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const2013 [10]
3 years ago
15

A cube had edge length 11 inches. Select all the expressions that could represent it’s volume. Two answers. A cube had edge leng

th 11 inches. Select all the expressions that could represent its surface area?
Mathematics
1 answer:
const2013 [10]3 years ago
6 0

Answer:

6(11 ⋅  11) and    6(112) I think

Step-by-step explanation:

yea

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We don't actually need the angle. We only need to know the sign of the cosine.

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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
kirill115 [55]
(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)

3 0
3 years ago
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