Can anyone help plssssssss
2 answers:
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Step-by-step explanation:
1)
Considering the sequence
2, 9, 16, 23,...
This sequence is an arithmetic sequence as the common difference between consecutive terms is constant.
i.e. ,
,
2)
Considering the sequence
3, 15, 75, 375,...
This sequence is geometric sequence as the common ratio between consecutive terms is constant.
i.e. r = 15/3 = 5, r = 75/15 = 5
3)
Considering the sequence
0,4,4,8,...
This sequence is not in arithmetic sequence as the common difference is not same.
This sequence is also not in geometric sequence as the common ratio is not same.
As the 2nd and 3rd term is repeating, it means the next term i.e. 5th would be 8 as the 4th term is 8.
So, it will be a recursive sequence.
4)
As the base of this exponential function is greater than 1.
i.e. because 1.1 > 1.
Therefore, this function will have exponential growth.
5)
As the base of this exponential function is less than 1. i.e. because 1/4 < 1.
Therefore, this function will have exponential decay.
Keywords: exponential decay, exponential growth, arithmetic sequence, geometric sequence, recursive sequence
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Answer:
19.7%
Step-by-step explanation:
Given that,
In 2000, the world population was 6.1 billion.
In 2015, the world population was 7.3 billion.
We need to find the percentage increase in population. The percent increase in this case is given by :
So, the increase in population is 19.7%.
Answer:
The equation after translation is x² + y² + 16x - 8y + 73 = 0 ⇒ answer (a)
Step-by-step explanation:
* Lets study the type of the equation:
∵ Ax² + Bxy + Cy² + Dx + Ey + F = 0 ⇒ general form of conic equation
- If D and E = zero
∴ The center of the graph is the origin point (0 , 0)
- If B = 0
∴ The equation is that of a circle
* Lets study our equation:
x² + y² = 7 ⇒ x² + y² - 7 =0
∵ B = 0 , D = 0 , E = 0
∴ It is the equation of a circle with center origin
- The equation of the circle with center origin in standard form is:
x² + y² = r²
∴ x² + y² = 7 is the equation of a circle withe center (0 , 0)
and its radius = √7
* We have two translation one horizontally and the other vertically
- Horizontal: x-coordinate moves right (+ve value) or left (-ve value)
- Vertical: y-coordinate moves up (+ve value) down (-ve value)
∵ The point of translation is (-8 , 4)
∵ x = -8 (-ve value) , y = 4 (+ve value)
∴ The circle moves 8 units to the left and 4 units up
* now lets change the x- coordinate and the y-coordinate
of the center (0 , 0)
∴ x-coordinate of the center will be -8
∵ y-coordinate of the center will be 4
* That means the center of the circle will be at point (-8 , 4)
- the standard form of the equation of the circle with center (h , k) is
(x - h)² + (y - k)² = r²
∵ h = -8 and y = 4
∴ The equation is: (x - -8)² + (y - 4)² = 7
∴ (x + 8)² + (y - 4)² = 7
* lets change the equation to the general form by open the brackets
∴ x² + 16x + 64 + y² - 8y + 16 - 7 = 0
* Lets collect the like terms
∴ x² + y² + 16x - 8y + 73 = 0
∴ The equation after translation is x² + y² + 16x - 8y + 73 = 0
* Look at the graph the blue circle is after translation
