Answer:
- a) (0,0), (-4, 1), (-1,2)
- b) None
Step-by-step explanation:
- <em>There are two ways of solving similar problems. One- substitute x and y with respective coordinates and verify if the inequalities are correct. Two- graph the lines and see if the points are in the intersection zones.</em>
- <em>We'll go with the first method. </em>
- <em>Remember both inequalities should be correct for the same point to accept it as a solution.</em>
<u>Given points </u>
<h3>a) <u>The system of inequalities</u></h3>
<u>Point (0,0)</u>
- 0 > 0 - 1 = -1 correct
- 0 < -1/2(0) + 2 = 2 - correct
- Yes
<u>Point (-4,1)</u>
- 1 > -4 - 1 = -5 - correct
- 1 < -1/2(-4) + 2 = 4 - correct
- Yes
<u>Point (-1,2)</u>
- 2 > -1 - 1= -2 - correct
- 2 < -1/2(-1) + 2 = 2.5 - correct
- Yes
<h3>b) <u>The system of inequalities</u></h3>
<u>Point (0, 0)</u>
- 0 - 2(0) = 0 ≥ 4 - incorrect
- 2(0) - 0 = 0 ≥ -1 - correct
- No
<u>Point (-4, 1)</u>
- -4 - 2(1) = - 6 ≥ 4 - incorrect
- 2(-4) - 1 = - 9 ≥ -1 - correct
- No
<u>Point (-1,2)</u>
- -1 - 2(2) = -5 ≥ 4 - incorrect
- 2(-1) - 2 = - 4 ≥ -1 - correct
- No
Step-by-step explanation:
2x^2-5x
f(x)= 2(4)^2-5(4)
2(16)-20
32-20= 12
It is given that:
![\begin{gathered} 2\cos 2x+\sqrt[]{2}=0 \\ 2\cos 2x=-\sqrt[]{2} \\ \cos 2x=-\frac{\sqrt[]{2}}{2} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%202%5Ccos%202x%2B%5Csqrt%5B%5D%7B2%7D%3D0%20%5C%5C%202%5Ccos%202x%3D-%5Csqrt%5B%5D%7B2%7D%20%5C%5C%20%5Ccos%202x%3D-%5Cfrac%7B%5Csqrt%5B%5D%7B2%7D%7D%7B2%7D%20%5Cend%7Bgathered%7D)
cos2x is negative square root 2 divided by 2 in the second and third quadrants, so it follows:
Here theta is given by:
So the solution is given by:
