The 1st , 3rd , 5th and 6th apply
Answer: There are two solutions and they are
theta = 135
theta = 225
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Explanation:
Recall that x = cos(theta). Since the given cosine value is negative, this indicates x < 0. Theta is somewhere to the left of the y axis, placing it in quadrant 2 or quadrant 3.
It turns out there are two solutions, with one solution per quadrant mentioned above. Use the unit circle to find that the two solutions are:
theta = 135
theta = 225
You're looking for points on the unit circle that have x coordinate equal to x = -sqrt(2)/2. Those two points correspond to the angles of 135 and 225, which are in quadrants 2 and 3 respectively.
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I recommend using your calculator to note that
-sqrt(2)/2 = -0.70710678
cos(135) = -0.70710678
cos(225) = -0.70710678
The decimal values are approximate. Make sure your calculator is in degree mode. Because those three results are the same decimal approximation, this indicates that cos(135) = cos(225) = -sqrt(2)/2.
The denominator is 14-x.
Since the denominator cannot be equal to zero, you take the denominator, set it equal to zero, and solve.
This ill give you the value or values that must be eliminated (cannot be in the domain).
14 - x = 0
add x to both sides
14 = x
The domain is x ≠ 14
OR
(- ∞, 14) ∪ (14, ∞)
OR
All real numbers except 14
Answer:
ITS B
Step-by-step explanation:
To solve for the solution of this system of linear equation, it is best to use substitution. From the first equation, x = 3y
Substituting the expression on the right for the value of x on the second equation,
-2(3y) + 3y = 16
Solving for the value of y gives y = -5 1/3
With this value of y, solving for x gives x = -16
Thus, the solution for this system of linear equation is (-16, -5 1/3)
