this leads us to a sturm-louiville problem in x. in each case the general solution in x is written with constants a and b
Answers
An example of a boundary value problem is the Sturm-Liouville problem, which entails determining the eigenvalues and eigenfunctions of a differential equation that complies with specific boundary requirements.
The general formula for the Sturm-Liouville problem's solution in x is y(x) = a * f(x) + b * g(x), where a and b are constants and f(x) and g(x) are the differential equation's eigenfunctions. When the differential equation and boundary conditions are solved, the eigenvalues and eigenfunctions are discovered.
For instance, if the differential equation has the following form: -y" + q(x)y = lambda* w(x)y where y is the dependent variable, y" is the second derivative of y, q(x) and w(x) are functions of x, and lambda is the eigenvalue, the boundary conditions can be of the following
form: where L is the length of the interval on which the differential equation is defined, y(0) = 0, and y(L) = 0.
The general solution in x can be expressed in the form: y(x) = a * f(x) + b * g(x), where a and b are constants and f(x) and g(x) are the eigenfunctions of the differential equation. The eigenvalues and eigenfunctions can be discovered by solving this differential equation and the boundary conditions.
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Related Questions
Is r = 6 a solution to the inequality below? 10 < r
Answers
Answer:
No
Step-by-step explanation:
10 is not less than 6, so 10 < r when r=6 is not true.
I have 47 question fast and right and no link or bot
Answers
Answer:
1 square root
2 irrational
3it a integer and a rational number(2)
Step-by-step explanation:
Arrange the steps in order to simplify the expression
Answers
Answer:
Step-by-step explanation:
For step explanation:
1. write the problem
2. distinguishing the neg sign
3. distributing 3
4. moving like terms next to each other through commutative property
5. Combining like terms
6. getting rid of parentheses
hot-air balloon is floating above a straight road. To calculate their height above the ground, the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon. The angles of depression are found to be 26∘ and 30∘.
How high (in feet) is the ballon?
Answers
The height of balloon is 1.99 miles above the ground.
What is angle of depression ?In the event when the line of sight is directed downhill from the horizontal line, an angle is created with it. Angle of depression is the angle produced between the horizontal line and the observer's line of sight when the object being observed is below the level of the observer.
Let's give the balloon's height above the earth and the distance it is from the first milepost horizontally a name.
We can state the following if the angle of this milepost's depression is 24 degrees:
Tan(24)=\(\frac{h}{b}\)
b = \(\frac{h}{tan(24)}\)
We can state the following for the following milepost as there will be (b+1)miles horizontal distance of and a 20 degree depression at that location.
tan(20)=\(\frac{h}{b+1}\)
b +1 = \(\frac{h}{tan(20)}\)
Therefore, substituting equation 1
\(\frac{h}{tan(24)}\) = \(\frac{h}{tan(20)} -1\)
1 = \(\frac{h}{tan(20)}\) - \(\frac{h}{tan(24)}\)
1 = h× ( \(\frac{h}{tan(20)}\) - \(\frac{h}{tan(24)}\) )
h = 1.99 miles
Consequently, the height of balloon is 1.99 miles above the ground.
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Find the eccentricity, b. identify the conic, c. give an equation of the directrix, and d. sketch the conic.
r=12/3--10 Cosθ
Answers
Answer:
a) 10/3
b) hyperbola
c) x = ± 6/5
Step-by-step explanation:
a) A conic section with a focus at the origin, a directrix of x = ±p where p is a positive real number and positive eccentricity (e) has a polar equation:
\(r=\frac{ep}{1\pm e*cos\theta}\)
Given the conic equation: \(r=\frac{12}{3-10cos\theta}\)
We have to make it to be in the form \(r=\frac{ep}{1\pm e*cos\theta}\):
\(r=\frac{12}{3-10cos\theta}\\\\multiply\ both\ sides\ by\ \frac{1}{3} \\\\r=\frac{12*\frac{1}{3}}{(3-10cos\theta)*\frac{1}{3}}\\\\r=\frac{12*\frac{1}{3}}{3*\frac{1}{3}-10cos\theta*\frac{1}{3}}\\\\r=\frac{4}{1-\frac{10}{3}cos\theta } \\\\r=\frac{\frac{10}{3}(\frac{6}{5} ) }{1-\frac{10}{3}cos\theta }\)
Comparing with \(r=\frac{ep}{1\pm e*cos\theta}\)
e = 10/3 = 3.3333, p = 6/5
b) since the eccentricity = 3.33 > 1, it is a hyperbola
c) The equation of the directrix is x = ±p = ± 6/5
Find the measure of the arc.
A
1460
E
B
mBC = [ ? ]0
![Find the measure of the arc.A1460EBmBC = [ ? ]0](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/ieYWgJHgsetMUGLNxwnD5f6E7hUYGVrm.png)
Answers
Answer:
see the attachment photo!
![Find the measure of the arc.A1460EBmBC = [ ? ]0](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/AFu2SusEZSdrlfiBFM2hN0WhByWPqvTJ.jpeg)
Evaluate each indefinite integral. SHOW STEPS
Answers
1. integrate 75x ^ 4 * cos(5x ^ 5 - 3) dx
Integral by substitution
2. integrate 3cos u du
Isolate the coefficient
3 * integrate cos u du
Evaluate the integral
4. 3sin u
Simplify and add the C
= 3sin(5x ^ 5 - 3) + C
Answer
3sin(5x ^ 5 - 3) + C
hope this will help u
please mark me as a brainliest
Answer:
\(3sin(5x^{5} -3) + C\)
Step-by-step explanation:
\(\frac{d}{dx}[sin (ax^{n}+b)] = [anx^{n-1}cos(ax^{n} + b)]\)
a and b are constants
∴\(\frac{d}{dy} sin(5x^{5} -3) = [(5)(5)x^{5-1}-0] cos(5x^{5} -3)\)
= \(25x^{4} cos(5x^{5} -3)\)
\(\int\ {75x^{4}cos(5x^{5} -3)} \, dx\)
Rewriting the above by applying algebraic manipulation:
\(\int\ (3)(25){x^{4}cos(5x^{4} -3)} \, dx\)
=\(3[\int\ 25{x^{4}cos(5x^{5} -3)} \, dx]\)
= \(3sin(5x^{5} - 3) + C\)
C is a constant, which is added to the above integration because there are no limits set. In other words, this is an indefinite integral.
Finish the sequence: 2/3,4/3,2,8/3,10/3
Answers
Answer:
4, 14/3, 16/3
Step-by-step explanation:
you add 2/3 to each number
Answer:
What similarities and differences do you see as compared to the muslim world?
Zachary recorded the grade-level and instrument of everyone in the middle school
School of Rock below.
Seventh Grade Students
Instrument # of Students
Guitar
Bass
Drums
Keyboard
7
14
15
9
Eighth Grade Students
Instrument # of Students
Guitar
Bass
Drums
Keyboard
2
15
2
11
Based on these results, express the probability that an eighth grader chosen at
random will play the drums as a percent to the nearest whole number.
Answers
Percent to the nearest whole number = 7%
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
Probability = (Number of possible outcomes)/(Total number of outcomes)
Total number of outcomes = 2 + 15 + 2 + 11 = 30
Number of possible outcomes = 2
Probability = 2/30 = 1/15 = 0.0666
Percent to the nearest whole number = 0.0666 *100 = 7%
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Answer:7
Step-by-step explanation:
solve the question 7 _ 2 3/7
Answers
Answer:
Do you mean 7 - 2 and 3/7?
If so:
Convert the mixed numbers to improper fractions, then find the LCD and combine.
Exact Form:
32 /7
Decimal Form:
4. 571428
Mixed Number Form:
4 and 4 /7
Step-by-step explanation:
Have a great day!
Answer:
3.7 the answer.........
-2|10 + 5x|-8=-16
How do I solve?
Answers
Answer:
so the answer is
x = -6/5, - 14/ 5
Step-by-step explanation:
i hope this is what your looking for
Answer:
5/6 and -26/5
Step-by-step explanation:
-16 divide -2 = 8
Add 8 = 16
Remove absolute value
Positive 16 - 10 = 6
Divide 5 = 6/5
Negative -16 - 10 = -26
Divide 5 = -26/5
Find the values of a and b such that
x^2 + 3x + 4 = (x + a)^2+ b
Answers
Answer:
\(x {}^{2} + 3x + 4 = (x + a) {}^{2} + b \\ x {}^{2} + 3x + 4 = x {}^{2} + 2ax + a {}^{2} + b \\ = x {}^{2} + a {}^{2} + 2ax + b \\ 2a = 3 \\ b = 4 \\ a = \frac{3}{2} \\ b = 4\)
Answer:
a=3/2
b=7/4
hope this help
) If the pattern shown continues, how many black keys appear on a portable keyboard with 49 white keys? Suggestion: use equivalent ratios or a rate table to confirm your answer.
Answers
Answer:
35
Step-by-step explanation:
Here we see 5 black keys for every 7 white keys.
So the ratio is 5:7
If we need 49 white keys, find the amount we scale the original ratio by:
49/7 = 7
So we are scaling by a factor of 7.
The number of black keys would be 5 * the scale of 7. = 35
So there should be 35 black keys.
Using proportions, it is found that 35 black keys appear on a portable keyboard with 49 white keys.
This question is solved by proportions, applying a rule of three.The equivalent ratio given, from the picture, is that for 7 white keys, there are 5 black keys. Hence, how many black keys will be there when there are 49 white keys?The rule of three is:
7 white keys - 5 black keys
49 white keys - x black keys
Applying cross multiplication:
\(7x = 49 \times 5\)
Simplifying both sides by 7:
\(x = 7 \times 5 = 35\)
Hence, 35 black keys will appear.
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A study of malaria transmission in Africa tested whether drinking beer increased attractiveness to mosquitoes. Yes, this is a real story (Lefevre et al. 2010. PLOS One5:e9546), and for simplicity I have changed some details from what they actually did. The researchers opened a container of 50 mosquitoes and looked at what proportion of the 50 mosquitoes left the container and flew towards the volunteer person. They did this experiment with 30 persons and each person was tested twice, once before they drank anything and then (an hour later) after they had consumed a beer. Assuming that the proportions of mosquitoes are normally distributed and the variances are similar, what would be the best test to see if more mosquitoes are attracted to people after drinking a beer
Answers
Answer:
The best test to see if more mosquitoes are attracted to people after drinking beer is the z-test for the difference in proportion of two populations
Step-by-step explanation:
The study tested if drinking bear increases the attractiveness to mosquitoes
The number of people the taking part in the study, n = 30 people
The total number of mosquitoes in the study = 50 mosquitoes
The proportion of mosquitoes flying to each volunteer is measured before and one hour after consuming bear
The mean number of mosquito flying towards a volunteer can be found by summing the other proportions that fly towards the 30 volunteers and dividing by n₁ = 30, before and n₂ = 30 after the respondents had bear to obtain \(\hat{p}_{1}\) and \(\hat{p}_{2}\)
Given that the variances are equal and the sum of the sample for the two tests, n₁ + n₂ = 60 > 30, it is, best to use the the z-test for the difference in proportion as follows;
\(Z=\dfrac{\hat{p}_1-\hat{p}_2}{\sqrt{\hat{p} \cdot (1-\hat{p}) \cdot \left (\dfrac{1}{n_{1}}+\dfrac{1}{n_{2}} \right )}}\)
Where the pooled mean, \(\hat p\), is given as follows;
\(\hat p = \dfrac{n_1 \cdot \hat p_1 + n_2 \cdot \hat p_2}{n_1 + n_2}\)
In a sequence of numbers,
a₁ = -6, a3 = 4, a5 = 14, a6 = 19,
and a 24. Based on this
information, which equation
can be used to find the nth
term in the sequence, an?
Answers
Answer:
Step-by-step explanation:
To find the equation for the nth term in the sequence, we need to determine the pattern or rule that generates the sequence.
From the given information, we can see that the sequence is not arithmetic because the differences between consecutive terms are not constant. Instead, the sequence appears to be quadratic because the second difference between consecutive terms is constant.
Using the given values of a₁, a₃, and a₅, we can find the first few differences:
a₃ - a₁ = 4 - (-6) = 10
a₅ - a₃ = 14 - 4 = 10
So, the first difference is 10, which indicates a linear term in the equation for an. We can now use the given value of a₁ and the first difference to find the constant term in the quadratic equation. Let d be the common difference, then we have:
a₂ = a₁ + d = -6 + 10 = 4
a₄ = a₃ + d = 4 + 10 = 14
a₆ = a₅ + d = 14 + 10 = 24 - 1
a₇ = a₆ + d = 24 - 1 + 10 = 33
Now, we can find the second difference between consecutive terms:
a₄ - 2a₃ + a₂ = 14 - 2(4) + (-6) = 0
a₆ - 2a₅ + a₄ = 19 - 2(14) + 4 = -5
a₇ - 2a₆ + a₅ = 33 - 2(19) + 14 = 9
Since the second difference is constant (-5), this confirms that the sequence has a quadratic term in its equation. Let's assume the equation for the nth term is:
an = an² + bn + c
Substituting the values we know, we get three equations:
a₁ = a₁² + b₁ + c --> -6 = c
a₃ = a₃² + b₃ + c --> 4 = 9a + b + c
a₅ = a₅² + b₅ + c --> 14 = 25a + 5b + c
Solving this system of equations, we get:
a = 1/2, b = 19/2, and c = -6
Therefore, the equation for the nth term in the sequence is:
an = (1/2)n² + (19/2)n - 6.
T(n)=5n-11
please help and tell me how you got the answer and I will give brainliest
Answers
Answer:
32
Step-by-step explanation:
you need to find out which number is 40% of 80 and to do that you go 40/100 is equal to what (x) over 80- x/80 and then you cross multiply so 100 times x is 100x = 40 times 80 which is 3200 and then divide 3200 by 100 so you get 32
Theres is a 10% chance of rain tomorrow. A spinner with 10 sections is spun to simulate the probability of rain, where spinning a 1 indicates rain. If the results are 3, 6, 1, 8, and 3, then what is the difference in the experimental probability from the simulation and the prediction?
Answers
Answer:
There is a difference of 10%
Step-by-step explanation:
In this situation, the theoretical probability, the probability of something based on logic, is 10%. This means that if the spinner was spun 10 times it would land on 1 once. However, the experimental probability, the probability determined by the results of an experiment, is 20%. This number can be found by finding how many times the spinner actually landed on 1. Out of 5 spins, the spinner landed on 1 once. So the experimental probability is 1/5, which is equal to 20%. Therefore, there is a 10% difference in the prediction and simulation.
Since 2 is further left on a number line than 5,2 -5
Answers
Answer:
lower right
Step-by-step explanation:
a diver dove to a location 6 3/5 meters below sea level. He then dove to a second location 8 1/5 meters below sea level. How many meters are there between the two locations?
Answers
Answer:
\(1\frac{3}{5}\) meter is the difference in depths of locations diver dove.
Step-by-step explanation:
Nancy has eight books. Three of them are nonfiction. Write a portion of Nancy’s book that are non-fiction decimal form.
Answers
Which of the following fractions is closest to 0? 5/12 , 2/3, 5/6,3/4
Answers
Answer:
5/12
Step-by-step explanation:
5/12 , 2/3, 5/6,3/4
Get a common denominator of 12
5/12, 2/3 *4/4, 5/6*2/2, 3/4 *3/3
5/12, 8/12, 10/12, 9/12
The numerator closest to 0 is the fraction closest to 0
5/12
Solve by the quadratic formula.
a) 5
b) -1
c) 1
d) -1/2
e) 4
Answers
Answer:
I hope this helps a little bit.
Step-by-step explanation:
the answer is -1/2 or -1
graph the equation y=-3x-1
Answers
The graph of y=-3x-1 is given in the attachment.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The given equation is y=-3x-1
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
In the given equation slope is -3.
Let us find few values of x and y.
x 0 1 2 3 4
y -1 -4 -7 -10 -13
Hence, the graph of y=-3x-1 is given in the attachment.
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Helpppppppppppppp I’ll mark u
Answers
I neeeeed heeeelp please
Answers
Answer:
10b/y^2
Step-by-step explanation:
Hope this helps! :)
The coldest temperature
recorded in Buffalo was-39°F. This was 12°F
warmer than the coldest temperature recorded
in Chicago. Which equation can be used to find
the coldest temperature recorded in Chicago?
What is the coldest temperature recorded in
Chicago?
A. C-12-39; -51°
B. C+12=-39; -27°
C. C-12-39; -27°
D. C+12=-39; -51°
Answers
Based on the coldest temperature in Buffalo and the difference in the temperature of Chicago, the equation that can be used to find the coldest temperature in Chicago is C. C - 12 = -39; -27°
What is the temperature at its coldest in Chicago?When temperatures are warmer, it means that they are higher. This means that to find the coldest temperature in Chicago, you need to add 12°F to the temperature of Buffalo.
The formula would therefore be:
C = -39 + 12
Making the Buffalo temperature the subject gives;
C - 12 = -39
The coldest temperature in Chicago is:
= -39 + 12
= -27°F
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Jessica needs to know how much water her new fish tank can hold:
A rectangular prism with a length of 8 inches, a width of 4 inches, and a height of 9 inches.
Determine the total volume of the fish tank.
Answers
The fish tank has a total volume of 288 inch³. As a result, Jessica's new fish tank has a capacity of 288 inch³ for water.
The volume of a rectangular prism can be calculated using the formula:
V = l x b x h..........(i)
where,
V ⇒ Volume
l ⇒ length
b ⇒ width
h ⇒ height
From the question, we are given the values,
l = 8 inches
b = 4 inches
h = 9 inches
Putting these values in equation (i), we get,
V = 8 x 4 x 9
⇒ V = 288 in³
Therefore, the fish tank has a total volume of 288 inch³. As a result, Jessica's new fish tank has a capacity of 288 inch³ for water.
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If the trip is 865 miles about how many miles will David drive
Answers
Answer:
865
Step-by-step explanation:
the trip is 865 miles so that is how many miles he will drive
A bag contain 50¢, 25¢ and 10¢ coins in the ratio 5 : 9 : 4, which amounts to $206. The number of coins of each type are
Answers
The number of 50¢ coins is 200, number of 25¢ coins is 360
and number of 10¢ coins is 160.
What is ratio?The quantitative relation between two or more amounts showing the number of times one value is contains or contained within other.
Now the given ratio is 5 : 9 : 4.
and total amount of the coins is $206.
There are three types of coins in the bag, 50¢, 25¢ and 10¢.
Suppose x be the the ratio of coins in the bag.
Hence, number of 50¢ coins = 5x
number of 25¢ coins = 9x
number of 10¢ coins = 4x
Now, given total amount = $206
and since $1 = 100¢
⇒ ($0.5)(5x) + ($0.25)(9x) + ($0.1)(4x) ¢ = $206
Solving them,
⇒ 2.5x + 2.25x + 0.4x = 206
⇒ 5.15x = 206
⇒ x = 40
Therefore,
number of 50¢ coins = 5*40 = 200
number of 25¢ coins = 9*40 = 360
number of 10¢ coins = 4*40 = 160
Hence, number of 50¢ coins is 200, number of 25¢ coins is 360
and number of 10¢ coins is 160.
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Chelseas school is selling tickets to o a play. On the first day of tickets sales the school sold 4 senior citizen tickets and 8 child tickets for a total of $68. The school took in $42 on the second day by selling the 2 seniors citizen tickets a 6 child tickets. What is the price each of one senior citizen ticket and one child ticket?
Answers
Answer:
The answer is 14 for each child and 8 each senior.
Step-by-step explanation:
0 + 1c = $14 for one child ticket
:
Find s using the equation 3s + 1c = 38, replace c with 14
3s + 14 = 38
3s = 38 - 14
3s = 24
s = 24/3
s = $8 for each senior
:
:
You can check these solutions using the 2n equation