A. 3,535.20
All you gotta do is Multiply 36 with 98.20 and boom, you got the answer
(3.4)/(12.92)
=(3+2/5)/(12+92/100)
=(15/5+2/5)/(1200/100+92/100)
=(17/5)/(1292/100)
=(17/5)*(100/1292)
=1700/6460
=170/646
=85/323
1,089 squared = (1,089) x (1,089) = 1,185,921 .
But 1,089 itself is a perfect square.
(33) x (33) = 1,089
Answer:
![\displaystyle \theta = \left\{\frac{7\pi}{6}, \, \frac{3\pi}{2}, \frac{11\pi}{6}\right\}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctheta%20%3D%20%5Cleft%5C%7B%5Cfrac%7B7%5Cpi%7D%7B6%7D%2C%20%5C%2C%20%5Cfrac%7B3%5Cpi%7D%7B2%7D%2C%20%5Cfrac%7B11%5Cpi%7D%7B6%7D%5Cright%5C%7D)
Step-by-step explanation:
We want to solve the equation:
![2\sin ^2 \theta + 3\sin \theta + 1 = 0](https://tex.z-dn.net/?f=2%5Csin%20%5E2%20%5Ctheta%20%2B%203%5Csin%20%5Ctheta%20%2B%201%20%3D%200)
In the interval [0, 2π).
Notice that this is in quadratic form. Namely, by letting u = sin(θ), we acquire:
![\displaystyle 2u^2 + 3u + 1 = 0](https://tex.z-dn.net/?f=%5Cdisplaystyle%202u%5E2%20%2B%203u%20%2B%201%20%3D%200)
Factor:
![\displaystyle (2u+1)(u+1) = 0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%282u%2B1%29%28u%2B1%29%20%3D%200)
By the Zero Product Property:
![\displaystyle 2u + 1 = 0\text{ or } u + 1 = 0](https://tex.z-dn.net/?f=%5Cdisplaystyle%202u%20%2B%201%20%3D%200%5Ctext%7B%20or%20%7D%20u%20%2B%201%20%3D%200)
Solve for each case:
![\displaystyle u = -\frac{1}{2} \text{ or } u = -1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20u%20%3D%20-%5Cfrac%7B1%7D%7B2%7D%20%5Ctext%7B%20or%20%7D%20u%20%3D%20-1)
Back-substitute:
![\displaystyle \sin \theta = -\frac{1}{2} \text{ or } \sin \theta =-1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csin%20%5Ctheta%20%3D%20-%5Cfrac%7B1%7D%7B2%7D%20%5Ctext%7B%20or%20%7D%20%5Csin%20%5Ctheta%20%3D-1)
Use the Unit Circle. Hence, our three solutions in the interval [0, 2π) are:
![\displaystyle \theta = \left\{\frac{7\pi}{6}, \, \frac{3\pi}{2}, \frac{11\pi}{6}\right\}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctheta%20%3D%20%5Cleft%5C%7B%5Cfrac%7B7%5Cpi%7D%7B6%7D%2C%20%5C%2C%20%5Cfrac%7B3%5Cpi%7D%7B2%7D%2C%20%5Cfrac%7B11%5Cpi%7D%7B6%7D%5Cright%5C%7D)
Answer:
32,000
Step-by-step explanation: