The height will be four, becaus 5 is the height of the base not the whole prism. You can tell be beacause when you find the area of the base and multiply it by the height you multiply it by 4 not 5.
1.
Answer C. (8)
2.
Answer C. [6x^(4/3)]
3.
Answer D. (the one with 36x²)
4.
Answer B. (2a^(2/3)b²)
5.
Answers C. and D.
Answer:
The required sequence is
. The average rate of change from n = 1 to n = 3 is -7.5.
Step-by-step explanation:
From the given graph it is clear that the sequence is a GP because the all terms are half of their previous terms.
Here, ![a_2=10,a_3=5,a_4=2.5,a_5=1.25](https://tex.z-dn.net/?f=a_2%3D10%2Ca_3%3D5%2Ca_4%3D2.5%2Ca_5%3D1.25)
![r=\frac{a_3}{a_2}=\frac{5}{10}=\frac{1}{2}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Ba_3%7D%7Ba_2%7D%3D%5Cfrac%7B5%7D%7B10%7D%3D%5Cfrac%7B1%7D%7B2%7D)
The common ratio of GP is 1/2.
![r=\frac{a_2}{a_1}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Ba_2%7D%7Ba_1%7D)
![\frac{1}{2}=\frac{10}{a_1}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%3D%5Cfrac%7B10%7D%7Ba_1%7D)
![a_1=20](https://tex.z-dn.net/?f=a_1%3D20)
The first term of the sequence is 20.
The formula for sequence is
![a_n=a(r)^{n-1}](https://tex.z-dn.net/?f=a_n%3Da%28r%29%5E%7Bn-1%7D)
Where a is first term and r is common difference.
The required sequence is
![a_n=20(\frac{1}{2})^{n-1}](https://tex.z-dn.net/?f=a_n%3D20%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7Bn-1%7D)
The formula for rate of change is
![m=\frac{f(x_2)-f(x_1)}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7Bf%28x_2%29-f%28x_1%29%7D%7Bx_2-x_1%7D)
The average rate of change from n = 1 to n = 3 is
![m=\frac{f(3)-f(1)}{3-1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7Bf%283%29-f%281%29%7D%7B3-1%7D)
![m=\frac{5-20}{3-1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B5-20%7D%7B3-1%7D)
![m=\frac{-15}{2}=-7.5](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-15%7D%7B2%7D%3D-7.5)
Therefore the required sequence is
. The average rate of change from n = 1 to n = 3 is -7.5.