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
Hello,
f(x)=7x²+42x=7(x²+2*3x+9)-63=7(x+3)²-63.
Answer:
15i
Step-by-step explanation:
-3+7i+3+8i
0+15i
Answer:
x = 1,650
Step-by-step explanation:
A real-world problem with a sample and a population is modeled by the proportion 66/100=x/2,500. Use the proportion to complete the sentences.
From the above question, we have to solve for x
Hence, we have the proportion
66/100=x/2,500
Cross Multiply
100 × x = 66 × 2,500
x = 66 × 2,500/100
x = 1,650
Answer:
k = 16 , (4, 0 )
Step-by-step explanation:
Using the discriminant Δ = b² - 4ac
• b² - 4ac = 0 , then 2 real and equal roots
Here
y = x² - 8x + k
with a = 1, b = - 8, c = k , then
b² - 4ac
= (- 8)² - (4 × 1 × k)
= 64 - 4k , and equating to zero
64 - 4k = 0 ( subtract 64 from both sides )
- 4k = - 64 ( divide both sides by - 4 )
k = 16
Then
y = x² - 8x + 16
Equate to zero to find the root
x² - 8x + 16 = 0 ← left side is a perfect square
(x - 4)² = 0
x - 4 = 0 ( add 4 to both sides )
x = 4
The point on the x- axis is (4, 0 )
