Answer:
x = π/3, x = 5π/3, x = 4π/3
Step-by-step explanation:
Let's split the given equation (2cosx-1)(2sinx+√3 ) = 0 into two parts, and solve each separately. These parts would be 2cos(x) - 1 = 0, and 2sin(x) + √3 = 0.
![2\cos \left(x\right)-1=0,\\2\cos \left(x\right)=1,\\\cos \left(x\right)=\frac{1}{2}](https://tex.z-dn.net/?f=2%5Ccos%20%5Cleft%28x%5Cright%29-1%3D0%2C%5C%5C2%5Ccos%20%5Cleft%28x%5Cright%29%3D1%2C%5C%5C%5Ccos%20%5Cleft%28x%5Cright%29%3D%5Cfrac%7B1%7D%7B2%7D)
Remember that the general solutions for cos(x) = 1/2 are x = π/3 + 2πn and x = 5π/3 + 2πn. In this case we are given the interval 0 ≤ x ≤2π, and therefore x = π/3, and x = 5π/3.
Similarly:
![\:2\sin \left(x\right)+\sqrt{3}=0,\\2\sin \left(x\right)=-\sqrt{3},\\\sin \left(x\right)=-\frac{\sqrt{3}}{2}](https://tex.z-dn.net/?f=%5C%3A2%5Csin%20%5Cleft%28x%5Cright%29%2B%5Csqrt%7B3%7D%3D0%2C%5C%5C2%5Csin%20%5Cleft%28x%5Cright%29%3D-%5Csqrt%7B3%7D%2C%5C%5C%5Csin%20%5Cleft%28x%5Cright%29%3D-%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D)
The general solutions for sin(x) = - √3/2 are x = 4π/3 + 2πn and x = 5π/3 + 2πn. Therefore x = 4π/3 and x = 5π/3 in this case.
So we have x = π/3, x = 5π/3, and x = 4π/3 as our solutions.
Answer:
241 clients
Step-by-step explanation:
His problem can be solved using the principle of proportionality or rule three.
We can take advantage of the proportion between respondents who tell us the number of respondents and how many expect to go on vacation and the total number of workers, therefore:
Respondents /// Whole company
Vacations 21 x
Total 45 516
then x equals:
x = (516 * 21) / (45)
x = 240.8
x = 241 clients
This means that approximately 241 clients expect to go on vacation throughout the company.
Hello.
17. ( 3 + 5 ) · 8 = 64
18. 4 · ( 6 - 2 ) + 7 = 23
19. 10 ÷ ( 3 + 2 ) · 4 = 8
20. ( 3 + 6 ) · 2 = 18
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Answer: how much did the calculators cost seperetely dummy
Step-by-step explanation: