Answer:
3x-36 is equivalent to 3(x-12)
is 0.3 greater than 0.38
Answer:
No
Step-by-step explanation:
Because 0.38 is 0.08 more than 0.3.
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
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
What is 25 % of 200?
Answer:
50
Step-by-step explanation:
25/100 × 200
= 25×2
=50
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?
Use basic facts and place value to find the quotient.
450 • 9 =
Your answer
How do I solve 10x = 100
Answer:
x = 10 since 10 x 10 = 100
Step-by-step explanation:
c(x)=85x+600 find C(25)
Answer:
Step-by-step explanation:
c(25) = 85(25) + 600 = 2725
Por favor si alguien sabe pliss
(escriba si o no)
Answer:
Respuesta: SI
Step-by-step explanation:
Números Racionales
Un número pertenece al conjunto de los números racionales (Q) si se puede expresar como una fracción de denominador diferente de cero, es decir, x es racional si:
[tex]\displaystyle x=\frac{a}{b}[/tex]
Donde a y b son número enteros y además b es diferente de cero
el número
[tex]\displaystyle -\frac{3}{5}[/tex]
Tiene un numerador igual a 3 y un denominador igual a 5 (independientemente del signo), por lo tanto cumple con las dos condicines y es efectivamente un número racional.
Respuesta: SI
Sylvia set a goal of saving at least $200 in a savings account.
She currently has $60 in the account. If she invests $5 of her weekly allowance per
week, how many weeks will it take her to reach her goal?
Define the variable.
Answer:
twenty eight more weeks till$200
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
what is a bar diagram
Answer:
A bar graph shows amounts as bars of different sizes and, sometimes, of different colors. Longer bars represent larger numbers.
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
Help!!! Find c.
Round to the nearest tenth:
Answer:
[tex]c = 14.9cm[/tex]
Step-by-step explanation:
Given
[tex]b = 10cm[/tex]
[tex]B = 12^{\circ}[/tex]
[tex]A = 150^{\circ}[/tex]
Required
Determine the length of c
First, we calculate C (the third angle of the triangle).
[tex]C = 180 - A - B[/tex]
[tex]C = 180 - 150 - 12[/tex]
[tex]C = 18^{\circ}[/tex]
Using Sine's law, we make use of:
[tex]\frac{sin\ B}{b} = \frac{sin C}{c}[/tex]
By substituting values, we have:
[tex]\frac{sin\ 12}{10} = \frac{sin 18}{c}[/tex]
Cross multiply
[tex]c* sin\ 12 = 10 * sin\ 18[/tex]
Make c the subject
[tex]c = \frac{10 * sin\ 18}{sin\ 12}[/tex]
[tex]c = \frac{10 * 0.3090}{0.2079}[/tex]
[tex]c = 14.9cm[/tex] approximated
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
PLEASE HELP !!! ILL GIVE BRAINLIEST!! *DONT SKIP* ILL GIVE 40 POINTS.
Answer:
5.5
Step-by-step explanation:
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%
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!!
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
Which of the following statements are not true about parallelograms?
Select all that apply.
1. The area of a parallelogram is half of the product of its length and width.
2. The angles formed by the diagonals of a parallelogram are complementary to each
other.
3. The diagonals of a parallelogram bisect each other.
4. A diagonal divides a parallelogram into two congruent triangles.
5. Two consecutive angles of a parallelogram are supplementary.
9514 1404 393
Answer:
1, 2
Step-by-step explanation:
1. The area of a parallelogram is the product of length and width. The given statement is FALSE.
2. The angles formed by the diagonals are linear pairs, so supplementary. The given statement is FALSE.
3. TRUE
4. TRUE
5. TRUE
__
Statements 1 and 2 are not true.
Explain how you could find the difference of 1 and 0.1978.
Answer:
0.8022
Step-by-step explanation:
difference=subtraction
so we take 1 - 0.1978 and it equals 0.8022
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
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
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]
Identify a secant that contains a diameter of M
Answer:
A. AC
Step-by-step explanation:
Find the degree measure of the indicated angle.
?
43°
75°
Alberto left the airport and traveled toward the capital. One hour later Danielle left traveling 10 km/h faster in an effort to catch up to him. After five hours Danielle finally caught up. What was Alberto's average speed?
Answer:
Step-by-step explanation:
Alberto traveled v km/h.
After 1 hour they are v km apart.
Danielle travels (v+10) km/h.
The distance between them decreases by 10 km/h.
They meet in 5 hours, after Danielle has traveled 5v+50 km and Alberto has traveled 6v km.
6v = 5v+50
v = 50 km/h
Alberto travels 50 km/h
Type the missing number that makes these fractions equal:
6
4.
8
Submit
please help i cany figure this one out
Answer:
acute angle
Step-by-step explanation:
Big brain
Answer:
Adjacent
Step-by-step explanation:
.3x+.65 x 175=.50(x+175)
Can you please explain this step by step? Kinda confused about how to figure it out.
Answer:
[tex]x=131.25[/tex]
Step-by-step explanation:
[tex]0.3x+0.65*175=0.5(x+175)[/tex]
[tex]0.3x+113.75=0.5x+87.5[/tex] (Simplify both sides of the equation by multiplying on the LHS and distributing on the RHS)
[tex]0.3x+113.75-0.5x=0.5x+87.5-0.5x[/tex] (Subtract [tex]0.5x[/tex] from both sides of the equation to get all [tex]x[/tex] terms to one side)
[tex]-0.2x+113.75=87.5[/tex] (Simplify)
[tex]-0.2x+113.75-113.75=87.5-113.75[/tex] (Subtract [tex]113.75[/tex] from both sides of the equation to isolate [tex]x[/tex])
[tex]-0.2x=-26.25[/tex] (Simplify)
[tex]\frac{-0.2x}{-0.2} =\frac{-26.25}{-0.2}[/tex] (Divide both sides of the equation by [tex]-0.2[/tex] to get rid of [tex]x[/tex]'s coefficient)
[tex]x=131.25[/tex] (Simplify)
Hope this helps!