 = 15

Long jump = ⅘ × 40 = 4 × 8 = 32

Let's look at the two extremes.

B. Most people will compete in only one event

Then the teams will overlap by seven members (Figure 1).

C. All those in Hurdles compete in the Long Jump

Then 15 members will compete in both Hurdles and Long Jump (Figure 2).

6 0

4 years ago

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