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.
-x+2 > 1
-x+2+x > 1+x .... add x to both sides
2 > 1+x
x+1 < 2
x+1-1 < 2-1 ... subtract 1 from both sides
x < 1
After solving for x, we get x < 1
To graph this, plot an open circle at 1 on the number line and shade to the left of this value. The open circle indicates that 1 is not part of the solution set.
If your teacher requires you to graph this on an xy grid, then draw a vertical line through 1 on the x axis. Make this vertical line a dashed line. Then shade the entire region to the left of this dashed line. Any point in this shaded region will have an x coordinate that is less than 1. The dashed line acts like the open circle. The dashed line tells the reader "any point on this dashed line is not part of the solution set"
Answer:
3, 4, 5
Step-by-step explanation:
Check the picture below.
now, to get how much is the area of the tiled section, we simply get the area of the whole pool, 53x26, which includes the tiles, and then subtract the area without the tile, the rectangle in the middle, and what's leftover, is the area of the tiled area.
Answer:
Step-by-step explanation:
An exponential function is of the form
where a is the initial value and b is the growth/decay rate. Our initial value is 64. That's easy to plug in. It goes in for a. So the first choice is out. Considering b now...
If the rate is decreasing at .5% per week, this means it still retains a rate of
100% - .5% = 99.5%
which is .995 in decimal form.
b is a rate of decay when it is greater than 0 but less than 1; b is a growth rate when it is greater than 1. .995 is less than 1 so it is a rate of decay. The exponential function is, in terms of t,
