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3 years ago

7

Working together, two pumps can drain a certain pool in 6 hours. If it takes the older pump 15 hours to drain the pool by itself

, how pump to drain the pool on its own?

1 answer:

stellarik [79]3 years ago

5 0

Answer:

10

Step-by-step explanation:

Rate of drainage for pump A and B = [1 pool drained]/[6 hours]

Rate of drainage for pump A (older pump) = [1 pool drained]/[15 hours]

Rate for pump B (newer pump) = [1 pool drained]/[t hours]

Thus, adding the rate of drainage of A and B,

1/t + 1/15 = 1/6

t=10

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Randall buys a wooden board that is 5 7/8 feet long. The cost of the wooden board is 0.25 per foot including tax. Enter the tota

AURORKA [14]

Answer:

Total Cost = $1.47

Step-by-step explanation:

Length of the wooden board = $5\frac{7}{8} =\frac{47}{8}$

Cost of the wooden board = $0.25 per foot

Total Cost = Cost per foot X Total Length in foot

= $0.25 X \frac{47}{8} =1.47$

Total Cost = $1.47

7 0

2 years ago

Let L be a tangent line to the hyperbola x y = 2 at x = 9 . Find the area of the triangle bounded by L and the coordinate axes.

mafiozo [28]

Answer:

$A = 4$

Step-by-step explanation:

The equation of the slope of the tangent line L is obtained by deriving the equation of the hyperbola:

$y = \frac{2}{x}$

$y'=-2\cdot x^{-2}$

The numerical value of the slope is:

$y' = -2 \cdot (9)^{-2}\\y' = -\frac{2}{81}$

The component of the y-axis is:

$y = \frac{2}{9}$

Now, the tangent line has the following mathematical model:

$y = m \cdot x + b$

The value of the intercept is found by isolating it within the equation and replacing all known variables:

$b = y - m \cdot x$

$b = \frac{2}{9}-(-\frac{2}{81} )\cdot (9)\\b = \frac{4}{9}$

Thus, the tangent line is:

$y = -\frac{2}{81}\cdot x + \frac{4}{9}$

The vertical distance between a point of the tangent line and the origin is given by the intercept.

$d_{y} = \frac{4}{9}$

In order to find horizontal distance between a point of the tangent line and the origin, let equalize y to zero and clear x:

$-\frac{2}{81}\cdot x + \frac{4}{9}=0$

$-\frac{2}{9}\cdot x + 4 = 0$

$x = 18$

$d_{x} = 18$

The area of the triangle is computed by this formula:

$A = \frac{1}{2}\cdot d_{x}\cdot d_{y}$

$A = \frac{1}{2}\cdot (18)\cdot (\frac{4}{9} )$

$A = 4$

4 0

3 years ago

1. Jane saved up 20 coins, all nickels and

kompoz [17]

Answer:

10 nickels and 10 quarters

Step-by-step explanation:

Given

Number of coins: 20

Vaiue of coins = $3.00

Required

Number of Nickels and Quarters;

<em>Let N =Nickels and Q =Quarters</em>

The total coins is represented as:

$N + Q = 20$

1 nickel is equivalent to $0.05 and 1 quarter is equivalent to $0.25; So

$0.05N + 0.25Q = 3$

Make N the subject of formula in the first equation

$N = 20 - Q$

Substitute this in the second equation

$0.05(20 - Q) + 0.25Q = 3$

$1 - 0.05Q + 0.25Q = 3$

Collect like terms

$-0.05Q + 0.25Q = 3 - 1$

$0.2Q = 2$

Multiply both sides by 5

$5 * 0.2Q = 2 * 5$

$Q = 10$

Recall that N = 20 - Q

$N = 20 - 10$

$N = 10$

6 0

3 years ago

Write an expression that will have a product less than both factors.

anzhelika [568]

$-2 * 3 = -6


-6 \ \textless \ -2 \ \textless \ 3$

6 0

3 years ago

Read 2 more answers

Wo numbers are in the ratio of 2 to 3. If the smaller number is 18, the larger number is

Zarrin [17]

The simplified ratio is 2:3. Since the smaller number when it's not simplified is 18, let's divide 18 by 2 to get our factor.
18/2 = 9.
So we can multiply 9 by 3 to get the missing larger number.
9 x 3 = 27.
Your missing number is 27, hope this helps!

5 0

3 years ago