.6 is ten times as much as
2 answers:
<u>Answer:</u> 0.6 is ten times as much as 0.06
<u>Step-by-step explanation:</u>
We are given a statement:
0.6 is ten times as much as
Let the number be considered as 'x'
'Times' in the above statement means multiplication operation.
So, the equation for the given statement becomes:
To solve the value of 'x', we shift the number '10' to other side of the equation and operation applied will be division.
Solving the above equation, we get:
Hence, 0.6 is ten times as much as 0.06
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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.