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
mafiozo [28]
3 years ago
10

Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200 L of a dyesolution with a c

oncentration of 1 g/L. To prepare for the next experiment, the tank is to be rinsed with fresh water owing in at the rate of 2 L/min, the well-stirred solution owing out at the same rate.
a. Find the time that will elapse before the concentration of dye in the tank reaches 1% of its original value?
Mathematics
1 answer:
nordsb [41]3 years ago
7 0

Answer:

Time,t that it will elapse before the concerntration of the dye in the tank reaches1% of its original value is 460.52 seconds

Step-by-step explanation:

Let Q(t) = amount of dye for all time,t.

Let Q'= rate in - rate out.

But Q/200 = concerntration of dye

Therefore rate out= Q/200 ×2.

Q'/Q = - 1/100

Dividing by Q gives

Ln/Q/ + c = -1/100t + c1

Integrating both sides with respect to t

Ln/Q/ = -1/100t + c2.

c1 and c1 are just another constants

Q= c3e^-t/100

Exponentiating both sides will cause the absolute values to get absorbed into the constants giving rise to a new constant c3

200= c3-0/100

c3= 200

2= 200e^-t/100

Ln1/100= - t/100

Ln0.01 = - t/ 100

Cross multiply

t= Ln0.01 × 100

t = 4.6052 ×100

t = 460.52seconds

You might be interested in
Find the slope of the line through the point (4,-6) and (-2,-5)
Gnom [1K]

Answer:

-1/6

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-5-(-6))/(-2-4)

m=(-5+6)/-6

m=1/-6

4 0
3 years ago
Solve -4r + 18= 6 I need this equation
schepotkina [342]
The answer I got is R=3
3 0
3 years ago
Read 2 more answers
Find the missing length indicated?
kondor19780726 [428]

Answer:

D. 15

Step-by-step explanation:

Let the missing length be represented as x.

Thus:

(24 - x)/12 = x/20 => angle bisector theorem

Cross multiply

20(24 - x) = x(12)

480 - 20x = 12x

480 - 20x + 20x = 12x + 20x

480 = 32x

480/32 = 32x/32

15 = x

Missing length = x = 15

6 0
2 years ago
which of the functions have a range of real numbers greater than or equal to 1 or less than or equal to-1​
lilavasa [31]

The question is incomplete. Here is the complete question:

Which of the functions have a range of all real numbers greater than or equal to 1 or less than or equal to -1? check all that apply.

A. y=\sec x

B. y= \tan x

C. y= \cot x

D. y= \csc x

Answer:

A. y=\sec x

D. y=\csc x

Step-by-step explanation:

Given:

The range is greater than or equal to 1 or less than or equal to -1.

The given choices are:

Choice A: y=\sec x

We know that, the \sec x=\frac{1}{\cos x}

The range of \cos x is from -1 to 1 given as [-1, 1]. So,

|\cos x|\leq 1\\\textrm{Taking reciprocal, the inequality sign changes}\\\frac{1}{|\cos x|}\geq 1\\|\sec x|\geq 1

Therefore, on removing the absolute sign, we rewrite the secant function as:

\sec x\leq -1\ or\ \sec x\geq 1\\

Therefore, the range of y=\sec x is all real numbers greater than or equal to 1 or less than or equal to-1​.

Choice B: y= \tan x

We know that, the range of tangent function is all real numbers. So, choice B is incorrect.

Choice C: y= \cot x

We know that, the range of cotangent function is all real numbers. So, choice C is incorrect.

Choice D: y=\csc x

We know that, the \csc x=\frac{1}{\sin x}

The range of \sin x is from -1 to 1 given as [-1, 1]. So,

|\sin x|\leq 1\\\textrm{Taking reciprocal, the inequality sign changes}\\\frac{1}{|\sin x|}\geq 1\\|\csc x|\geq 1

Therefore, on removing the absolute sign, we rewrite the cosecant function as:

\csc x\leq -1\ or\ \csc x\geq 1\\

Therefore, the range of y=\csc x is all real numbers greater than or equal to 1 or less than or equal to-1​.

6 0
3 years ago
T/0.3 = 1.7/0.9 ( the one I'm pointing at)
Vikentia [17]
I hope this helps you

3 0
3 years ago
Other questions:
  • F(x)=<img src="https://tex.z-dn.net/?f=%5Csqrt%7Bx%2B4%7D" id="TexFormula1" title="\sqrt{x+4}" alt="\sqrt{x+4}" align="absmiddle
    13·1 answer
  • Plz help only 5 questions
    14·1 answer
  • Given ΔDEF : ΔRST, find the scale factor.
    9·2 answers
  • Whar is 56 percebt as a fraction
    8·2 answers
  • If f(x) = x^2 + 1 and g(x) = x - 4, which value is equivalent to (fºg)(10)?
    13·1 answer
  • What is 4 1/2 - 3 5/4 = but don’t find the quotient I need an estimate!!?
    9·1 answer
  • An airplane can travel 365mph in still air. If it travels 2716 miles with the wind in the same length of time it travels 2394 mi
    7·1 answer
  • You can buy 5 cans for green beans at the Village Market-for-$4.00- You can buy 10 of the same cans of beans at Sam's Club for $
    14·2 answers
  • Preimage Poster = 9 in by 12 in
    14·1 answer
  • Please help with this!!
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!