Solution
Part A
The general form of the n-th term = a + (n-1)d
Here we are given the 8th term A8 = 28
, common difference (d) = 6
A8 = a + (n - 1) 6
28 = a + (8- 1)6
28 = a + 7*6
28 = a + 42
a = 28 - 42
a = -14
Part B
n-th term is 760. a = -14 and d = 6.
Plugging in the values in the general form, we get
760 = -14 + (n -1)6
760 = -14 + 6n - 6
760 = -20 + 6n
6n = 760 + 20
6n = 780
Dividing both sides by 6, we get
n = 780/6 = 130
The value of n is 130
Answer:
$56,320 is the year 2 profit
Step-by-step explanation:
$ 32,000 x .76 = $24,320
$32,000 + $24,320 = $56,320
Answer:
![a^3 + b^3 = -4](https://tex.z-dn.net/?f=a%5E3%20%2B%20b%5E3%20%3D%20-4)
Step-by-step explanation:
Given
![a + b = 3ab = 2](https://tex.z-dn.net/?f=a%20%2B%20b%20%3D%203ab%20%3D%202)
Required
Solve: ![a^3 + b^3](https://tex.z-dn.net/?f=a%5E3%20%2B%20b%5E3)
Rewrite the expression as:
![a^3 + b^3 = a^3 - a^2b +ab^2 + a^2b - ab^2 + b^3](https://tex.z-dn.net/?f=a%5E3%20%2B%20b%5E3%20%3D%20a%5E3%20-%20a%5E2b%20%2Bab%5E2%20%2B%20a%5E2b%20-%20ab%5E2%20%2B%20b%5E3)
Factorize
![a^3 + b^3 = a(a^2 - ab +b^2) + b(a^2 - ab + b^2)](https://tex.z-dn.net/?f=a%5E3%20%2B%20b%5E3%20%3D%20a%28a%5E2%20-%20ab%20%2Bb%5E2%29%20%2B%20b%28a%5E2%20-%20ab%20%2B%20b%5E2%29)
![a^3 + b^3 = (a + b)(a^2 - ab + b^2)](https://tex.z-dn.net/?f=a%5E3%20%2B%20b%5E3%20%3D%20%28a%20%2B%20b%29%28a%5E2%20-%20ab%20%2B%20b%5E2%29)
Rewrite as:
![a^3 + b^3 = (a + b)(a^2 + b^2- ab)](https://tex.z-dn.net/?f=a%5E3%20%2B%20b%5E3%20%3D%20%28a%20%2B%20b%29%28a%5E2%20%20%2B%20b%5E2-%20ab%29)
![a^3 + b^3 = (a + b)(a^2 + b^2+2ab - 3ab)](https://tex.z-dn.net/?f=a%5E3%20%2B%20b%5E3%20%3D%20%28a%20%2B%20b%29%28a%5E2%20%20%2B%20b%5E2%2B2ab%20-%203ab%29)
Factorize
![a^3 + b^3 = (a + b)((a + b)^2 - 3ab)](https://tex.z-dn.net/?f=a%5E3%20%2B%20b%5E3%20%3D%20%28a%20%2B%20b%29%28%28a%20%20%2B%20b%29%5E2%20-%203ab%29)
Open brackets
![a^3 + b^3 = (a + b)^3 - 3ab(a + b)](https://tex.z-dn.net/?f=a%5E3%20%2B%20b%5E3%20%3D%20%28a%20%20%2B%20b%29%5E3%20-%203ab%28a%20%20%2B%20b%29)
Given that:
![a + b = 3ab = 2](https://tex.z-dn.net/?f=a%20%2B%20b%20%3D%203ab%20%3D%202)
This means that:
and ![3ab = 2](https://tex.z-dn.net/?f=3ab%20%3D%202)
So, we have:
![a^3 + b^3 = (a + b)^3 - 3ab(a + b)](https://tex.z-dn.net/?f=a%5E3%20%2B%20b%5E3%20%3D%20%28a%20%20%2B%20b%29%5E3%20-%203ab%28a%20%20%2B%20b%29)
![a^3 + b^3 = 2^3 - 3 * 2 * 2](https://tex.z-dn.net/?f=a%5E3%20%2B%20b%5E3%20%3D%202%5E3%20-%203%20%2A%202%20%2A%202)
![a^3 + b^3 = 8 - 12](https://tex.z-dn.net/?f=a%5E3%20%2B%20b%5E3%20%3D%208%20-%2012)
![a^3 + b^3 = -4](https://tex.z-dn.net/?f=a%5E3%20%2B%20b%5E3%20%3D%20-4)
Answer:
3x^2 +3xh +h^2 -10 x- sh + 1, H=0
Step-by-step explanation: