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Mathematics

1 answer:

Serga [27]4 years ago

6 0

Answer OK I WILL

Step-by-step explanation:

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Freddie put an empty bucket underneath a leaking pipe. After 3/4 hours, Freddie collected 1/2 cups of water. What is the rate, i

lidiya [134]

0.35 cups/hour

To be able to determine the rate at which the water is leaking from the pipe with the information given, you have to divide the number of cups by the number of hours in which they were collected:
12 cups/34 hours= 0.35 cups/hour
According to this, the answer is that the rate at which the water is leaking from the pipe is 0.35 cups/hour.

Hope this helps!!

5 0

3 years ago

Let f be a continuous function defined on the interval [0,1] such that f(0) = f(1). Show that there exists a number 0 <= a &l

Leni [432]

Explanation:

In order to prove that affirmation, we define the function g over the interval [0, 1/2] with the formula $g(x) = f(x+1/2)-f(x) .$

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

$0 = g(c) = f(c+1/2)-f(c)$