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Oduvanchick [21]
3 years ago
11

A pool has 2 pipes, one to fill and one to empty it. Ms.Charles wants to fill the pool, but she mistakenly turns on both pipes a

t the same time. The pipe that fills the pool can fill in 6 hours and the one that drains it can do that job in 10 hours. How long will it take to fill the now that both pipes are filling and emptying it at the same time?
Mathematics
1 answer:
dolphi86 [110]3 years ago
6 0

-- The filler pipe can fill 1/6 of the pool every hour.

-- The drainer pipe can drain 1/10 of the pool every hour.

-- When they're filling and draining at the same time, the filler pipe
will win eventually, because it finishes more of the pool in an hour
than what the drain pipe can finish in an hour.

-- When they're filling and draining at the same time, then every hour,
1/6 of the pool fills and 1/10 of it empties.  The difference is   (1/6) - (1/10).

To do that subtraction, we need a common denominator.
The smallest denominator that works is 30.

       1/6  =  5/30

     1/10  =  3/30 .

So in every hour,  5/30 of the pool fills, and  3/30 of the pool empties.
The result of both at the same time is that  2/30 = 1/15  fills each hour.

If nobody notices what's going on and closes the drain pipe, it will take
<em><u>15 hours</u></em> to fill the pool.


If the drain pipe had <em><u>not</u></em> been open, the filler pipe alone could have filled
the pool <em><u>2-1/2 times</u></em> in that same 15 hours.  With both pipes open,
1-1/2 pool's worth of water went straight down the drain during that time,
and it was wasted. 

I would say that the school should take the cost of 1-1/2 poolsworth out
of Ms. Charles' pay at the rate of $5 a week.  I would, but that would
guarantee her more job security than she deserves after pulling a stunt
like that.

I hope this did not take place in California.


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gtnhenbr [62]

The closest point is (3.5, 1.9) and the distance is 1.96 units

<h3>How to determine the point and the distance?</h3>

The coordinate is given as:

(4, 0)

The equation of the function is

y = √x

The distance between two points is calculated using

d = √(x2 - x1)^2 + (y2 - y1)^2

So, we have the following points

(x1, y1) = (4, 0) and (x2, y2) = (x, 0)

This gives

d = √(x - 4)^2 + (√x - 0)^2

Evaluate the difference

d = √(x - 4)^2 + (√x)^2

Evaluate the exponent

d = √x^2 - 8x + 16 + x

Evaluate the like terms

d = √x^2 - 7x + 16

Next, we differentiate using a graphing calculator

d' = (2x - 7)/[2√(x^2 - 7x + 16)]

Set to 0

(2x - 7)/[2√(x^2 - 7x + 16)] = 0

Cross multiply

2x - 7 = 0

Add 7 to both sides

2x = 7

Divide by 2

x = 3.5

So, we have:

Substitute x = 3.5 in y = √x

y = √3.5

Evaluate

y = 1.9

So, the point is (3.5, 1.9)

The distance is then calculated as:

d = √(x2 - x1)^2 + (y2 - y1)^2

This gives

d = √(3.5 - 4)^2 + (1.9 - 0)^2

Evaluate

d = 1.96

Hence, the closest point is (3.5, 1.9) and the distance is 1.96 units

Read more about distance at:

brainly.com/question/23848540

#SPJ1

3 0
1 year ago
Simplify: -4b^6 + (-26b^6)
DENIUS [597]

Answer:

-30b^{6}

Step-by-step explanation:

-4b^6 + -24b^6 = -30b^6

7 0
3 years ago
Define the function add_mn that takes two integers m, n as arguments and returns m + 10 * n. For instance, add_mn 3 5 = 3 + 10*5
jok3333 [9.3K]

Answer:

// C++ Program to arithmetic operationf on 2 Numbers using Recursion

// Comments are used for explanatory purpose

#include <bits/stdc++.h>

using namespace std;

// add10 recursive function to perform arithmetic operations

int add10(int m, int n)

{

return (m + product(n, 10)); //Result of m + n * 10

return 0;

}

// Main Methods Starts here

int main()

{

int m, n; // 2 Variables m and n declared as integer

cin>>m; // accept input for m

cin>>n; // accept input for n

cout << "Result : "<<add10(m,n); // Print results which is calculated by m + 10 * n

return 0;

}

8 0
3 years ago
Geometry, help please ! :)
Dovator [93]

The bottom rectangle is 52 ft by 27 ft.

The top rectangle is 30 ft by 17 ft (calculated as 57 ft - 27 ft - 13 ft = 17 ft).

The connector rectangle is 13 ft by 9 ft (calculated as 30 ft - 21 ft = 9 ft).

total area = 52 ft * 27 ft + 30 ft * 17 ft + 13 ft * 9 ft

total area = 1404 ft^2 + 510 ft^2 + 117 ft^2

total area = 2031 ft^2

weight = 2031 ft^2 * 12 lb/ft^2

weight = 24,372 lb

4 0
3 years ago
Suppose two dice are tossed and the numbers on the upper faces are observed. Let S denote the set of all possible pairs that can
lesya [120]

Answer:

The set A={(1,2),(2,2),(3,2),(4,2),(5,2),(6,2),(1,4),(2,4),(3,4),(4,4),(5,4),(6,4),(1,(2,6),(3,6),(4,6),(5,6),(6,6)}

B={(2,2),(4,2),(6,2),(2,4),(2,6),(1,3),(1,5),(1,1),(3,1),(3,3),(3,5),(4,4),(4,6),(5,1),(5,3),(5,5),(6,4),(6,6)}

C={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,3),(2,5),(3,3),(3,5),(3,4),(3,6),(4,1),(4,3),(4,5),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,3),(6,5)}.

A∩B:{(2,2),(4,2),(6,2),(2,4),(2,6),(4,4),(4,6),(6,4),(6,6)}

A∪B={(1,2),(2,2),(4,2),(6,2),(2,4),(2,6),(4,4),(4,6),(6,4),(6,6),(3,2),(5,2),(1,4),(3,4),(5,4),(1,6),(3,6),(5,6),(1,3),(1,5),(1,1)(3,1),(3,3),(3,5),(5,1),(5,3),(5,5)}

A∩C={(1,2),(1,4),(1,6),(3,2),(3,4),(3,6),(5,2),(5,4),(5,6)}

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
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