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
PilotLPTM [1.2K]
3 years ago
10

Water flows into a tank according to the rate F of t equals the quotient of 6 plus t and the quantity 1 plus t, and at the same

time empties out at the rate E of t equals the quotient of the natural log of the quantity t plus 2 and the quantity t plus 1, with both F(t) and E(t) measured in gallons per minute. How much water, to the nearest gallon, is in the tank at time t
Mathematics
1 answer:
diamong [38]3 years ago
8 0

Answer:

Step-by-step explanation:

The complete question is

Water flows into a tank according to the rate F(t)= (t+6)/(1+t), and at the same time empties out at the rate E(t)= (ln(t+2))/(t+1), with both F(t) and E(t) measured in gallons per minute. How much water, to the nearest galllon, is in the tank at time t=10 minutes.

Let C(t) be the amount of water in the tank at time t. We now that the rate of change of the tank is given by

\frac{dC}{dt}=[\tex]rate at which water flows in- rate at which water flows out. Then [tex]\frac{dC}{dt}=\frac{t+6}{t+1}-\frac{\ln(t+2)}{(t+1)}[\tex]so, the desired expression is obtained by integrating with respect to t. This leads us to [tex]C(t)  = \int \frac{t+1}{t+1}+ \frac{5}{t+1} - \frac{\ln(t+2)}{(t+1)} dt=t+ 5 \ln (|t+1|)-\int \frac{\ln(t+2)}{(t+1)} dt +C

Unfortunately, the integral \int \frac{\ln(t+2)}{(t+1)} dt cannot be expressed using fundamental functions. So, the problem cannot have an specific function (if you are willing to know the complete answer, the integral of this function uses the  polylogarithm function with n=2).

Since you want the exact amount of water at time, you need to give C a value, that is, you need to know an initial condition for the problem. This means, you need to know the amount of water in the tank at time 0

You might be interested in
Indicate in standard form the equation of the line passing through the given point and having the given slope. R(4,0), m=5
liberstina [14]
First you put the equation in point slope form- Y-0= 5x - 4
Then add the zero to the 4.
Final answer: y= 5x -4
7 0
3 years ago
This expression is factored what is it's trinomal form?<br> (5x+2)(x-3)
Mkey [24]

Answer:

5x² - 13x - 6

Step-by-step explanation:

Each term in the second factor is multiplied by each term in the first factor, that is

5x(x - 3) + 2(x - 3) ← distribute both parenthesis

= 5x² - 15x + 2x - 6 ← collect like terms

= 5x² - 13x - 6

8 0
3 years ago
2. Jim has $57 in her bank account. He wants to buy a video game that costs $69. Should
levacccp [35]

Answer:

Well I would say John shouldn’t buy any vidoe games becuase first he can’t afford it and no one’s gonna borrow 12 dollars for a video gamer. Plus he can buy it when he has enough.

5 0
3 years ago
What is the value of 4 to the 3 power divided by 2 to the third power?
Sholpan [36]

Answer:

8

Please Vote Me Brainliest. Thank You.

7 0
2 years ago
Read 2 more answers
Write the equation of a line perpendicular to 8xplus5yequals2 that passes through the point ​(2​,negative 7​).
SSSSS [86.1K]

8x + 5y = 2   →   5y = - 8x + 2   →   y = (-8/5)x + 2  ⇒ m = -8/5

perpendicular slope = 5/8

Point-Slope formula: y - y₁ = m(x - x₁)  ; where (x₁, y₁) is the given point

y - (-7) = (5/8)(x - 2)

y + 7 = (5/8)(x - 2)

8(y + 7) = 5(x - 2)

8y + 56 = 5x - 10

8y + 66 = 5x

        66 = 5x - 8y   ⇒   5x - 8y = 66

Answer: 5x - 8y = 66


7 0
3 years ago
Other questions:
  • The quotient of any two integers is an intiger? True or false
    11·1 answer
  • Terri wrote the equation using slope-intercept form for the line that passes through the points (4,6) and (-2,3). Which best des
    15·1 answer
  • One side of a triangle is half the longest side. The third side is
    13·1 answer
  • Find the y-intercept and x-intercept of the line.
    10·1 answer
  • At a rugby match the ratio of children to adults is 2:3 .There are 80 children in the crowd .How many adults are in the crowd?​
    8·2 answers
  • Expand and simplify 4(2x +7) – 3(x + 5)
    11·1 answer
  • Find the solution set of the inequality
    8·2 answers
  • A cone has a height of 12 inches and a radius of 12 inches. What is its volume.
    13·1 answer
  • Can somebody help me as soon as possible
    5·1 answer
  • The rectangle ABCD shown on the coordinate plane represents an overhead view of a piece of land. Each until represents 1,000 fee
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!