3. (3 pts) Find the general solution of the following homogeneous differential equations. 2xyy' + (x² - y²) = 0
Answers
The general solution of the given homogeneous differential equation is:y = ±x√(Cx² + 2)
The given differential equation is: 2xyy' + (x² - y²) = 0
We have to find the general solution of the given homogeneous differential equation. To solve the above differential equation, we will use the substitution method.
Put y = vx and y' = v + xv'
Differentiating both sides w.r.t x: y' = v + xv' ⇒ v' = (y' - v)/x
Differentiating again w.r.t x: y'' = v' + xv'' + v' ⇒ y'' = (y'' - 2y'v + v² + xv')/x
Substituting these values in the given differential equation:
2x(v)(v + xv') + (x² - v²x²) = 0
2v + 2x²v' + x - v² = 0
2x²v' + 2v/x - v³/x = -1/x
We can write the above differential equation as:
2x²dv/dx + 2v/x = v³/x - 1/x
Separating the variables and integrating both sides:
∫dx/x = ∫[v/(v² - 2)]dv/x
⇒ ln |x| + ln |v² - 2| + C
⇒ ln |x(v² - 2)| = ln |Cx|
⇒ v² - 2 = Cx² (where C is a constant)
⇒ v = ±√(Cx² + 2)
Putting the value of v in y = vx, we get:
y = x√(Cx² + 2) and y = -x√(Cx² + 2)
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Related Questions
Your hospital has just reset the safety stock level for sleeping pills to be 220 pills.
If your hospital consumes an average of 1,155 per day with a standard deviation of 81 pills, what is the chance that your hospital will run out of sleeping pills on any day? (Keep four decimal places in your answer, which should be a number not a percentage)
Answers
The chance that the hospital will run out of sleeping pills on any given day is 0.5000 (or 0.5000 with four decimal places).
To calculate the chance that the hospital will run out of sleeping pills on any given day, we can use the normal distribution and Z-score.
First, let's calculate the Z-score using the formula:
Z = (X - μ) / σ
Where:
X = consumption rate per day (1,155 pills)
μ = average consumption rate per day (1,155 pills)
σ = standard deviation (81 pills)
Z = (1,155 - 1,155) / 81
Z = 0
Now, we need to find the probability associated with this Z-score. However, since the demand for sleeping pills can be considered continuous and not discrete, we need to calculate the area under the curve from negative infinity up to the Z-score. This represents the probability of not running out of sleeping pills.
We discover that the region to the left of a Z-score of 0 is 0.5000 using a basic normal distribution table or statistical software.
To find the probability of running out of sleeping pills, we subtract this probability from 1:
Probability of running out of sleeping pills = 1 - 0.5000
Probability of running out of sleeping pills = 0.5000
Therefore, on any given day, the hospital has a 0.5000 (or 0.5000 with four decimal places) chance of running out of sleeping tablets.
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Whose answer is correct? Explain your reasoning.
Answers
PLEASE HELP!!!! offering 45 points with brainiest
Answers
Answer:
\(\huge\boxed{12 \ people}\)
Step-by-step explanation:
By looking at the range of histogram , we come to know that:
People who walked for 0-2 hours = 5
People who walked for 2-4 hours = 17
People who walked for 4-6 hours = 12
People who walked for 6-8 hours = 9
People who walked for 8-10 hours = 3
Answer:
12 people
Step-by-step explanation:
We want to find the number of people between 4 and 6 hours
Reading the chart, the third bar is between 4 and 6 hours
12 people
when the positive integer n is divided by 3, the remainder is 2, and when n is divided by 5, the remainder is 1. what is the least possible value of n ?
Answers
The smallest number that appears in both lists is 11. Therefore, the least possible value of n that satisfies both conditions is 11.
To find the least possible value of n, we need to find the smallest number that satisfies both conditions.
We can start by listing out some numbers that have a remainder of 2 when divided by 3: 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95, 98, 101, 104, 107, 110, 113, 116, 119, 122, 125, 128, 131, 134, 137, 140, 143, 146, 149, 152, 155, 158, 161, 164, 167, 170, 173, 176, 179, 182, 185, 188, 191, 194, 197, 200, 203, 206, 209, 212, 215, 218, 221, 224, 227, 230, 233, 236, 239, 242, 245, 248, 251, 254, 257, 260, 263, 266, 269, 272, 275, 278, 281, 284, 287, 290, 293, 296, 299, and so on.
Out of these numbers, we need to find the ones that also have a remainder of 1 when divided by 5. The numbers that have a remainder of 1 when divided by 5 are: 1, 6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71, 76, 81, 86, 91, 96, and so on.
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3(x+2)=36
Please help
Answers
Answer:
Step-by-step explanation:
3(x+2)=36
3x+6=36
3x=30
x=10
Answer:
3 (10+2)=36
Step-by-step explanation:
Hope this helps
ill give brainliest to the correct and best explained answer :))
Answers
Answer:
Step-by-step explanation:
To find the median, arrange the data in ascending order
10,20,30,40,50,60,70,80,90
Number of data = 9 . It is a odd number
So, median will be the (n+1)/2 th term
\(\left(\dfrac{9+1}{2} \right)^{th \ term} = (\dfrac{10}{2})^{th \ term} = 5^{th \ term}\)
Median = 50
Solution:
Step-1: Re-arrange the following data from biggest to smallest.
30, 10, 40, 20, 60, 50, 80, 70, 90=> 90, 80, 70, 60, 50, 40, 30, 20, 10Step-2: Refer to the following:
1. If there is an even number of digits, you will use the formula:
(Total number of digits)/22. If there is an odd number of digits, you will use the formula:
(Total number of digits + 1)/2Step-3: Find the median:
If we count the number of digits in the data, we can say that nine numbers are in this data. Thus, we will use the formula "(Total number of digits + 1)/2"
=> (Total number of digits + 1)/2 term=> (9 + 1)/2 term=> 10/2 term=> 5th termThe fifth term of the group is the median.
Step-4: Review the "biggest to smallest" data.
90, 80, 70, 60, 50, 40, 30, 20, 10Since 50 is the 5th term, the median is 50.
........ edges 1- Assume G is a complete graph has 100 vertices, then G must has. a) 4950 b) 10000 c) 99 d) 200 2- Assume G is a connected graph has 100 vertices, then G must has at least..............edges a) 4950 b) 10000 c) 99 d) 200 3- Consider the following algorithm For i=1 to n kn while k>=1 do k=k/2 The complexity of the above algorithm is a) 2 (n²) b) 0 (n lg n) c) 8( ilgn) (d) 0( Ign) 4- Minimum Spanning Tree algorithm is a ................ Method a) Backtracking b) Dynamic c) Greedy 5-if G has a path between each two vertices then G is a.......................Graph a) Complete b) Connected c) Complete and Connected 6- Any problem in NP-Complete class is in a) NP-class b) P-class c) NP-Hard d) a + c 7- The ................. algorithm has a linear complexity a) Binary search b) Matrix multiplication c) Max is in-place Algorithm a) Insertion sort b) Selection sort c) Min Algorithm 9- The worst case analysis of insertion sort is a) 0(n²) b) 8 (n lg n) c) 0 (n¹5) 10-An example of greedy method is a) Dijkstra b) Quick Sort 8- The......... c) Min&Max d) 0(¹25) d)All d) Divide& conquer d) None d) Merge sort d) All
Answers
The complete graph with 100 vertices will have \(\( \binom{100}{2} = 4950 \)\)edges. Therefore, the correct option is (a) 4950. A connected graph with 100 vertices must have at least 99 edges.
1. A complete graph with 100 vertices means that there is an edge between every pair of vertices. The number of edges in a complete graph with n vertices is given by the formula \(\( \binom{n}{2} = \frac{n(n-1)}{2} \)\). Substituting n = 100, we get\(\( \frac{100 \cdot 99}{2} = 4950 \)\) edges.
2. In a connected graph with n vertices, the minimum number of edges required to ensure connectivity is n - 1. Therefore, a connected graph with 100 vertices must have at least 99 edges.
3. The given algorithm has a loop that divides the value of k by 2 in each iteration. As long as k is greater than or equal to 1, the loop continues. Since the value of k is halved in each iteration, the loop will run approximately \log ntimes. Therefore, the complexity of the algorithm is \(\( O(\log n) \)\).
4. The Minimum Spanning Tree algorithm is a Greedy method because it makes locally optimal choices at each step to construct the minimum spanning tree.
5. A graph is called connected if there is a path between every pair of vertices. Therefore, if a graph has a path between each two vertices, it is a connected graph.
6. NP-Complete problems are a subset of problems in the NP-class and are also NP-Hard. Therefore, any problem in the NP-Complete class is in both NP-class and NP-Hard class.
7. The algorithm with linear complexity is the Max is in-place Algorithm, which finds the maximum element in an array by comparing each element with the current maximum and updating it if necessary.
8. The worst-case time complexity of Insertion Sort is\(\( O(n^2) \)\) because in the worst case, for each element, it may need to be compared and shifted with every element to its left.
9. Dijkstra's algorithm is an example of the Greedy method for finding the shortest path in a graph.
10. The correct option is not provided for question 10, as none of the given options
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A complete collection of all elements (scores, people, measurements, and so on) to be studied is called the Group of answer choices sample population parameter grade
Answers
The correct option is B. The complete collection of all elements, individuals, measurements, scores, or other entities that are of interest and relevant to a particular study or analysis is called the population.
A collection is a group of items that have been gathered or accumulated together based on a particular theme or purpose. Collections can be made up of physical objects such as books, stamps, coins, or artwork, as well as digital items like photos, music, or videos. Collections can also refer to data structures in computer programming that hold groups of related items.
People often collect items as a hobby or passion, and the act of collecting can bring a sense of fulfillment, enjoyment, and satisfaction. Collections can have both sentimental and monetary value, and they may be displayed in personal or public settings, such as museums or galleries. The process of collecting often involves researching and acquiring new items, as well as organizing and preserving the existing collection.
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Joey rode his bicycle 125 yds. The diameter tire is 25 inches. How many whole revolutions did the tire make (1 yd= 36 inches) ?
Answers
Answer:
Step-by-step explanation:
which fraction is greater 7/10 or 2/6
Answers
Answer:
7/10
Step-by-step explanation:
Answer:
7/0
Step-by-step explanation:
Find the smallest value of k, such that 16k is a perfect cube.
Answers
Answer:
k = 4
Step-by-step explanation:
16k = 16(4) = 64 and
64 = 4 × 4 × 4
\(\sqrt[3]{64}\)
= \(\sqrt[3]{4^{3} }\)
= 4
Determine the surface area of a cereal box with these dimensions width: 3 inches length: 8 inches height: 12 inches
Answers
|-0.8 x 10| Help pls
Answers
solution steps: |-0.8 × 10|
Multiply -0.8 and 10 to get -8.
|8|
The absolute value of a real number a is
a when a > 0, or -a when a < 0. The
absolute value of -8 is 8.
8
18x2 - 54x – 20
Expand and simplify
Answers
Answer:
36x- 54x-20
-18x-20
-38
PLEASE HELP ASAP
Which is NOT true of the construction of an angle bisector?
A)You start with any angle
B) When you're finished, you have a line that bisects your segment
C) You must draw an arc using the vertex as the center
D) When you're finished, you have a ray that bisects your angle
Answers
Answer:
B) When you're finished, you have a line that bisects your segment
Step-by-step explanation:
An angle bisector is a ray that divides a given angle into two congruent parts. There is no line segment involved.
__
The statement that is not true about this construction is ...
B) When you're finished, you have a line that bisects your segment
_____
Additional comment
The construction effectively creates an arc of a circle, then creates the perpendicular bisector of the chord of that arc. The center of the circular arc is the vertex of the angle being bisected. The constructed perpendicular bisector of the chord also bisects the angle. (The chord is never actually drawn, and the "circular arc" may be two short arcs across the rays of the angle being bisected.)
Terry's house is 32 feet wide and the peak of the roof line is at 24 feet. write the absolute value equation to model the roof line
Answers
The peak is at y = 24 feet, the vertex point (h, k) is (16, 24). Plugging these values into the equation, we get:
y = |x - 16| + 24
This equation models the roof line of Terry's house.
To model the roof line of Terry's house, we can use the concept of absolute value. The equation for an absolute value function can be written as:
y = |x - h| + k
where (h, k) represents the vertex of the absolute value graph.
In this case, the peak of the roof line is at 24 feet. Since the width of the house is 32 feet, the vertex of the absolute value graph will be at the midpoint of the width, which is 16 feet. Therefore, h = 16.
Since the peak is at y = 24 feet, the vertex point (h, k) is (16, 24). Plugging these values into the equation, we get:
y = |x - 16| + 24
This equation models the roof line of Terry's house.
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A line passes through (-8,1)and has a slope of -5/4
write an equation in slope-intercept form for this line.
please help!
Answers
\( \Large{\boxed{\sf y = - \dfrac{5}{4}x - 9}} \)
\( \\ \)
Explanation:First, let's recall what is an equation of a line in slope-intercept form:
\( \Large{\left[ \begin{array}{c c c} \underline{\tt Slope-Intercept \ Form \text{:}} \\ ~ \\ \tt y = mx + b \end{array} \right] } \)
Where:
(x , y) is a point on the line.m is the slope of the line.b is the y-intercept.\( \\ \)
Since we are given the value of the slope, we can subtitute it into the equation:
\( \sf y =- \dfrac{5}{4}x + b \)
\( \\ \)
We know that the line passes through (-8 , 1), which means that the coordinates of this point verify the equation of the line. Therefore, we can substitute its coordinates into the equation and solve for b:
\( \sf (\underbrace{\sf -8}_{x} \ , \ \overbrace{\sf 1}^{y} ) \\ \\ \\ \rightarrow \sf 1 = - \dfrac{5}{4} \cdot (-8) + b \\ \\ \\ \rightarrow \sf 1 = -\dfrac{5 \cdot (-8) }{4} + b \\ \\ \\ \rightarrow \sf 1 = -\dfrac{- 40}{4} + b \\ \\ \\ \rightarrow \sf 1 = 10 + b \\ \\ \\ \rightarrow \boxed{\sf b = -9} \)
\( \\ \)
Therefore, the equation of the line in slope-intercept form is:
\( \boxed{\boxed{\sf y = - \dfrac{5}{4}x - 9}} \)
\( \\ \)
\( \hrulefill \)
\( \\ \)
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To write the equation of a line in slope-intercept form, we can use the formula:
\(\qquad\Large\begin{aligned}\bigstar\:\boxed{\rm{\:\:y = mx + b\:\:}}\end{aligned}\)
where:
m is the slope.b is the y-intercept.\(\\\)
As per the provided information, we know that the line passes through the point (-8, 1) and has a slope of -5/4, we can substitute these values into the equation to find the y-intercept.
\(\\\)
Let's solve for b:
\(\Large\quad\begin{aligned}\rm\dashrightarrow{y}& = \rm{mx + b} \\\\\rm\dashrightarrow{1}& = \rm{ {\large{-\frac{5}{4}}} \cdot -8 + b} \\\\\rm\dashrightarrow{1}& = \rm{{ \large{\frac{40}{4}}} + b} \\\\\rm\dashrightarrow{1}& = \rm{10 + b} \\\\\rm\dashrightarrow{b}& = \rm{1 - 10} \\\\\rm\dashrightarrow{b}& = \rm{-9}\end{aligned}\)
\(\\\)
Now that we have the slope m = -5/4 and the y-intercept b = -9, we can write the equation of the line:
\(\Large\quad\begin{aligned}\boxed{\boxed{\rm{\:\:y = -\dfrac{5}{4}x - 9\:\:}}}\: \overline{\quad} \: \large{\red{\sf{answer}}}\end{aligned}\)
\(\\\\\\\)
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Given m||n, find the value of x.
kt
(6x+5)°
(7X-40°
Answers
Answer:
x = 9
Step-by-step explanation:
These are alternate exterior angles and alternate exterior angles are equal if m is parallel to n
6x+5 = 7x-4
Subtract 6x from each side
6x -6x+5 = 7x-6x-4
5 = x -4
Add 4 to each side
5+4 =x-4+4
9 =x
2 birds are building a nest. Bird A is flying toward the nest at the same time bird B is flying away from it
Answers
Answer:
Step-by-step explanation:
is it that 1 bird is at the nest and the other is flying away ?
Lane uses counters to make a 4 X 7 array and a 1 X 7 array. What size array can he make using all of these counters?3rd grade subject
Answers
Answer:
5 x 7 array
Explanation:
Lane makes a 4 X 7 array and a 1 X 7 array.
Note that the second number 7 is the same in both cases.
Therefore, the array size that he can make using all of the counters is:
\(\begin{gathered} (4\times7)+(1\times7) \\ =(4+1)\times7 \\ =5\times7 \end{gathered}\)Lane can make a 5 x 7 array using all of the counters.
i need help I am haveing trouble understanding
Answers
Answer: y= x + 4
Step-by-step explanation:
helpp if you can tyy <3
Answers
Step-by-step explanation:
please mark me as brainlest
A sample of helium gas occupies 12. 4 L at 23oC and 0. 956 atm. What volume will it occupy at 40oC and 0. 956 atm?
Answers
The helium gas will occupy approximately 13.09 L at 40°C and 0.956 atm.
To solve this problem, we can use the combined gas law equation, which states:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = Initial pressure
V1 = Initial volume
T1 = Initial temperature (in Kelvin)
P2 = Final pressure
V2 = Final volume (what we need to find)
T2 = Final temperature (in Kelvin)
First, let's convert the temperatures to Kelvin:
Initial temperature T1 = 23°C + 273.15 = 296.15 K
Final temperature T2 = 40°C + 273.15 = 313.15 K
Now, let's substitute the given values into the equation:
(0.956 atm * 12.4 L) / (296.15 K) = (0.956 atm * V2) / (313.15 K)
Now we can solve for V2:
(0.956 atm * 12.4 L * 313.15 K) / (0.956 atm * 296.15 K) = V2
Simplifying the equation, we find:
V2 ≈ 13.09 L
Therefore, the helium gas will occupy approximately 13.09 L at 40°C and 0.956 atm.
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Can someone help me on this?
Answers
5s + 10a = 3000
x = students
y = adults
5x + 10y = 3000
follow the instructions to find x/y intercept;
for example;
5(0) + 10y = 3000
10y = 3000
y = 300;
you would then want to solve for “x” by plugging “y” for 0.
I can explain further if you’d like;
Math is hard help !!!!!
Answers
Answer:
3000
Step-by-step explanation:
x = original amount of GHC
\(\frac{1}{3} (\frac{1}{2}x)\) --> 1/6x = 500
x= 3000
What would be the opportunity cost of spending $90,000 on advertising but only producing 12,000 units? Potential sales (before advertising) of 12,000 units, Price of $16, Fixed costs of $48,000, Variable costs $8, Advertising $90,000 Assume advertising multiplier is (30,000+ advertising)/30,000
$76,800
$576,000
$192,000
−$191,936
$768,000
Answers
The opportunity cost of spending $90,000 on advertising but only producing 12,000 units can be calculated by comparing the benefits of the advertising investment to the potential alternative uses of that money.
First, let's calculate the total cost of producing 12,000 units. Fixed costs amount to $48,000, and variable costs are $8 per unit, resulting in a total cost of $48,000 + ($8 × 12,000) = $144,000.
Next, we need to calculate the potential sales revenue without advertising. With a price of $16 per unit, the potential sales revenue would be $16 × 12,000 = $192,000.
Now, let's calculate the potential sales revenue after advertising. The advertising multiplier is given as (30,000 + advertising) / 30,000. In this case, the multiplier would be (30,000 + 90,000) / 30,000 = 4.
Therefore, the potential sales revenue after advertising would be $192,000 × 4 = $768,000.
The opportunity cost is the difference between the potential sales revenue after advertising ($768,000) and the potential sales revenue without advertising ($192,000), which is $768,000 - $192,000 = $576,000.
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HELP! Find the slope of the line in the graph below using any method you want:
1. 4/5
2. - 5/4
3. 5/4
4. - 4/5
Answers
Answer:
-4/5
Step-by-step explanation:
its going down 4, and to the right 5 units.
PLS HELP ASAP¡!!!
A P E X MATH
Answers
Answer:
Step-by-step explanation:
Is there an image to see?
Mr Louis wants to top-up his central heating oil tank.
The oil tank can take up to 1400 litres of oil.
There are already 150 litres of oil in the tank.
The price of oil is 80. 5p per litre.
As a loyal customer, Mr Louis gets a 6. 5% discount on the price of the oil.
How much discount does Mr Louis get on this purchase?
Give your answer in £.
Answers
If Mr Louis gets a 6. 5% discount on the price of the oil, Mr. Louis gets a discount of £65.41 on this purchase.
First, let's find out how many litres of oil Mr. Louis needs to fill his tank:
Maximum capacity of the tank: 1,400 litres
Current oil in the tank: 150 litres
Litres needed to top up: 1,400 - 150 = 1,250 litres
Next, we'll calculate the original price of the oil without the discount:
Price per litre: £0.805
Cost of oil needed: 1,250 litres * £0.805 = £1,006.25
Now, let's calculate the discount amount:
Discount percentage: 6.5%
Discount amount: £1,006.25 * 0.065 = £65.41
So, Mr. Louis gets a discount of £65.41 on this purchase.
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Find the perimeter of the figure.
istg i am going crazy :) i hate math
Answers
Answer:
30 centimeters
Step-by-step explanation:
P = 6 + 4 + 4 + 6.5 + 9.5 = 30