Answer:
![Sum=4*[\frac{n^2-1}{n^2}]](https://tex.z-dn.net/?f=Sum%3D4%2A%5B%5Cfrac%7Bn%5E2-1%7D%7Bn%5E2%7D%5D)
For n=10:
Sum=3.96
For n=100:
Sum=3.9996
For n=1000:
Sum=3.999996
For n= 10000:
Sum=3.99999996
Step-by-step explanation:
Formula:
Rearranging the above formula:
Eq (1)
According to summation formula:
Putt these in Eq (1), and we will get:
![=\frac{12}{n^3}[\frac{n(n+1)(2n+1)}{6}-\frac{n(n+1)}{2}]\\Taking\ n\ as\ common\\=n*\frac{12}{n^3}[\frac{(n+1)(2n+1)}{6}-\frac{(n+1)}{2}] \\=\frac{12}{n^2}*[\frac{(n+1)(2n+1)}{6}]-\frac{12}{n^2}*[\frac{(n+1)}{2}] \\=\frac{2*(n+1)(2n+1)}{n^2}-\frac{6(n+1)}{n^2}\\](https://tex.z-dn.net/?f=%3D%5Cfrac%7B12%7D%7Bn%5E3%7D%5B%5Cfrac%7Bn%28n%2B1%29%282n%2B1%29%7D%7B6%7D-%5Cfrac%7Bn%28n%2B1%29%7D%7B2%7D%5D%5C%5CTaking%5C%20n%5C%20as%5C%20common%5C%5C%3Dn%2A%5Cfrac%7B12%7D%7Bn%5E3%7D%5B%5Cfrac%7B%28n%2B1%29%282n%2B1%29%7D%7B6%7D-%5Cfrac%7B%28n%2B1%29%7D%7B2%7D%5D%20%5C%5C%3D%5Cfrac%7B12%7D%7Bn%5E2%7D%2A%5B%5Cfrac%7B%28n%2B1%29%282n%2B1%29%7D%7B6%7D%5D-%5Cfrac%7B12%7D%7Bn%5E2%7D%2A%5B%5Cfrac%7B%28n%2B1%29%7D%7B2%7D%5D%20%5C%5C%3D%5Cfrac%7B2%2A%28n%2B1%29%282n%2B1%29%7D%7Bn%5E2%7D-%5Cfrac%7B6%28n%2B1%29%7D%7Bn%5E2%7D%5C%5C)
Taking 
as common:
After more simplifying,
Now ,for n=10:
![Sum=4[\frac{(10^{2})-1}{10^{2}}]\\Sum=3.96](https://tex.z-dn.net/?f=Sum%3D4%5B%5Cfrac%7B%2810%5E%7B2%7D%29-1%7D%7B10%5E%7B2%7D%7D%5D%5C%5CSum%3D3.96)
For n=100:
![Sum=4[\frac{(100^{2})-1}{100^{2}}]\\Sum=3.9996](https://tex.z-dn.net/?f=Sum%3D4%5B%5Cfrac%7B%28100%5E%7B2%7D%29-1%7D%7B100%5E%7B2%7D%7D%5D%5C%5CSum%3D3.9996)
For n=1000
![Sum=4[\frac{(1000^{2})-1}{1000^{2}}]\\Sum=3.999996](https://tex.z-dn.net/?f=Sum%3D4%5B%5Cfrac%7B%281000%5E%7B2%7D%29-1%7D%7B1000%5E%7B2%7D%7D%5D%5C%5CSum%3D3.999996)
For n=10000:
![Sum=4[\frac{(10000^{2})-1}{10000^{2}}]\\Sum=3.99999996](https://tex.z-dn.net/?f=Sum%3D4%5B%5Cfrac%7B%2810000%5E%7B2%7D%29-1%7D%7B10000%5E%7B2%7D%7D%5D%5C%5CSum%3D3.99999996)
Answer:
Step-by-step explanation:
This equation does not represent the situation because to find the fraction of the rain gauge we need to : divide the fraction of gauge filled by the raining fraction of an hour
But, Diego wrote the incorrect division equation so, it does not represent the current situation.
Now, to find the required division and multiplication equations :
Answer:
The 3rd and 4th option
Explanation:
A function only works when the input (x) only has one output (y).
The first, second, and the last option has the input has two or more outputs.
Fun Fact:
It is okay for the outputs to have more then in input, but not okay for the input to have more then one output.
I hope this help and have a nice day :)
Answer:
It'll take 128 cubes to fill the prism.
Step-by-step explanation:
In order to solve this question we first need to find the volume of the cubes. The volume of a cube is given by the following formula:
volume = length³
So the cubes have the following volume:
volume = (1/4)³ = 1/64
Since we want to know how many of these cubes are needed to fill the prism, we need to divide prism's volume by the volume of the smaller cubes. We have:
number of cubes = (volume of prism)/(volume of cubes)
number of cubes = 2/(1/64)
number of cubes = 2*(64/1)
number of cubes = 128
It'll take 128 cubes to fill the prism.
