The concentration of a drug, denoted by c(t), is given by the function c(t) = [tex]0.1t^{2/11}[/tex], where t is the time in hours after the drug is injected.
To find the time when the concentration is at its maximum, we need to determine the critical points of the function by taking the first derivative and setting it equal to zero.
The first derivative of c(t) with respect to t is:
c'(t) = [tex]\frac{d}{dt}[/tex] [tex]0.1t^{2/11}[/tex] =[tex]\frac{0.1}{11}[/tex] x 2t = [tex]\frac{0.2t}{11}[/tex]
To find the critical points, set c'(t) equal to zero and solve for t:
[tex]\frac{0.2t}{11}[/tex] = 0
t = 0
Since there is only one critical point, t = 0, this is the time when the concentration is at its maximum. However, this answer indicates that the concentration is at its maximum immediately after the drug is injected. This result may be due to the simplified model used to describe the concentration of the drug. In conclusion, according to the given function, the concentration of the drug is at its maximum at t = 0 hours, immediately after being injected. The answer is accurate to at least two decimal places (t = 0.00 hours).
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3 times the length of a field increased by 4 times the width gives 24 units. Two times the length decreased by 3 times the width is -1 unit. Find the dimensions
Answer:
width = 3
length = 4
Step-by-step explanation:
Ok so you can form a system of equations where w is the width and l is the length:
3l + 4w = 24
2l - 3w = -1
you want to eliminate one of the variables and then solve, so you can first take the top equation and multiply both sides by 2:
6l + 8w = 48
next, multiply the second equation by 3:
6l - 9w = -3
now that both include 6l, you can subtract the two equations
6l + 8w = 48
- (6l - 9w = -3)
17w = 51
divide both sides by 17
w = 3
Plug w = 3 into the equation 3l + 4w = 24:
3l + 4 * 3 = 24
3l + 12 = 24
subtract 12 from both sides
3l = 12
divide both sides by 3
l = 4
A human heart beats an average of 80 beats per minute. How many beats is this in an hour?
Answer:
4800 beats an hour
Step-by-step explanation:
there are 60 minutes in and hour
the heart beats 80 times per minute( that is actually a very high heart rate)
80*60=4800 per hour
Find the radius of a circle in which an inscribed square has a side of 8 inches.
Answer:
r = 4
Step-by-step explanation:
side of square is the same as the diameter of the circle
if diameter is 8 then radius is 4
Solve the inequality x+4>6. Then graph the solutions. What are the solutions? Select the correct choice below and fill in the answer box to complete your choice.
Answer:
The ineqaulity is x > 2
Step-by-step explanation:
please answer this question
Answer:
activity2
1. ( 14.4) adn
2.(0.616) adn
3.( 5-36) adn
Solve the system of linear equations by elimination. Check your solution. 3x + 2y = 7 -3x + 4y = 5
Answer:
(3x+2y=7-3x+4y)=5
3x+3x+2y-4y-7=5
6x-2y-7=5
6x-2y=5+7
=12
2(3x-y)=12
3x-y=12/2
= 6
-10(n+30)=1/2(24-14n)
Ryan can mow 15 lawns in 5 days. How many lawns can he mow each day?
Answer:
3
Step-by-step explanation:
MARK BRAINLIEST
Mrs. Dyson is making trail mix for Christmas gifts. She needs 4 cups of nuts, 6 ups of raisins, and 5 cups of chocolate chips. What percent of the trail mix are
raisins
HINT: Use Part to Whole and Reduce
A.60%
B.40%
C.6%
D.15%
Answer:
b
Step-by-step explanation:
15/6=2.5
100/2.5=40
Please help! Complete answers please.
Answer:
m3 = 103 degrees
m4 = 77 degrees
Step-by-step explanation:
comment if you want me to explain please :)
The interior angles of ∆AUL (or any triangle for that matter) sum to 180°, so
∠3 + 20° + 57° = 180°
===> ∠3 = 103°
Angles ∠3 and ∠4 occur on the same ray LP, so they are supplementary to one another. In other words,
∠3 + ∠4 = 180°
so that
∠4 = 180° - 103° = 77°
Kelly works at her own nail
salon. Today, she did 11
manicures and received $52.25
overall in tips. If x represents the
cost of each manicure, which of
the following equations can be
used to find the total amount of
money she earned, including
tips, for her nail salon today?
A. y = 11(x + 52.25)
B. y = 52.25x + 11
c. y = 52.25(x + 11)
D. y = 11x + 52.25
Answer:
(x×11)÷52.25
Step-by-step explanation:
if 11=52.25 and y=x then x11÷52.25 i think that is the answer
john makes $400 per week. What does it mean for him to get a 150% salary raise? Explain in words and then give an example showing a calculation.
plzzzzzzzzzzzzzzzzzzzzzz help me
Answer:
1200
Step-by-step explanation:
400 x 300 because double
Please I need formula and faces
Answer:
+3[36 hahahahhh Sana all mag hanap ka nlg sa iba
What’s the radius of a circle with the circumference of 37.68 feet
Answer:
r≈6ft
Step-by-step explanation:
Using the formula
C=2πr
Solving forr
r=C
2π=37.68
2·π≈5.99696ft
pls mark as brainliest
Please work out -80 ÷ -8
Answer:
10
Step-by-step explanation:
-80 / -8 = 10
the negatives cancel each other out
-80÷-8=10
.....................
Nita needs at least $85 to buy a skateboard. She already has $61. Which graph best represents all the possible dollar amounts that Nita can save to buy a skateboard? (5 points)
Number line graph with open circle on 24 and shading to the right.
Number line graph with closed circle on 24 and shading to the right.
Number line graph with open circles on 0 and 24 and shading in between.
Number line graph with closed circles on 0 and 24 and shading in between.
Answer:
Number line graph with closed circle on 24 and shading to the right.
Step-by-step explanation:
First, the graph has to have a closed circle on only 24.
Since she has $61 and needs at least $85 to buy a skateboard, she needs to have at least $24 saved to buy one.
This means the last 2 answer choices are wrong, because there cannot be shading in between.
The first answer choice is also wrong because it puts a open circle, instead of a closed one, on 24.
So, the correct answer is Number line graph with closed circle on 24 and shading to the right.
give the other brainliest
Finding a percentage of o total amount without a calculator...
An item is regularly priced at $35. It is on sale for 40% off the regular price. How much (In dollars) Is discounted from the regular price?
Amount discounted: si
х
5
?
9514 1404 393
Answer:
$14
Step-by-step explanation:
Computing 40% can be done a couple of ways.
40% = 40/100 = 4/10 = 2/5
40% of 35 = (2/5)(35) = 2(35/5) = 2(7) = 14
__
40% = 4/10 = 2(2(1/10))
40% of 36 = 2(2(1/10)(35)) = 2(2(3.5)) = 2(7) = 14
The amount discounted is $14.
can someone help asap ill give brainiest plus 50 points if you answer right.
Examine the following graph of a nonlinear function.
Graph of a nonlinear function passing through (0, negative 3), (1, negative 2), (2, 0), & (3, 4).
What is the average rate of change over the interval 1≤x≤3?
Enter your answer as a number, like this: 42
Answer:
the answer is 3
Step-by-step explanation:
just guessed and got it right since it wasn't 1 or 2 because i tried searching up the answer and they were around 2 but rlly close to 3
The rate of change of y with respect to x is 3.
We have a graph of a Non - linear function.
We have to determine the average rate of change over the interval
1 ≤ x ≤ 3.
What do you understand by the Average rate of change of two quantities plotted along X and Y axis respectively?It indicates the rate of change of y with respect to x. Mathematically -
[tex]$r=\frac{dy}{dx}[/tex]
or
[tex]$r =\frac{y(2)-y(1)}{x(2) -x(1)}[/tex]
According to the question -
The coordinate points plotted area s follows -
X Y
1 -2
2 0
3 4
Now, the average rate of change →
[tex]$r =\frac{y(2)-y(1)}{x(2) -x(1)}[/tex]
[tex]$r =\frac{4-(-2)}{3-1}[/tex]
r = 3
Hence, the rate of change of y with respect to x is 3.
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Michael needs to gain weight. He weighs 120 pounds and thinks he can gain 2 pounds a week. He wants to weigh at least 165 pounds. How long will it take him to reach this goal? inequality: solution:
Answer:
The answer is B
Step-by-step explanation:
You deposit $500 in an account that earns 6.5% annual interest compounded yearly. Write a function that represents the balance y (in dollars) after x years.
Answer:
f(x)=.65+y
Step-by-step explanation:
.
The function for compound interest is A = 500 ( 1.065 )ˣ
What is Compound Interest?Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.
The formula for calculating Compound Interest is
A = P ( 1 + r/n )ⁿᵇ
where A = Final Amount
P = Principal
r = rate of interest
n = number of times interest is applied
b = number of time periods elapsed
Given data ,
Let the compound interest amount be represented as A
Now , the interest rate r = 6.5 %
The number of times the interest is applied = yearly
The principal amount P = $ 500
n = 1 ( compounded yearly )
t = x ( number of years )
So, the function that represents the balance y (in dollars) after x years is:
y ( x ) = 500 ( 1 + 0.065/1 )ˣ
On simplifying , we get
y ( x ) = 500 ( 1.065 )ˣ
Hence , the function is A = 500 ( 1.065 )ˣ
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Help pls!!!!!!!!!!!!!!!!!!!!!!!
Answer:
9x6=54 ur welcome:)
Step-by-step explanation:
Answer:
30
Step-by-step explanation:
The perimeter of a rectangle formula is P = 2*Length + 2*Width
The length is the largest side, so it's 9.
The width is the smallest side, so it's 6.
So, our formula would be like this: P = 2*9 + 2*6.
If you know that a denominator in your ratio table is 12 and one of
the other ratios is 1/3, what numerator should you apply to your
12 denominator to make that ratio have the same value?
Answer:
the numerator is 4
Step-by-step explanation:
1/3 = ?/12
How did the values of the denominator change from 3 in the fraction 1/3 to 12 in the fraction ?/12? 3 was multiplied by 4 to get 12.
Then, since 12 is 4 times 3, then the missing numerator must be 4 times 1.
1/3 = 4/12
Answer: the numerator is 4
here are 36 points lovely person but first any advice for a student - kid
Ava pours 3 gallons of paint equally into 5 cans. How many gallons of paint will there be in each can?
Answer:
0.6
Step-by-step explanation:
first you well have a 3 and then dived it by 5 and after you dived them to you well get the answer 0.6
solve using quadratic equation
Answer:
±5 is your answer
Step-by-step explanation:
x²-25=0
comparing above equation with ax²+bx+c
we get
a=1
b=0
c=-25
by using quadratic equation
x=(-b±√(b²-4ac))/2a=(-0±√(0²-4×1×-25))/2×1
=±{√(100)}/2=±(√10²)/2=±10/2=±5
Answer:
5, - 5
Step-by-step explanation:
x^2 = 25
x = ± √25
= ± 5
x = 5, - 5
Item 4 Find the distance between the two points. (4, −5), (−1, 7)
Answer:
yes , the distance between the two points is 13 units
A CIRCLE HAS A CIRCUMFENCE 43.96 YD FIND THE RADUIS OF THE CIRCLE
Answer:
≈ 7
Step-by-step explanation:
How do you list all of the rational zeros of g(x)=x^4-3x^3-53x^2-9x?
I only know how to list them for when the last number doesn’t have the variable x.
Answer:
No lo se
Step-by-step explanation:
Hi! PLS HELP!!! 20 POINTS!
A children's pool contains 17,500 milliliters. How many liters are in the pool?
1.75 liters
17.5 liters
175 liters
1,750 liters
pls help!
If u put something of the topic imma report u
Have a great day! :)
(its not a I did it and got it wrong!!)
Answer:
17.5 liters
Step-by-step explanation:
hope its the answer your looking for
A student was given the following instructions:
"Given f(x) = 6x + 4, find f(4)."