Answer:
r ≥ 6
Step-by-step explanation:
37+15r ≥ 127
-37 -37 37 cancels and you're left with 15r
15r ≥ 90
/ 15 /15 15 cancels and you're left with r
r ≥ 6
I’ll solve it radius of 10 and a height of 13
Answer:
360
Step-by-step explanation:
Here we are required to find ![_^{6}\textrm{P}_{4}](https://tex.z-dn.net/?f=_%5E%7B6%7D%5Ctextrm%7BP%7D_%7B4%7D)
It is a problem of Permutation and we must understand the formula for finding permutations.
The general formula for finding the permutation is given as below:
![_^{m}\textrm{P}_{n}=\frac{m!}{(m-n)!}](https://tex.z-dn.net/?f=_%5E%7Bm%7D%5Ctextrm%7BP%7D_%7Bn%7D%3D%5Cfrac%7Bm%21%7D%7B%28m-n%29%21%7D)
Hence
![_^{6}\textrm{P}_{4}=\frac{6!}{(6-4)!}](https://tex.z-dn.net/?f=_%5E%7B6%7D%5Ctextrm%7BP%7D_%7B4%7D%3D%5Cfrac%7B6%21%7D%7B%286-4%29%21%7D)
![_^{6}\textrm{P}_{4}=\frac{6!}{2!}](https://tex.z-dn.net/?f=_%5E%7B6%7D%5Ctextrm%7BP%7D_%7B4%7D%3D%5Cfrac%7B6%21%7D%7B2%21%7D)
Where
![m!=m\times(m-1)\times\(m-2)\times\cdot\cdot\cdot\codt\cdot3\times2\times1](https://tex.z-dn.net/?f=m%21%3Dm%5Ctimes%28m-1%29%5Ctimes%5C%28m-2%29%5Ctimes%5Ccdot%5Ccdot%5Ccdot%5Ccodt%5Ccdot3%5Ctimes2%5Ctimes1)
![6!=6\times5\times4\times3\times2\times1](https://tex.z-dn.net/?f=6%21%3D6%5Ctimes5%5Ctimes4%5Ctimes3%5Ctimes2%5Ctimes1)
![2!=2\times1](https://tex.z-dn.net/?f=2%21%3D2%5Ctimes1)
Hence
![_^{6}\textrm{P}_{4}=\frac{6\times5\times4\times3\times2\times1}{2\times1}](https://tex.z-dn.net/?f=_%5E%7B6%7D%5Ctextrm%7BP%7D_%7B4%7D%3D%5Cfrac%7B6%5Ctimes5%5Ctimes4%5Ctimes3%5Ctimes2%5Ctimes1%7D%7B2%5Ctimes1%7D)
![_^{6}\textrm{P}_{4}=6\times5\times4\times3](https://tex.z-dn.net/?f=_%5E%7B6%7D%5Ctextrm%7BP%7D_%7B4%7D%3D6%5Ctimes5%5Ctimes4%5Ctimes3)
![_^{6}\textrm{P}_{4}=360](https://tex.z-dn.net/?f=_%5E%7B6%7D%5Ctextrm%7BP%7D_%7B4%7D%3D360)
A graph shows the limit to be 1/2.
https://www.desmos.com/calculator/qrf6ay47tw
Since the value of the function is the indeterminate form 0/0, L'Hôpital's rule applies. The ratio of derivatives of numerator and denominator is
.. x/
![\sqrt{x^{2}+3 }](https://tex.z-dn.net/?f=%20%5Csqrt%7Bx%5E%7B2%7D%2B3%20%7D)
Evaluated at x=1, this is
.. 1/
![\sqrt{1^{2}+3 }](https://tex.z-dn.net/?f=%20%5Csqrt%7B1%5E%7B2%7D%2B3%20%7D)
= 1/2
In its present form, there's not enough information to answer the question.
We'll need to know what you mean by the "radius" of an equilateral triangle,
or for that matter, the 'radius' of any triangle.