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3 years ago

5/9 of a piece of metal has a mass of 7 kg. What is the mass of 2/7 of the piece of metal

Mathematics

1 answer:

Eddi Din [679]3 years ago

8 0

Answer:

3.6 kg

Step-by-step explanation:

5/9 piece of metal has a mass=7kg

1 piece of metal has a mass =7/5/9 kg

=63/5 kg

Hence,

2/7 piece of metal has a mass=63/5*2/7

=18/5kg

=3.6 kg

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(1 point) a tank contains 1060 l of pure water. a solution that contains 0.06 kg of sugar per liter enters the tank at the rate

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(a) There is 0 kg of sugar in the tank at the beginning since it contains pure water at the start. The sugar only comes from the solution.

(b)

$S' = f(t,S) = \left(0.06 \dfrac{\text{kg}}{\text{L}}\right)\left(9\dfrac{\text{L}}{\text{min}}\right) - \left(\dfrac{S}{1060} \dfrac{\text{kg}}{\text{L}}\right)\left(9\dfrac{\text{L}}{\text{min}}\right) \ \Rightarrow \\ \\ S' = 0.54 \text{ kg}/\text{min} - \dfrac{9S}{1060}$

So yes, you enter S' = 0.54 - (9S/1060)

(c)

$\displaystyle\frac{dS}{dt} = 0.54 - \frac{9S}{1060} \ \Rightarrow\ \frac{dS}{dt} = \frac{572.4 - 9S}{1060}\ \Rightarrow\ \dfrac{dS}{572.4 - 9S} = \frac{1}{1060} dt\ \Rightarrow \\ \\
\int \dfrac{dS}{572.4 - 9S} = \int \frac{1}{1060} dt\ \Rightarrow\textstyle\ -\frac{1}{9}\ln|572.4 - 9S| = \frac{1}{1060}t + C \\ \\
S(0) = 0 \ \Rightarrow\ -\frac{1}{9}\ln|572.4 - 0| = \frac{1}{1060}(0) + C\ \Rightarrow\ C = -\frac{1}{9} \ln 572.4$

$-\frac{1}{9}\ln|572.4 - 9S| = \frac{1}{1060}t -\frac{1}{9} \ln 572.4\ \Rightarrow \\ \\
\ln|572.4 - 9S| = \ln 572.4 - \frac{9}{1060}t \ \Rightarrow \\ \\
|572.4 - 9S| = e^{\ln 572.4 - 9t/1060}\ \Rightarrow \\ \\
572.4 - 9S= \pm 572.4 e^{-9t/1060}\ \Rightarrow \\ \\
S = \frac{-1}{9}\left(-572.4 \pm 572.4 e^{-9t/1060}\right)$

But only (+) satisfies $S(0) = 0$

$S= -\frac{1}{9}\left(-572.4 + 572.4 e^{-9t/1060}\right) \\ \\
S= 63.6 - 63.6 e^{-9t/1060}\text{ kg}$

Enter in S = 63.6 - 63.6 * e^(-9t/1060)

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5/9 of a piece of metal has a mass of 7 kg. What is the mass of 2/7 of the piece of metal​

5/9 of a piece of metal has a mass of 7 kg. What is the mass of 2/7 of the piece of metal