Given:
The set is
To find:
The correct option for the given set which represents the quality that is not in the given set.
Solution:
We have,
It is the set of ordered pairs. So, it is a relation.
For each x-value there is a unique y-value value. So, it is a function.
All elements are real numbers but they not distinct and they are in ordered pairs. So, the given set is not a set of real numbers.
In one to one functions each image has exactly one preimage and each preimage has exactly one image.
In the given set 4 has two preimages 3 and 4. So, the given set is not a one to one function.
Therefore, the correct options are C and D.
Use pythagorean theorem:
sin^2 + cos^2 = 1
(-1/3)^2 + cos^2 = 1
1/9 + cos^2 = 1
cos^2 = 8/9
cos = +- sqrt(8)/sqrt(9) = +- 2sqrt(2)/3
Determine whether cos is positive or negative by looking at which quadrant the angle is in.
pi < theta < 3pi/2 ---> this is 3rd quadrant where x or cos is negative
Therefore cos(theta) = -2sqrt(2)/3
Answer: Choice D) ordered pair is <u>not</u> a solution to the second equation
We can see this by replacing x and y with 1 and -4 respectively
2x + y = 4
2*1 + y = 4 .... replace x with 1
2*1 + (-4) = 4 ... replace y with -4
2 - 4 = 4
-2 = 4 .... this equation is false because -2 and 4 are different values
The last equation being false means that the original equation 2x+y = 4 is also false when (x,y) = (1,-4). Therefore, this ordered pair is not a solution to the second equation 2x+y = 4
A solution to the system must make BOTH equations true simultaneously, not just one.
Visually again I’m not really sure but a average arm would be the same size
