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3 years ago

What is the smallest power of 10 that exceeds this number 235,452

Mathematics

1 answer:

Oliga [24]3 years ago

8 0

Answer:

$10^{6}$

Step-by-step explanation:

1. You have the following number given in the problem above:

235,452

2. As you can see, it is smaller than a number with seven digits as 1,000,000.

3. You can rewrite 1,000,000 as an integer power of 10, which must have the following form:

$10^{n}$

Where $n$ is the exponent that indicates the number of times that 10 is multiplied by itself.

4. Therefore, you have:

$1,000,000=10^{6}$

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Use the divergence theorem to calculate the surface integral s f · ds; that is, calculate the flux of f across s. f(x, y, z) = x

valkas [14]

$\mathbf f(x,y,z)=x^4\,\mathbf i-x^3z^2\,\mathbf j+4xy^2z\,\mathbf k$
$\mathrm{div}(\mathbf f)=\dfrac{\partial(x^4)}{\partial x}+\dfrac{\partial(-x^3z^2)}{\partial y}+\dfrac{\partial(4xy^2z)}{\partial z}=4x^3+0+4xy^2=4x(x^2+y^2)$

Let $\mathcal D$ be the region whose boundary is $\mathcal S$ . Then by the divergence theorem,

$\displaystyle\iint_{\mathcal S}\mathbf f\cdot\mathrm d\mathbf S=\iiint_{\mathcal D}4x(x^2+y^2)\,\mathrm dV$

Convert to cylindrical coordinates, setting

$x=r\cos\theta$
$y=r\sin\theta$

and keeping $z$ as is. Then the volume element becomes

$\mathrm dV=r\,\mathrm dr\,\mathrm d\theta\,\mathrm dz$

and the integral is

$\displaystyle\iiint_{\mathcal D}4x(x^2+y^2)\,\mathrm dV=\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}\int_{z=0}^{z=r\cos\theta+7}4r\cos\theta\cdot r^2\cdot r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$
$=\displaystyle4\iiint_{\mathcal D}r^4\cos\theta\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$
$=\dfrac{2\pi}3$

4 0

3 years ago

A set of middle school student heights are normally distributed with a mean of 150 centimeters and a standard deviation of 20 ce

julsineya [31]

Answer:

The proportion of students whose height are lower than Darnell's height is 71.57%

Step-by-step explanation:

The complete question is:

A set of middle school student heights are normally distributed with a mean of 150 centimeters and a standard deviation of 20 centimeters. Darnel is a middle school student with a height of 161.4cm.

What proportion of proportion of students height are lower than Darnell's height.

Answer:

We first calculate the z-score corresponding to Darnell's height using:

$Z=\frac{X-\mu}{\sigma}$

We substitute x=161.4 , $\mu=150$ , and $\sigma=20$ to get:

$Z=\frac{161.4-150}{20} \\Z=0.57$

From the normal distribution table, we read 0.5 under 7.

The corresponding area is 0.7157

Therefore the proportion of students whose height are lower than Darnell's height is 71.57%

8 0

3 years ago

Identify the domain of the graph given. *Don't forget the parenthesis or brackets*

anzhelika [568]

Answer:

(-4,3)

Step-by-step explanation:

The domain of a function is all of its possible x-values. In this graph, there is a y-value for every x-value between -4 and 3 except -4 and 3, because there are open dots at those points. Therefore, the domain is (-4,3). Use parenthesis because the function is not defined at x=-4 or x=3.

5 0

3 years ago

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ch4aika [34]

Answer:

A, D, E

Step-by-step explanation:

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6 0

3 years ago

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lions [1.4K]

D they all have the same slope.

8 0

3 years ago