find the general solution of the following differential equation. primes denote derivatives with respect to x. 3xy^2y'
Answers
To find the general solution of the differential equation 3xy^2y' = 0, we can separate the variables and integrate both sides with respect to x.
First, we can rewrite the equation as:
y^2 dy/dx = 0
Now, we can separate the variables by dividing both sides by y^2 and multiplying both sides by dx:dy/y^2 = 0 dx
Integrating both sides, we get:∫ dy/y^2 = ∫ 0 dx
Using the power rule for integration, we can integrate the left-hand side:
-1/y = C1 + x
where C1 is the constant of integration.
To solve for y, we can isolate it by taking the reciprocal of both sides:y = -1/(C1 + x)
where C1 is an arbitrary constant.
Therefore, the general solution of the differential equation 3xy^2y' = 0 is y = -1/(C1 + x)
where C1 is an arbitrary constant.
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Related Questions
Can you pls explain how you got te answer
Answers
Solving the equation, 1 = 2k - 1 for k, we have that k = 1
What is an equation?An equation is a mathematical expression that shows the relationship between two variables.
Since we have the equation 1 = 2k - 1 and we desire to solve for k, we proceed as follows.
1 = 2k - 1
Now first, we desire to isolate the 2k term by adding 1 to both sides of the equation. so, we have that
1 = 2k - 1
1 + 1 = 2k - 1 + 1
2 = 2k + 0
2 = 2k
Now to isolate k, we divide both sides by 2. so, we have that
2k = 2
2k/2 = 2/2
k = 1
so, k = 1
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Chris's car was rear-ended by another driver and Chris decided to file a claim for the body damage. Which deductible would he have to pay before he receives a payment from the insurance company?
A) Premium
B) Comprehensive
C) Collision
D) He would not have to pay any deductible because he was not at fault.
[A P E X Per sonal Fin ance Sem 2]
Answers
Answer:
D
Step-by-step explanation:
1. When you hear the word MONEY what's the first thing that comes to mind?
Answers
Answer:
I think of bills/notes.
Step-by-step explanation:
Money is the mode or medium of exchange for goods and services.
What is currency?Currency is a type of money that is used as a medium of exchange in a specific country or region. It is a standardized unit of value that is accepted as payment for goods and services within the jurisdiction where it is used. Currency can take the form of physical banknotes and coins, or digital representations of money that can be used for online transactions.
Here,
Money is medium of exchange or a unit of account that is used to purchase goods and services. It is a tangible or intangible asset that represents value and is accepted by individuals, businesses, and governments in exchange for goods or services. Money is a fundamental component of modern economies, and its importance cannot be overstated.
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2. (a) [5pts.] Length and Dot Product in R¹. Suppose u and v' are unit vectors in R". Prove > || u’ – V || = √2√√1 – u - v (b) [5pts.] Orthonormal Bases. Suppose U = {₁,..., un} is an orthonormal basis for R" and x ER". Prove if x' u₁ = || u}'|| for all i, 1 ≤ i ≤n, then x = U₁ + ... + un -
Answers
(a) To prove the equation ||u' - v|| = √2√(1 - u · v) in R², where u and v are unit vectors, we can use the properties of the dot product and vector norms.
First, let's expand the norm on the left side of the equation:
||u' - v||² = (u' - v) · (u' - v)
Expanding the dot product, we have:
||u' - v||² = (u' · u') - 2(u' · v) + (v · v)
Since both u and v are unit vectors, their norms are equal to 1:
||u' - v||² = (1) - 2(u' · v) + (1)
Simplifying, we have:
||u' - v||² = 2 - 2(u' · v)
Now, let's focus on the right side of the equation:
√2√(1 - u · v) = √2√(1 - (u' · v))
Taking the square of both sides, we have:
2 - 2(u' · v) = 2 - 2(u' · v)
Therefore, the equation ||u' - v|| = √2√(1 - u · v) holds in R².
(b) To prove that if x'ui = ||ui|| for all i, 1 ≤ i ≤ n, where U = {u₁, ..., un} is an orthonormal basis for Rⁿ and x ∈ Rⁿ, then x = u₁ + ... + un.
Since U is an orthonormal basis, each ui is a unit vector, and they are linearly independent, forming a basis for Rⁿ. We can write any vector x ∈ Rⁿ as a linear combination of the basis vectors:
x = c₁u₁ + c₂u₂ + ... + cnun
Now, let's calculate the dot product of x with each basis vector ui:
x · ui = (c₁u₁ + c₂u₂ + ... + cnun) · ui
= c₁(u₁ · ui) + c₂(u₂ · ui) + ... + cn(un · ui)
Since the basis vectors are orthonormal, the dot product of any two distinct basis vectors is zero:
(uj · ui) = 0 (for j ≠ i)
Therefore, the dot product simplifies to:
x · ui = ci(u · ui)
Given that x · ui = ||ui|| for all i, we have:
ci(u · ui) = ||ui||
Since ui is a unit vector, the dot product (u · ui) is equal to the norm of u:
ci ||ui|| = ||ui||
This equation holds for all i, 1 ≤ i ≤ n. Since ||ui|| is non-zero (as ui is a unit vector), we can divide both sides of the equation by ||ui||:
ci = 1
Hence, each coefficient ci is equal to 1. Therefore, we can rewrite x as:
x = u₁ + u₂ + ... + un
If x'ui = ||ui|| for all i, 1 ≤ i ≤ n, where U = {u₁, ..., un} is an orthonormal basis for Rⁿ, then x can be written as the sum of the basis vectors: x = u₁ + u₂ + ... + un.
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1. The list shows the amounts of money student council collected from students for a field trip. Each student paid the same amount. What is the most the field trip could cost per student? Wednesday $36 Thursday $54 Friday $72 The most the field trip could cost is $ per student.
Answers
Answer:
Step-by-step explanation:
First find the LCM and it is going to be 18.
There are 24 students in a class that play basketball. If 75% are boys how many of the students are girls? Answer and Explanation.
Answers
Answer:
there are 18 boys and 6 girls
Step-by-step explanation:
suppose your class has 12 students, and the professor places students into 3 teams of 4 over the course of the semester, with 1 of the 4 students serving as the team lead. how many times does the professor need to form groups such that the 3 team compositions (and team leads) are guaranteed to repeat?
Answers
To guarantee that the 3 team compositions (and team leads) are repeated, the professor would need to form groups a total of 3 times over the course of the semester. Each time the professor forms groups, there would be 3 possible team compositions (since the team lead can change within each group) and after 3 formations, all 3 compositions would have been used and repeated.
To determine the number of possible unique team compositions and team leads that can be formed.
1. First, we'll find the number of ways to choose team leads for each group:
There are 12 students and 3 team leads needed, so there are 12 choose 3 ways to pick the team leads, which is calculated as C(12,3) = 12! / (3! * (12-3)!) = 220.
2. Now, we'll calculate the number of ways to divide the remaining 9 students into 3 groups of 3 students each. We can use the multinomial coefficient formula, which is:
C(9,3,3,3) = 9! / (3! * 3! * 3!) = 1680
3. To find the total number of unique team compositions (including team leads), we multiply the results from steps 1 and 2 Total unique team compositions = 220 * 1680 = 369,600
4. The professor needs to form the groups 369,601 times in order to guarantee that the 3 team compositions (and team leads) will repeat.
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In triangle ABD, AC is a median. The value of AC is?
Answers
Step 1
A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side.
Therefore,
\(\begin{gathered} Since\text{ C is the midpoint, }\bar{\text{DC}}\text{=}\bar{\text{CB}}\text{ } \\ 28=x+2 \\ x=28-2 \\ x=26 \end{gathered}\)Step 2
Find the value of Line AC the median.
\(\begin{gathered} \bar{AC}=x+8 \\ \bar{AC}=26+8=\text{ 34} \end{gathered}\)Hence, the value of line AC is 34
in what one year period of the study did the rabbit populations see the greatest decrease?
Answers
Answer- The rabbit population decreased in 2013 and 2015 in some areas of up to 80%
You can infer causality from a correlational result, but only when the r value is greater than ?A. 0B. 5C. 1
Answers
You can infer causality from a correlational result, but only when the r value is greater than:
C. 1
Causality refers to a situation in which one event causes another. When there is a correlation between two variables, it means that they tend to move in the same direction.
However, this does not necessarily mean that one event causes the other. In order for a correlation to indicate causality, the correlation coefficient (r) must be greater than 1. If the correlation coefficient is below 1, then there is not enough evidence to suggest that one event causes the other.
In addition, there are other factors that need to be considered when assessing causality from a correlational result.
For example, the strength of the relationship between the variables, the direction of the relationship, and the consistency of the results over time. It is also important to consider the context in which the research was conducted, as this may have an effect on the results.
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хWhich statements about comparing two numbers are correct? Select all that apply.A The number with fewer digits is always smallerB. The number with more digits is always smallerC. The number with the larger number in the ones place is always greater
Answers
Step 1:
The number with fewer digits is always smaller (Option A is correct)
Step 2
Numbers with different numbers of digits are never equal. (Option E is correct).
PLS ANSWER AS SOON AS POSSIBLE
Answers
Answer:
5p^2+5q^2-3pq^2
Step-by-step explanation:
3q^2+4p^2-2pq^2-(2pq^2-3p^2)
3q^2+4p^2-2pq^2-2pq^2+3p^2
7p^2+3q^2-4pq^2+(pq^2-5p^2+q^2+3p^2+q^2)
7p^2+3q^2-4pq^2+pq^2-2p^2+2q^2
5p^2+5q^2-3pq^2
Answer:36
Step-by-step explanation:
Determine for each x-value whether it is in the domain of f or not. -
Answers
Answer:
-7 is in our domain.
0 is in our domain
7 is not in our domain.
Step-by-step explanation:
So we have the rational function:
\(f(x)=\frac{x}{x-7}\)
The domain restrictions of rational functions are the zeros of the denominator. In other words, the domain of rational functions are always all real numbers except for the zeros of the denominator.
So, solve for the denominator by setting it to 0:
\(x-7=0\)
Add 7 to both sides:
\(x=7\)
So, our domain is all real numbers except for 7.
(When x=7, we have 7/0, which is undefined.)
Therefore:
-7 is in our domain.
0 is in our domain
7 is not in our domain.
Answer:
the picture has it all!
whatever equals zero is not the domain and whatever doesnt equal zero is the domain!
hope i helped :)
g(n) = 4n+ 3
f(n) =n +4
Find -5g (9) + 5f (9)
Answers
Answer: -130
Step-by-step explanation:
on donne A(-1,2). Determiner les coordonnées du point B tel que AOB soit un triangle direct,rectangle et isocèle en O.
Answers
Answer:
donald trump
Step-by-step explanation:
William and Debra Pierce are celebrating their 20th anniversary by having a reception at a local reception hall. They have budgeted $2,500 for their reception. If the reception hall charges a $100 cleanup fee plus $38 per person, find the greatest number of people that they may invite and still stay within their budget.
Answers
The greatest number of people that William and Debra may invite and still stay within their budget is 63.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Since William and Debra have budgeted $2,500 for their reception. Therefore, their total expenses should be equal to the total expenses in the reception.
Budget = Total expenses
Budget = Reception hall Cleanup charge + $38 per person fee
Let the number of people invited to the party be represented by x,
$2,500 = $100 + $38(x)
2500 = 100 + 38x
2500 - 100 = 38x
2400 = 38x
x = 2400 / 38
x = 63.157 ≈ 63
Hence, the greatest number of people that William and Debra may invite and still stay within their budget is 63.
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Part BHow much does Rosa earn for working 19 1/2 hours. Rpund to the nearest cent if necessary. Part ARosa earns 12.25$ per hpur at an ice cream shop.
Answers
Given data:
The amount Rosa earned per hour is 12.25$.
The expression for the given statement is,
\(1\text{ hour = \$12.25}\)Multiply the above expression by 19 1/2 on both sides.
\(\begin{gathered} 19\frac{1}{2}(1\text{ hour)=19}\frac{1}{2}(12.25) \\ 19\frac{1}{2}\text{ hours =19.5(12.25)} \\ =238.875 \\ =238.87 \end{gathered}\)Thus, the amount earned by Rosa in 19 1/2 hours is $238.87.
Which table represents a linear function?
୦
X
1
no
2
4
y
-2
-6
-2
-6
Answers
Because the graph always has a consistent slope of +2, the table x|y-2| 4|0| 6|2| is an illustration of a linear function table.
In order for a table to represent a linear function, there must be a constant rate of change (slope) between any two points on the graph. In other words, the relationship between the x-values and y-values should follow a consistent pattern.
The correct table that represents a linear function is: x|y-2| 4|0| 6|2|This is because there is a constant rate of change of +2 between any two points on the graph. For example, when x goes from 2 to 4, y increases from -2 to 0. When x goes from 4 to 6, y increases from 0 to 2.
This constant rate of change indicates that the relationship between x and y is linear.
In summary, a table represents a linear function when there is a constant rate of change between any two points on the graph. The table x|y-2| 4|0| 6|2| is an example of a linear function table because there is a consistent slope of +2 between any two points on the graph.
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Find the value of x if 12x=34^2 - 26^2
Answers
Answer:
40
Step-by-step explanation:
\( 12x = 34^2 - 26^2 \\
12x = (34+26)(34-26)\\
12x = 60\times 8\\\\
x = \frac{60\times 8}{12}\\\\
x = 5\times 8\\
x = 40\)
What is the range of the function shown in the graph?
Answers
Answer:
D. -∞ < y < 5
Step-by-step explanation:
The range are all the possible values for y that the function can take. In the graph we can see that the highest value for y is 5 and there isn't a lowest value for y. It means that the range are values between -∞ and 5.
So the range is:
-∞ < y < 5
Can i pls have help with is soooooooooo confused
Answers
500.
Solution: 210 is 42% of X
Equation: Y = P% * X
Solving our equation for X
X = Y/P%
X = 210/42%
Converting percent to decimal:
p = 42%/100 = 0.42
X = 210/0.42
X = 500
The points (- 1, – 2), (1, 0), (- 1, 2), (- 3, 0) forms a quadrilateral of type:
Answers
Answer:
A square.
Step-by-step explanation:
answer quickly
Write an equation of the cosine function with amplitude 2 and period 6π.
Answers
The cosine function with amplitude 2 and period 6π is given by:
y = 2cos(x/3).
What is the standard cosine function?The standard cosine function is given by:
y = Acos(Bx).
In which:
The amplitude is A.The period is of 2pi/B.For a cosine function with amplitude 2 and period 6π, we have that A = 2 and B = 1/3, hence:
y = 2cos(x/3).
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For each type of effect listedâmain effects, two-way interactions, and three-way interactionsâidentify the maximum number of possible effects that could be tested in a 2 Ã 2 Ã 2 factorial design. - 3 main effects- 1 three- way interaction- 3 two-way interactions
Answers
The maximum number of possible effects that could be tested in a 2x2x2 factorial design with 3 main effects, 3 two-way interactions, and 1 three-way interaction is 7.
In a 2 x 2 x 2 factorial design, we can test the following maximum number of possible effects:
Main effects:
There are 3 main effects in this design, one for each factor (A, B, and C). You would analyze the effect of each factor independently on the outcome variable.
Two-way interactions:
There are 3 possible two-way interactions that can be tested in this design: AxB, AxC, and BxC.
These interactions examine the combined effects of two factors on the outcome variable.
Three-way interactions:
There is 1 possible three-way interaction that can be tested in this design: AxBxC.
This interaction examines the combined effect of all three factors (A, B, and C) on the outcome variable.
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A function is given. PREVIOUS ANSWERS g(x) = x 4 gi x+9 (a) Determine the net change between the given values of the variable. (b) Determine the average rate of change between the given values of the variable
Answers
The average rate of change between the given values of the variable is 89 and the net change is 607.
The given function is
g(x) = x4 + 9.
Find the net change between the given values of the variable.
Net change = g(x₂) - g(x₁)
Net change = g(5) - g(-2)
Let x = 5
Net change = g(5) = 59
Net change = 625
Let x = -2
Net change = g(-2) = (-2)⁴ + 9
Net change = 25 - 7
Net change = 18
Therefore, the net change between the given values of the variable is
625 - 18 = 607.
Determine the average rate of change between the given values of the variable.
Average rate of change = (g(x₂) - g(x₁)) / (x₂ - x₁)
Average rate of change = (g(5) - g(-2)) / (5 - (-2))
Average rate of change = (625 - 18) / 7
Average rate of change = 89
Therefore, the average rate of change between the given values of the variable is 89.
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Draw the image of ABC under a dilation whose center is P and scale factor is 1/3
Answers
Answer:
there
Step-by-step explanation:
Answer:
khan
Step-by-step explanation:
Solve the simultaneous equations 3x- 4y =20 and 4x-2y = 25
Answers
Answer:
(6, - \(\frac{1}{2}\) )
Step-by-step explanation:
Given the 2 equations
3x - 4y = 20 → (1)
4x - 2y = 25 → (2)
Multiplying (2) by - 2 and adding to (1) eliminates the y- term
- 8x + 4y = - 50 → (3)
Add (1) and (3) term by term to eliminate y
- 5x = - 30 ( divide both sides by - 5 )
x = 6
Substitute x = 6 into either of the 2 equations and evaluate for y
Substituting into (1)
3(6) - 4y = 20
18 - 4y = 20 ( subtract 18 from both sides )
- 4y = 2 ( divide both sides by - 4 )
y = \(\frac{2}{-4}\) = - \(\frac{1}{2}\)
Solution is (6, - \(\frac{1}{2}\) )
The solution of the linear equations 3x - 4y = 20 and 4x - 2y = 25 will be (6, -0.50).
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The linear equations are given below.
3x - 4y = 20 ...1
4x - 2y = 25
8x - 4y = 50 ...2
Subtract equation 1 from equation 1, then we have
8x - 4y - 3x + 4y = 50 - 20
5x = 30
x = 6
The value of the variable 'y' will be given as,
3(6) - 4y = 20
18 - 4y = 20
4y = - 2
y = - 0.50
The solution of the linear equations 3x - 4y = 20 and 4x - 2y = 25 will be (6, -0.50).
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At what point do the curves r1 = < t, 4 - t, 12 + t2 > and r2 = < 6 - s, s - 2, s2 > intersect?
Answers
To calculate the intersection point equate the pair of components to each other. The equations can be rewritten as:
\(t = 6 - s; \\ 4 - t = s - 2 ; \\ 12+t^{2} =s^{2};\)
Simplifying the above three equations by substituting the value of “\(t = 6 - s\)” in the last equation.
Therefore,
\(12+(6 - s)^{2} = s^{2} \\ 12s =60\\ s=5\)
Now, substitute the value of "s" and calculate the value of "t".
Therefore,
\(t = 6-s\\ t=1\)
Substituting the value of \(s = 5; t= 1\) in all the three equations we get intersect points as \((1,1,25).\)
What are the intersecting lines?
When two or more lines cross each other then it is called intersecting lines. The intersecting lines meet at a single point which is known as a point of intersection.
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10 Points<>I need help ASAP!!!
Answers
Answer:
Step-by-step explanation:
A and D
Someone help me ples
Answers
Answer:
24
Step-by-step explanation:
You should draw a picture to let everything fall into place:
.................2x.......................
N ----x+7------ O ---10---- P
Then you can easily see that
x+7 + 10 = 2x
17 = 2x - x
so x = 17
NP = 2x = 2*17 = 34
NO = x+7 = 17+7 = 24
OP = 10
NO + OP = 24 + 10 = 34 = NP