A differential equation with some initial conditions is used to solve an initial value problem.
The required particular solution is given by the relation:
[tex]$4y^{(3/2)} = 9e^{(-2x/3)} + 23[/tex]
What is meant by an initial-value problem?An initial value problem in multivariable calculus is an ordinary differential equation with an initial condition that specifies the value of the unknown function at a given point in the domain. In physics or other sciences, modeling a system frequently entails solving an initial value problem.
Let the given equation be [tex]$y^{1/2} dy\ dx y^{3/2} = 1[/tex], y(0) = 9
[tex]$(\sqrt{y } ) y^{\prime}+\sqrt{(y^3\right\left) }=1[/tex] …..(1)
Divide the given equation (1) by [tex]$\sqrt{ y} $[/tex] giving
[tex]$y^{\prime}+y=y^{(-1 / 2)} \ldots(2)$[/tex], which is in Bernoulli's form.
Put [tex]$u=y^{(1+1 / 2)}=y^{(3 / 2)}$[/tex]
Then [tex]$(3 / 2) y^{(1 / 2)} \cdot y^{\prime}=u^{\prime}$[/tex].
Multiply (2) by [tex]$\sqrt{ } y$[/tex] and we get
[tex]y^{(1 / 2)} y^{\prime}+y^{(3 / 2)}=1[/tex]
(2/3) [tex]u^{\prime}+u=1$[/tex] or [tex]$u^{\prime}+(3 / 2) y=3 / 2$[/tex],
which is a first order linear equation with an integrating factor
exp[Int{(2/3)dx}] = exp(2x/3) and a general solution is
[tex]u. $e^{(2 x / 3)}=(3 / 2) \ln \[\left[e^{(2 x / 3)} d x\right]+c\right.$[/tex] or
[tex]\mathrm{y}^{(3 / 2)} \cdot \mathrm{e}^{(2x / 3)}=(9 / 4) \mathrm{e}^{(2x / 3)}+{c}[/tex]
To obtain the particular solution satisfying y(0) = 4,
put x = 0, y = 4, then
8 = (9/4) + c
c = (23/4)
Hence, the required particular solution is given by the relation:
[tex]$4y^{(3/2)} = 9e^{(-2x/3)} + 23[/tex]
To learn more about initial-value problem, refer to:
https://brainly.com/question/14744043
#SPJ4
Two students are running on a circular path. It takes the first student 20 minutes to complete one lap, and it takes the second student 35 minutes to complete one lap. If they both start at the same time and run in the same direction, when will they meet each other at the starting point?
5 minutes
55 minutes
140 minutes
175 minutes
The time they would both meet at the starting point is 140 minutes (third option).
When would they meet at the starting point?The time they would both meet at the starting point will be a common multiple of the time it takes each of them to complete a lap.
A multiple of a number is the product of an integer and that number. A common multiple is a multiple that is common to two or more numbers.
Multiple of 20 = 20, 40, 60, 80, 100, 120, 140
Multiple of 35 = 35, 70, 105, 140, 175
Lowest common multiple of 20 and 35 = 140
To learn more about multiples, please check: https://brainly.com/question/26030133
#SPJ1
Scatter plots are used to visualize association in samples of paired data (x, y). group starts
a. true
b. false
A high school has 36 players on the football team. the summary of the players' weights is given in the box plot. what is the interquartile range of the players' weights?
The interquartile range of the players' weights = 48 pounds.
The boxplot attached to this question is missing. It was obtained online and is attached to this solution of the question.
It should be noted that the following is true for a boxplot.
A box plot gives a visual representation of the distribution of the data, showing where most values lie and those values that greatly differ from the rest, called outliers.
The elements of the box plot are described thus;
The bottom side of the box represents the first quartile, and the top side, the third quartile. Therefore, the width of the central box represents the inter-quartile range.
The horizontal line inside the box is the median.
The lines extending from the box reach out to the minimum and the maximum values in the data set, as long as these values are not outliers. The ends of the whiskers are marked by two shorter horizontal lines.
Variables in the dataset, higher than Q3+(1.5×IQR) or lower than Q1-(1.5×IQR) are considered outliers and are usually shown using dots above the top whisker or below the bottom whisker.
So, it is evident that for this question,
First quartile = 174 pounds
Third quartile = 222 pounds
Inter Quartile Range = (Third quartile) - (First quartile)
= 222 - 174
= 48 pounds.
To know more about "interquartile"
Refer this link:
https://brainly.com/question/16988652
#SPJ4
A basic slime recipe calls for 1 part borax, 24 parts white glue, and 48 parts water. The relationship between borax, white glue and water is proportional. If Catalina has 3 tablespoons of borax and will use it all, how many cups of white glue will she need
Answer:
I am more on the sure side it's 8
Step-by-step explanation:
And if it isn't im so so sorry
[tex]\sqrt[3]{x} = 3[/tex]
Answer:
x = 27
Step-by-step explanation:
You need to cube each side.
[tex]\sqrt[3]{x} ^{3}[/tex] = [tex]3^{3}[/tex]
x = 27
What's the Gcf of 16,44, and 28 (greatest common factor)
Answer:
4
16 / 4 = 4
44 / 4 = 11
28 / 4 = 3
easy
In a recent national football league season tom brady philip rivers and aaron rodgers throw a total of 94 touchdown passes if we first had two more touchdowns and roger and six fewer than brady how many did brady have
Answer:
88 is the answer to the question
Type the expression that results from the following series of steps:
Start with
n
, add 5, multiply by 4, then subtract 7.
Answer:
n + 5 x 4 - 7
Step-by-step explanation:
Answer:
4(n+)7
Step-by-step explanation:
n+5
(n+5) x 4 = 4 ( n + 5)
4( n+5)-7
In the word grapefruit the ratio of vowels to consonants is 2:3 .find the ratios of vowels to consonats in the word pineapple and strawberry. give each ratio in its simplest form.
Answer:
48 because of the vowels it became 48 .
Step-by-step explanation:
I Quesliod. Make sure you start new workings. In the word grapefruit, the ratio of vowels to consonants is . Find the ratios of vowels to consonants in the words pineapple and strawberry. Give each ratio in its simplest form. grapefruit Vowels :Consonants Remember: vowels are a, e, i, o, u
Segment AC has a length of 60. Find the following values.
DG = 60
Therefore,[tex]4x - 3 + 2x + 21 = 60[/tex]
→[tex]6x+18 = 60 \\ 6x = 60 - 18[/tex]
→[tex]6x = 42[/tex]
Divide both sides by 6
→[tex]x = 7[/tex]
DO =[tex]4x - 3 [/tex]
→[tex]4(7) - 3 \\ 28 - 3[/tex]
DO [tex]= 25[/tex]
OG [tex]= 2x + 21[/tex]
→[tex]2(7) + 21 \\ 14 +21[/tex]
OG [tex]= 35[/tex]
Therefore:
[tex]x = 7[/tex]
[tex]DO = 25 ft[/tex]
[tex]OG = 35 ft[/tex]
I hope this helpsThe answer to 5√12 × √7, given in its simplest form, is t√√u, where t and u are integers.
Calculate the values of t and u.
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
Exact Form: 10√21 where t = 10 and u =21
let f(x)= 7x-2 and g(x)= sqrt (x) + 2x. what are (f+g)(x) and (f-g)(x)?
Answer:
• [tex](f+g) (x)[/tex] = [tex]9x + \sqrt{x} -2[/tex]
• [tex](f-g)(x)[/tex] = [tex]5x - \sqrt x - 2[/tex]
Step-by-step explanation:
[tex]f(x) = 7x - 2[/tex]
[tex]g(x) = \sqrt{x} + 2x[/tex]
To calculate [tex](f+g) (x)[/tex] and [tex](f-g)(x)[/tex], we have to add and subtract [tex]f(x)[/tex] and [tex]g(x)[/tex] respectively:
• [tex](f+g) (x)[/tex]
⇒ [tex]f(x) + g(x)[/tex]
⇒ [tex]7x - 2 \: + \sqrt{x} + 2x[/tex]
⇒ [tex]9x + \sqrt{x} -2[/tex]
• [tex](f-g)(x)[/tex]
⇒ [tex]7x - 2 - (\sqrt x + 2x)[/tex]
⇒ [tex]7x - 2 - \sqrt x - 2x[/tex]
⇒ [tex]5x - \sqrt x - 2[/tex]
Evaluate the following function when x = -1 and x = 2 and determine the sum of the two results:
Answer:
J. 1
Step-by-step explanation:
Plug the x values into the equation:
f(-1)=3-(-1)^2
f(2)=3-(2)^2
Solve each one, then add.
3-(-1)^2=
=3-1=2
3-(2)^2=
=3-4=-1
Combine the answers together.
2-1=1
The answer is J. 1.
Hope this helps!
Please mark as brainliest if correct!
four more than five times x is the same as x increased by 26
Four more than five times x is the same as x increased by 26. The value of x is x=5.5
Given information can be written in the form of algebraic equation is :
5x+4=x+26
5x-x=26-4
4x=22
x=5.5
The equal to (=) symbol is used to unite two algebraic expressions to form an algebraic equation. Because polynomials are included on both sides of the equal sign, algebraic equations are sometimes referred to as polynomial equations. Variables, coefficients, constants, and algebraic operations like addition, subtraction, multiplication, division, and exponentiation are all components of an algebraic equation.
A mathematical statement with two equal algebraic expressions is called an algebraic equation. When P and Q are polynomials, the usual form of an algebraic equation is P = 0 or P = Q. Equations in algebra with only one variable are referred to as univariate equations, whereas equations with several variables are referred to as multivariate equations. The solution of an algebraic problem is always balanced.
To learn more about this algebraic equation visit , https://brainly.com/question/25421217
#SPJ9
Iron has a density of 7.9 g/cm³. Gold has a density of 19.3 g/cm³.
I have a piece of metal that has a volume of 200 cm³ and a mass of 3.86 kg. Is it gold or iron?
pls hurry! i will give brainliest!!
-
What is the measure of angle x?
Enter your answer in the box.
Answer:
43
Step-by-step explanation:
The Florida Fish and Wildlife Conservation Commission is conducting a study on wildlife patterns and behaviors in a specific area of the Florida
Everglades. A stationary camera is placed where the area being observed can be filmed and recorded for 96 hours. Researchers found that the footage
revealed that the Cape Sable Seaside Sparrows were observed in the area once every 4 hours and the Florida Leafwing Butterfly was observed in the
area once every 9 hours. What is the least amount of hours of footage the observers need to review to see the Cape Sable seaside sparrow and the
Florida leafwing butterfly in the area at the same time?
96
36
4
9
The least amount of hours of footage the observers need to review to see the Cape Sable seaside sparrow and the Florida leafwing butterfly in the area at the same time is B. 36 hours.
What is the least common multiple?The least common multiple (LCM) is the smallest multiple of two or more numbers.
The LCM of 9 and 4 is 36 (4 x 9).
Data and Calculations:The total number of hours of filming and recording by the stationary camera is 96.
The regularity of observing the Cape Sable Seaside Sparrows = every 4 hours
The regularity of observing the Florida Leafwing Butterfly = every 9 hours
Using their LCM as 36,
The Cape Sable Seaside Sparrows will be observed 9 times when they meet the Florida Leafwing Butterfly at its 4th observation.
Thus, the least amount of hours of footage the observers need to review to see the Cape Sable seaside sparrow and the Florida leafwing butterfly in the area at the same time is B. 36 hours.
Learn more about the least common multiple at https://brainly.com/question/16054958
#SPJ1
There are two types of memberships for a book club
- an unlimited use of memebership for $50 per month or
- a monthly fee if $5 per book
Enter an equation needed to determine how many books in a month are needed for both plans to cost the same?
Answer:
9 books are needed for the plans to cost the same
Step-by-step explanation:
50 = 5 + 5x
45 = 5x
x = 9
Round 452,906 to the nearest hundred.
Answer : 500,000 450,000 453,000 452,900 452,910 step-by-step explanation:
look to the right one digit of the place they are asking to round . if it is either greater than or equal to5, then you round up the place they want. if it is not, then it says the same. then all he number to right of it becomes 0s.
9x+1-x^2
write in standard form
Answer:
−[tex]x^{2}[/tex] + 9x + 1
Step-by-step explanation:
You are planning a vacation and have found a great rate on a hotel. The hotel is $99 per night, plus tax and a
resort fee. The expression 99(1.05)+ 25 represents the total cost of the hotel for nights. What is the tax
rate and the resort fee? Explain how you know
Answer:
resort fee is 25
tax rate is 1.05
Step-by-step explanation:
how is solving |ax| + b = c different from solving |ax+b| = c?
Step-by-step explanation:
they are different because the first equation only ax is in absolute but in the second equation both ax and b are in absolute, so we could solve them differently.
A rock sample containing an isotope with a half-life of 28 million years has an initial mass of 184 grams. how much time has elapsed after three half-lives?
The half life period is the time in which only half of the given population remains. It can be represented through this equation:
[tex]f(t)=a\times(1/2)^{\frac{t}{h}}[/tex]
t = time passeda = y-intercepth = half lifeSolving the QuestionWe're given:
h = 28 million yearsa = 184 grams (this is the initial mass, after 0 time has passed)For most questions like this, we would have to plug these values into the equation mentioned above. However, this question asks for the time elapsed after 3 half-lives.
This can be calculated simply by multiplying the given half-life by 3:
28 million years x 3
= 84 million years
Answer84 million years
help needed. with show work
If a population has 500 individuals in it in 2010, and the per capita birth rate is 0.3 and the per capita death rate is 0.2, is the population growing or shrinking?
The population is growing as the births are more than deaths in an year.
What is Population Growth?Increases in a population's or a dispersed group's membership are referred to as population growth.
Given:
Total population = 500Per capita birth rate = 0.3Per capita death rate = 0.2To find: Is population growing or shrinking?
Finding:
Number of new-borns in an year = total population (per capita birth rate) = 500(0.3) = 150Number of deaths in an year = total population (per capita death rate) = 500(0.2) = 100Difference in the number of births and deaths = 150 - 100 = 50Hence the population is growing as the births are more than deaths in an year.
To learn more about population growth, refer to the link:https://brainly.com/question/1437549
#SPJ4
what is the formula of (a+b)²
Hey there!
Finding the the answer to the [Binomial]
(a + b)^2
CONVERT:
= (a + b)(a + b)
DISTRIBUTE
= a(a) + a(b) + b(a) + b(b)
= a^2 + ab + ab + b^2
COMBINE the LIKE TERMS
= (a^2) + (ab + ab) + (b^2)
= a^2 + ab + ab + b^2
= a^2 + 1ab + 1ab + b^2
= a^2 + 2ab + b^2
Therefore, your answer should be:
a^2 + 2ab + b^2
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
I need help please!
Answer:
cho kevin and sydney qualify
Step-by-step explanation:
If a number is chosen at random from the set {1, 2, 3, 4, . . ., 18}, what is the probability that the number chosen is a factor of 17?
Answer two questions about systems a and b: ​ x−7y=−3 4x y=7 ​ ​ 4x y=7 x−7y=−3 ​
our ordered pair is ( 2 , 1/2).
What is linear equations in two variables?
If an equation is written in the form ax + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero, then it is said to be a linear equation in two variables. Examples of two-variable linear equations are 10x+4y = 3 and -x+5y = 2.Let's first move the y's to the left side in the first equation.
4x - y = 3y + 7
4x - 4y = 7
Dividing both sides by 4,
x - y = 7/4
Our other equation is
x + 8y = 4
Subtracting the first equation from the second, we get
9y = 9/4
y = 1/4
We plug this into one of the equations
x + 2 = 4
x = 2
So our ordered pair is ( 2 , 1/2)
Learn more about linear equations in two variables
brainly.com/question/24085666
#SPJ4
There are 38 pencils in the drawer. Sam took 24
pencils from the drawer. How many pencils are now in the drawer ?
Answer: 14
Step-by-step explanation: