1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
N76 [4]
3 years ago
7

(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

9 l/min. the solution is mixed and drains from the tank at the same rate. (a) how much sugar is in the tank at the beginning? y(0)= 0kg (include units) (b) with s representing the amount of sugar (in kg) at time t (in minutes) write a differential equation which models this situation. s′=f(t,s)= 0.54-(9s/1060) . note: make sure you use a capital s, (and don't use s(t), it confuses the computer). don't enter units for this function. (c) find the amount of sugar (in kg) after t minutes.
Mathematics
1 answer:
kirill115 [55]3 years ago
3 0
(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)

You might be interested in
6.
Nadusha1986 [10]
Easy I think it is 14
6 0
3 years ago
How does the graph of g(x) = −(x + 3)^4 compare to the parent function of f(x) = x^4
kotykmax [81]

Answer: Option D

g(x) is shifted 3 units to the left and reflected over the x-axis.

Step-by-step explanation:

If we have a main function f (x) = x ^ 4

And we perform the transformation:

g (x) = f (x + h) = (x + h) ^ 4

Then it is fulfilled that:

If h> 0 the graph of f(x) moves horizontally h units to the left

If h the graph of f(x) moves horizontally h units to the right

If we have a main function f (x) = x ^ 4

And we perform the transformation:

g (x) = -f(x) = -x ^ 4

Then it is fulfilled that:

The graph of g(x) is equal to the graph of f(x) reflected on the x axis

In this case we have to:

g(x) = -(x + 3)^4 and f(x) = x^4

Therefore h=3>0 and g(x) = -f(x)

This mean that: g(x) is shifted 3 units to the left and reflected over the x-axis.

6 0
3 years ago
The metal in a penny is worth about 0.505 cent . How much cents is this written as a fraction?\
Ratling [72]
0.505 means 505 * 0.001, or 505 * 1/1000. This is equivalent to 505/1000, or 101/200.
8 0
3 years ago
The tangent to the circle x^2+y^2=18 is parallel to the tangent x+y=6
liubo4ka [24]

Answer:

y = -x - 6

Step-by-step explanation:

If we are looking for the equation of the line tangent to the circle, we have to find the first derivative of the circle function.  If that tangent line is to be parallel to the given tangent line, we need to find the slope of the the given tangent line and make sure the slope of the line we are looking for is the same.  First let's find the slope of the given tangent.  If the given tangent is x+y=6, then to find the slope, solve for y:

y = -x + 6.  So the slope of that line, and also the slope of the tangent we are solving for, is -1.  Hold that thought while we find the derivative of the function.  Using implicit differentiation, we find the derivative to be:

2x+2y\frac{dy}{dx}=0

Solving for the slope (dy/dx) gives us:

2y\frac{dy}{dx}=-2x and

\frac{dy}{dx}=\frac{-2x}{2y} so

\frac{dy}{dx}=-\frac{x}{y}

Subbing in the value of the slope we found:

-1=-\frac{x}{y} so

-y = -x or, equivalently,

y = x.  Now that we know that y and x are the same value, we can go back to the original circle to find out what they both are by substitution.  If y = x, we make the substution:

If x^2+y^2=18, then

y^2+y^2=18 and

2y^2=18 and

y^2=9 so

y = ±3

We will choose the negative root (you'll see why in a second) and sub that in for both y and x since y and x are th same number.  Going back to the fact that the slope is -1:

y - (-3) = -1(x - (-3)) simplifies a bit to:

y + 3 = -x - 3 which gives us, in slope-intercept form:

y = -x - 6

That is the equation of the tangent to the circle that is parallel to the given tangent.

If we would have chosen the principle (or positive) root of 3, our equation would have looked like this:

y - 3 = -1(x - 3) and

y = -x + 3 + 3 so

y = -x + 6.  Notice that that is the EXACT SAME EQUATION as the given tangent.  That's why we have to pick the negative 3 as our root.

Good luck in your calculus class!  Make sure you post your questions in here!  Many of us LOVE the challenge of calculus!

3 0
3 years ago
Find the area of the circle. Round your answer to the nearest hundredth.
Hoochie [10]
Area is 706.858, rounded is 707
6 0
3 years ago
Read 2 more answers
Other questions:
  • What is 1.2 -0.145 because last time I did this I got it wrong
    15·2 answers
  • when Marla round and 19.95 to the nearest tenth she found the number change to 20. Explain how this is right plz
    8·1 answer
  • Mrs. Nelson has a rectangular flower box that is 5 feet long and 2 feet tall. She wants the width of the box to no more than 5 f
    7·1 answer
  • ​ Quadrilateral ABCD ​ is inscribed in this circle.
    11·1 answer
  • laura purchased a prepaid phone card for $25 . long distance calls cost 8 cents a minute using this card. laura used her card on
    9·1 answer
  • Emma buys and sells truck parts she bought two tires for $35 each and later sold them for $65 each she bought three rooms for $7
    15·2 answers
  • Pls help me with these problems
    11·2 answers
  • I need to solve for x ​
    8·2 answers
  • Determine whether the system has no one, or infinitely many solutions.<br>y = 2x + 6 <br>y = -x - 3​
    10·2 answers
  • Represent the following sentence as an algebraic expression, where "a number" is the
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!