Answer:
-1.5
Step-by-step explanation:
A drug is administered intravenously at a constant rate of r mg/hour and is excreted at a rate proportional to the quantity present, with constant of proportionality k > 0.
(a) Set up a differential equation for the quantity, Q, in milligrams, of the drug in the body at time t hours. (Your answer will contain the unknown constants r and k.)
(b) Solve this differential equation, assuming there is no drug in the body initially. (Your answer will contain r and k.)
(c) What is the limiting long-run value of Q?
Answer:
a.)Q' = -kQ + r
b.)Q = [tex]\frac{r}{k} [ 1 - e^{-kt} ][/tex]
c.) Limiting long run value of Q = [tex]\frac{r}{k}[/tex]
Step-by-step explanation:
a.)
The rate of change is directly proportional to the quantity, Q
⇒[tex]\frac{dQ}{dt}[/tex] ∝ Q
⇒[tex]\frac{dQ}{dt}[/tex] = -kQ ( because it is decreasing )
Also given, quantity is increasing with a constant rate r
⇒[tex]\frac{dQ}{dt}[/tex] = -kQ + r
⇒Q' = -kQ + r
b.)
As we have
[tex]\frac{dQ}{dt}[/tex] = -kQ + r
⇒[tex]\frac{dQ}{-kQ + r}[/tex] = dt
⇒∫[tex]\frac{dQ}{-kQ + r}[/tex] = ∫dt
⇒-[tex]\frac{1}{k}log(-kQ + r) = t + C[/tex]
⇒log(-kQ + r) = -kt -kC
Taking exponential both side, we get
⇒-kQ + r = [tex]e^{-kt +A}[/tex]
⇒-kQ = -r + [tex]e^{-kt +A}[/tex]
⇒Q = [tex]\frac{r}{k}[/tex] - [tex]\frac{1}{k}[/tex][tex]e^{-kt +A}[/tex]
⇒Q = [tex]\frac{r}{k}[/tex] - [tex]\frac{1}{k}[/tex][tex]e^{-kt}.e^{A}[/tex]
⇒Q = [tex]\frac{r}{k}[/tex] - [tex]\frac{1}{k}[/tex][tex]Be^{-kt}[/tex] .......(1)
Now,
At t = 0, Q = 0
0 = [tex]\frac{r}{k}[/tex] - [tex]\frac{1}{k}[/tex]B
⇒[tex]\frac{1}{k}B = \frac{r}{k}[/tex]
⇒B = r
∴ equation (1) becomes
Q = [tex]\frac{r}{k}[/tex] - [tex]\frac{r}{k}[/tex][tex]e^{-kt}[/tex]
⇒Q = [tex]\frac{r}{k} [ 1 - e^{-kt} ][/tex]
c.)
for limiting long run value of Q
[tex]\lim_{n \to \infty} Q = \lim_{n \to \infty}[/tex] [tex]\frac{r}{k} [ 1 - e^{-kt} ][/tex]
= [tex]\frac{r}{k}[/tex][tex]\lim_{n \to \infty} [ 1 - e^{-kt} ]= \frac{r}{k} [ 1 - e^{\infty} ] = \frac{r}{k}[ 1-0][/tex]
= [tex]\frac{r}{k}[/tex]
⇒Limiting long run value of Q = [tex]\frac{r}{k}[/tex]
Q' = -kQ + r
Q = r/k (1- [tex]\rm e^{-kt}[/tex])
The limiting long-run value of Q = [tex]\rm \frac{r}{k}[/tex]
A drug is administered intravenously at a constant rate of r mg/hour and is excreted at a rate proportional to the quantity present, with a constant of proportionality k > 0.
What is a differential equation?The differential equation is an equation that contains the derivative of the unknown function.
a) It is given that the rate of change is directly proportional to the quantity Q
[tex]\rm \frac{dQ}{dt}[/tex] ∝ Q
[tex]\rm \frac{dQ}{dt}[/tex] = -kQ
So, Q' = -kQ + r
where quantity Q is increasing with constant rate r and k is unknown constant.
b) Q' = -kQ + r
[tex]\rm \frac{dQ}{dt}[/tex] = -kQ + r
[tex]\rm \frac{dQ}{-kQ+r}=dt\\[/tex]
[tex]\int\limits {\rm \frac{dQ}{-kQ+r} = \int\limits dt[/tex]
log(-kQ + r) = -kt -kC
by taking exponential both side, we get
-kQ + r = [tex]e^{-kt+A}[/tex]
-kQ = -r + [tex]e^{-kt+A}[/tex]
-Q /k= -r/k + [tex]e^{-kt+A}[/tex]/k
Q = -r/k -[tex]\rm \frac{1}{k}Be^{-kt}[/tex]
At t = 0, Q = 0
[tex]\rm \frac{1}{k} B=\frac{r}{k}[/tex]
B = r
by substituting the value in the above equation
Q = r/k (1- [tex]\rm e^{-kt}[/tex])
c) The limiting long-run value of Q
[tex]\rm \lim_{n \to \infty} Q= \lim_{n \to \infty} \frac{r}{k} [1-e^{-kt} ]\\\rm= \frac{r}{k}\lim_{n \to \infty} [1-e^{-kt} ]\\\rm =\frac{r}{k}[1-0]\\\rm=\frac{r}{k}[/tex]
The value Q =[tex]\rm \frac{r}{k}[/tex]
Learn more about differential equations here:
https://brainly.com/question/25731911
Reflect (5,-5) in (a) the x-axis and (b) the y-axis.
Answer:
a. (5,5)
b. (-5,-5)
Step-by-step explanation:
reflection over x-axis flips the sign of y-coordinate
reflection over y-axis flips the sign of x-coordinate
William receives a weekly allowance according to the following formula: For each day that he remembers to do his chores, he eams 51.50, and for each day that he doesn't remember to do his chores, he loses
50.25. What amount of allowance would William receive for a week in which he remembers to do his chores on five days and forgets to do them on two days?
Damian went shopping for a new pair of sneakers. Sales tax where he lives is 5.5%. The price of the pair of sneakers is $48. Find the total price including tax. Round to the nearest cent.
Ezra’s dad is building a cover for his sandbox. The sandbox is in the shape of a kite as shown.
A kite has a width of 6 feet and a height of 4 feet.’
What is the area of the sandbox cover?
6 square feet
12 square feet
18 square feet
24 square feet
Answer:
12
Step-by-step explanation:
its either 12 or 18 try 12 first
Express the recurring decimal 0.004 as a fraction.
Answer:
The recurring decimal 0.004 in friction is 1/250
Answer:
Step-by-step explanation:
Let x=0.004444....
1000x-100x=4.444... -0.444...
900x=4
x=4/900=1/225
The national weather service keeps records of rainfall in valleys. Records indicate that in a certain valley the annual rainfall has a mean of 95 inches and a standard deviation of 12 inches. Suppose the rainfalls are sampled during randomly picked years and x is the mean amount of rain in these years. For samples of size 36 determine the mean and standard deviation of x.
Answer:
The mean is 95 and the standard deviation is 2
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
Population:
Mean 95, Standard deviation 12
Samples of size 36:
By the Central Limit Theorem,
Mean 95
Standard deviation [tex]s = \frac{12}{\sqrt{36}} = 2[/tex]
please help i cany figure this one out
Answer:
acute angle
Step-by-step explanation:
Big brain
Answer:
Adjacent
Step-by-step explanation:
c(x)=85x+600 find C(25)
Answer:
Step-by-step explanation:
c(25) = 85(25) + 600 = 2725
Sarah's fish tank holds 32 litters of water. Sarah uses a 4 liter container to fill the tank. how many times will Sarah need to fill the 4 liter container in order to fill the fish tank.
Answer:
8 times,
Step-by-step explanation:
4 x 8 is 32
then 42 letter Pat rotational Athlone for tea towel
describe the transformations of the following functions from their parent function
Answer:
see explanation
Step-by-step explanation:
22
- [tex]\sqrt{x}[/tex] is a reflection of [tex]\sqrt{x}[/tex] in the x- axis
Given f(x) then f(x) + c is a vertical translation of f(x)
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Thus
g(x) = - [tex]\sqrt{x}[/tex] - 4
is a reflection in the x- axis, followed by a vertical translation 4 units down
23
Given f(x) then f(x + a) is a horizontal translation of f(x)
• If a > 0 then a shift left of a units
• If a < 0 then a shift right of a units
Thus
h(x) = [tex]\sqrt[3]{x+1}[/tex] + 5
is a horizontal translation 1 unit left and a vertical translation of 5 units up
Answer:
22
- \sqrt{x}
x
is a reflection of \sqrt{x}
x
in the x- axis
Given f(x) then f(x) + c is a vertical translation of f(x)
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Thus
Which statements describe the graph of 2 8/9 ≥ x on a number line? Select three options.
Answer:
✔️The graph contains point zero
✔️There's a closed circle on 2⁸/9
✔️The arrow points to the left
Step-by-step explanation:
The inequality, 2⁸/9 ≥ x, implies that 2⁸/9 is either equal to x or more than x. In other words, the highest value of x is 2⁸/9. Possible value of x is equal to or less than 2⁸/9.
This, on a number line, we would graph the information as follows:
✔️The graph contains point zero
Rationale: point zero is less than 2⁸/9
✔️There's a closed circle on 2⁸/9
Rationale: this indicates 2⁸/9 is included in the possible value of x
✔️The arrow points to the left
Rationale: possible value of x ranges from 2⁸/9 and below.
Answer: b c d
Step-by-step explanation:
heart it please ;) your welcome
What impact did the American Revolution have on Haiti?
What impact did the Haitian Revolution have on the United States?
Please help
Answer:
What impact did the American Revolution have on Haiti? The American Revolution occurred first and in part inspired the Haitian and French Revolutions. ... The Haitian Revolution was the first and only slave uprising that led to the establishment of a free state without slavery and ruled by non-whites and former slaves.
What impact did the Haitian Revolution have on the United States?The Haitian Revolution had many international repercussions. It ended Napoleon's attempts to create a French empire in the Western Hemisphere and arguably caused France to decide to sell its North American holdings to the United States (the Louisiana Purchase)—thus enabling the expansion of slavery into that territory.
Step-by-step explanation:
BRAINLIST PLEASE!!
A 0.025 kg bullet enters a 2.35-kg watermelon with a speed of 217 m/s
and exits the opposite side with a speed of 109 m/s. If the melon was
originally at rest, then what speed will it have as the bullet leaves its
opposite side?
Answer:
1.15m/s
Step-by-step explanation:
Given data
m1=0.025 kg
m2= 2.35kg
u1= 217 m/s
v1= 109 m/s
u2= 0
v2=???
Applying the law of conservation of linear momentum
m1u1+m2u2=m1v1+m2v2
substitute
0.025*217+2.35*0= 0.025*109+2.35*v2
5.425= 2.725+ 2.35v2
5.425-2.725=2.35v2
2.7=2.35v2
divide both sides by 2.35
v2= 2.7/2.35
v2=1.15 m/s
Hence the speed of the watermelon will be 1.15m/s
2) James paid x dollars plus 3% sales tax for a pen. Write an algebraic Expression for the amount of
money he paid for the pen.
3) Seven watermelons each weighs w pounds a basket can hold 11 pounds less than two-fifths of the
weight of the watermelons. What weight can the basket hold?
(US)
Text Predictions: On
100%
Algebraic expression for #3
Answer:
What’s the answer?!? Ok
Step-by-step explanation:
What is 25 % of 200?
Answer:
50
Step-by-step explanation:
25/100 × 200
= 25×2
=50
Out of these, which is not an inequality?
a. 435 ≥ 5p + 4
b. g - 7 < 100
c. 18x + 9y
d. a > 6b
Answer:
C. 18x+9y
Step-by-step explanation:
Answer:
I think its the third one, C. Hope this helps!
A copy machine makes 102 copies in 4 minutes and 15 seconds how many copies did it make per minute
Answer:
24 pages
Step-by-step explanation:
102 copies in 4 1/4 minutes
102 / 1 ÷ 17 / 4
102 / 1 × 4 / 17 = 24
Which is the correct calculation for the volume of the prism??
3units
5units
4units
3+5+4=12units3
3(4)+6=17units3
3(4)=12units3
3+(5)(4)=60units3
Answer:
3+5+4=12units3
Step-by-step explanation:
A prism has a length of 3 units, height of 5 units, and width of 4 units. 3 + 5 + 4 = 12 Units cubed 3(4) + 5 = 17 Units cubed.
Answer:
He is wrong its really 60 units
Step-by-step explanation:
cuánto es 1+1 = es dos jaja
Answer:
El raigañu cuadráu corresponder cola radicación d'índiz 2 o, equivalentemente, cola potenciación d'esponente 1/2.
Cualquier númberu real non negativu {\displaystyle x}x tien un únicu raigañu cuadráu positiva o raigañu cuadráu principal[2] y denotada como {\displaystyle {\sqrt {x}}}{\displaystyle {\sqrt {x}}} onde {\displaystyle {\sqrt {\;}}}{\displaystyle {\sqrt {\;}}} ye'l símbolu raigañu y {\displaystyle x}x ye'l aniciando.
Cuando se riquir denotar dos raigaños cuadraos una negativa, {\displaystyle -{\sqrt {x}}}{\displaystyle -{\sqrt {x}}}, y otra positiva, {\displaystyle {\sqrt {x}}}{\displaystyle {\sqrt {x}}}, suelen denotarse curioso como {\displaystyle \pm {\sqrt {x}}}{\displaystyle \pm {\sqrt {x}}} o bien como {\displaystyle \mp {\sqrt {x}}}{\displaystyle \mp {\sqrt {x}}} según l'orde precisáu.
El conceutu de raigañu cuadráu puede estendese a cualquier aniellu alxebraicu, asina ye posible definir el raigañu cuadráu d'un númberu real negativu o'l raigañu cuadráu de delles matrices. Nos númberos cuaterniónicos los reales negativos almiten un númberu infinitu de raigaños cuadraos, sicasí'l restu de cuaterniones distintos de cero almiten solu dos raigaños cuadraos. Nel aniellu non conmutativu de les funciones reales de variable real cola adición y la composición de funciones si fºf = g, puede plantegase que f ye la "raigañu cuadráu" de g.[3]
Step-by-step explanationY segun todos mis calculos es 2 :
(10 Points) Tanya is visiting New Orleans, and she wants to bring back T-shirts for all her friends. She’s
found T-shirts she likes for $5, $10, and $15. She has budgeted $40 for the gifts. make a systematic list
to answer the following questions.
(i) List how many ways she can spend exactly $30 if she is determined to buy one or more than one
$15 T-shirts?
(ii) List how many ways she can spend exactly $25.
Help its due in 1 hour plzzz!!!!!!! can you show your work to
Answer:
ok.
1. Tanya spends exactly $30.
She can spend $15.00 each for 2 t shirts and spend $30.00
15 x 2 = 30
She can buy one $15.00 t shirt, one $10.00 t shirt and one $5.00 t shirt for exactly $30.00.
15 + 10 + 5 = 30
She can buy one $15.00 t shirt, and three $5.00 t shirts for exactly $30.00
15 + 5 + 5 +5 = 30
2. To spend exactly $25.00, Tanya can spend it :
5 of the $5.00 t shirts
5 x 5 = 25
2 of the $10 t shirts and one of the $5 t shirts
10 + 10 + 5 = 25
1 of the $15 t shirts and one of the $10 t shirts
15 + 10 = 25
1 of the $15 t shirts and 2 of the $5 t shirts
15 + 5 + 5 = 25
can somebody solve this question for me and explain it
Answer:2
Step-by-step explanation:
X+4b=72. If x=12, what’s the value of b?
Answer:
Step-by-step explanation:
12 + 4b = 72
Subtract 12 on both sides
4b = 60
b = 15
How do I solve 10x = 100
Answer:
x = 10 since 10 x 10 = 100
Step-by-step explanation:
A boat moves at a rate of 11 mph in Stillwater if the rivers current flow at a rate of 2 mph how long does it take the boat to travel 26 miles upstream
Answer:
2 hours 52 minutes
Step-by-step explanation:
11-2=9
26/9=2.87
To offset college expenses, at the beginning of your freshman year you obtain a nonsubsidized student loan for $15,000. Interest on this loan accrues at a rate of 4.11% compounded monthly. However, you do not have to make any payments against either the principal or the interest until after you graduate.
Required:
a. Write a function that gives the total amount, F, you will owe on this loan after t years in college. F(t) = ?
b. What is the APR?%
c. What is the APY? (Round your answer to two decimal places.)
Answer:
15000(1.003425)^12t ;
4.11%
4.188%
Step-by-step explanation:
Given that:
Loan amount = principal = $15000
Interest rate, r = 4.11% = 0.0411
n = number of times compounded per period, monthly = 12 (number of months in a year)
Total amount, F owed, after t years in college ;
F(t) = P(1 + r/n)^nt
F(t) = 15000(1 + 0.0411/12)^12t
F(t) = 15000(1.003425)^12t
2.) The annual percentage rate is the interest rate without compounding = 4.11%
3.)
The APY
APY = (1 + APR/n)^n - 1
APY = (1 + 0.0411/12)^12 - 1
APY = (1.003425)^12 - 1
APY = 1.04188 - 1
APY = 0.04188
APY = 0.04188 * 100% = 4.188%
one of the root of the quadratic equation dx²-cx+p=0 is twice other. find the relationship between d, c, and p
please help...I don't understand atall
Answer:
The relationship between d, c and p is that [tex]p = \frac{4c^2}{9d}[/tex]
Step-by-step explanation:
Roots of a quadratic equation:
The roots [tex]r_1[/tex] and [tex]r_2[/tex] of a quadratic equation in the following format:
[tex]ax^2 + bx + c = 0[/tex]
Can be given by:
[tex]r_1 + r_2 = -\frac{b}{a}[/tex]
[tex]r_1r_2 = \frac{c}{a}[/tex]
In this question:
We have the following quadratic equation:
[tex]dx^2 - cx + p = 0[/tex]
So [tex]a = d, b = -c, c = p[/tex]
One of the roots is twice the other:
So [tex]r_2 = 2r_1[/tex]
First relation:
[tex]r_1 + r_2 = -\frac{b}{a}[/tex]
[tex]r_1 + 2r_1 = -\frac{(-c)}{d}[/tex]
[tex]3r_1 = \frac{c}{d}[/tex]
[tex]r_1 = \frac{c}{3d}[/tex]
Second relation:
[tex]r_1r_2 = \frac{c}{a}[/tex]
[tex]r_1*2r_1 = \frac{p}{d}[/tex]
[tex]2r_{1}^{2} = \frac{p}{d}[/tex]
[tex](\frac{2c}{3d})^2 = \frac{p}{d}[/tex]
[tex]\frac{4c^2}{9d^2} = \frac{p}{d}[/tex]
[tex]p = \frac{4c^2}{9d}[/tex]
The relationship between d, c and p is that [tex]p = \frac{4c^2}{9d}[/tex]
un cuerpo es dejado caer desde una altura de 3000 centímetros
Answer:
what is your question
Step-by-step explanation: am not trying to steal ur points
Martha jogged 7.8 miles. Erica jogged 0.5 times as far. How dar did erica jog
Answer: 3.9
Step-by-step explanation:
7.8 miles x 0.5 = 3.9 miles