The answer should be C. 8 because two times the amount that Charles ate which is 4 equals 8 and 4+8=12
Answer:
![a(x)=\dfrac{1}{1+2x}](https://tex.z-dn.net/?f=a%28x%29%3D%5Cdfrac%7B1%7D%7B1%2B2x%7D)
Step-by-step explanation:
The generating function a(x) produces a power series ...
![a(x)=a_0+a_1x+a_2x^2+a_3x^3+\dots](https://tex.z-dn.net/?f=a%28x%29%3Da_0%2Ba_1x%2Ba_2x%5E2%2Ba_3x%5E3%2B%5Cdots)
where the coefficients are the elements of the given sequence.
We observe that the given sequence has the recurrence relation ...
![a_0=1;a_n=-2a_{n-1} \quad\text{for n $>$ 0}](https://tex.z-dn.net/?f=a_0%3D1%3Ba_n%3D-2a_%7Bn-1%7D%20%5Cquad%5Ctext%7Bfor%20n%20%24%3E%24%200%7D)
This can be rearranged to ...
![a_n+2a_{n-1}=0](https://tex.z-dn.net/?f=a_n%2B2a_%7Bn-1%7D%3D0)
We can formulate this in terms of a(x) as follows, then solve for a(x).
![\sum\limits^{\infty}_{n=1} {a_{n}x^n} =a(x)-a_0 \quad\text{and}\\\\\sum\limits^{\infty}_{n=1} {2a_{n-1}x^n} =(2x)a(x) \quad\text{so}\\\\\sum\limits^{\infty}_{n=1} {(a_n+2a_{n-1})x^n}=0=a(x)-a_0+2xa(x)\\\\a(x)=\dfrac{a_0}{1+2x}=\dfrac{1}{1+2x}](https://tex.z-dn.net/?f=%5Csum%5Climits%5E%7B%5Cinfty%7D_%7Bn%3D1%7D%20%7Ba_%7Bn%7Dx%5En%7D%20%3Da%28x%29-a_0%20%5Cquad%5Ctext%7Band%7D%5C%5C%5C%5C%5Csum%5Climits%5E%7B%5Cinfty%7D_%7Bn%3D1%7D%20%7B2a_%7Bn-1%7Dx%5En%7D%20%3D%282x%29a%28x%29%20%5Cquad%5Ctext%7Bso%7D%5C%5C%5C%5C%5Csum%5Climits%5E%7B%5Cinfty%7D_%7Bn%3D1%7D%20%7B%28a_n%2B2a_%7Bn-1%7D%29x%5En%7D%3D0%3Da%28x%29-a_0%2B2xa%28x%29%5C%5C%5C%5Ca%28x%29%3D%5Cdfrac%7Ba_0%7D%7B1%2B2x%7D%3D%5Cdfrac%7B1%7D%7B1%2B2x%7D)
The generating function is ...
a(x) = 1/(1+2x)
Answer:
<h2><u><em>
The lengths of the sides of a small cube are = foot. Volume of cube = side x side x side. V = = cubic foot. Number of small cubes that can be packed in the prism = = = = 180 cubes. Hence, 180 cubes can be packed into rectangular prism. Part B: Unit cube volume is 1x1x1 =1 cubic foot. So, 180 cubes will have 180 cubic foot volume.</em></u></h2>
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
the volume of the cylinder is 3769.91
the volume of the cube is 1000
so the cylinder's volume is clearly larger than the cube's volume.