Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response of a particular drug's effects. The concentration, C, in mg/L, of a particular medication after being injected into a patient can be given by the function C of t is equal to the quantity negative 10 times t squared plus 50 times t end quantity over the quantity t squared plus 4 times t plus 3 end quantity comma where the time, t, is hours after injection. Part A: What is the domain of the function C(t) based on the context of the problem? Show all necessary calculations. (5 points) Part B: Graph the function to determine the greatest concentration of the medication that a patient will have in their body. (5 points)
Answers
Graphs are used to show the relationship between variables, where the variables are represented by a pair of axes.
The domain of the function is [tex]t \ge 0[/tex] The greatest concentration of the medication is 5mg/LGiven that:
[tex]C(t) = \frac{-10t^2 + 50t}{t^2 + 4t + 3 }[/tex]
(a): The domain of the function
Because the medication concentration C(t) is a function of time (t), the domain is the possible values t can take.
t, cannot take negative values (i.e. it is not possible to have a negative time).
The least possible value of t is 0
So, the domain of the function based on the context is:
[tex]t \ge 0[/tex]
(b) The greatest concentration of the medication
From the graph (see attachment), the maximum y-value is 5.
Hence, the greatest concentration of the medication is 5 mg/L
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A function assigns the values. The greatest concentration of the medication that a patient will have in their body is when the time is t=1.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
A.) Given the function of the concentration of medication in the body as to[tex]C(t)=\ \frac{\left(-10t^{2}+50t\right)}{t^{2}+4t+3}[/tex] where t is the time. Since the time can not be negative, therefore, the domain of the function is t≥0.
B.) The graph of the function can be plotted as shown below. Now, the greatest concentration of the medication that a patient will have in their body is when the time is t=1.
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Related Questions
Simplify square root of -200
Answers
Answer:
14.1421356i
Step-by-step explanation:
hope it helps
Seven teenagers were asked what they charge hourly for babysitting,
The results are shown below. What is the median of these prices?
$8.00, $8.50, $9.00, $9.25, $9.50, $10.75, $11.00
Answers
Median- is the middle value whereby the values are place in order (ascending)
$9.25 is the median of these prices
Solve for M
-3+m/ 9 = 10
Answers
Step-by-step explanation:
-3+m/9=10
m/9=10+3
m/9=13
m=13×9
m=117
Note:if you need to ask any question please let me know.
(4) ^ (1/3) * (3 ^ (1/3) * 3 ^ (1/2)) ^ 7 / (9 ^ (3/4))
Answers
Answer:
[tex] \sqrt[3]{4} \times {3}^{ \frac{35 \sqrt{3} }{54} } [/tex]
Step-by-step explanation:
attached
can anyone help me solve this function please?
Answers
Answer:
f(-5) = 19
Step-by-step explanation:
f(t) = -3t+4
Let f(t) = 19
19 = -3t+4
Subtract 4 from each side
19 - 4 =-3t+4-4
15 = -3t
Divide each side by -3
15/-3 = -3t/-3
-5 = t
Answer:
the answer is -5
Step-by-step explanation:
F(t)=-3(t)+4
it told you that F(t) is equal to 19
so -3*-5=15+4=19
Find the coordinates of the image of J (−5, −1) after the translation (x, y) → (x − 2, y).
A. (−7, −3)
B. (−5, −3)
C. (−3, −1)
D. (−7, −1)
Answers
Hope it helpss
The coordinates of the image of J (−5, −1) after the translation (x, y) → (x − 2, y) will be (−7, −1). Then the correct option is D.
What is a transformation of a point?A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.
The rule of the translation is given below.
(x, y) → (x − 2, y)
The coordinates of the image of J (−5, −1). Then the location of the point J after the translation will be
(x, y) → (x − 2, y)
(−5, −1) → (−5 −2, −1)
(−5, −1) → (−7, −1)
The coordinates of the image of J (−5, −1) after the translation (x, y) → (x − 2, y) will be (−7, −1). Then the correct option is D.
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At a competition with 7 runners, medals are awarded for first, second, and
third places. Each of the 3 medals is different. How many ways are there to
award the medals?
Decide if this is a permutation or a combination, and find the number of ways
to award the medals.
Answers
Answer:
35 different combinations
Step-by-step explanation:
This would be a combination because the same person cannot get all three medals so permutation is not the correct way to calculate this. We use the formula C(n,r)=(nr)=n!(r!(n−r)!)=? where n is the number of total objects and r is the number of objects taken from the total.
brainliest pls . . . uwu
Describe a relationship between two sets that you can describe mathematically
Answers
Answer:
LOVE and CARING for each other
Step-by-step explanation:
What does heredity mean?
DNA make RNA, and RNA makes proteins
a human genetic disorder
traits passed down from parent and grandparents to offspring
the process of DNA replicating into two strands
Answers
A piece of wire 6 cm long weighs 30 grams. What is the weight of an 8 m length of the same wire?
A) 400 grams
B) 425 grams
C) 640 grams
D) 4000 grams
Answers
Answer:
4000 gm
Step-by-step explanation:
We can use ratios to solve
Change 8 m to cm
8m * 100cm/1m = 800 cm
6 cm 800 cm
------------- = ------------
30 grams x gm
Using cross products
6 * x = 800 * 30
6x = 24000
Divide by 6
6x/6 = 24000/6
x = 4000 gm
Which graph shows the function f(x) = x with an input of f(x – 3)?
Answers
the number 126 is divisible by what numbers ? 2,3,4,5,6,9,10
Answers
Answer:
1,
Step-by-step explanation:
You may also be interested to know that all the numbers that 126 is divisible by are also known as the factors of 126. Not only that, but all the numbers that are divisible by 126 are the divisors of 126.
Given that
a
= 3 cm and
b
= 21 cm, work out
θ
rounded to 1 DP.
Answers
Answer:
I am sorry I not no
this question
Step-by-step explanation:
sorry dear friend
Xian and his cousin Kal both collect stamps. Xian has 52 stamps, and Kal has 68 stamps. The boys recently
joined different stamp-collecting dubs. Xian's club will send him 20 new stamps per month. Kai's club will
send him 16 new stamps per month. After how many months will Xlan and Kal have the same number of
stamps? How many stamps will each have?
Answers
Answer:
In 4 months, they will both have 132 stamps.
Step-by-step explanation:
Let x = # of months
52 + 20x = 68 + 16x
4x = 16
x = 4
Plug x value into both expressions and see if it checks out
52 + 20(4) = 68 + 16(4)
52 + 80 = 68 + 64
132 = 132
Perform the indicated operations. Write the answer in standard form, a+bi.
5 - 3i / -2-9
Answers
[tex] \huge \boxed{\mathfrak{Answer} \downarrow}[/tex]
[tex] \large \bf\frac { 5 - 3 i } { - 2 - 9 } \\ [/tex]
Subtract 9 from -2 to get -11.
[tex] \large \bf \: Re(\frac{5-3i}{-11}) \\ [/tex]
Divide 5-3i by -11 to get [tex]\sf-\frac{5}{11}+\frac{3}{11}i \\ [/tex].
[tex] \large \bf \: Re(-\frac{5}{11}+\frac{3}{11}i) \\ [/tex]
The real part of [tex]\sf-\frac{5}{11}+\frac{3}{11}i \\ [/tex]is [tex]\sf-\frac{5}{11} \\ [/tex].
[tex] \large \boxed{\bf-\frac{5}{11} \approx -0.4545..} \\ [/tex]
Answer:
[tex] \frac{5 - 3i}{ - 2 - 9} \\ = \frac{ 5 - 3i}{ - 11} \\ = \frac{5}{ - 11} + \frac{3i}{11} \\ thank \: you[/tex]
Picture shown!
Complete the remainder of the table for the given function rule:
y=-x-9
x | -2 -1 0 2
y |-7 [?] [ ?] [? ] [? ]
Answers
Step-by-step explanation:
-8
-9
-10
-11
just subtituted the remaining values of x.
Answer:
x= -1 —> y= –8
x=0 —> y= –9
x=1—> y= –10
x=2—>y= —11
Step-by-step explanation:
x= -1 —>y= -(-1)-9= +1-9 = –8
x=0 —> y= -(0)-9= –9
x=1—> y= -(1)-9= -1-9= –10
x=2—>y= -(2)-9 = —11
I hope I helped you^_^
one half of a number plus 7
Answers
Answer:
1/2n + 7
n = unkown number
Step-by-step explanation:
Answer:
1/2(x) + 7
Step-by-step explanation:
x= unknown number
Pls help how do I solve this?
Answers
Answer:
area is just multiplication of sides so..
(4.2x^2 - 3xy) (5)
= 21 x^2 - 15 xy
doneeeeee
A soda company has determined that it's profit during lunch on a given day
could be modeled by the function P(s)=-1/3s^2+ 10s + 8 where P is the profit
and s is the number of sodas sold. Determine the amount of sodas that would
maximize profit and how much the company would earn.
Answers
9514 1404 393
Answer:
15 sodas will give a maximum profit of 83
Step-by-step explanation:
For quadratic ax^2 +bx +c, the maximum occurs at x = -b/(2a). Here, we have ...
a = -1/3, b = 10
x = -b/(2a) = -10/(2(-1/3)) = 15
The profit for sale of 15 sodas is ...
P(15) = (-1/3s +10)s +8 = (-1/3(15) +10)(15) +8 = 5(15) +8 = 83
The company would earn a maximum of 83 from sale of 15 sodas.
Mrs. Eskew saved her money for 32 years and had $4,119,184 in the bank. She used her money to go a vacation for a month and spent $978,349. How much did she have left after her vacation?
Answers
Answer:
$3,140,835
Step-by-step explanation:
4,119,184-978,349=3,140,835
hope this helped!
Simplify
(m^3)^6 - m^18
Answers
Answer:
x
2
+
x
−
7
x
+
2
Step-by-step explanation:
Answer:
0
Step-by-step explanation:
m^18 - m^18 (using power law of indices)
0
Subtract: 2 -(-6)
I don’t get it at all :/
Answers
Answer: 2 -(-6) = 2 + 6 = 8
* (+) - (-) = (+)
If helpful, brainliest please !
Answer and Step-by-step explanation:
If you're confused by what this expression means by looking at it, then try writing or saying out loud the expression.
Two minus negative 6. (2 - (-6))
We know from math that when two negative numbers multiply together, they result in a positive.
We have here the negative 1 (represented as just -, because it isn't necessary to include 1 in the expression) multiply the negative 6.
-1 * -6 = +6.
Now we have the expression 2 + 6.
Add them together.
2 + 6 =
8
8 is the answer.
#teamtrees #PAW (Plant And Water)
I hope this helps!
A goat is grazing outside of a rectangular barn that has dimensions 20 ft by 30 ft.
He's tied to a corner of the barn with a 12 ft rope. Find the grazing area of the goat.
Answers
Answer:
108π ft² or 339.29 ft²Step-by-step explanation:
Refer to attached picture.
The grazing area of the goat is 3/4 of area of circle with 12 ft radius:
A = 3/4(πr²) = 3/4(π*12²) = 108π or 339.29 ft²Tied to the corner
Means 1part among 4parts of circle or a quarter area
So grazing field
πr²-1/4πr²3/4πr²3/4(12)²π3/4(144)π108π339.3ft²What does the term "cube root" mean?
Answers
What is one of the best ways to stop procrastinating and study More
Answers
Answer:
use the two minute rule. you tell yourself you will study for two minutes or ten minutes and then if you're in a flow you keep going. hope this helps :)
5
Select the correct answer from each drop-down menu.
Amélie runs a bakery. She wants to find out whether her cake sales are affected by the weather conditions. She recorded the daily
temperature and the number of cakes she sold on different days of the year. The table shows the data she gathered.
Daily Temperature (°F) Cakes Sold
42
39
45
52
48
31
54
61
59
72
62
35
64
61
65
34
67
58
75
45
84
24
The correlation coefficient is close to
Based on this information, we can conclude that Amélie's cake sales are
affected by the daily temperature,
Reset
Next
Answers
The correct answer is : -0.7
A correlation coefficient is a statistical indicator of how well changes in one variable's value predict changes in another. There is a common tendency to assume that a change in one variable must be the result of a change in the other when the fluctuation of one variable predicts a similar fluctuation in another variable with high accuracy.
Correlation does not necessarily indicate cause, though. For instance, there might be an unidentified factor that has a similar impact on both variables. When it comes to consumer data patterns, being able to distinguish between correlation and causation can be useful and provide insightful information. In the context of marketing, the beer and diapers example is frequently used to illustrate this.
The correlation coefficient is close to: -0.7 (negative because there is an inverse relationship)
Based on this information, we can conclude that Amélie's cake sales are affected by the daily temperature.
Therefore, the final answer is : -0.7.
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cos(-x) = -cosx for all values of x.
True or false?
Answers
What’s the answer to this? Please send help
Answers
Answer:
C
Step-by-step explanation:
will mark brainliest if correct
Answers
Hi :)
6
6 is a whole number
6 is an integer
and 6 is a natural number
Answer:
Natural number is 6 here
Whole number is 6 too and so is integer. 4.9 and (-1/2) are a rational number while pi is an irrational number
Find the midpoint between two points on a coordinate plane whose coordinates are (5, 7) and (-3, 1).
A. (4,4)
B. 12,8)
C. (8,8)
D. (1.4)
Answers
Answer:
(1,4)
Step-by-step explanation:
To find the x coordinate of the midpoint, average the x coordinates of the endpoints
(5+-3)/2 = 2/2 =1
To find the y coordinate of the midpoint, average the y coordinates of the endpoints
(7+1)/2 = 8/2 =4
(1,4)
Answer:
D. (1.4)
Step-by-step explanation:
