Answer:
a. dQ/dt = -kQ
b. [tex]Q = 9e^{-kt}[/tex]
c. k = 0.178
d. Q = 1.063 mg
Step-by-step explanation:
a) Write a differential equation for the quantity Q of hydrocodone bitartrate in the body at time t, in hours, since the drug was fully absorbed.
Let Q be the quantity of drug left in the body.
Since the rate of decrease of the quantity of drug -dQ/dt is directly proportional to the quantity of drug left, Q then
-dQ/dt ∝ Q
-dQ/dt = kQ
dQ/dt = -kQ
This is the required differential equation.
b) Solve your differential equation, assuming that at the patient has just absorbed the full 9 mg dose of the drug.
with t = 0, Q(0) = 9 mg
dQ/dt = -kQ
separating the variables, we have
dQ/Q = -kdt
Integrating we have
∫dQ/Q = ∫-kdt
㏑Q = -kt + c
[tex]Q = e^{-kt + c}\\Q = e^{-kt}e^{c}\\Q = Ae^{-kt} (A = e^{c})[/tex]
when t = 0, Q = 9
[tex]Q = Ae^{-kt} \\9 = Ae^{-k0}\\9 = Ae^{0}\\9 = A\\A = 9[/tex]
So, [tex]Q = 9e^{-kt}[/tex]
c) Use the half-life to find the constant of proportionality k.
At half-life, Q = 9/2 = 4.5 mg and t = 3.9 hours
So,
[tex]Q = 9e^{-kt}\\4.5 = 9e^{-kX3.9}\\\frac{4.5}{9} = e^{-kX3.9}\\\frac{1}{2} = e^{-3.9k}\\[/tex]
taking natural logarithm of both sides, we have
[tex]ln\frac{1}{2} = ln(e^{-3.9k})\\\\-ln2 = -3.9k\\k = -ln2/-3,9 \\k = -0.693/-3.9\\k = 0.178[/tex]
d) How much of the 9 mg dose is still in the body after 12 hours?
Since k = 0.178,
[tex]Q = 9e^{-0.178t}[/tex]
when t = 12 hours,
[tex]Q = 9e^{-0.178t}\\Q = 9e^{-0.178X12}\\Q = 9e^{-2.136}\\Q = 9 X 0.1181\\Q = 1.063 mg[/tex]
Given the number 254, 476, 951
What number is in the TEN THOUSAND's SPOT?
Step-by-step explanation: 1 is in the ten thousand places and has a place value of 10,000. 3 is in the thousand's place and has a place value of 3,000. 5 is in the hundreds and has a place value of 500.
summarize how you can find the slope of a perpendicular line.
Since "slope" tells us the angle of the line being graphed, the word "slope" is commonly used in mathematics.
Planar geometry states that all lines have slopes. Any slope can be calculated by comparing it to another line, usually the x-axis. A line's slope, or angle, in relation to that x-axis value is how steep it is.
In mathematics, slope is the proportion of the change in the y value to the change in the x value.
Two perpendicular lines have a slope such that the reciprocal of the negative slope of one line equals the slope of the other. The slope of perpendicular lines is -1 as a result.
The relationship between the slopes of parallel lines can be demonstrated using the formula m1.m2 = -1, if the slopes of the two perpendicular lines are m1, m2.
Like a fraction, a slope works by favoring the rise, up-and-down movement, over-the-run, or side-to-side movement. If a line rose up one unit for every rightward unit traveled, the slope would be a positive one.
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PS lies on the perpendicular bisector of QR. Select all the statements about the figure that must be true.
Of the given statements, only the option number {5} and {6} are true.
What is perpendicular bisector?The perpendicular bisectors of a triangle are lines passing through the midpoint of each side which are perpendicular to the given side. A triangle's three perpendicular bisectors meet at a point. known as the circumcenter, which is also the center of the triangle's circumcircle.
Given is a triangle as shown in the image.
Since PS is the perpendicular bisector of QR, we can write -
QS = SR
6n + 3 = 4n + 11
2n = 8
n = 4
QR = QS + SR
QR = 6n + 3 + 4n + 11
QR = 10n + 14
QR = 10 x 4 + 14
QR = 54
and
SR = 4n + 11
SR = 16 + 11
SR = 27
Therefore, of the given statements, only the option number {5} and {6} are true.
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I thought of a number, added 26 to it, and then divided the result by 20. What is my number?
Answer:
12?
Step-by-step explanation:
If f(x) = 2x4 - 3x + 3, then what is the remainder when f(x) is divided by x - 1?
The remainder on dividing 2x⁴-3x+3 by x-1 is 2
What are functions?Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given here: 2x⁴-3x+3 by x-1
The remainder theorem states that when a polynomial p(x) is divided by (x - a), then the remainder = f(a)
∴ The remainder would is f(1) = 2×1-3+3
=2
Hence, The remainder on dividing 2x⁴-3x+3 by x-1 is 2
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You find a mutual fund that offers approximately 6% APR compounded
monthly. How much will you need to invest each month for the next year in
order to have $1000?
Answer:
$81.06
A P E X :)
5 in. 3 8 in. What is the volume, in cubic inches, of the prism? cubic inches
Answer:
70in^3
Step-by-step explanation:
Ok so the the formula for volume for a cube is V= L x W x H
so if the dimensions are 5in by 3in by 8in, the volume of the cube is 5x8x3 = 70 inches^3
Debby deposits 25% if the money that she earns each week in a savibgs account if debby earns $72 each week, how much money will she deposit next week
need help solving this problem please
Step-by-step explanation:
[tex] \cos( \frac{ \alpha }{2} ) = \sqrt{ \frac{1 - \cos( \alpha ) }{2} } \\ = \sqrt{ \frac{1 - ( - \frac{15}{17}) }{2} } \\ = \sqrt{ \frac{32}{34} } [/tex]
i dont understand this help
laucs ori nisiquiera estoy en universidad estoy en eseyo pe
It takes 3 eggs to make a cake .how many cakes can you make with 37 eggs
Answer:
12 cakes
Step-by-step explanation:
37 / 3 = 12.33333
Determine a system of linear equations that represents the problem. Be sure to explain how you created the equations.
Answer:
a-
3x+3y=11.25
4x+2y=10
What is the probability of tossing a coin and getting heads three times in a row?
What is the chance that the next toss will be heads? What is the chance that the next toss will be tails?
The probability of tossing 3 heads in a row is P = 0.125, and after that, because the events are independent, the probability of getting heads (or tails) still is p = 0.5
How to find the probability?Assuming that we have a fair coin, we assume that both outcomes have the same probability, so:
P(tails) = 0.5
P(heads) = 0.5
Then the probability of getting heads 3 times in a row, is the product of the probability of getting heads 3 times, this will be:
P(3 heads) = 0.5*0.5*0.5
P(3 heads) = 0.5^3
P(3 heads) = 0.125
Now, after this point, what is the probability of getting heads or tails?
Remember that each toss of the coin is independent of the previous one, so the probability of getting tails still is 0,5, and the same for the probability of getting heads.
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if someone takes your food is it still sharing
Answer:
not unless you want them to have it :)
Step-by-step explanation:
If f(x)=-4x-5 and g(x)= 3-x, what is g(-4) +f(1)?
A.-10
B.7
C.-9
D.-2
Answer:
-2
Step-by-step explanation:
sustitue -4 into x for 3-x which would equal 7 because a negative times a negative equals positive. Then substitue 1 in for x in -4x-5 which would get you -9
give brainliest pls
-5(6x+3y-1)
Simplify
Answer:
-30x+15y+5 is the simplified answer
A movie theater sells popcorn in bags that open to form similar prisms, as shown. The large bag has a volume of 576 cubic inches. The small bag is 12 in tall and the large bag is 16 in tall. What is the volume of the small bag?
speeeeeeeedddddddddddddddddddddddddddddddd
Answer:
I would be ...
75/8
multiple 9 by 8 and then add 3
Hope this helps!
Step-by-step explanation:
;)
Answer:
75/8!
Step-by-step explanation:
Solve for the value of c (2c-4) (5c+3)
Answer:
its 13
Step-by-step explanation:
There are 5 yellow golf balls, 3 red golf balls, and 10 white golf balls in a bag. What are the odds of randomly choosing a yellow golf ball?
Answer:
5/18
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
1+1=2
- Joy and John MacAllister have agreed to purchase a house for $79,900. First
National Savings & Loan is willing to lend the money at 7.5 percent for
25 years, provided the MacAllisters can make a $19,900 down payment. The
total closing cost is 3.5 percent of the amount of the mortgage. What is their
total closing cost?
Answer:
Step-by-step explanation:
A cylindrical paint can has a diameter of 12 centimeters and
height of 16 centimeters. Which is closest to the volume of
the paint can in cubic centimeters?
Answer:
Step-by-step explanation:
you could find the area of the circle , then multiply that by the height
area of circle = [tex]\pi[/tex][tex]r^{2}[/tex]
[tex]\pi[/tex][tex]6^{2}[/tex]=113.0973355
16*113.0973355=1809.5573
The volume of the paint can in cubic centimeters 1808.64 cm³.
what is Volume?The amount of space occupied by a three-dimensional figure as measured in cubic units.
given: radius= 6cm and height= 16 cm
Volume of cylinder= πr²h
= 3.14*6*6*16
= 1808.64 cm³
Thus, the volume of the paint can in cubic centimeters 1808.64 cm³.
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I need help with this question please help me with this
By basic algebra, the part to be cut is equal to 17/45. When the numerator exceeds or is equal to the denominator, the fraction is said to be improper. 5/2 and 8/5, for instance, are improper fractions. Each fraction has two components.
In math, what is a fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Let x part is cut to shorten
then,
[tex]\frac{3}{2}-x=\frac{2}{9}\\\\x=\frac{3}{5} -\frac{2}{9} \\\\x=\frac{17}{45}[/tex]
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HELPPP MEE THANK U, 20 POINTS!~
Answer:
B
Step-by-step explanation:
The second box plot starts later then the first one on the number line.
A house 20 meters long and 15 meters wide is surrounded by a verandah of uniform width of 3 meters. Find the cost of the flooring the verandah at RS 200 per square meter
Answer:
49200 rs. so the cost of flooring =246*200=49200 rs
Step-by-step explanation:
we measure the area of veranda by taking width in addition of length and breadth- house area
it means
area of veranda =outer rectangle-inner rectangle
⇒area= (20+3+3)*(15+3+3)-20*15
⇒area=26*21-300
⇒area= 546-300
⇒area=246 m²
Hence , the cost of flooring =246*200=49200 rs.
35×75(46×13-55)-76=?
Answer:
1,425,299
Step-by-step explanation:
Answer:
1425299
Step-by-step explanation:
35×75(46×13-55)-76
multiply stuff in parenthesis
35×75(598-55)-76
subtract stuff in parenthesis
35×75(543)-76
multiply
1425375-76
subtract
1425299
A principal of $3600 is invested at 3.5% interest, compounded annually. How much will the investment be worth after 12 years? Use the calculator provided and round your answer to the nearest dollar. X S
Answer:
$5043
Step-by-step explanation:
To find the value of the investment after 12 years, you can use the following formula:
A = P * (1 + r/n)^(nt)
Where:
A = final amount
P = principal
r = interest rate
n = number of times the interest is compounded per year
t = number of years
Plugging in the values from the problem, we get:
A = 3600 * (1 + 3.5/100)^(1*12)
Solving this equation, we get:
A = $5043.33
So, after 12 years, the investment will be worth $5043.33.
HELP MEEEEEE PLEASESEE PLEASE
Answer:
240 grams
Step-by-step explanation:
720-480=240
Answer:
240
Step-by-step explanation:
subtraction
720-480
Two car dealerships pay their employees a monthly salary plus a commission on cars that they sell.
The person who is right on the dealership that pays a higher commission, is Tyson because Dealership A pays the higher commission.
How to find the commission paid ?The commission paid on Dealership A cars can be found by the formula :
= ( Monthly income for 4 cars - Monthly income for 1 car ) / Difference in number of cars
= ( 3, 850 - 1, 900 ) / ( 4 - 1 )
= $ 650
The commission paid on Dealership B cars would be:
= ( Monthly income for 4 cars - Monthly income for 1 car ) / Difference in number of cars
= ( 3, 500 - 2, 000 ) / ( 4 - 1 )
= 1, 500 / 3
= $ 500
Dealership A pays the higher commission.
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AB=25 , BD=4, Solve for the radius?
Please help!!!!!
9514 1404 393
Answer:
r = 14.5
Step-by-step explanation:
AD is the perpendicular bisector of chord EC, so is the diameter of the circle. The radius is half the diameter.
r = AD/2 = (AB +BD)/2 = (25 +4)/2 = 29/2
r = 14.5
__
Segments BE and BC are 10 = √(25·4)