Answer:
Equation: y = 65x
Randomly pick a x and y value and plug into above equation, if they don't equal then the x and y you've picked cannot be on this table.
Step-by-step explanation:
Pick any two points to find slope, let's got with (3, 195) and (4, 260):
slope m = (y₂- y₁) / (x₂ - x₁)
= (260 - 195) / (4 - 3)
= 65 / 1
m = 65
Find y-intercept by using m from above and another point from your table, let's go with (5, 325):
y = mx + b
325 = 65(5) + b
325 = 325 + b
b = 0
Use m and b to form equation of line:
y = mx + b
y = 65x + 0
y = 65x
Check:
point (3, 195): 195 = 65(3) ====> 195 = 195
point (4, 260): 260 = 65(4) ====> 260 = 260
point (5, 325): 325 = 65(5) ====> 325 = 325
point (6, 390): 390 = 65(6) ====> 390 = 390
Example of a point that doesn't belong on table:
point (8, 500): 500 = 65(8) ====> 500 ≠ 520
The explicit formula for the geometric sequence
is
![c_{n}=6(\frac{-1}{3})^{n-1}](https://tex.z-dn.net/?f=c_%7Bn%7D%3D6%28%5Cfrac%7B-1%7D%7B3%7D%29%5E%7Bn-1%7D)
Step-by-step explanation:
The formula of the nth term of a geometric sequence is
, where:
- a is the first term of the sequence
- r is the common ratio between the consecutive terms
The geometric sequence of
is 6 , -2 ,
,
, ![\frac{2}{27}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B27%7D)
∵
= 6
∵ ![r=\frac{c_{2}}{c_{1}}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Bc_%7B2%7D%7D%7Bc_%7B1%7D%7D)
∵
= -2
∴ ![r=\frac{-2}{6}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B-2%7D%7B6%7D)
- Divide both term by 2 to simplify it
∴ ![r=\frac{-1}{3}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B-1%7D%7B3%7D)
∵ ![c_{n}=c_{1}(r)^{n-1}](https://tex.z-dn.net/?f=c_%7Bn%7D%3Dc_%7B1%7D%28r%29%5E%7Bn-1%7D)
- Substitute the value of
and r in the rule above
∴ ![c_{n}=6(\frac{-1}{3})^{n-1}](https://tex.z-dn.net/?f=c_%7Bn%7D%3D6%28%5Cfrac%7B-1%7D%7B3%7D%29%5E%7Bn-1%7D)
The explicit formula for the geometric sequence
is
![c_{n}=6(\frac{-1}{3})^{n-1}](https://tex.z-dn.net/?f=c_%7Bn%7D%3D6%28%5Cfrac%7B-1%7D%7B3%7D%29%5E%7Bn-1%7D)
Learn more:
You can learn more about the geometric sequence in brainly.com/question/1522572
#LearnwithBrainly
From the given figure, it can be seen that triangle JMS was formed from triangle DPW by performing the following transformations.
Triangle DPW was shifted 1 unit to the left, then it was shifted 5 units down and then it was rotated by 90 degrees to the left.
Answer:
42pi
Step-by-step explanation:
to solve for the circumference you do 2pi x radius
2*21*pi=42pi