Let C(t) be the concentration of a drug in the bloodstream. As the body eliminates the drug, C(t) decreases at a rate that is proportional to the amount of the drug that is present at the time. Thus C 0 (t) = −2kC(t), where 2k is a positive number. Here is it is half of the elimination constant of the drug. (a) If Co is the concentration at time t = 0, find the concentration at time . (b) If the body eliminates half the drug in 30 hours, how long does it take to eliminate 80% of the drug?
Answers
Answer:
See explanation below
Step-by-step explanation:
In this case, let's answer this by parts:
a) Concentration at time t when Co is concentration at t = 0:
In this case, we will use the initial expression but without the 2, so:
C(t) = -kC
In this case, we want to know the concentration at time t so:
C'(t) = -kC(t) derivating:
dC/dt = -kC
dC/C = -kdt From here, we can do integrals so:
lnC = -kt + C₁ (1)
Now, it's time to replace t = 0 and C = C₀:
lnC₀ = -k(0) + C₁
lnC₀ = C₁ (2)
Replacing (2) in (1) we have:
lnC = -kt + lnC₀
lnC - lnC₀ = -kt
ln(C/C₀) = -kt
C/C₀ = e^(-kt)
C(t) = C₀ e^(-kt) (3)
This is the expression for C at given time t.
2. time to eliminate 80% of the drug:
With the first data, we need to calculate the value of k, which will be constant at any given time so:
C(t) = C₀ e^(-kt)
0.5C₀ = C₀ e^(-30k)
0.5 = e^(-30k)
ln(0.5) = -30k
k = 0.02310
Now with this value we can calculate the time to eliminate 80% of the drug or simply in other words, that we just have a remaining of 0.2C₀:
0.2C₀ = C₀ e^(-0.0231t)
ln(0.2) = -0.0231t
-ln(0.2) / 0.0231 = t
t = 69.67 h
This is the time to eliminate 80% of the drug
Related Questions
IF A SOUP RECIPE YIELDS 20 GALLONS, HOW MANY 5-FLUID OUNCE PORTIONS WILL THE RECIPE YIELD?
Answers
The number of 5 fluid ounce portions needed in 20 gallons is a total of 512 portions
Calculating the number of ounce portions neededTo solve this problem, we first need to convert the volume of the soup recipe from gallons to fluid ounces, and then divide by the size of each portion to find the total number of portions.
Given that
1 gallon = 128 fluid ounces
Therefore, the recipe yields:
20 gallons x 128 fluid ounces per gallon = 2560 fluid ounces
Now, we can find the number of 5-fluid ounce portions by dividing the total volume by the portion size:
2560 fluid ounces / 5 fluid ounces per portion = 512 portions
Therefore, the soup recipe yields 512 portions of 5 fluid ounces each.
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The ratio of 5 to 15
Answers
Answer:
the ratio of 5 to 15 is
1/3 hope i helped please check out my latest question i need help with homework
Step-by-step explanation:
its simplified
On his way out to meet a friend for lunch, David realized that his financial record was not up to date. He notices that he forgot to record three transactions. The first transaction was on August 2nd in the amount of $12.32, another transaction on that same day in the amount or $52.34, and finally a transaction on August 8th in the amount of $85.35. Determine David's balance carried forward for the 8th of August using the table below and the information provided. A check register. The Balance on August fifth is 1,049 dollars and 16 cents. a. $975.32 b. $899.15 c. $1,049.16 d. $848.84
Answers
Answer:
b
Step-by-step explanation:
add the three numbers together then minus from the main total
Answer:
B. $899.15
Step-by-step explanation:
Plz plz hurry plz hurry plz hurry
Answers
Answer:
C
I took the same assignment, have a nice day.
this as a fraction in simplest form
Answers
Answer:
-1/2
Step-by-step explanation:
i used my calculator. i cant really give a explanation
A bag contains 14 yellow balls, 2 violet balls, and 9 red balls. You pick one without looking. Explain the probability that the marble will be either yellow or violet. * 10 points
Answers
Answer:
yell 14:25 violet 2:15 for both it would be 16:25
Step-by-step explanation:
so there is a total of 25
Ullany TVd How much 20k stamps can #2.00 buy
Answers
Answer: 4000
Step-by-step explanation:
Perform the following operation, and report the answer to the correct number of significant figures. 3.47 x 6.7
Answers
Answer:
23
Step-by-step explanation:
3.47 = 3 sig. figs.
6.7 = 2 sig. figs.
Since these two numbers are being multiplied, you would round to the smallest number of sig. figs. of the two. In this case, it would be 2 significant figures.
3.47 * 6.7 = 23.249 (dont forget to round to 2 sig. figs. ) --> 23
Verify algebra radically if the function is even, odd, or neither.Need help with #7
Answers
SOLUTION
(7). For a function to be even, then
\(f(x)=f(-x)\)And if a function is odd, then
\(f(x)=-f(-x)\)Now, let us check
\(\begin{gathered} f(x)=x\sqrt[]{4-x^2} \\ f(-x)\text{ becomes , that is replacing }x\text{ with -}x \\ f(-x)=-x\sqrt[]{4-(-x)^2} \\ f(-x)=-x\sqrt[]{4-x^2} \\ So,\text{ }f(x)=x\sqrt[]{4-x^2}\text{ and }f(-x)=-x\sqrt[]{4-x^2}\text{ } \\ we\text{ can s}ee\text{ that }f(x)\ne f(-x) \end{gathered}\)Hence, the function is not even.
Let's check for odd
\(\begin{gathered} \text{For odd} \\ f(x)=-f(-x) \\ f(x)=x\sqrt[]{4-x^2}\text{ } \\ -f(-x)=-(-x\sqrt[]{4-(-x)^2} \\ -f(-x)=-(-x\sqrt[]{4-x^2} \\ -f(-x)=x\sqrt[]{4-x^2} \\ \text{Now we can s}ee\text{ that }f(x)=x\sqrt[]{4-x^2}\text{ and }-f(-x)=x\sqrt[]{4-x^2} \\ So,\text{ }f(x)=-f(-x) \end{gathered}\)Hence the function is odd
Ok now what do I press?
Answers
Answer:
Notification
Step-by-step explanation:
A professor of philosophy hypothesizes that an introductory course in logic will affect college students with their other studies. To test this hypothesis, a random sample of 25 first year students is selected. These students are required to complete a logic course during their first year. At the time of graduation, the final GPA is computed or each of these students. The mean GPA for this sample is 2.58 with a SS of 6.
Required:
Can the professor conclude that the grades for the sample were significantly different from the rest of the graduating class, which had an average GPA of 2.33?
Answers
Answer:
NO.
Step-by-step explanation:
The Professor's hypothesis:
An introductory course in Logic will affect college students with their other studies (will affect their Great Point Average - GPA).
25 students are used as the experimental group while the rest of the class are the control group.
The mean GPA in a sample size (SS) of 6 is = 2.58
The mean GPA in the full sample size of 25 would be = 10.75 by crossmultiplying.
This makes me believe the question was written wrongly. I assume SD (standard deviation) of 0.6 instead of SS (sample size) of 6.
Going by this, if standard deviation is 0.6 then the interval within which the GPA of the experimental group (the 25 students) falls is:
[2.58 - 0.6] to [2.58 + 0.6]
= 1.98 to 3.18
The rest of the graduating class (the control group) had a mean GPA of 2.33
Can the professor conclude that the GPA for the sample is significantly different from that of the control group?
The answer is NO because the GPA of the control group falls within the GPA interval of the experimental group!
After Verifying that the functions 1 2 satisfy the corresponding homogeneous equation of the given equation, find a particular solution of the non-homogeneous equation and then the general solution of the equation .
x²y'' + xy' + (x² - 0.25 ) y = 3x √xsinx
x> 0
y1(x) = sin (x) / √x
y2(x) = cos (x) / √x
Answers
To find a particular solution of the non-homogeneous equation and the general solution of the equation, we can use the method of variation of parameters.
First, let's find the Wronskian of the homogeneous solutions y1(x) and y2(x):
W(y1, y2) = | y1 y2 |
| y1' y2' |
We have y1(x) = sin(x) / √x and y2(x) = cos(x) / √x. Differentiating these functions, we get:
y1'(x) = (cos(x) / √x - sin(x) / (2√x^3))
y2'(x) = (-sin(x) / √x - cos(x) / (2√x^3))
Substituting these values into the Wronskian:
W(y1, y2) = | sin(x) / √x cos(x) / √x |
| (cos(x) / √x - sin(x) / (2√x^3)) (-sin(x) / √x - cos(x) / (2√x^3)) |
Expanding the determinant:
W(y1, y2) = (sin(x) / √x) * (-sin(x) / √x - cos(x) / (2√x^3)) - (cos(x) / √x) * (cos(x) / √x - sin(x) / (2√x^3))
Simplifying:
W(y1, y2) = -1 / (2√x)
Now, we can find the particular solution using the variation of parameters formula:
y_p(x) = -y1(x) * ∫(y2(x) * g(x)) / W(y1, y2) dx + y2(x) * ∫(y1(x) * g(x)) / W(y1, y2) dx
Here, g(x) = 3x√xsin(x). Substituting the values:
y_p(x) = -((sin(x) / √x) * ∫((3x√xsin(x)) * (-1 / (2√x))) dx + (cos(x) / √x) * ∫((3x√xsin(x)) / (2√x)) dx
Simplifying the integrals:
y_p(x) = -(∫(-3sin^2(x)) dx) + (∫(3xcos(x)sin(x)) dx)
Integrating:
y_p(x) = 3/2 (xsin^2(x) - cos^2(x)) - 3/2 (xcos^2(x) + sin^2(x)) + C
Simplifying:
y_p(x) = 3x(sin^2(x) - cos^2(x)) + C
The general solution of the equation is given by the sum of the homogeneous solutions and the particular solution:
y(x) = C1 * (sin(x) / √x) + C2 * (cos(x) / √x) + 3x(sin^2(x) - cos^2(x)) + C
where C1, C2, and C are arbitrary constants.
5x²-11x +6 . factories the expression
Answers
Answer:
5
x
2
−
11
(
x
)
+
6
Step-by-step explanation:
\(5x^2-11x+6\\\\=5x^2-5x-6x+6\\\\=5x(x-1) - 6(x-1)\\\\=(x-1)(5x-6)\)
Which is equivalent to
Answers
Answer:
2·2·2·2 = 16
Step-by-step explanation:
everytime a number is raised by another, that means you are going to multiply the base number times itself as many times as the exponents tells you. this is a little but tricky to explain, so let me give you some examples:
2² → in this case the base number is 2 and the exponent is 2 as well, so you will multiply 2 times itself, 2 times:
2² = 2 · 2 = 4
2³ → in this case the base number is 2 and the exponent is 3, so you will multiply 2 times itself, 3 times:
2³ = 2 · 2 · 2 = 8
In the question asked, 2 is being raised by 4, so you will multiply 2 times itself, 4 times:
2^4 = 2·2·2·2 = 16
the same format will be used regardless of the base number and the exponent
i hope this helps! :)
I need help as soon as posible pls
Answers
which function BEST represents the graph shown?
A) y=2x +4
B) y=4x +2
C) y=2x -4
D) y=4x -2
Answers
What is an equation of the line that passes through the point ) (8,−5) and is parallel to the line
5x+4y=24?
Answers
By rearranging the equation, we get the equation of the line parallel to 5x + 4y = 24 that passes through the point (8, -5) as y = (-5/4)x + 5.To find the equation of a line parallel to another line, we need to determine the slope of the given line.
The equation of a line can be written in slope-intercept form as y = mx + b, where m represents the slope.
To determine the slope of the given line 5x + 4y = 24, we need to rearrange the equation in slope-intercept form. First, subtract 5x from both sides: 4y = -5x + 24. Next, divide all terms by 4: y = (-5/4)x + 6. Therefore, the slope of the given line is -5/4.
Since the line we are looking for is parallel to this line, it will also have a slope of -5/4. Now we can use the point-slope form of a line to find the equation. The point-slope form is given as y - y1 = m(x - x1), where (x1, y1) represents the given point (8, -5) and m is the slope.
Substituting the values into the equation, we have y - (-5) = (-5/4)(x - 8). Simplifying further, y + 5 = (-5/4)x + 10.
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question is in the image below
Answers
The perimeter of Sam's string is 178 inches.
Given information:
Sam has a rectangular shaped window.
Length = 65 inches.
Width = 24 inches.
To find the perimeter:
you can use the formula:
Perimeter = 2 x (Length + Width)
Substituting the values into the formula, we have:
Perimeter = 2 x (65 + 24)
Perimeter = 2 x 89
Perimeter = 178 inches
Therefore, the perimeter of the rectangular window is 178 inches.
So, the perimeter of the rectangular window is 178 inches. This means that if you were to walk along the outline of the window, you would cover a total distance of 178 inches. It's important to note that the perimeter represents the total length of all the sides combined, and it is measured in the same unit (in this case, inches) as the length and width of the window.
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what decimal is equivalent to 41 over 100 (pls keep it simple i am only in 5th grade )
Answers
Answer: 0.41
Step-by-step explanation:
To find the decimal point of a fraction, divide the numerator (the top half of the fraction) by the denominator (the bottom half of the fraction).
41 over 100 as a decimal point would be 41 divided by 100
Which produces the equivalent decimal, 0.41
P.S this is also how you find the percent of a number. To get the percent, move the decimal point 2 digits over (0.41 to 41.) and then add the percentage sign to the end of the number (41%)
0.41 = 41%
so 41 over 100 is 0.41, and 41 is also 41% of 100 (per cent means per 100)
Best of luck in 5th grade :)
2 In the grocery store, eggs are sold in cartons of 12. Write five
ordered pairs made from the corresponding terms of these
two patterns, based on selling 0 to 4 cartons of eggs.
Pattern A: number of cartons sold
Pattern B: number of eggs sold
Plot the points in the coordinate plane to the right.
Describe the relationship between the coordinates of the
ordered pairs.
Answers
The ordered pairs is as follow:
(0, 0)
(1, 12)
(2, 24)
(3, 36)
(4, 48)
The relationship is a linear proportional relationship
How to find the relationshipInformation from the problem include:
eggs are sold in cartons of 12The equation is set up using the information given
number of eggs sold (y) = 12 x number of cartons sold (x)
y = 12x
the ordered pair is as follow: (Pattern A, Pattern B)
(0, 0)
(1, 12)
(2, 24)
(3, 36)
(4, 48)
The graph of the proportional relationship is attached
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Quadrilateral YFGT can be mapped onto quadrilateral MKNR by a translation. If TY = 2, find RM.
Answers
Based on the information given, we can conclude that RM = 2, but we cannot determine the lengths of the other sides of the quadrilaterals without further information.
Given that quadrilateral YFGT can be mapped onto quadrilateral MKNR by a translation, we can use the information to determine the length of RM.
A translation is a transformation that moves every point of a figure by the same distance and in the same direction. In this case, the translation is such that the corresponding sides of the quadrilaterals are parallel.
Since TY = 2, and the translation moves every point by the same distance, we can conclude that the distance between the corresponding points R and M is also 2 units.
Therefore, RM = 2.
By the properties of a translation, corresponding sides of the two quadrilaterals are congruent. Hence, side YG of quadrilateral YFGT is congruent to side MK of quadrilateral MKNR, and side GT is congruent to NR. However, the given information does not provide any additional details or measurements to determine the lengths of these sides.
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Tina is having a party with 11 of her friends she wants each person including herself to get 1/4 of a sandwich .how many sandwiches will she need to order for her party?
(There are 12 people)
Answers
Answer:
3
Step-by-step explanation:
Jack is taller than Pater and Bill is shorter than Jack. what is accurate?
Bill is taller than Peter
Answers
(-5, -1), 6
Write an equation of a circle with the given center & radius
Answers
Step-by-step explanation:
The equation of a circle with the given center and radius.
center = (-5,-1) and radius is 6
x²-y²-10x-2y-6=0.
What is the equation of circle?
The equation of the circle is the equation which is used to represent the circle in the algebraic equation form with the value of center point in the coordinate plane and measure of radius.
The standard form of the equation of the circle can be given as,
Here (h,k) is the center of the circle and (r) is the radius of the circle.
The equation of a circle with the given center and radius. center (-5,-1) and radius 6 has to be written. Use the above equation,
Thus, the equation of a circle with the given center and radius.
center (-5,-1) and radius is 6
x²-y²-10x-2y-6=0.
Line segment Q R , Line segment R S and Line segment S Q are midsegments of ΔWXY.
Triangle R Q S is inside triangle X Y W. Point R is the midpoint of side X Y, point S is the midpoint of side Y W, and point Q is the midpoint of side X W. The length of Q R is 2.93 centimeters, the length of R S is 2.04 centimeters, and the length of Q S is 2.28 centimeters.
What is the perimeter of ΔWXY?
11.57 cm
12.22 cm
12.46 cm
14.50 cm
Answers
Answer:
14.50 cm
Step-by-step explanation:
Based on the midsegment theorem:
The midsegment connecting two sides of triangle is parallel to the third side of the triangle and the length of the midsegment line is half the length of the third side parallel to the midsegment.
From the diagram ;
QR // ZY
XY = 2 * 2.93 = 5.86
RS // XZ
XZ = 2 * 2.04 = 4.08
QS // XY
XY = 2 * 2.28 = 4.56
The perimeter :
(XY + XZ + XY)
5.86 + 4.08 + 4.56
= 14.50 m
Answer:
d
Step-by-step explanation:
What meaning of the statement this?
Answers
Note that the notation "∪C = {x : x ∈ for some S ∈ C} = ∪ { S:S ∈ C}" represents a mathematical statement involving sets.
What is the explanation of this ?∪C : This represents the union (∪) of the sets in C.
{x : x ∈ for some S ∈ C}: This is the description or definition of the elements in the set formed by the union of sets in C.
It states that an element x belongs to the union of sets in C if and only if x belongs to at least one set S that is an element of the set C.
= ∪{ S:S ∈ C} : This means that the union (∪) of sets in C is equal to the union of all sets S that belong to the set C.
In summary, the statement is saying that the union of sets in C consists of all elements that belong to at least one set in C. It is the combined collection of elements from all sets in C.
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I WILL GIVE BRAINLIEST
How can you make a 95% confidence interval smaller without changing the confidence level?
I NEED EXPLANATION
Answers
Answer:
In Picture
Step-by-step explanation:
In Picture
Sorry if you cant read cursive :> I hope this helped :D
What are the new coordinates if the figure were rotated 90 degrees counterclockwise
Answers
Answer:
third option
Step-by-step explanation:
under a counterclockwise rotation of 90° about the origin
a point (x, y ) → (y, - x )
Then
A (- 1, - 2 ) → (- 2, - (- 1) ) → (- 2, 1 )
B (2, - 2 ) → (- 2, - 2 )
C (1, - 4 ) → (- 4, - 1 )
The new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)
How to determine the new coordinates rotating by 90 degrees counterclockwiseFrom the question, we have the following parameters that can be used in our computation:
The figure,
Where, we have
A = (-1, -2)
B = (2, -2)
C = (1, -4)
The rule of 90 degrees counterclockwise is
(x, y) = (-y, x)
Using the above as a guide, we have the following:
A = (2, -1)
B = (2, 2)
C = (4, 1)
Hence, the new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)
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Montel Edwards bought a 20-oz package of ham for $8.75. He can buy a 3-ib package of ham for $15.60. How much will he save per ounce by buying the 3-ib. package of
ham instead of the 20-oz. package (Note: 1 lb. = 16 ounces)?
9.6 cents ter ounce
10.5 cents per ounce
11.3 cents per ounce
12.8 cents per ounce
None of these choices are correct.
Answers
The 20-oz ham is $8.75/20 ounces = $0.4375/ounce
The 3-lb ham is 3 x 16 ounces = 48 ounces. Cost is $15.60/48 ounces = $0.325/ounce.
The difference in cost per ounce is 0.4375 - 0.325 = $0.1125 = 11.3 cents/ounce, rounded.
Suppose P(x) = 3x 2−4x−7 is a quadratic function and we suspect that 8 3 is a zero of P(x). How can we confirm our suspicion?
Answers
P(8/3) is not equal to zero, we can conclude that 8/3 is not a zero of P(x). Therefore, our suspicion was incorrect.
What is quadratic equation and how to solve it ?
A quadratic equation is a second-degree polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable.
To solve a quadratic equation, there are different methods, such as factoring, completing the square, and using the quadratic formula. The quadratic formula is the most general method and can be used for any quadratic equation.
It states that the solutions to the equation ax^2 + bx + c = 0 are given by the formula
x = (-b ± sqrt(b^2 - 4ac)) / (2a).
We can use this formula to find the roots of the equation by substituting the values of a, b, and c into the formula and simplifying.
To confirm if 8/3 is a zero of the quadratic function P(x) = 3x^2 - 4x - 7, we can substitute 8/3 for x in the equation and check if the resulting expression is equal to zero. If P(8/3) equals zero, then we can confirm that 8/3 is indeed a zero of P(x).
P(8/3) = 3(8/3)^2 - 4(8/3) - 7
= 3(64/9) - 32/3 - 7
= 64/3 - 32/3 - 21/3
= 11/3
Since P(8/3) is not equal to zero, we can conclude that 8/3 is not a zero of P(x). Therefore, our suspicion was incorrect. If we want to find the zeros of P(x), we can use the quadratic formula or factor the equation into (3x + 1)(x - 7) = 0 to get the roots x = -1/3 and x = 7.
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