Imagine that a person enters an area downstream of a power plant, and the air in this location is contaminated with noxious gas species Poisonall. As the person breathes, Poisonall enters the bloodstream at a constant rater (units of g/hr) and is biologically eliminated from the bloodstream at a rate proportional to the concentration of Poisonal in the bloodstream at time t, with proportionality constant k (units of m3/hr). Assume that initially (i.e. right before the person enters the polluted zone), the person's blood contains no Poisonal. Assume the concentration of Poisonal in the blood is the same everywhere throughout the body (e.g. the blood is well mixed). Let V = 1 m be the volume of blood in the body. Starting from the equation for mass balance, derive the first-order differential equation that describes dC/dt, where is the concentration of Poisonall in the bloodstream. Then find the particular solution if r = 2 mg/hr and k = 0.5 m^3/hr.
Answers
The particular solution for the given values of r and k is: C(t) = (C(0) - 1 mg) e^(-2t) + 4 mg.
The mass balance equation for Poisonal in the bloodstream can be written as:
Rate of Poisonal entering the bloodstream - Rate of Poisonal leaving the bloodstream = Rate of change of Poisonal in the bloodstream
Let C(t) be the concentration of Poisonal in the bloodstream at time t. Then, the rate of Poisonal entering the bloodstream is given by r, and the rate of Poisonal leaving the bloodstream is proportional to the concentration of Poisonal in the bloodstream, with proportionality constant kV, where V is the volume of blood in the body. Therefore, we can write:
r - kVC(t) = dC(t)/dt
This is a first-order differential equation that describes the concentration of Poisonal in the bloodstream over time.
To find the particular solution for this differential equation, we need to solve it using separation of variables:
(dC(t)/dt) + kVC(t) = r
Multiplying both sides by dt and dividing both sides by (C(t))(kV-r) gives:
(dC(t))/(C(t)(kV-r)) = r/(kV-r) dt
Integrating both sides from 0 to t gives:
∫[0,t] (dC(t))/(C(t)(kV-r)) dt = ∫[0,t] r/(kV-r) dt
Using the fact that the integral of (1/x) dx is ln|x| + C, we get:
ln|C(t)/(C(0)-kVr)| = (r/(kV-r)) t
Rearranging this equation, we get:
C(t) = (C(0) - kVr) e^(-kt/V) + (r/k)
Substituting r = 2 mg/hr and k = 0.5 m^3/hr, we get:
C(t) = (C(0) - 1 mg) e^(-2t) + 4 mg
Therefore, the particular solution for the given values of r and k is:
C(t) = (C(0) - 1 mg) e^(-2t) + 4 mg.
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Related Questions
X + 7= -12i need it step by step
Answers
Answer: x = -19
Step-by-step explanation:
Given
x + 7 = - 12
Subtract 7 on both sides
x + 7 - 7 = -12 - 7
\(\boxed{x=-19}\)
Hope this helps!! :)
Please let me know if you have any questions
Answer:
X=-19
Step-by-step explanation:
X+7=-12
subtract 7 from both sides
X=-19
help! i need to answer this before midnight! ( its 10:00pm)
Answers
Answer:
D.
Step-by-step explanation:
length times width times height
Solve for v.
8 + 5v = -12
Simplify your answer as much as possible.
Answers
8 +5v=-12
-8 -8
________
5v=-20
—- ——
5 5
v=-4
If the true means of the k populations are equal in an ANOVA model, then MSTR/MSE should be: a. more than 1.00 b. close to 1.00 c. close to 0.00 d. close to -1.00 e. a negative value between 0 and - 1 f. not enough information to make a decision
Answers
The correct answer is b. close to 1.00. Ratio close to 1.00 indicates that the between-group variation is similar to the within-group variation.
In an ANOVA (Analysis of Variance) model, MSTR refers to the mean square treatment (or between-group variation), while MSE refers to the mean square error (or within-group variation).
If the true means of the k populations are equal, it means that the between-group variation is similar to the within-group variation, and there is no significant difference between the group means.
In this scenario, we would expect the MSTR/MSE ratio to be close to 1.00 (answer b). A ratio close to 1.00 indicates that the between-group variation is similar to the within-group variation, supporting the assumption that the true means of the populations are equal.
Therefore, the correct answer is b. close to 1.00.
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A gardener will use up to square feet for planting flowers and vegetables. She wants the area used for vegetables to be at least three times the area used for flowers. Let denote the area (in square feet) used for flowers. Let denote the area (in square feet) used for vegetables. Shade the region corresponding to all values of and that s
Answers
The graph attached with inequality x + y ≤ 240 and y ≥ 3x.
What is Graph?The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.
In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.
Usually, data that varies over time is represented with a line graph.
Given:
Area= 240 feet square
You may calculate x + y ≤ 240
since the overall planted space (240 square feet) will be made up of a flowering area (x) and a vegetable area (y) because he will use up to 240 square feet.
Also, the area of vegetables will be at least three times the area used for flowers.
So, the inequality is y ≥ 3x
The graph is attached below.
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What do the side lengths tell you about the angle measures?
Answers
Answer:
You can use the side lengths to determine the angle by using trig. Sin, cosins, and tangent.
If someone can answer this your a life saver
Answers
Answer:
m = 2
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
P = (-5, 2) Q = (-3, 6)
We see the y increase by 4 and x increase by 2, so the slope is
m = 4/2 = 2
Combine like terms to create an equivalent expression.
Enter any coefficients as simplified proper or improper fractions or integers.
-2/3p+ 1/5 -1+ 5/6p
Answers
Answer:
\(\frac{1}{6}\) p - \(\frac{4}{5}\)
Step-by-step explanation:
collect like terms
- \(\frac{2}{3}\) p + \(\frac{5}{6}\) p + \(\frac{1}{5}\) - 1
= - \(\frac{2(2)}{2(3)}\) p + \(\frac{5}{6}\) p + \(\frac{1}{5}\) - \(\frac{5}{5}\)
= - \(\frac{4}{6}\) p + \(\frac{5}{6}\) p - \(\frac{4}{5}\)
= \(\frac{1}{6}\) p - \(\frac{4}{5}\)
Find the volume.
V=1/3h(a^2+ab+b^2)
Answers
Answer:
1092 in³Step-by-step explanation:
We have formula and values given:
V = 1/3h(a² + ab + b²)h = 12 ina = 5√7 ina = 2√7 inSubstitute the values and calculate:
V = 1/3*12*[(5√7)² + (5√7)(2√7) + (2√7)²] =
= 4*(25*7 + 10*7 + 4*7) =
= 4* 273 =
= 1092 in³
A smart phone is bought at ₹ 46000. Its value depreciated at the rate of 12% per annum. Find its value after one year.
please answer fast please :)
Answers
Answer:
40480
Step-by-step explanation:
find 12% of 46000 and subtract it by 46000
brainliest pls
Answer:
40480
Step-by-step explanation
take 12% of the cost
46000*.12=5520
subtract answer from original number
46000-5520=40480
16. Consider the inequalities -2.x < 10 and -6 < -2x.
a. Is x = 0 a solution to both inequalities?
b. Is x = 4 a solution to both inequalities?
c. Find another value of x that is a solution to both inequalities.
Answers
a) The value of x=0 will be a solution for both the inequalities .
b) One equality is false and only one in correct when value of x = 4
What is inequalities?
In Mathematics, the relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.a) x =0
i) -2.x < 10
-2(0) < 10
0 < 10
ii) -6 < -2x
-6 < -2(0)
-6 < 0
The value of x will be a solution for both the inequalities .
b) x = 4
i) -2.x < 10
-2(4) < 10
-8< 10
ii) -6 < -2x
-6 < -2(4)
-6 < -8
Hence, one inequality is false and only one in correct when the value of x =4.
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Solve the first one asap please
Answers
Answer:
x=2. y=3. x=4. y=7x=6. y=11Step-by-step explanation:
y=2x-1
x=2
y=2*2-1=4-1=3
x=4
y=2*4-1=8-1=7
x=6
y=2*6-1=12-1=11
If she traveled 400 miles, how many hours did she drive?
Answers
Answer:
it is 8 hours................
Answer:
takes you 8 hours
Step-by-step explanation:
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. I estimate that the probability of my getting married in the next 3 years is 0.7. math
Answers
The statement "I estimate that the probability of my getting married in the next 3 years is 0.7" does make sense.
As individuals, we can make personal estimates or predictions about events that are relevant to our lives, such as the probability of getting married in a certain timeframe. These estimates are based on our own subjective beliefs, experiences, and expectations. While they may not be based on precise mathematical calculations or rigorous statistical analysis, they can still reflect our personal opinions or perceptions.
In this case, the person is providing an estimate that they believe there is a 0.7 (or 70%) probability of getting married within the next 3 years. This estimate is a subjective assessment of their own chances based on various factors such as their current relationship status, personal goals, or cultural norms.
It is important to note that personal estimates like this are not necessarily based on concrete evidence or universally applicable probabilities. They can vary greatly from person to person and are subjective in nature. However, they can still hold personal meaning and influence one's decision-making or expectations regarding future events.
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Hello, i was wondering if anyone could help me with questions 2 and 3? Thanks :)
I know the page is a bit blurry so here’s what question 2 says:
Hal is munching his garden. He has 5 3/4 bags of much. Each bag covers 105.2 sq. how much area can he cover?
the options are:
A. 520.2
B. 525.75
C 574.5
D 604.9
Answers
Answer: 2:D 3: 1/3 of the fruit, or 80 oranges
Step-by-step explanation:
Answer:
Step-by-step explanation: 5x105.2=526 75% of 105.2 is 78.9 so 105.2+78.9=184.1
I really need help ASAP ILL GIVE BRAINLY
Answers
Answer: D.
Step-by-step explanation:
You can start out with the form AX = B and solve for matrix X that would yield the answer
Then X = (A^-1)(B)
A = [1 -1]
[1 1]
A^-1 = (1/(1 - (1)(-1)))*[1 1]
[-1 1]
which can be written as (1/2) * [1 1]
[-1 1]
B = [26]
[6]
(A^-1)(B) = (1/2)*[1 1] [6]
[-1 1] [26]
= (1/2)*[32]
[20]
= [16]
[10]
plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
Answers
...................
Answer:
Shredder A shreds about 3.67 pounds of paper per minute.
Step-by-step explanation:
1100 pounds/(5 * 60 minutes)
1100 pounds/300 minutes
3.6666...7 pounds/minute
3.67 lb/min
Suppose that in a large bag of socks, there are 100 pairs of each of red, blue, black, and white socks. One draws 2 socks at random. What is the probability that the chosen pair is a uni-color one?
Answers
The probability of choosing a uni-color pair of socks from the bag is 199/799.
The probability of choosing a uni-color pair of socks from a large bag with 100 pairs of each of red, blue, black, and white socks is calculated as follows:
Step 1: Calculate the total number of socks in the bag.
There are 100 pairs of each color, and each pair consists of 2 socks, so there are 100 x 2 = 200 socks of each color.
The total number of socks in the bag is 200 x 4 = 800 socks.
Step 2: Calculate the probability of choosing a uni-color pair of socks.
The probability of choosing a red sock on the first draw is 200/800 = 1/4.
The probability of choosing another red sock on the second draw is 199/799.
The probability of choosing a red pair is (1/4) x (199/799) = 199/3196.
Similarly, the probability of choosing a blue pair, a black pair, or a white pair is also 199/3196.
The probability of choosing a uni-color pair is the sum of the probabilities of choosing a red pair, a blue pair, a black pair, and a white pair.
So the probability of choosing a uni-color pair is (199/3196) x 4 = 796/3196 = 199/799.
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Which type of front creates a ramp-shaped collision?
Warm fronts
Cold fronts
Answers
A ramp-shaped collision is created by a warm front.
When a warm front moves into an area, it brings warm air that rises above the colder air ahead of it. As the warm air rises, it cools and condenses, forming clouds and precipitation. This creates a ramp-like structure where the warm air is lifted over the colder air, leading to a gradual slope of weather systems along the frontal boundary.
The warm air gradually replaces the cold air, resulting in a change in weather conditions.
In contrast, a cold front creates a steeper and more abrupt collision. When a cold front moves into an area, it pushes the warm air ahead of it upwards rapidly. This causes the warm air to cool and condense quickly, resulting in more intense weather conditions such as thunderstorms and heavy rainfall.
In summary, a warm front creates a ramp-shaped collision where warm air rises above colder air, leading to gradual weather changes.
On the other hand, a cold front creates a steeper and more abrupt collision, causing rapid changes in weather conditions.
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if the area of a circle is 64 square meters then what is the radius
Answers
Answer:
Radius = 4.51
Step-by-step explanation:
Answer:
r≈4.51m is surely correct ✔︎
State the slope and y-intercept of the graph of y=-2/5x+2
Answers
Answer:
34y
Step-by-step explanation:
. Generally, which one of the following is the least appropriate measure of central tendency for a data set that contains outliers? a.mean b.median c.2ndquartile d.50thpercentile
Answers
The following is the least appropriate measure of central tendency for a data set that contains outliers is 2ndquartile.
A single number that seeks to characterise a set of data by pinpointing the centre position within that set of data is referred to as a measure of central tendency. As a result, measures of central location are occasionally used to refer to measures of central tendency. They also fit within the category of summary statistics. You are probably most familiar with the mean (sometimes known as the average), but there are additional central tendency measures, including the median and the mode.
The mean, median, and mode are all reliable indicators of central tendency, however depending on the situation, some indicators are more useful than others.
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the producer price index (ppi) is the best index to measure average price changes faced by
Answers
The producer price index (ppi) is the best index to measure average price changes faced by Producers.
The Producer Price Index (PPI) measures the average change in prices received by domestic producers for their output. It is designed to measure price changes for goods and services sold in the primary marketplace by producers.
Therefore, the PPI is an indicator of inflationary trends in the production sector of the economy, and it is used by businesses, policymakers, and analysts to monitor changes in the cost of inputs for goods and services.
It is not the best index to measure average price changes faced by consumers, importers, or labor unions negotiating COLAs (cost-of-living adjustments).
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Yesterday, Grace drove 38 1/2 miles. She used 1 1/4 gallons of gasoline. What is the unit rate for miles per gallon?
Answers
Answer:
The unit rate for miles per gallon is 30 3/5
miles per gallon
Step-by-step explanation:
To get the unit rate for miles per gallon, we simply divide the number of moles by the amount of gallons
Number of miles is 38 1/2 which is 77/2 miles
Number of gallons = 1 1/4 = 5/4
So unit rate will be;
77/2 divided by 5/4
= 77/2 * 4/5 = 154/5 = 30 3/5 miles per gallon
The remote interior angles of a triangle measure 45° and 60°. What is the measure of the exterior angle?
Answers
please help with my math
Answers
Answer:
B.) \(6^{\frac{1}{2}}\)
Step-by-step explanation:
Use the exponent rule that states \(a^{\frac{1}{m}}=\sqrt[m]{a}\). For this problem, let
a=6
m=2
So,
\(\sqrt6=6^{\frac{1}{2}}\)
 PLEASE HURRY I WILL GIVE BRAINLIEST AND 5 STAR AND HEART! THANK YOU!
Answers
Answer:
I believe it is 55°.
I can't remember the exact steps for this tho.
I hope it is right! good luck!
{(47,37 (12,17) (63,60)}
Answers
Answer:
is it domain and range bc if so the first parts of the points are domain and second is range
Step-by-step explanation:
brainleist pls
part A: if McDonald's wanted to fence in the square where pasture and Barbed wire fencing cost a $1.50 per foot, then determine the cost to fence in the pasture.Part b: if MacDonald wants to cover the square pasture and fertilizer and then he needs to determine the area of the pasture. What is the area of the pasture in the nearest hundredth?
Answers
A) To fence the squere, we have to calculate the perimeter of the figure so first we have to calculate the side of the square, so we can use the trigonometric identity of sin so:
\(\sin (45)=\frac{x}{750}\)and we solve for x so:
\(\begin{gathered} x=750\sin (45) \\ x=530.33 \end{gathered}\)Now the perimeter will be:
\(\begin{gathered} P=530.33\cdot4+750 \\ P=2871.32 \end{gathered}\)Now the cost will be the perimeter times the cost per foot so:
\(\begin{gathered} C=2871.32\cdot1.50 \\ C=4306.98 \end{gathered}\)B) The are of the pasture will be the addition of the area of the squate plus the area of the triangle so:
\(\begin{gathered} A=A_t+A_s \\ A=\frac{530.33\cdot530.33}{2}+530.33\cdot530.33 \\ A=530.33+1060.66 \\ A=1590.99 \end{gathered}\)Required information Problem 1-35A (Algo) Recording events in a horizontal statements model LO 1-3, 1-4, 1-5, 1-6, 1-7, 1-8, 1-9, 1-10 [The following information applies to the questions displayed below.] Maben Company was started on January 1, Year 1 , and experienced the following events during its first year of operation: 1. Acquired $38,000 cash from the issue of common stock. 2. Borrowed $32,000 cash from National Bank. 3. Earned cash revenues of $56,000 for performing services. 4. Paid cash expenses of $49,000. 5. Paid a $1,800 cash dividend to the stockholders. 6. Acquired an additional $28,000 cash from the issue of common stock. 7. Paid $8,000 cash to reduce the principal balance of the bank note. 8. Paid $61,000 cash to purchase land. 9. Determined that the market value of the land is $85,000.
Answers
In Maben Company's first year of operation, events included issuing common stock for $38,000, borrowing $32,000 from National Bank, earning $56,000 in cash revenues, paying $49,000 in cash expenses, paying a $1,800 cash dividend, acquiring $28,000 from issuing more common stock, paying $8,000 to reduce the bank note, and purchasing land for $61,000. The market value of the land was determined to be $85,000.
The company acquired $38,000 cash from the issue of common stock. This means that individuals or investors provided funds to the company in exchange for ownership (shares) in the company.
Maben Company borrowed $32,000 cash from National Bank. This indicates that the company obtained a loan from the bank, and it is obligated to repay the borrowed amount in the future.
The company earned cash revenues of $56,000 for performing services. This represents the income generated by providing services to customers or clients. The revenue increases the company's cash balance.
Maben Company paid $49,000 cash for various expenses. This includes costs such as salaries, utilities, supplies, and other operating expenses. The payment decreases the company's cash balance.
A $1,800 cash dividend was paid to the stockholders. This means that the company distributed a portion of its profits to the shareholders as a return on their investment.
An additional $28,000 cash was acquired from the issue of common stock. This indicates that the company issued more shares of common stock and received cash in return.
The company paid $8,000 cash to reduce the principal balance of the bank note. This represents a partial repayment of the loan obtained from the bank.
Maben Company paid $61,000 cash to purchase land. This implies that the company acquired a piece of land for its operations or as an investment.
It was determined that the market value of the land is $85,000. This is the estimated value of the land based on market conditions and comparable sales. It provides insight into the company's assets and potential future value.
Overall, these events highlight the inflow and outflow of cash, financing activities, revenue generation, and the acquisition of assets during Maben Company's first year of operation.
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