The distance between the two points on the number line is of 
units.
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- The distance between two numbers on the number line is given by the <u>subtraction of the greater by the smaller number.</u>
- The greater number is
- The smaller is
. - The distance is:
Thus, distance of units.
A similar problem is given at brainly.com/question/10795861
Answer:
We want to find:
![\lim_{n \to \infty} \frac{\sqrt[n]{n!} }{n}](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B%5Csqrt%5Bn%5D%7Bn%21%7D%20%7D%7Bn%7D)
Here we can use Stirling's approximation, which says that for large values of n, we get:
Because here we are taking the limit when n tends to infinity, we can use this approximation.
Then we get.
![\lim_{n \to \infty} \frac{\sqrt[n]{n!} }{n} = \lim_{n \to \infty} \frac{\sqrt[n]{\sqrt{2*\pi*n} *(\frac{n}{e} )^n} }{n} = \lim_{n \to \infty} \frac{n}{e*n} *\sqrt[2*n]{2*\pi*n}](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B%5Csqrt%5Bn%5D%7Bn%21%7D%20%7D%7Bn%7D%20%3D%20%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B%5Csqrt%5Bn%5D%7B%5Csqrt%7B2%2A%5Cpi%2An%7D%20%2A%28%5Cfrac%7Bn%7D%7Be%7D%20%29%5En%7D%20%7D%7Bn%7D%20%3D%20%20%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7Bn%7D%7Be%2An%7D%20%2A%5Csqrt%5B2%2An%5D%7B2%2A%5Cpi%2An%7D)
Now we can just simplify this, so we get:
![\lim_{n \to \infty} \frac{1}{e} *\sqrt[2*n]{2*\pi*n} \\](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B1%7D%7Be%7D%20%2A%5Csqrt%5B2%2An%5D%7B2%2A%5Cpi%2An%7D%20%5C%5C)
And we can rewrite it as:
The important part here is the exponent, as n tends to infinite, the exponent tends to zero.
Thus:
The measure of <ABD, <DBC and <ABC are 67, 67 and 134 degrees respectively.
<h3>Bisection of angles</h3>
Angles are bisected if they are divided into two equal parts.
If the angle BC bisects <ABC, hence <ABD and <DBC are equal, hence;
2(11x + 23) = <ABC
Given the following parameters
<ABC = 25x + 34
2(11x + 23) = 25x + 34
Expand
22x +46 = 25x + 34
22x-25x = 34 - 46
-3x = -12
x = 4
Determine the measure of the angles
<ABD = 11x + 23 = <DBC
<ABD = 11(4) + 23
<ABD = 44 + 23
<ABD = 67 degrees
<ABC = 2(67)
<ABC = 134 degrees
Hence the measure of <ABD, <DBC and <ABC are 67, 67 and 134 degrees respectively.
Learn more on bisection of angles here: brainly.com/question/25770607
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Answer:
$34,240
Step-by-step explanation:
7% of $32,000 is $2,240
$32,000+$2,240=$34,240
Answer:
-6>-8
Step-by-step explanation:
-6 is more than -8.
