Answer:
Find out the what is the eighth term in the arithmetic sequence defined by the explicit formula.
![a_{n} = 2n + 7](https://tex.z-dn.net/?f=a_%7Bn%7D%20%3D%202n%20%2B%207)
To prove
As given the explicit formula for the arithmetic sequence .
![a_{n} = 2n + 7](https://tex.z-dn.net/?f=a_%7Bn%7D%20%3D%202n%20%2B%207)
Put n = 8
![a_{8} = 2\times 8 + 7](https://tex.z-dn.net/?f=a_%7B8%7D%20%3D%202%5Ctimes%208%20%2B%207)
![a_{8} = 16 + 7](https://tex.z-dn.net/?f=a_%7B8%7D%20%3D%2016%20%2B%207)
![a_{8} = 23](https://tex.z-dn.net/?f=a_%7B8%7D%20%3D%2023)
Therefore the eighth term in the arithmetic sequence is 23 .
X = velocity of plane
y = velocity of wind
x - y = 1680/5 = 336 mph .....(1) [ plane flying against the wind]
&
x + y = 1680/4 = 420 mph....(2) [ plane flying with the wind]
Adding (1) and (2) to eliminate y gives
2x = 756
x = 378 mph is the speed of the plane with no wind.
It can be written as 1.0625
Given the equation - x² + 5x = 3, which can be rewritten as:
- x² + 5x - 3 = 0
where a = -1, b = 5 and c = -3.
Quadratic formula:
![\frac{-b\text{ }\pm\text{ }\sqrt[]{b^2\text{ - 4ac}}}{2a}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%5Ctext%7B%20%7D%5Cpm%5Ctext%7B%20%7D%5Csqrt%5B%5D%7Bb%5E2%5Ctext%7B%20-%204ac%7D%7D%7D%7B2a%7D)
Now, we just replace the values of a, b and c on the equation above.
![\frac{-5\text{ }\pm\text{ }\sqrt[]{5^2\text{ - 4(-1)(3)}}}{2(-1)}](https://tex.z-dn.net/?f=%5Cfrac%7B-5%5Ctext%7B%20%7D%5Cpm%5Ctext%7B%20%7D%5Csqrt%5B%5D%7B5%5E2%5Ctext%7B%20-%204%28-1%29%283%29%7D%7D%7D%7B2%28-1%29%7D)
=
Im pretty sure its 1.09375