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
Natalija [7]
3 years ago
7

Please help with the question below!

Mathematics
1 answer:
Flura [38]3 years ago
5 0

Answer:

ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddd

Step-by-step explanation:

You might be interested in
A 75-gallon tank is filled with brine (water nearly saturated with salt; used as a preservative) holding 11 pounds of salt in so
Debora [2.8K]

Let A(t) = amount of salt (in pounds) in the tank at time t (in minutes). Then A(0) = 11.

Salt flows in at a rate

\left(0.6\dfrac{\rm lb}{\rm gal}\right) \left(3\dfrac{\rm gal}{\rm min}\right) = \dfrac95 \dfrac{\rm lb}{\rm min}

and flows out at a rate

\left(\dfrac{A(t)\,\rm lb}{75\,\rm gal + \left(3\frac{\rm gal}{\rm min} - 3.25\frac{\rm gal}{\rm min}\right)t}\right) \left(3.25\dfrac{\rm gal}{\rm min}\right) = \dfrac{13A(t)}{300-t} \dfrac{\rm lb}{\rm min}

where 4 quarts = 1 gallon so 13 quarts = 3.25 gallon.

Then the net rate of salt flow is given by the differential equation

\dfrac{dA}{dt} = \dfrac95 - \dfrac{13A}{300-t}

which I'll solve with the integrating factor method.

\dfrac{dA}{dt} + \dfrac{13}{300-t} A = \dfrac95

-\dfrac1{(300-t)^{13}} \dfrac{dA}{dt} - \dfrac{13}{(300-t)^{14}} A = -\dfrac9{5(300-t)^{13}}

\dfrac d{dt} \left(-\dfrac1{(300-t)^{13}} A\right) = -\dfrac9{5(300-t)^{13}}

Integrate both sides. By the fundamental theorem of calculus,

\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac1{(300-t)^{13}} A\bigg|_{t=0} - \frac95 \int_0^t \frac{du}{(300-u)^{13}}

\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac{11}{300^{13}} - \frac95 \times \dfrac1{12} \left(\frac1{(300-t)^{12}} - \frac1{300^{12}}\right)

\displaystyle -\dfrac1{(300-t)^{13}} A = \dfrac{34}{300^{13}} - \frac3{20}\frac1{(300-t)^{12}}

\displaystyle A = \frac3{20} (300-t) - \dfrac{34}{300^{13}}(300-t)^{13}

\displaystyle A = 45 \left(1 - \frac t{300}\right) - 34 \left(1 - \frac t{300}\right)^{13}

After 1 hour = 60 minutes, the tank will contain

A(60) = 45 \left(1 - \dfrac {60}{300}\right) - 34 \left(1 - \dfrac {60}{300}\right)^{13} = 45\left(\dfrac45\right) - 34 \left(\dfrac45\right)^{13} \approx 34.131

pounds of salt.

7 0
2 years ago
Which function has a greater y-intercept?
Natali5045456 [20]

Answer:

Option C, both functions have an y-intersect equal to 2.

Step-by-step explanation:

When we have a function f(x), the y-intercept is the value f(0). This is the point where the graph of the function intersects the y-axis.

Then, for f(x) = -x^2 + 5*x + 2

The y-intercept is:

f(0) = -0^2 + 5*0 + 2 = 2

f(0) = 2

And for g(x) we do not have the equation, but we have the graph, so we can just look at which value of y does the graph intersects the y-axis.

We can see that the graph intersects the graph at y = 2

Then the y-intersect is: g(0) = 2

So both functions have the same y-intersect. Then the correct option is C.

4 0
3 years ago
What is the value of 5 in 564,242
saul85 [17]

Answer:

The value of 5 is 500,000

Step-by-step explanation:

becuse their is 5 numbers behind it making it equivilant to 500,000

3 0
2 years ago
Read 2 more answers
For which value of x( from 1 to 10) is y the greatest?
qwelly [4]

10 i think..... plz don't report me

4 0
4 years ago
Which graph represents the equation y = 3/4x - 3
Gnesinka [82]
The bottom left graph since it is the only one tp go through -3 and go up 3/4

5 0
3 years ago
Other questions:
  • The ratio of two supplementary angles is 16:29.
    12·1 answer
  • a kennel owner has 270 feet of fencing material to be used to divide a rectangular are into 10 equal pens. Find the dimensions t
    14·1 answer
  • Mattie Evans drove 150 miles in the same amount of time that it took a turbopropeller plane to travel 600 miles. The speed of th
    13·1 answer
  • Donald needs to stamp 145 pieces of mail. He has finished 97 pieces. How many more does he have to do?      A. 58 B. 48 C. 42 D.
    5·2 answers
  • If every pair of consecutive angles of a quadrilateral are supplementary, then the quadrilateral must be a parallelogram.
    12·1 answer
  • ** I NEED TO GET THIS RIGHT IM DOING TEST CORRECTION**
    7·1 answer
  • Round 3308.89 to the nearest australian dollar
    9·1 answer
  • Emilio borrows $1200 from a bank with 8% simple interest per year. How much will he have to pay back total in 2 years?
    6·2 answers
  • Use the Distributive Property to simplify the expression.<br> 8(5g+5−2)=
    9·2 answers
  • A map is drawn to a scale of 1 : 20 000.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!