Explanation:
In order to prove that affirmation, we define the function g over the interval [0, 1/2] with the formula 
If we evaluate g at the endpoints we have
g(0) = f(1/2)-f(0) = f(1/2) - f(1) (because f(0) = f(1))
g(1/2) = f(1) - f(1/2) = -g(0)
Since g(1/2) = -g(0), we have one chance out of three
- g(0) > 0 and g(1/2) < 0
- g(0) < 0 and g(1/2) > 0
- g(0) = g(1/2) = 0
We will prove that g has a zero on [0,1/2]. If g(0) = 0, then it is trivial. If g(0) ≠ 0, then we are in one of the first two cases, and therefore g(0) * g(1/2) < 0. Since f is continuous, so is g. Bolzano's Theorem assures that there exists c in (0,1/2) such that g(c) = 0. This proves that g has at least one zero on [0,1/2].
Let c be a 0 of g, then we have
Hence, f(c+1/2) = f(c) as we wanted.
The answer is ........
Shawty's like a melody in my head
That I can't keep out, got me singin' like
Na na na na everyday
It's like my iPod's stuck on replay
Replay-ay-ay-ay
Shawty's like a melody in my head
That I can't keep out, got me singin' like
Na na na na everyday
It's like my iPod's stuck on replay
Replay
Remember the first time we met
You was at the mall wit yo friend
I was scared to approach ya
But then you came closer
Hopin' you would give me a chance
Who would have ever knew
That we would ever be more than friends
We're real worldwide, breakin' all the rules
She like a song played again and again
That girl, like something off a poster
That girl, is a dime they say
That girl, is a gun to my holster
She's running through my mind all day, ay
Shawty's like a melody in my head
That I can't keep out, got me singin' like
Na na na na everyday
It's like my iPod's stuck on replay
Replay-ay-ay-ay
Shawty's like a melody in my head
That I can't keep out, got me singin' like
Na na na na everyday
It's like my iPod's stuck on replay
Replay-ay-ay-ay
See you been all around the globe
Not once did you leave my mind
We talk on the phone, from night 'til the morn'
Girl, you really changed my life
Doin' things I never do
I'm in the kitchen cookin' things she likes
We're real worldwide, breakin' all the rules
Someday I wanna make you my wife
That girl, like something off a poster
That girl, is a dime they say (Hey)
That girl, is a gun to my holster
She's running through my mind all day, ay
Shawty's like a melody in my head
That I can't keep out, got me singin' like
Na na na na everyday
It's like my iPod's stuck on replay
Replay-ay-ay-ay
Shawty's like a melody in my head
That I can't keep out, got me singin' like
Na na na na everyday
It's like my iPod's stuck on replay
Replay-ay-ay-ay
I can be your melody
Oh, girl, I could write you a symphony
The one that could fill your fantasies
So come baby girl let's sing with me, ay
I can be your melody
Oh, girl, I could write you a symphony
The one that could fill your fantasies
So come baby girl let's sing with me, ay
Na na na na na na na
Na na na na na na
Shawty got me singin'
Na na na na na na na
Na na na na na na
Now she got me singin'
Answer:
Step-by-step explanation:
To write the equation of a circle, use the formula 
where the center of the circle is (h, k).
This means the equation is 
.
Find the radius r by dividing the diameter of 10 in 2. The radius is 5.
So the equation of the circle is
Answer:
52 miles per hour.
Step-by-step explanation:
Divide 234 by 4.5, as that is what you must divide 4.5 by to get 1.
234/4.5 = 52 miles per hour.
Step-by-step explanation:
Answer: 16 and 5/4 tbsp of sugar.
7 ÷ 2 = 3.5
Don't worry about the decimal for now, just find how many tbsp of sugar she needs for 6 tbsp of milk.
6 ÷ 2 = 3
3 x 5 = 15
Now, we will focus in the 0.5 tbsp of milk.
Find how much 1/2 a tbsp of milk can get for sugar.
4 1/2 tbsp of milk is 5 tbsp of sugar.
5 ÷ 4 = 1.25
So 16 and 5/4 tbsp of sugar is required.
(Answer for Part A)
