Answer: Choice C
![\left[0 , \frac{\pi}{2}\right) \ \ \text{ and } \ \ \left(\frac{\pi}{2}, \pi\right]](https://tex.z-dn.net/?f=%5Cleft%5B0%20%2C%20%5Cfrac%7B%5Cpi%7D%7B2%7D%5Cright%29%20%5C%20%5C%20%5Ctext%7B%20and%20%7D%20%5C%20%5C%20%5Cleft%28%5Cfrac%7B%5Cpi%7D%7B2%7D%2C%20%5Cpi%5Cright%5D)
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Explanation:
Let's look at the function y = sec(x) first, which is the secant function.
Recall that secant is 1 over cosine, so sec(x) = 1/cos(x)
We can't divide by zero, so cos(x) = 0 can't be allowed. If x = pi/2, then cos(pi/2) = 0 will happen. So we must exclude pi/2 from the domain of sec(x).
If we look at the interval from 0 to pi, then the domain of sec(x) is 
we can condense that into the interval notation
Note the use of curved parenthesis to exclude the endpoint; while the square bracket includes the endpoint.
So effectively we just poked at hole at x = pi/2 to kick that out of the domain. I'm only focusing on the interval from 0 to pi so that secant is one to one on this interval. That way we can apply the inverse. When we apply the inverse, the domain and range swap places. So the range of arcsecant, or 
is going to also be
Answer:
How do you figure out if a relation is a function? You could set up the relation as a table of ordered pairs. Then, test to see if each element in the domain is matched with exactly one element in the range. If so, you have a function!
Step-by-step explanation:
Answer: the length of the field is 70 yards. The width of the field is 35 yards
Step-by-step explanation:
Let L represent the length of the rectangular athletic field.
Let W represent the width of the rectangular athletic field.
A rectangular athletic field is twice as long as it is wide. This means that
L = 2W
The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(L + W)
If the perimeter of the athletic field is 210 yards, it means that
210 = 2(L + W)
L + W = 210/2 = 105
Substituting L = 2W into L + W = 105, it becomes
2W + W = 105
3W = 105
W = 105/3 = 35
L = 2W = 2 × 35
L = 70
Answer:
3/2
Step-by-step explanation:
Answer:
Inez worked for 2 hours 32 minutes more than Joe
Step-by-step explanation:
Here, we are to calculate the difference in the amount of time in which both of them spent working.
Mathematically, that would be the time spent by Inez minus the time spent by Joe
= 7 hrs 23 minutes - 4 hrs 51 minutes
This works like normal arithmetic subtraction;
Since we cannot subtract 51 minutes from 23 minutes, we need to borrow 1 hour ( 60 minutes) from 7 , and it becomes 6 while our minutes become (60 + 23 = 83 minutes).
So the difference here will be (6-4)hrs and (83-51) minutes = 2 hrs 32 minutes
