Answer:
J + 9 = 63
Jackson = 54 inches
Step-by-step explanation:
Using the variable 'J' for the height of Jackson, we know that Elliott is Jackson's height, plus an additional 9 inches. Since Elliott is 64 inches tall in total, we can add Jackson's height plus 9 to get Elliot's height:
Jackson's height + 9 inches = Elliot's height
J + 9 = 63
Subtract '9' from both sides: J + 9 - 9 = 63 - 9 or J = 54
So, Jackson is 54 inches tall.
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:
I just had a test on this lol perfect timing. Anyways the answer would be 3 times bigger bc the circumference of a circle with the radius of 3 is 6pi and the circumference of a circle with the radius of 1 is 2pi which makes the first circle 3 times bigger
Step-by-step explanation: the answer for this question should be 81.64 because to find the circumference you need to know the circumference formulas which is C=TT times d or C= 2 times TT times r.
C= 3.14 times 26 C= 2 times 3.14 times 13
C= 81.64
C= 81.64
so the answer is 81.64 for the circle's circumference so hopefully that is the correct answer and have a great day
