A glucose solution is administered intravenously into the bloodstream at a constant rate r. As the glucose is added, it is converted into other substances and removed from the bloodstream at a rate that is proportional to the concentration at that time. Thus a model for the concentration C = C(t) of the glucose solution in the bloodstream is dC/dt = r - kC where k is a positive constant. Assuming that C0 < r/k, find lim t→[infinity] C(t) and interpret your answer
Answers
Answer:
\(C(t) =\dfrac{ r}{k} - \left (\dfrac{r-kC_{0}}{k} \right )e^{ -kt}\)
\(C(t) =\dfrac{ r}{k}- e^{ -kt}\) we can conclude that the function is an increasing function.
Step-by-step explanation:
Given that:
\(\dfrac{dC}{dt}= r-kC\)
\(\dfrac{dC}{r-kC}= dt\)
By taking integration on both sides ;
\(\int\limits\dfrac{dC}{r-kC}= \int\limits \ dt\)
\(- \dfrac{1}{k}In (r-kC)= t +D\)
\(In(r-kC) = -kt - kD \\ \\ r- kC = e^{-kt - kD} \\ \\ r- kC = e^{-kt} e^{ - kD} \\ \\r- kC = Ae^{-kt} \\ \\ kC = r - Ae^{-kt} \\ \\ C = \dfrac{r}{k} - \dfrac{A}{k}e ^{-kt} \\ \\\)
\(C(t) =\frac{ r}{k} - \frac{A}{k}e^{ -kt}\)
where;
A is an integration constant
In order to determine A, we have C(0) = C0
\(C(0) =\frac{ r}{k} - \frac{A}{k}e^{0}\)
\(C_0 =\frac{r}{k}- \frac{A}{k}\)
\(C_{0} =\frac{ r-A}{k}\)
\(kC_{0} =r-A\)
\(A =r-kC_{0}\)
Thus:
\(C(t) =\dfrac{ r}{k} - \left (\dfrac{r-kC_{0}}{k} \right )e^{ -kt}\)
b ) Assuming that C0 < r/k, find lim t→[infinity] C(t) and interpret your answer
\(C_{0} < \lim_{t \to \infty }C(t)\)
\(C_0 < \dfrac{r}{k}\)
\(kC_0 <r\)
The equation for C(t) can therefore be re-written as :
\(C(t) =\dfrac{ r}{k} - \left (\dfrac{r-kC_{0}}{k} \right )e^{ -kt}\)
\(C(t) =\dfrac{ r}{k} - \left (+ve \right )e^{ -kt} \\ \\C(t) =\dfrac{ r}{k}- e^{ -kt}\)
Thus; we can conclude that the above function is an increasing function.
Related Questions
Help! I’m confused and need help finding the answer!
Answers
Answer:
y=11x
Step-by-step explanation:
we use formula y2-y1/x2-x1 with 2 of the order pairs
22-11/2-1
11/1
11 is the slope
We find y intercept by finding when x is equal to zero and we subtract 11 until we find the 0 x unit since it goes down 11 every time
When x is zero y is zero so we write it like this
Y=11x
Hopes this helps please mark brainliest
PLEASE HELP ME ITS ALGEBRA THANK YOUUUU
Answers
Answer: 171 attendees
Step-by-step explanation:
I answered another similar question by you earlier, so I really hope you read through this explanation, as I will go far in depth. It's important you learn to do this so as not to simply skate through homework, then struggle with assessment.
For this problem, you have to find something called a unit price.
A unit price is the price in dollars per thing.
In this case, the price in dollars for the whole group is $132 for many things, 66 attendees.
Because 66 attendees costs $132, to find out how much money a single attendee costs, simply divide $132 by 66 to get 2$ for 1 attendee.
With this information, it is very straightforward to determine the number of attendees for $342. Simply divide $342 by $2 to get 171 attendees.
I really hope it helps :) and please, let me know if you want me to explain in more depth, the unit you are currently in is a fundamental part of early math, and it is important you understand it.
This year you earned $75,500. Last year you earned $72,400. What was the rate of change on your earnings since last year
Answers
Answer:
4.28%
Step-by-step explanation:
We Know
Last year you earned $72,400
This year you earned $75,500
What was the rate of change in your earnings since last year?
We Take
(75,500 ÷ 72,400) x 100 ≈ 104.28%
Then We Take
104.28 - 100 = 4.28%
So, the earning increased by about 4.28%.
There are 38 buses in the parking lot and each bus holds 74 people how many people are able to ride the buses
Answers
Answer:
2812 people
Step-by-step explanation: There are 38 buses and each holds 74 people so 38 x 74= 2812
Hope this helps :)
PLZZZ HELP!!!!!!!!!1
What is the median and Q1 of the data set represented on the plot?
Median = 30; Q1 = 20
Median = 33; Q1 = 20
Median = 30; Q1 = 25
Median = 33; Q1 = 25
Answers
Answer:
i cant put the picture
Step-by-step explanation:
d. Median=33;Q1=25 the median is represented by the line in between the two boxes. Q1 is represented by the line on the far left of the box in the picture Q1 is marked for quadrent 1 and m is for median
carry out the following subracting involving rational number 13/36-2/40
Answers
Answer:
14/45
Explanation:
Make the denominator of both fractions the same
13/36=130/360
2/40=18/360
130/360-18/360=112/360
112/360=14/45
A limousine company charges $1.50 per mile plus a mandatory $25 tip. Ms. Warwick gave the limousine driver a total of $62.50. What is the total miles driven and the equation to solve it?
Answers
Answer:
25 total miles the equation is 1.50x+25=62.50
Step-by-step explanation:
Answer:25 MILES driven
subtract 25 from 62.50 which is 37.50.
Then: Divide 37.50 to 1.5 which is 25.
Step-by-step explanation:
Find the slope of the line through the given points (-7, 7), (-1,10)
Answers
Answer:
The slope would be 1/2.
Step-by-step explanation:
When solving questions like these, make sure to plug in the points into the formula: \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}} = slope\) . y2 would stand for the y coordinate of the second point, y1 would stand for the y coordinate of the first point. While x2 would stand for the x coordinate of the second point and x1 for the x coordinate of the first point. Once plugged in, it should look like this: \(\frac{10-7}{-1-(-7)}\). That should then give you the slope of 1/2. Hope this helps!! :D
Which choice is the slope-intercept equation of the line shown below?5+(0.2)(-4, 0)X55-5
Answers
The line passes through the points (0,2) and (-4,0).
Determine the equation of line passing though the points.
\(\begin{gathered} y-2=\frac{0-2}{-4-0}(x-0) \\ y-2=-\frac{2}{-4}x \\ y=\frac{1}{2}x+2 \\ =0.5x+2 \end{gathered}\)So slope intercept form of equation for line is y = 0.5x + 2.
Option A is correct.
Can someone help and explain how to do this
Answers
Answer: yeah
Step-by-step explanation: So what you do is ask a question and then add a picture so people know what the fawk you talkin bout lol.
Consider parallelogram QRST below. Use the information given in the figure to find m
Answers
The missing values are
<UTQ = 41 degree
x= 1
<UQT = 47 degree
We have a parallelogram QRST.
We know that the opposite sides of the parallelogram is equal and parallel then
QR || ST
QT || SR
Then, <SRT = <RTQ (<UTQ) (alternate Interior Angle)
<UTQ = 41
Similarly, <UQT = <SRQ = 47
Now, RU = UT
2x + 1= 3
2x = 2
x= 1
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HELP NEEDED! Thanks if you do!!
Answers
Answer:
We conclude that:
csc (U) = 26 / 24
Step-by-step explanation:
Given
The angle ∠U The opposite of the angle ∠U = 24The hypotenuse = 26To determine
csc (U) = ?
Using the trigonometric ration
sin Ф = opposite / hypotenuse
substituting Ф = U, opposite = 24, hypotenuse = 26
sin (U) = 24/26
We know that: csc (U) = [1 ] / [sin(U)]
Therefore,
csc (U) = [1 ] / [sin(U)]
= 26 / 24
Therefore, we conclude that:
csc (U) = 26 / 24
Solve for x and y by substitution method
a) 0.4x-1.5=6.5
0.3x+0.2=0.9
b) x+y=8
2x-3y=1
Answers
Answer:
A
Step-by-step explanation:
Because if you simplify you get that
Answer:
15 and 4+4
Step-by-step explanation:
i think its correct
Twice the difference of a number and is 2equal to8 . Use the variable y for the unknown number.
Answers
The answer of the given question based on the equation is , the unknown number is 6.
What is Equation?An equation is the mathematical statement that asserts equality of the two expressions. It typically consists of the two expressions separated by equal sign " = ". The expressions can include variables, constants, and mathematical operations like addition, subtraction, multiplication, division, and exponentiation. Solving an equation involves finding the value(s) of the variable(s) that make the equation true.
The statement can be translated into an equation as follows:
2(y - 2) = 8
Simplifying the equation, we can distribute the 2 on the left-hand side:
2y - 4 = 8
Then, we can add 4 to both sides to isolate the variable:
2y = 12
Finally, we divide both sides by 2 to solve for y:
y = 6
Therefore, the unknown number is 6.
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Please help if you can, this is due in two days.
Answers
The lengths of side \(\overline{AB}\) and \(\overline{AC}\), found using the angle bisector theorem are;
AB = 28, AC = 42
What is the angle bisector theorem?The angle bisector theorem states that the bisector of an angle in a triangle, intersects the opposite side at a point such that the opposite side are divided into proportions that is equivalent to the ratio or proportion of the other two sides.
AB = x - 7
AC = x + 7
According to the angle bisector theorem, we get;
8/12 = (x - 7)/(x + 7)
8·(x + 7) = 12·(x - 7)
8·x + 8 × 7 = 12·x - 12 × 7
8·x + 56 = 12·x - 84
12·x - 8·x = 56 + 84 = 140
4·x = 140
x = 140 ÷ 4 = 35
x = 35
Therefore;
AB = 35 - 7 = 28
AC = 35 + 7 = 42
The correct option is therefore;
AB = 28, AC = 42
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What percent of 125 is 375?
A) 33.33%
B) 250%
C) 300%
D) 468.75%
Show work
Answers
Answer:
To find the percent of 125 that 375 is, we need to divide 375 by 125 and then multiply by 100.
375 / 125 = 3
So 375 is 3 times 125. Multiplying 3 by 100, we get:
3 * 100 = 300%
So the correct answer is C) 300%.
Succes!
Answer:
C) 300%
Step-by-step explanation:
Percent of 125 means the value of x/125.
Where x is the value 375.
375/125 = 3
3 * 1 =
3 * 100% = 300%
It can be mistaken as 33.33% since 125 is 33.33% of 375.
^^ This question is asking 125 is what percent of 375.
But remember, the question, 'What percent of 125 is 375?', is asking 375 is what percent of 125, not the other way around.
56. How many tangent lines to the curve \(y=x /(x+1)\) pass through the point (1,2)? At which points do these tangent lines touch the curve?
Answers
There are 2 tangent lines that pass through the point
\(y=\frac{1}{(-1+\sqrt{3)^2} } (x-1)+2\)
and
\(y=\frac{1}{(-1-\sqrt{3)^2} } (x-1)+2\)
Explanation:
Given:
\(y=\frac{x}{x+1}\)
The point-slope form of the equation of a line tells us that the form of the tangent lines must be:
\(y=m(x-1)+2\) \([1]\)
For the lines to be tangent to the curve, we must substitute the first derivative of the curve for \(m\):
\(\frac{dy}{dx} =\frac{d(x)}{dx}(x+1)-x^\frac{d(x+1)}{dx} \\ \\\)
\(\frac{dy}{dx} =\frac{x+1-x}{(x+1)^2}\)
\(\frac{dy}{dx}= \frac{1}{(x+1)^2}\)
\(m=\frac{1}{(x+1)^2}\) \([2]\)
Substitute equation [2] into equation [1]:
\(y=\frac{x-1}{(x+1)^2}+2\) \([1.1]\)
Because the line must touch the curve, we may substitute \(y=\frac{x}{x+1}:\)
\(\frac{x}{x+1}=\frac{x-1}{(x+1)^2}+2\)
Solve for x:
\(x(x+1)=(x-1)+2(x+1)^2\)
\(x^2+x=x-1+2x^2+4x+2\)
\(x^2+4x+1\)
\(x\frac{-4±\sqrt{4^2-4(1)(1)} }{2(1)}\)
\(x=-2\) ± \(\sqrt{3}\)
\(x=-2\) ± \(\sqrt{3}\) \(and\) \(x=-2-\sqrt{3}\)
There are 2 tangent lines.
\(y=\frac{1}{(-1+\sqrt{3)^2} } (x-1)+2\)
and
\(y=\frac{1}{(-1-\sqrt{3)^2} } (x-1)+2\)
What is the standard deviation of this data set ?Reporting 2 more decimal places than the original data. 69.2,85.2,85.2,73.8,57.9,42.6,59,67.2,85.2,61
Answers
Answer:6.986
Step-by-step explanation:
To find the standard deviation of a set of data I find it easiest to make a chart. First you must find the mean of your data. In this case it is 476.85. Then you must subtract the mean from each data point, and square each number. Now you take your new set of data that has been squared and find the mean of these numbers. This is 48.8006. Lastly, take the square root of this number. In this case your standard deviation is 6.986.
Answer: Standard deviation is 6.986.
Step-by-step explanation:
Given an data 69.2,85.2,85.2,73.8,57.9,42.6,59,67.2,85.2,61 and have to calculate standard deviation
To find the standard deviation of a set of data I find it easiest to make a chart. First you must find the mean of your data. In this case it is 476.85. Then you must subtract the mean from each data point, and square each number.
Now you take your new set of data that has been squared and find the mean of these numbers. This is 48.8006. Lastly, take the square root of this number.
In this case standard deviation is 6.986.
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2 Write 386 in expanded form
Answers
Answer:
300+ 80+6
Step-by-step explanation:
i think i not sure
where is 1/2x- y = 2 on a graph
Answers
Answer: in the 4th quadrant
Step-by-step explanation:
it needs to be in y=mx+b (slope form) so it would be
-y=-1/2x+2 then divide everything by -1 which is y=1/2 -2 b=-2 m=1/2 if you were to graph it, the line would be in the 4th quadrant24. This week, Cristina eamed P594.65 from selling burgers for 35 days. How much he will earn in 5 days?
A. P84.95
B. P94.95
C. P104.95
D. P114.95
25. You have four quizzes in your math subject in a quarter. You got 88.75 for the first quiz, 85.5, 90.5, and 87.25 in the second, third and fourth quizzes, respectively. What is your average in the four quizzes this quarter?
A. 86.5
B. 88
C. 89.5
D. 90 26. Amberich put P580.00 into a savings account for one year. The rate of interest on the account was 6.5%. How much was the interest for one year in pesos and centavos?
A. P67.70
B. P37.70
C. P57.70
D. P17.70
24. This week , Cristina eamed P594.65 from selling burgers for 35 days . How much he will earn in 5 days ?
A. P84.95
B. P94.95
C. P104.95
D. P114.95
25. You have four quizzes in your math subject in a quarter . You got 88.75 for the first quiz , 85.5 , 90.5 , and 87.25 in the second , third and fourth quizzes , respectively . What is your average in the four quizzes this quarter ?
A. 86.5
B. 88
C. 89.5
D. 90
26. Amberich put P580.00 into a savings account for one year . The rate of interest on the account was 6.5 % . How much was the interest for one year in pesos and centavos ?
A. P67.70
B. P37.70
C. P57.70
D. P17.70
Answers
Question 24 :
P594.65 : 35 days
P594.65/7 : 35/7 days
P84.95 : 5 days
⇒ A. P84.95
Question 25 :
88.75 + 85.5 + 90.5 + 87.25 / 4
352/4
88
⇒ B. 88
Question 26 :
I = P × r × t
I = 580.00 × 0.065 × 1
I = P37.70
⇒ B. P37.70
(v/5 is a fraction my thing is broken so i need to do that)
v/5 - 6 = -1
Answers
It should be noted that the value of v in the fraction v/5 - 6 = -1 is 25.
How to illustrate the information?It should be noted that from the information that's illustrated, it was written that:
v/5 - 6 = -1
The goal here is to simply calculate the value of v.
Add +6 to both sides
v/5 - 6 + 6 = -1 + 6
v / 5 = 5
Cross multiply
v = 5 × 5
v = 25
Therefore, it should be noted that the value of v in the fraction v/5 - 6 = -1 is 25.
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The mug is 5/8 full, the mug contains 3/4 of water find the capacity of the mug
Answers
The capacity of the mug is 1.2. The capacity of the mug can be found by using the equation C = (3/4) ÷ (5/8).
What is capacity?It is the maximum amount of output that can be produced in a given period of time. Capacity is usually expressed in terms of units per unit of time, such as gallons per minute or passengers per hour.
In this equation, 3/4 represents the amount of water in the mug, and 5/8 represents the amount the mug is full.
Let the capacity of the mug be x.
Given,
Mug is 5/8 full and contains 3/4 of water
So, 5/8 of the mug is filled with water
Therefore,
5/8 of x = 3/4
(5/8 )x = (3/4)
x = (3/4) × (8/5)
x = (24/20)
x = 1.2
Therefore, the capacity of the mug is 1.2.
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find the direction angle of the given vector. give your answer in degrees in the interval . round to the nearest hundredth (2 decimal places). give just the number without the degree symbol.
Answers
The Direction Angle Of The Given Vector is θ = 59.086
Given :
The Direction Angle Of The Given Vector. V <-3,5) Give Your Answer In Degrees In The Interval [0°, 360°). round to the nearest hundredth (2 decimal places). give just the number without the degree symbol.
what is Direction angle of vector ?
The direction angle of a vector v is the angle from the positive x -axis to v .using the arc tangent of the ratio of the vertical component of the vector and the horizontal component of the vector.
tan θ = b / a
= 5 / -3
= -5 / 3
= 1.67
θ = tan^-1 ( 1.67 )
θ = 59.086
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A number pattern has the rule divide by 3 the fifth term of the pattern is 2 what is the second term of the pattern.
Answers
1. Mildred Dunbar works as a waitress at Famous Foods.
She earns $1.75 per hour plus tips. Last week she
worked 39 hours and received $241.75 in tips. What was
her gross pay for the week?
Answers
Answer:
310
Step-by-step explanation:
1.75×39=68.25
241.75+68.25=310
Answer: $310.00
Explanation:
$1.75 × 39 = $68.25
$241.75 + $68.25 = $310.00
Find the volume of a pyramid with a square base, where the side length of the base is
10.6
in
10.6 in and the height of the pyramid is
12.3
in
12.3 in. Round your answer to the nearest tenth of a cubic inch.
Answers
Answer:
V = 460.68
Step-by-step explanation:
V=(lwh)/3
Volume = (1/3) * base area * height
In this case, the base of the pyramid is a square with a side length of 10.6 inches, so the base area can be calculated as:
Base area = side length * side length
Let's calculate the base area first:
Base area = 10.6 in * 10.6 in
Next, we'll substitute the values into the volume formula:
Volume = (1/3) * (10.6 in * 10.6 in) * 12.3 in
Calculating this expression will give us the volume of the pyramid. Rounding the answer to the nearest tenth of a cubic inch will provide the final result.
What are the values for the coefficients and constant term of 2 + 3x² - 5x?
a=
B=
C=
Answers
Answer:
a=3
b=-5
c=2
Step-by-step explanation:
Because first arrange them in decreasing order by their variables powers like this 3x²-5x+2 after that take the the coefficients
Triangle ABC has vertices at A(−3, 3), B(0, 7), and C(−3, 0). Determine the coordinates of the vertices for the image if the preimage is translated 3 units up.
A′(−3, 0), B′(0, 4), C′(−3, −3)
A′(−3, 6), B′(0, 10), C′(−3, 3)
A′(−6, 3), B′(−3, 7), C′(0, 0)
A′(0, 3), B′(3, 5), C′(0, 0)
Answers
Answer:
To translate triangle ABC 3 units up, we need to add 3 to the y-coordinate of each vertex:
A' = (-3, 3 + 3) = (-3, 6)
B' = (0, 7 + 3) = (0, 10)
C' = (-3, 0 + 3) = (-3, 3)
Therefore, the coordinates of the vertices for the image triangle A'B'C' are A'(-3, 6), B'(0, 10), and C'(-3, 3).
So the correct answer is: A′(−3, 6), B′(0, 10), C′(−3, 3).
Create two different 5 number summaries for the data below
A. 72, 56, 81, 84, 75, 26, 39, 62, 65, 66, 85, 71, 74, 68, 73, 66, 83, 60, 58, 72
B. 44, 45, 51, 51, 53, 53, 55, 57, 58, 62, 65, 66, 69, 69, 70, 73, 75, 77, 78, 79
Answers
The two different 5 number summaries for the data is shown in the table both data size is 20.
What is the box and whisker plot?A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.
It is given that:
Two data set:
Data set A:
72, 56, 81, 84, 75, 26, 39, 62, 65, 66, 85, 71, 74, 68, 73, 66, 83, 60, 58, 72
Population size: 20
Median: 69.5
Minimum: 26
Maximum: 85
First quartile: 60.5
Third quartile: 74.75
Data set B:
44, 45, 51, 51, 53, 53, 55, 57, 58, 62, 65, 66, 69, 69, 70, 73, 75, 77, 78, 79
Population size: 20
Median: 63.5
Minimum: 44
Maximum: 79
First quartile: 53
Third quartile: 72.25
Thus, the two different 5 number summaries for the data is shown in the table both data size is 20.
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