Answer:176
Step-by-step explanation:
Answer would be C because the cost is independent
The formula is ![\frac{n(n+1)(2n+1)}{6}](https://tex.z-dn.net/?f=%5Cfrac%7Bn%28n%2B1%29%282n%2B1%29%7D%7B6%7D)
What are series?
In mathematics, we can describe a series as adding infinitely many numbers or quantities to a given starting number or amount.
We will find the formula as shown as below:
Let ![S=1+2^2+3^2+4^2+................+n^2](https://tex.z-dn.net/?f=S%3D1%2B2%5E2%2B3%5E2%2B4%5E2%2B................%2Bn%5E2)
We know ![(n+1)^3=n^3+3n^2+3n+1](https://tex.z-dn.net/?f=%28n%2B1%29%5E3%3Dn%5E3%2B3n%5E2%2B3n%2B1)
![(1+1)^3=1^3+3(1)^2+3(1)+1](https://tex.z-dn.net/?f=%281%2B1%29%5E3%3D1%5E3%2B3%281%29%5E2%2B3%281%29%2B1)
![(2+1)^3=2^3+3(2)^2+3(2)+1](https://tex.z-dn.net/?f=%282%2B1%29%5E3%3D2%5E3%2B3%282%29%5E2%2B3%282%29%2B1)
![(3+1)^3=3^3+3(3)^2+3(3)+1](https://tex.z-dn.net/?f=%283%2B1%29%5E3%3D3%5E3%2B3%283%29%5E2%2B3%283%29%2B1)
.
.
![(n+1)^3=n^3+3(n)^2+3(n)+1](https://tex.z-dn.net/?f=%28n%2B1%29%5E3%3Dn%5E3%2B3%28n%29%5E2%2B3%28n%29%2B1)
On adding
![2^3+3^3+4^3......(n+1)^3=(1^3+2^3+3^3+.....+n^3)+3(1^2+2^2+.....+n^2)+3(1+2+3....n)+(1+1+1+....+1)](https://tex.z-dn.net/?f=2%5E3%2B3%5E3%2B4%5E3......%28n%2B1%29%5E3%3D%281%5E3%2B2%5E3%2B3%5E3%2B.....%2Bn%5E3%29%2B3%281%5E2%2B2%5E2%2B.....%2Bn%5E2%29%2B3%281%2B2%2B3....n%29%2B%281%2B1%2B1%2B....%2B1%29)
![2^3+3^3+4^3......(n+1)^3-(1^3+2^3+3^3+.....+n^3)=3S+\frac{3n(n+1)}{2}+(1+1+1+....+1)](https://tex.z-dn.net/?f=2%5E3%2B3%5E3%2B4%5E3......%28n%2B1%29%5E3-%281%5E3%2B2%5E3%2B3%5E3%2B.....%2Bn%5E3%29%3D3S%2B%5Cfrac%7B3n%28n%2B1%29%7D%7B2%7D%2B%281%2B1%2B1%2B....%2B1%29)
![(n+1)^3-1^3=3S+\frac{3n(n+1)}{2} +n](https://tex.z-dn.net/?f=%28n%2B1%29%5E3-1%5E3%3D3S%2B%5Cfrac%7B3n%28n%2B1%29%7D%7B2%7D%20%2Bn)
![n^3+3(n)^2+3(n)+1-1=3S+\frac{3n(n+1)}{2} +n](https://tex.z-dn.net/?f=n%5E3%2B3%28n%29%5E2%2B3%28n%29%2B1-1%3D3S%2B%5Cfrac%7B3n%28n%2B1%29%7D%7B2%7D%20%2Bn)
![2n^3+6n^2+6n=6S+3n^2+3n+2n](https://tex.z-dn.net/?f=2n%5E3%2B6n%5E2%2B6n%3D6S%2B3n%5E2%2B3n%2B2n)
![6S=2n^3+3n^2+n](https://tex.z-dn.net/?f=6S%3D2n%5E3%2B3n%5E2%2Bn)
![6S=2n^2(n+1)+n(n+1)](https://tex.z-dn.net/?f=6S%3D2n%5E2%28n%2B1%29%2Bn%28n%2B1%29)
![6S=(n+1)(2n^2+n)](https://tex.z-dn.net/?f=6S%3D%28n%2B1%29%282n%5E2%2Bn%29)
![6S=n(n+1)(2n+1)](https://tex.z-dn.net/?f=6S%3Dn%28n%2B1%29%282n%2B1%29)
![S=\frac{n(n+1)(2n+1)}{6}](https://tex.z-dn.net/?f=S%3D%5Cfrac%7Bn%28n%2B1%29%282n%2B1%29%7D%7B6%7D)
Hence, the formula is ![\frac{n(n+1)(2n+1)}{6}](https://tex.z-dn.net/?f=%5Cfrac%7Bn%28n%2B1%29%282n%2B1%29%7D%7B6%7D)
Learn more about Series here:
brainly.com/question/24643676
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Answer:
f(t) = 62 ⋅ 0.9953t
Step-by-step explanation:
The function decreases at a rate of 0.47%
That will mean, the initial value decreases by 0.47?
100% - 0.47% = 99.53%
The next value will be 99.53% of the initial value.
∴ 99.53% × 62 = 0.9953 × 62.
After a time t, the value will be:
0.9953t × 62
∴ Answer = 62 × 0.9953
Answer:
216 cubic inches
Step-by-step explanation:
The volume of a right rectangular prism is given by the area of the base rectangle multiplied by the height.
Now, see the given figures with the question.
The base of the prism is a rectangle, and its area is (6 × 12) = 72 square inches.
Now, the volume of the prism will be (72 × 3) = 216 cubic inches (Answer)