Answer:
1. 12
2. 4
3. 6.8
4. 4.5
5 1.2
Step-by-step explanation:
![2+\cot A=1\implies \cot A=-1\implies \tan A=-1](https://tex.z-dn.net/?f=2%2B%5Ccot%20A%3D1%5Cimplies%20%5Ccot%20A%3D-1%5Cimplies%20%5Ctan%20A%3D-1)
This happens whenever
![A=\dfrac{3\pi}4](https://tex.z-dn.net/?f=A%3D%5Cdfrac%7B3%5Cpi%7D4)
or
![A=\dfrac{7\pi}4](https://tex.z-dn.net/?f=A%3D%5Cdfrac%7B7%5Cpi%7D4)
. More generally,
![\tan A=-1](https://tex.z-dn.net/?f=%5Ctan%20A%3D-1)
whenever you start with one of these angles and add any multiple of
![\pi](https://tex.z-dn.net/?f=%5Cpi)
, so the general solution would be
![A=\dfrac{3\pi}4+n\pi](https://tex.z-dn.net/?f=A%3D%5Cdfrac%7B3%5Cpi%7D4%2Bn%5Cpi)
, where
![n](https://tex.z-dn.net/?f=n)
is any integer. (Notice that when
![n=1](https://tex.z-dn.net/?f=n%3D1)
, you end up with
![\dfrac{7\pi}4](https://tex.z-dn.net/?f=%5Cdfrac%7B7%5Cpi%7D4)
.)
Answer:
1) k = (-8)/5
2) x = 5
Step-by-step explanation:
1)
![6 {k}^{2} + 16k = 0](https://tex.z-dn.net/?f=6%20%7Bk%7D%5E%7B2%7D%20%20%2B%2016k%20%3D%200)
![= > 2k(3k + 8) = 0](https://tex.z-dn.net/?f=%20%3D%20%20%3E%202k%283k%20%2B%208%29%20%3D%200)
![= > 3k + 8 = \frac{0}{2k} = 0](https://tex.z-dn.net/?f=%20%3D%20%20%3E%203k%20%2B%208%20%3D%20%20%5Cfrac%7B0%7D%7B2k%7D%20%20%3D%200)
![= > 3k = - 8](https://tex.z-dn.net/?f=%20%3D%20%20%3E%203k%20%3D%20%20-%208)
![= > k = \frac{ - 8}{3}](https://tex.z-dn.net/?f=%20%3D%20%20%3E%20k%20%3D%20%20%5Cfrac%7B%20-%208%7D%7B3%7D%20)
2)
![{x}^{2} - 5x = 0](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20%20-%205x%20%3D%200)
![= > x(x - 5) = 0](https://tex.z-dn.net/?f=%20%3D%20%20%3E%20x%28x%20-%205%29%20%3D%200)
![= > x - 5 = \frac{0}{x} = 0](https://tex.z-dn.net/?f=%20%3D%20%20%3E%20x%20-%205%20%3D%20%20%5Cfrac%7B0%7D%7Bx%7D%20%20%3D%200)
![= > x = 5](https://tex.z-dn.net/?f=%20%3D%20%20%3E%20x%20%3D%205)