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Vinvika [58]
3 years ago
5

An inlet pipe on a swimming pool can be used to fill the pool in 38 hours. The drain pipe can be used to empty the pool in 40 ho

urs. If the pool is 14 filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool?
Answer
Mathematics
1 answer:
AlexFokin [52]3 years ago
6 0

To solve this problem you must apply the proccedure shown below:

1. In a hour you have \frac{1}{38} of the pool filled and \frac{1}{40}.Taking \frac{1}{4} of the pool filled, you have the following expression:

\frac{1}{38}-\frac{1}{40}=\frac{1}{4}/t

2. Solve for t, as following:

t=\frac{760}{4}\\ t=190 hours

The answer is: 190 hours

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Step-by-step explanation:

(a)

Using the definition given from the problem

f(A) = \{x^2  \, : \, x \in [0,2]\} = [0,4]\\f(B) = \{x^2  \, : \, x \in [1,4]\} = [1,16]\\f(A) \cap f(B) = [1,4]  = f(A \cap B)\\

Therefore it is true for intersection. Now for union, we have that

A \cup B = [0,4]\\f(A\cup B ) = [0,16]\\f(A) = [0,4]\\f(B)= [1,16]\\f(A) \cup f(B) = [0,16]

Therefore, for this case, it would be true that f(A\cup B) = f(A)\cup f(B).

(b)

1 is not a set.

(c)

To begin with  

A\cap B \subset A,B

Therefore

g(A\cap B) \subset g(A) \cap g(B)

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g(A)\cap g(B) \subset  g(A \cap B), therefore  g(A)\cap g(B)  =  g(A \cap B).

(d)

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7 0
3 years ago
Which method will not work?
katen-ka-za [31]
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3 years ago
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Triss [41]

Answer:

Row 1 -

1/3, 1/2, 1/3, 2/3, 2/3, 8/15, 1/2.

Row 2 -

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Row 3 -

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Answer:

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Step-by-step explanation:

sorry I'm doing a competition for who ever reaches 1k points

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