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.
Problem 1
One possible answer is y = -x+5
This equation has a slope of -1 as does the first equation y = -x+3. Parallel lines have equal slopes but different y intercepts.
You can change the "+5" to any number you want.
=====================================
Problem 2
One possible answer is y = (3/4)x - 2. Like before, parallel lines have the same slope, just a different y intercept. The "-2" can be any number (negative or positive) you want as long as the slope remains 3/4.
Answer:
4 1/6
Step-by-step explanation:
5 5/4 divided by 1 1/2 = 4 1/6
Answer:
2.72 ml
Step-by-step explanation:
4 lb = 1814.37 gm
1814.37 gm * .09 mg/gm / ( 60 mg/ml) = 2.72 ml
Answer:
B
Step-by-step explanation:
18 x 2 = 36
20 x 2 = 40
36 + 40 = 76 miles