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Romashka-Z-Leto [24]
3 years ago
5

It takes 12 minutes to fill an entire bathtub using both the cold and hot water. if just the cold water is used, it takes 18 min

utes to fill the bathtub. how long would it take to fill the bathtub if just the hot water were used?
Mathematics
1 answer:
Lemur [1.5K]3 years ago
3 0
Roughly 30 minutes to fill the bathtub due to vaporization.
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Write an expression, using an exponent, that is equivalent to 9\times 9\times 9\times 9\times 9\times 9\times 99×9×9×9×9×9×9
jeka57 [31]
Nine to the eighth power
7 0
3 years ago
Read 2 more answers
A tank with a capacity of 1000 L is full of a mixture of water and chlorine with a concentration of 0.02 g of chlorine per liter
faltersainse [42]

At the start, the tank contains

(0.02 g/L) * (1000 L) = 20 g

of chlorine. Let <em>c</em> (<em>t</em> ) denote the amount of chlorine (in grams) in the tank at time <em>t </em>.

Pure water is pumped into the tank, so no chlorine is flowing into it, but is flowing out at a rate of

(<em>c</em> (<em>t</em> )/(1000 + (10 - 25)<em>t</em> ) g/L) * (25 L/s) = 5<em>c</em> (<em>t</em> ) /(200 - 3<em>t</em> ) g/s

In case it's unclear why this is the case:

The amount of liquid in the tank at the start is 1000 L. If water is pumped in at a rate of 10 L/s, then after <em>t</em> s there will be (1000 + 10<em>t</em> ) L of liquid in the tank. But we're also removing 25 L from the tank per second, so there is a net "gain" of 10 - 25 = -15 L of liquid each second. So the volume of liquid in the tank at time <em>t</em> is (1000 - 15<em>t </em>) L. Then the concentration of chlorine per unit volume is <em>c</em> (<em>t</em> ) divided by this volume.

So the amount of chlorine in the tank changes according to

\dfrac{\mathrm dc(t)}{\mathrm dt}=-\dfrac{5c(t)}{200-3t}

which is a linear equation. Move the non-derivative term to the left, then multiply both sides by the integrating factor 1/(200 - 5<em>t</em> )^(5/3), then integrate both sides to solve for <em>c</em> (<em>t</em> ):

\dfrac{\mathrm dc(t)}{\mathrm dt}+\dfrac{5c(t)}{200-3t}=0

\dfrac1{(200-3t)^{5/3}}\dfrac{\mathrm dc(t)}{\mathrm dt}+\dfrac{5c(t)}{(200-3t)^{8/3}}=0

\dfrac{\mathrm d}{\mathrm dt}\left[\dfrac{c(t)}{(200-3t)^{5/3}}\right]=0

\dfrac{c(t)}{(200-3t)^{5/3}}=C

c(t)=C(200-3t)^{5/3}

There are 20 g of chlorine at the start, so <em>c</em> (0) = 20. Use this to solve for <em>C</em> :

20=C(200)^{5/3}\implies C=\dfrac1{200\cdot5^{1/3}}

\implies\boxed{c(t)=\dfrac1{200}\sqrt[3]{\dfrac{(200-3t)^5}5}}

7 0
3 years ago
from 2002 to 2012, the number of a particular make of cars sold at a dealership yearly declined to 500. The number is expected t
Alinara [238K]
To determine the number of cars that will be sold by the year 2020, we will use the equation,

     N = (N1)(1 - r)^(t)

where N1 is the starting number of cars, r is the rate of the decrease, and t is the number of years from 2012. Substituting the konwn values,

   N = (500)(1 - 0.028)^(8)
    N = 398.38

The closest integer to the calculated value is 398. Thus, the answer is 398 cars. 
3 0
3 years ago
How do -11.5 and -9.5 compare?
DIA [1.3K]

Answer:

-9.5 is larger by 2 units

Step-by-step explanation:

-9.5 - (-11.5)

= -9.5 + 11.5

= 2.

5 0
3 years ago
Un rombo tiene un ángulo de 22 grados. Cuanto vale la suma de sus ángulos que no midan 22 grados?
Igoryamba

Answer:

The sum of the angles that do not measure 22 degrees is equal to 316°

Step-by-step explanation:

The question in English is

A rhombus has a 22-degree angle. How much is the sum of its angles that do not measure 22 degrees worth?

we know that

The opposite internal angles of a rhombus are equal and the adjacent internal angles are supplementary

so

Let

x -----> the measure of an adjacent angle to 22 degrees in the rhombus

x+22°=180°

x=180°-22°=158°

therefore

The sum of the angles that do not measure 22 degrees is equal to

158°+158°=316°

5 0
3 years ago
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