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
Read more about functions and graphs at:
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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.
Learn more about Function:
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Related Questions
please help me with this and explain your answer
Answers
Answer:
B
Step-by-step explanation:
t=4x+c
Since we are looking for x,
t-c=4x
Divide through by the coefficient of x which is 4
4x/4=t-c/4
Therefore, x=t-c/4
raise the quotient of r and 6 to the 3rd power!!!!!!!!! IF YOU HELP RIGHT AWAY YOU GET A BRAINLY THIS IS 7th GRADE!!!!!!!
Answers
Explanation:
The expression r/6 is the quotient of r and 6. The quotient is the result of a division problem. For example, the quotient of 100 and 25 is 4 because 100/25 = 4.
We'll then raise r/6 to the 3rd power to get the final answer (r/6)^3
We could rewrite it in its equivalent form (r/6)^3 = (r^3)/(6^3) = (r^3)/216, but the answer in bold is sufficient in my opinion.
What’s the answer? ANSWER THIS NOW PLEASE
Answers
Answer:
v=4
Step-by-step explanation:
-23=3v+9-11v
-23=9-8v
-32=-8v
v=4
Answer:
v=4
Step-by-step explanation:
-23=-8v+9
-23-9=-8v
-32=-8v
-32/-8=v two negatives make a positive
4=v
Samuel invested money in his bank account. He had a principal, P, of $100 in his account at the beginning of the period, which increased at a rate, r, of 0.15 per year. At the end of the period, he had interest, I, of $105 in his account. Use the simple interest formula I = Prt, to solve for the time, t, in months that it took to earn this amount.
Answers
Hey there! I'm happy to help!
Let's see what we have for each variable.
I = 105
P = 100
r = 0.15
Now, let's plug it in and solve for our t (time)
105=100(0.15)(t)
Swap sides so t is on the left.
100(0.15)(t)=105
Divide both sides by 100.
0.15t=1.05
Divide both sides by 0.15
t=700
So, we see that it takes 700 months to earn this amount.
Have a wonderful day and keep on learning! :D
The number of months that it took to earn this amount will be 84 months.
What is simple interest?Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.
I = (PRT)/100
Where P is the principal, R is the rate of interest in percentage, and T is the time.
Samuel invested money in his bank account.
He had a principal, P, of $100 in his account at the beginning of the period, which increased at a rate, R, of 0.15 per year.
At the end of the period, he had interest, I, of $105 in his account.
105 = 100 x 0.15 x t
t = 1.05 / 0.15
t = 7 years
The number of months that it took to earn this amount will be
⇒ 7 x 12
⇒ 84 months
The number of months that it took to earn this amount will be 84 months.
More about the simple interest link is given below.
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7. What is the perimeter of the
rectangle?
Answers
Answer:
I don't see anything but Perimeter is Length + Width × 2
Solve: VII multiplied by IX. Show your answer in standard form. Standard Number 1 Roman Numeral 5 V 10 50 100 500 1,000 X-003 A) 36 B) 63 C) 77
Answers
63
Step-by-step explanation:
i gotchu keep these coming
Please help me with this-
Answers
ALGEBRA 1 MATH PLEASE HELP !!!
Answers
Answer:
|x + 2|
Step-by-step explanation:
Translating to the left and right has the number on the inside with the variable. Adding goes left and subtracting goes right.
(if you want an explanation on why it's opposite like that then just comment)
Please send me an answer sheet for this paper.
Answers
Answer:
Q.1. x=8-5
x=3
Q.2. -3x=16-7
-3x=9
x=-9/3
x=-6
Q.3. 3p=6*7
3p=42
p=42/3
p=16
Q.4. 2(x+5)=24
2x+10=24
2x=24-10
2x=14
x=14/2
x=7
Step-by-step explanation:
For Q1.
1. x + 5 = 8
x = 8 - 5
x = 3
2. -3x + 7 = 16
-3x = 16 - 7
-3x = 9
x = 9/-3
x = -3
3. 3P/7 = 6
3P = 6*7
3P = 42
P = 42/3
P = 14
4. 2(x + 5) = 24
2x + 10 = 24
2x = 24 - 10
x = 14/2
x = 7
5. x/5 - 8 = 9
x/5 = 9 - 8
x = 5
For Q.2:
1. 12 + 4(x + 3(x + 4)) = 108
12 + 4(x + 3x + 12) = 108
12 + 4x + 12x + 48 = 108
60 + 16x = 108
6x = 108 - 60
x = 48/6
x = 8
2. 5x + 7(4 - (x + 3)) = 31
5x + 28 - x + 3 = 31
6x + 31 = 31
6x = 0
x = 0
3. 2(3y - 2(y + 5) + 3) = -4
2(3y - 2y + 10 + 3) = -4
2(y + 13) = -4
2y + 26 = -4
2y = 30
y = 15
4. 20 - 2(2x -(2 - x) + 10) = -44
20 - 2(2x - 2 + x + 10) = -44
20 - 2(3x + 8) = -44
20 - 6x - 16 = -44
4 - 6x = -44
-6x = -44 - 4
-6x = -48
x = -48/-6
x = 8
5. 5(3x - 4(x + 2) + 5(2x + 1)) = 60
5(3x - 4x - 8 + 10x + 5) = 60
5(3x - 4x + 10x - 8 + 5) = 60
5(9x - 3) = 60
45x -15 = 60
45x = 60 + 15
x = 75/45
x = 1.67
For Q.3:
1. x/2 + x/3 = 10
(3x + 2x)/6 = 10
5x/6 = 10
5x = 60
x = 12
2. 1/3(2x/7 - 1) = 3
1/3(2x - 7/7) = 3
2x - 7/7 = 3/(1/3)
2x - 7/7 = 1
2x - 7 = 7
2x = 14
x = 7
3. (P + 2/2) + ( 2P - 6/4) = 5
(2P + 4 + 2P - 6)/4 = 5
(4P - 2)/4 = 5
4P - 2 = 20
4P = 22
P = 5.5
4. x/3 - (2x + 1)/3 - (x - 3)/5
(x - 2x + 1)/3 - (x - 3)/5
(1 - x)/3 - (x - 3)/5
(5 - 5x - 3x - 9)/15
(-8x - 4)/15
5. (y - 2)/3 + (2y + 5)/5 - (y + 7)/3
5/3 + (2y + 5)/5
(25 + 6y + 15)/15
(40 + 6y)/15
Help me pleaseee!!
Would appreciate ^^
**BRAINLIST, thanks and points***
Answers
Answer:
4900
Step-by-step explanation:
because it is square root of 70 and it means
sol?
square of 70 =70²=70×70=4900
Answer:
22. 30
prime factorization of 30
2 × 3 × 5
so there is no simplification needed here
23. 126
2 × 3 × 3 × 7
simplification
2 × [tex]3^{2}[/tex] × 7
24. 4900
2 ×2 × 5 × 5 × 7 ×7
simplification
[tex]2^{2}[/tex] × [tex]5^{2}[/tex] × [tex]7^{2}[/tex]
25. 39204
2 × 2 × 3 × 3 × 3 × 3 × 11 × 11
simplification
[tex]2^{2}[/tex] × [tex]3^{4}[/tex] × [tex]11^{2}[/tex]
26 .
Yes 4900 is a square number it's square root is 70
you can even cross-check
70 × 70
= 4900
and even 39204 is a square number it's square root is 198
you can even cross-check
198 × 198
= 39204
Hence 2 numbers 4900 and 39204 are square numbers
27 .
i. highest common factor of 30 and 126
factors of 30 are 2 × 3 × 5
factors of 126 are 2 × 3 × 3 × 7
now find common between them
common factors are 2 and 3
so multiply 2 and 3
2 × 3
= 6
6 is the highest common factor
ii. 126 and 39204
factors of 126 are 2 × 3 × 3 × 7
factors of 39204 are 2 × 2 × 3 × 3 × 3 × 3 × 11 × 11
now find common between them
common factors are 2 × 3 × 3
= 18
18 is the highest common factor
28 .
1 . 126 and 4900
factors of 126 are 2 × 3 × 3 × 7
factors of 4900 are 2 ×2 × 5 × 5 × 7 ×7
make the pairs of the numbers
2 ×2 × 5 × 5 × 3 × 3 × 7 ×7
= 44100 least common multiple
ii. 4900 and 39204
factors of 39204 are 2 × 2 × 3 × 3 × 3 × 3 × 11 × 11
factors of 4900 are 2 ×2 × 5 × 5 × 7 ×7
make the pairs of the numbers
2 ×2 × 3 x 3 x 3 x 3 x 5 x 5 x 7 x 7 x 11 x 11
= 48024900 least common multiple
55 is the sum of 24 and Delia's age.
Use the variable d to represent Delia's age.
Answers
Answer:
d + 24 = 55
Step-by-step explanation:
hope this helps have a great day
9 + x + 1 + 2x
Can someone help me out with this :)
Answers
3x + 10
Step-by-step explanation:
9 + x + 1 + 2x
Combine like terms
2x + x = 3x
Combine like terms
9 + 1 = 10
We’re left with 3x + 10
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\text{9 + x + 1 + 2x}[/tex]
[tex]\huge\text{= 9 + 1x + 1 + 2x}[/tex]
[tex]\huge\textsf{COMBINE the LIKE TERMS}[/tex]
[tex]\huge\text{= (9 + 1) + (1x + 2x)}[/tex]
[tex]\huge\text{= 10 + 3x or 3x + 10}[/tex]
[tex]\huge\text{Answer: \textsf{3x + 10}}[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
help?????????????????
Answers
Answer:
[tex] 1)-\sqrt{2.25} = - \sqrt{225 \times {10}^{ - 2} } \\ = -\sqrt{225} \times \sqrt{ {10}^{ - 2} } \\ =- 15 \times {10}^{ - 1} =- 1.5 = -\frac{3}{2} \\ 2) -\frac{3}{2} = -1.5 \\ thank \: you[/tex]
what is the midpoint of (2,3) and (11,16)
Answers
Answer: Midpoint = (11.5, 14.5)
Concept:
Here, we need to know the idea of the midpoint formula.
[tex]Midpoint=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} )[/tex]
Solve:
Given information
(x₁. y₁) = (2, 3)
(x₂, y₂) = (11, 16)
Given expression
[tex]Midpoint=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} )[/tex]
Substitute values into the expression
[tex]Midpoint=(\frac{2+11}{2}, \frac{3+16}{2} )[/tex]
Simplify the numerator by addition
[tex]Midpoint=(\frac{13}{2}, \frac{19}{2} )[/tex]
Simplify by division
[tex]\boxed{Midpoint=(11.5, 14.5 )}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
kendra revived a bonus that was 30%of her monthly earnings is her monthly earnings were 930 how much was kendras bonus
Answers
Hey there! I'm happy to help!
30% is the same thing as 0.3 because 0.3 is 30% of 1. If you multiply something by 1, it will just stay the same, so you need that percent of 1.
To convert a decimal to a percent, you move the decimal to the left two spaces.
Now, we simply multiply this by 930.
0.3×930=279
So, Kendra will receive a bonus of $279.
Have a wonderful day and keep on learning! :D
The ratio of boys to girls in a college marching band is 5:6. If there are 121 total students in this band, how many boys are in the band?
Answers
Answer:
Step-by-step explanation:
The ratio of boys to girls in the band is 5:6 and there are a total of 121 people.
We can call each bit of the ratio 'parts'.
So, there are a total of 5+6=11 parts in total, and there are a total of 121 people.
Therefore, each part of the ratio is equal to 121 ÷ 11 = 11.
Since there are 5 parts assigned to the number of boys in the band, then the total number of boys in the band is equal to 11 × 5, which is equal to 55 boys.
The solution set for -18 < 5x - 3 is _____. 3 > x -3 > x 3 < x -3 < x
Answers
Answer:
x < -3.
x is less than negative 3
Step-by-step explanation:
-18 < 5x - 3
-18 + 3 < 5x (- 3 + 3)
-15 < 5x
-15/5 < 5x/5
-3 > x
x < -3
What is 30% of $37.50
Answers
11.25 US $
What is the product?
-1
Answers
Answer:
3.(-2/0) this is your answer
What is the answer to -4x-5x work
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\text{-4x - 5x}[/tex]
[tex]\huge\text{= -4x + (-5x)}[/tex]
[tex]\huge\textsf{COMBINE the LIKE TERMS}[/tex]
[tex]\huge\text{= (-4x - 5x)}[/tex]
[tex]\huge\text{= -9x}[/tex]
[tex]\huge\boxed{\mathsf{Answer: -9x}}[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]
Answer:
-9x
Step-by-step explanation:
-4x-5x
Combine like terms
-4x-5x
-9x
Given g(x)=-x+2g(x)=−x+2, find g(5)g(5).
Answers
Answer:
g(5) = -3
Step-by-step explanation:
Hi there!
[tex]g(x)=-x+2[/tex]
To find g(5), replace x with 5:
[tex]g(5)=-5+2\\g(5)=-3[/tex]
I hope this helps!
Answer:
g(5) = -3
Step-by-step explanation:
given:
[tex]g(x) = -x + 2[/tex]
find:
[tex]g(5)[/tex]
replace the x with 5
~~~~~~~~~~~~
➡️ [tex] g(5) = -5 + 2[/tex]
➡️ [tex] g(5) = -3 [/tex]
Find the 13th term of the geometric sequence 4,-8,16
Answers
Answer:
4, -8, 16
scale factor = x-2
4, -8, 16, -32, 64, -128, 256, -512, 1024, -2048, 4096, -8192, 16384
answer = 16,384
No. of acute angles in the given figure:_____
Answers
Answer:
looks like there's 5
Step-by-step explanation:
acute angles are under 90°
obtuse are over 90°
right angles are 90°
Show your work:
(5n^4 - 2n²) – (4n² + 4n^4) + (3n² + 2n^4)
Answers
Collect terms
3n^4-3n^2
Answer:
3[tex]n^{4}[/tex] - 3n²
Step-by-step explanation:
(5[tex]n^{4}[/tex] - 2n²) - (4n² + 4[tex]n^{4}[/tex]) + (3n² + 2[tex]n^{4}[/tex])
Remove parenthesis, distributing the second one by - 1
= 5[tex]n^{4}[/tex] - 2n² - 4n² - 4[tex]n^{4}[/tex] + 3n² + 2[tex]n^{4}[/tex] ← collect like terms
= (5 - 4 + 2)[tex]n^{4}[/tex] + (- 2 - 4 + 3)n²
= 3[tex]n^{4}[/tex] + (- 3)n²
= 3[tex]n^{4}[/tex] - 3n²
what two numbers would give a sum of 30, a difference of 24, product of 81 and a quotient of 9
Answers
Answer:
27 and 3
Step by Step explanation:
Just list the factors of 81 and find the two numbers
A swimmer wins the 50-yard freestyle with a time of 24.76 seconds. Find the swimmer’s average speed to the nearest hundredth of a yard per second.
Answers
Answer:
2.02 yards per second
Step-by-step explanation:
Distance/time= Average speed or speed
50yard/ 24.76sec= 2.01938 yards per second ~ 2.02 yards per second
please help fast please
Answers
Answer:
6.6
Step-by-step explanation:
What is the measure of ZA?
Select the best answer from the choices provided.
A. 35
B. 55°
С.70°
D.110°
Answers
Answer:
55°
Step-by-step explanation:
Since two of the sides are the same length, that means ∠A and ∠B are the same.
All angles of a triangle add up to 180°
180 - 70 = 110
To find ∠A, we just divide 110 by 2
110 ÷ 2 = 55
Both ∠A and ∠B are 55°
B. 55°
Step-by-step explanation:
The triangle shown is a isosceles triangle meaning two angles measure the same value and one angle measures different from the others
To find m∠A, subtract 180 since it’s the total ° among the angle minus 70° to be left with the two angles
180° - 70° = 110°
The two angles can’t each be measured 110° so we must divide 110° by 2 for the two angles to have the same degree
Thus, m∠A = m∠B and m∠A = 55°
what is 1000,0000t -100x=
Answers
Answer:
100(10t-x)
Step-by-step explanation:
factor 100 out from the expression
Which number is a rational number that is NOT a whole number?
F.) 2
G.) 12
H.) 30/10
J.) 17/5
Answers
Answer:
J (17/5)
Step-by-step explanation:
Whole numbers cannot contain decimal values so 17/5 is not a whole number.