Answer:
Reference angle is and tan
= -1
Step-by-step explanation:
lies in the 4th quadrant
and reference angle for angle in 4th quadrant is 2π - x , where x is the angle given.
and reference angle for is
2π- =
and tan = -tan
= -1
Since tan is negative in 4th quadrant ,therefore value will be negative for the given angle.
Answer:
Mean 1.580666667 1.769333333
Standard Deviation 0.890741799 1.123161779
Step-by-step explanation:
When we run the commands in the R software we get the graphs as follows.
The commands were
qqnorm(c(0.32,0.52,0.77,0.81,0.96,1.2,1.31,1.43,1.62,1.87,1.95,2.1,2.48,3,3.37))
and
qqnorm(c(0.47,0.59,0.81,0.9,1.18,1.2,1.35,1.51,1.74,1.89,2.05,2.2,2.81,3.09,4.75))
We can plot the graphs in any other plotting software .
The results would be same .
We see there's a slight difference between the two graphs.
One curve goes above ( Minneapolis) for 0.4 and the other ( for St Paul) is below 0.4
Answer:
When we have a quadratic equation:
a*x^2 + b*x + c = 0
There is something called the determinant, and this is:
D = b^2 - 4*a*c
If D < 0, then the we will have complex solutions.
In our case, we have
5*x^2 - 10*x + c = 0
Then the determinant is:
D = (-10)^2 - 4*5*c = 100 - 4*5*c
And we want this to be smaller than zero, then let's find the value of c such that the determinant is exactly zero:
D = 0 = 100 - 4*5*c
4*5*c = 100
20*c = 100
c = 100/20 = 5
As c is multiplicating the negative term in the equation, if c increases, then we will have that D < 0.
This means that c must be larger than 5 if we want to have complex solutions,
c > 5.
I can not represent this in your number line, but this would be represented with a white dot in the five, that extends infinitely to the right, something like the image below:
