Solve the initial value problem: y(x) dy dx +6y= 4, y(0) = 0 Solve the initial value problem for 0 < t < and y(π/2) = 13. Put the problem in standard form. Then find the integrating factor, p(t) and finally find y(t) = dy 5(sin(t) du + t + cos(t)y) = cos(t) sinº(t), Solve the initial value problem for t > -1 with y(0) = 4. Put the problem in standard form. Then find the integrating factor, p(t) and finally find y(t) = 10(t+1) dy dt - 8y = 16t,
Answers
The solution to the initial value problem y(x) dy/dx + 6y = 4, y(0) = 0 is
\(y = (4x)^{1/7}.\)
We have,
The initial value problem:
y(x) dy/dx + 6y = 4, y(0) = 0
First, let's rewrite the equation in standard form:
dy/dx + (6/y) = 4/y
Comparing this with the standard form equation, we have:
P(x) = 6/y, Q(x) = 4/y
Now, we need to find the integrating factor, denoted by μ(x), which is given by:
μ(x) = exp(∫P(x)dx)
μ(x) = exp(∫(6/y)dx)
μ(x) = exp(6ln|y|)
μ(x) = \(y^6\)
Multiplying the entire equation by the integrating factor, we get:
\(y^6(dy/dx) + 6y^7/y = 4y^6/y\)
Simplifying further:
\(d/dx(y^7) = 4\)
Integrating both sides with respect to x:
\(\int d/dx(y^7) dx = ∫4 dx\)
\(y^7 = 4x + C1\)
(where C1 is the constant of integration)
Applying the initial condition y(0) = 0:
\(0^7 = 4(0) + C1\)
C1 = 0
Therefore, the solution to the initial value problem is:
\(y^7 = 4x\)
Taking the seventh root of both sides, we get:
\(y = (4x)^{1/7}\)
Thus,
The solution to the initial value problem y(x) dy/dx + 6y = 4, y(0) = 0 is
\(y = (4x)^{1/7}.\)
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The complete question:
Solve the initial value problem:
y(x) dy/dx + 6y = 4, y(0) = 0
Related Questions
Some please help me with this question
Answers
Answer:
y = - 2x + 9
Step-by-step explanation:
From y = -2x + 1
comparing with y = mx + c
slope (m) = - 2
Writing in point slope form
y - y1 = m(x - x1)
y - 1 = -2( x - 4)
y - 1 = -2x + 8
Now writing in slope intercept form
y = - 2x + 8 + 1
y = -2x + 9
Hope it will help :)
I had $5.00. My mom gave me $10.00 while my Dad Gave me $30.00. My aunt and uncle gave me $100.00. I had another $5.00. How much did I have? I won against Tada Yazhe
Answers
Answer:
Is it $150?
Step-by-step explanation:
Step 1: Add it all together
5 + 10 + 30 + 100 + 5
All adds up to 150.
Probably got it wrong though haha.
The value of a collectible coin can be represented by the equation y = 2 x + 9.74, where x represents the number of years that Consuello has owned the coin and y represents the total value, in dollars, of the coin. What was the value of the coin when Consuello originally purchased it? $4.87 $7.74 $9.74 $19.48
Answers
Answer:
you would multiply 2 * 4.87 and then add that to 9.74 and then you do that to everyone and then one of them will get you your answer and I am not sure about the answer but I think its b
Step-by-step explanation:
Answer:
The value of the coin when Consuelo originally purchased it is $9.74 ⇒ C
Step-by-step explanation:
The form of the linear equation is;
y = m x + b, where
m is the slope of the line (The rate)
b is the y-intercept (initial amount, value y at x = 0)
∵ The value of a collectible coin can be represented by the equation
y = 2 x + 9.74
→ Compare it with the form of the linear equation above
∴ m = 2
∴ b = 9.74
∵ x represents the number of years that Consuelo has owned the coin
∵ y represents the total value, in dollars, of the coin
→ That means the value of y at x = 0 is the value of the coin when
Consuelo originally purchased it
∵ b represents the value of y at x = 0
∵ b = 9.74
∴ The value of the coin when Consuelo originally purchased it is $9.74
the shop keeper at an inn receives 175 letters a week (7 days). How many letters does he receive in a day
Answers
Answer:
25
Step-by-step explanation:
175 divided by 7 =25
Answer:
25 letters
Step-by-step explanation:
the word problem can be expressed as 175=7x
there are 7 days in a week and you want to find home many there are in one of those days
divide 175 by 7, your answer is 25.
Is it possible to subtract a loss from a positive number and result in a negative number?
Answers
Answer:
yes that's possible for example -3-5=-8
One of your users calls you with a complaint that he can't reach the site www.. You try and access the site and discover you can't connect either but you can ping the site with its IP address. What is the most probable culprit
Answers
The site and discover can't connect either but can ping the site with its IP address is given by,
The most probable culprit in this scenario is a Domain Name System issue.
DNS is responsible for translating human-readable domain names into IP addresses that computers can understand.
When you enter a domain name into a web browser, it relies on DNS to resolve the domain name to the corresponding IP address.
If you are unable to access the site using its domain name .
But can ping the site successfully using its IP address, it suggests that the DNS resolution is failing.
The IP address connectivity indicates that the site itself is reachable and accessible, but the domain name is not being resolved correctly.
There are a few potential reasons for this DNS issue.
DNS server problems,
The DNS server you are using might be experiencing issues or downtime.
This can occur if the DNS server is misconfigured, overloaded, or undergoing maintenance.
DNS cache issue,
Your local DNS cache or the DNS cache of your internet service provider may have incorrect or outdated information.
Clearing the DNS cache on your computer or using alternative DNS servers can help resolve this issue.
DNS misconfiguration,
There might be a misconfiguration in the DNS settings for the domain itself.
This could include incorrect DNS records or problems with the domain's authoritative DNS servers.
Network connectivity issue,
There could be a network connectivity problem between your computer and the DNS server, preventing the resolution of domain names.
To troubleshoot and resolve the issue, you can try the following steps.
Clear your DNS cache,
Flush the DNS cache on your computer to ensure that any incorrect or outdated DNS information is cleared.
Change DNS servers,
Temporarily switch to alternative DNS servers, such as DNS or OpenDNS, to see if the issue persists.
Contact your ISP,
If the issue persists, contact your internet service provider and inform them about the problem.
They may be able to provide assistance or identify any broader DNS issues.
Check domain configuration,
If you are responsible for managing the domain, review the DNS settings and ensure they are correctly configured.
By investigating and addressing the DNS issue,
Able to resolve the problem and regain access to the site using its domain name.
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Solve 6x + c = k for x
Answers
Answer:
106 bucks
Step-by-step explanation:
Answer:
x = - 1/6c + 1/6k
Step-by-step explanation:
...........
GIVING AWAY BRAINLIEST TO THE FIRST ANSWER. Find the primary root only for (4-3i)^1/5. Round to 3 decimal places for accuracy.
Answers
Rounding to 3 decimal places, the primary root of (4-3i)^(1/5) is approximately:
(4-3i)^(1/5) = 1.380(cos(-0.129) + i sin(-0.129))
Root calculation.
To find the primary root of the complex number (4-3i)^(1/5), we can use the polar form of complex numbers.
First, we need to find the modulus (or absolute value) and the argument (or angle) of the complex number (4-3i):
|4-3i| = sqrt(4^2 + (-3)^2) = 5
Arg(4-3i) = arctan(-3/4) = -0.6435 (rounded to 4 decimal places)
Next, we can write the complex number (4-3i) in polar form as:
4-3i = 5(cos(-0.6435) + i sin(-0.6435))
To find the primary root, we need to take the fifth root of the modulus and divide the argument by 5:
|4-3i|^(1/5) = 5^(1/5) = 1.3797 (rounded to 4 decimal places)
Arg(4-3i) / 5 = -0.1287 (rounded to 4 decimal places)
Finally, we can write the primary root in rectangular form by multiplying the modulus by the cosine of the argument divided by 5 for the real part and multiplying the modulus by the sine of the argument divided by 5 for the imaginary part:
(4-3i)^(1/5) = 1.3797(cos(-0.1287) + i sin(-0.1287))
Rounding to 3 decimal places, the primary root of (4-3i)^(1/5) is approximately:
(4-3i)^(1/5) = 1.380(cos(-0.129) + i sin(-0.129))
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a soccer team has 13 players. a starting lineup consist of 11 players, one of whom is a goalkeeper and the other 10 regular players (players are interchangeable). how many different starting lineups can the team have?
Answers
The soccer team can have 1,716 different starting lineups. The number of ways to choose 1 player out of 13 for the goalkeeper position is given by the combination formula: C(13, 1) = 13.
To calculate the number of different starting lineups, we need to determine the combinations of players that can be chosen for the starting lineup. Since there are 13 players on the team and 11 positions in the starting lineup, we need to choose 1 player for the goalkeeper position and 10 players for the regular positions. Similarly, the number of ways to choose 10 players out of the remaining 12 players for the regular positions is given by the combination formula:
C(12, 10) = 66.
To find the total number of different starting lineups, we multiply the number of choices for the goalkeeper position by the number of choices for the regular positions: 13 * 66 = 858.
However, the order of the players in the lineup doesn't matter, so we need to divide the result by the number of permutations of the 10 regular players: 858 / 10! = 1716. The soccer team can have 1,716 different starting lineups.
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10. A developmental psychologist believes that language learning in preschool girls differs from boys. For example, girls are more likely to use more complex sentences structures earlier than boys. The researcher believes that a second factor affecting language skills is the presence of older siblings; that is, preschool children with older siblings will generate more complex speech than older children. The researcher carefully records the speech of a classroom of 40 preschool children (20 females, 20 males), half of whom have older siblings. The speech of each child is then given a complexity score. Which method of analysis should the researcher use? Explain. b. Make of diagram of this design. a.
Answers
Girls are more likely to use more complex sentence structures earlier than boys, and preschool children with older siblings generate more complex speech than older children.
Preschool language differences: Gender and siblings?Language learning in preschool children can be influenced by gender and the presence of older siblings. Research suggests that girls tend to exhibit more advanced language skills, including the use of complex sentence structures, at an earlier age compared to boys.
This difference may be attributed to various factors, such as socialization patterns and exposure to language models. Additionally, having older siblings can contribute to the development of more complex speech in preschool children, as they may be exposed to a richer linguistic environment and have more opportunities for interaction and learning.
Understanding these factors can help in tailoring language interventions and support for children with different backgrounds and needs.
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700,000,000+10,000,000+1,000,000+100,000+40,000+2,000+200+7 write the standard form above
Answers
Answer:
712,402,207
Step-by-step explanation:
;)
Answer: 711,142,207
Step-by-step explanation:
A tank in the form of a right-circular cylinder standing on end is leaking water through a circular hole in its bottom. As we saw in (10) of Section 1.3, when friction and contraction of water at the hole are ignored, the height h of water in the tank in feet after t seconds is described by dh dt А. 2gh AW where A and A, are the cross-sectional areas of the water and the hole in square feet, respectively. (a) Solve for h(t) if the initial height of the water is H. Give its interval I of definition in terms of the symbols Awr An, and H. Use g = 32 ft/s2. (4„VH – 44,4) h(t) = osts 4A 4VĀ By hand, sketch the graph of h(t). h h H H/2 t h h H/2H H t (b) Suppose the tank is 11 ft high and has radius 2 ft and the circular hole has radius in. If the tank is initially full, how long will it take to empty? (Round your answer to two decimal places.) sec
Answers
The height of water in the tank in feet after t seconds can be expressed as h(t) = H - (Aw/Ah) 2gh t2, where Aw and Ah are the cross-sectional areas of the water and the hole in square feet respectively,
and g is the gravitational acceleration (32 ft/s2). The interval of definition for h(t) is 0 ≤ t ≤ H/2gh.
The graph of h(t) is a parabola with its vertex at (H/2gh, H) and is symmetric about the line t = H/2gh. It starts at (0, H) and gradually decreases to (H/2gh, 0).
Given the tank is 11 ft high, has radius 2 ft and the circular hole has radius in, and it is initially full, the time it will take to empty can be calculated as: t = √(2H/gAh) = √(22/(32 x π(0.52))) = 3.87 seconds. Therefore, it will take approximately 3.87 seconds to empty.
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Drag the labels to the correct locations on the image. Not all labels will be used.
Consider function h.
Answers
Answer:
-∞ < y < ∞
Step-by-step explanation:
Range corresponds to the values on the y-axis and Domain corresponds to values on the x-axis. Here if see the graph the range depends on values on y-axis and we can see that the the graph goes to -∞(-negative infinity) to +∞(positive infinity) so the answer is
-∞ < y < ∞
Answer:
The range is -∞< y < ∞, below is the explanation of how to get range.
Step-by-step explanation:
Given:
Graph of a function h(x).
To find:
The range of the function in inequality notation.
The range is all possible y-values of the function. Let's find all possible y values from the graph.
If we see the graph, it has a vertical asymptote at x=1 and a slant asymptote.
But it tool all y values from -infinity to infinity.
So, we can write range as -∞< y < ∞ because both sides of the function go and so on below the x-axis and go and so on above the x-axis.
The range is -∞< y < ∞ .
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If∠
Answers
Answer:
where is tge other half question?
Can you help me with this
Answers
Answer:
\( - 3x - 9y = 21\)
Step-by-step explanation:
\( - 3x - 9 - 9y = 12 \\ - 3x - 9y = 12 + 9 \\ - 3x - 9y = 21 \\ \)
If the two figures are congruent, which statement is true?
A. BCDA ≅ FEHG
B. ABCD ≅ EFGH
C. BADC ≅ EFGH
D. ADCB ≅ HGFE
Answers
Answer:
A
Step-by-step explanation:
the order of letter should resemble the same shape
3. Frank is considering two cell phone plans. The first company charges $120 for the
phone and $30 per month for the calling plan that Juan wants. The second company
charges $40 for the same phone but charges $45 per month for the calling plan that
Juan wants. After how many months would the total cost of the two plans be the same?
Representations:
Equations:
Answers
Answer:
5.333 months
Step-by-step explanation:
Company A: 120+30x
Company B: 40+ 45x
120+30x=40+45x
80=15x
80/15=x
5.33333=x
Professor Rosencrantz flips a fair coin once. Professor Guildenstern flips a fair coin three times. What is the probability that Professor Rosencrantz obtains more heads than Professor Guildenstern
Answers
Answer:
9/13 = 0.6923
Step-by-step explanation:
We start by defining
A as event that head was flipped
B1 = event that coin is biased
B2 = event that it is unbiased
P(B1) = 3/5
P(B2) = 2/5
P(A|B1) = 3/4
P(A|B2) = 2/4 = 1/2
When we solve this using bayes theorem we have to find
p(B1|A) = [P(B1) x P(A|B1)]/[P(B1) x P(A|B1) + P(B2) x P(A|B2)
= 0.6 x 0.75 / 0.6 x 0.75 + 0.4x0.5
= 0.45/0.45+0.2
= 0.45/0.65
= 0.6923
please brainliest
Please help i’m not sure what to do and how to do a certain step ....
Answers
Step-by-step explanation:
The perimeter of Ms.Burner garden will be 3 times greater than Mrs.Kesler garden.The area of Ms.Burner garden will be larger than Mrs.Kelser garden.Suppose that we have 100 apples. In order to determine the integrity of the entire batch of apples, we carefully examine n randomly-chosen apples; if any of the apples is rotten, the whole batch of apples is discarded. Suppose that 50 of the apples are rotten, but we do not know this during the inspection process. (a) Calculate the probability that the whole batch is discarded for n = 1, 2, 3, 4, 5, 6. (b) Find all values of n for which the probability of discarding the whole batch of apples is at least 99% = 99 100*
Answers
To calculate the probability that the whole batch is discarded for a given value of n, we need to consider the probability of selecting at least one rotten apple out of the n apples examined.
Let's calculate the probabilities for n = 1, 2, 3, 4, 5, and 6: For n = 1: The probability of selecting at least one rotten apple is 50/100 = 0.5 since we know that 50 out of the 100 apples are rotten. Therefore, the probability of discarding the whole batch is also 0.5. For n = 2: The probability of selecting at least one rotten apple out of two apples is given by the complement of selecting two fresh apples, which is 1 - (50/100) * (49/99) = 1 - 0.2525 = 0.7475. Therefore, the probability of discarding the whole batch is 0.7475. For n = 3: The probability of selecting at least one rotten apple out of three apples is 1 - (50/100) * (49/99) * (48/98) = 1 - 0.3788 = 0.6212. Therefore, the probability of discarding the whole batch is 0.6212. For n = 4: The probability of selecting at least one rotten apple out of four apples is 1 - (50/100) * (49/99) * (48/98) * (47/97) = 1 - 0.4998 = 0.5002. Therefore, the probability of discarding the whole batch is 0.5002. For n = 5: The probability of selecting at least one rotten apple out of five apples is 1 - (50/100) * (49/99) * (48/98) * (47/97) * (46/96) = 1 - 0.6094 = 0.3906. Therefore, the probability of discarding the whole batch is 0.3906. For n = 6: The probability of selecting at least one rotten apple out of six apples is 1 - (50/100) * (49/99) * (48/98) * (47/97) * (46/96) * (45/95) = 1 - 0.5086 = 0.4914. Therefore, the probability of discarding the whole batch is 0.4914. (b) To find the values of n for which the probability of discarding the whole batch is at least 99%, we can examine the probabilities calculated above and identify the smallest value of n that gives a probability greater than or equal to 0.99.
From the calculations, we find that for n = 2, the probability of discarding the whole batch is 0.7475, which is already greater than 0.99. Therefore, the value of n that satisfies the condition is n = 2.
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please help!!!!!! Thanks!!
Answers
Answer:
60
Step-by-step explanation:
Answer:
60
Step-by-step explanation:
Angle on a staright line is 180 degrees so 180 - 120 is 60 degrees and 6y degrees is opposite 60 degrees so 6y is 60
4x + 6 = 2(2x +3) is an example of what type of equation?
Answers
Answer:
Simplifying
4x + -6 = 2(2x + 3)
Reorder the terms:
-6 + 4x = 2(2x + 3)
Reorder the terms:
-6 + 4x = 2(3 + 2x)
-6 + 4x = (3 * 2 + 2x * 2)
-6 + 4x = (6 + 4x)
Add '-4x' to each side of the equation.
-6 + 4x + -4x = 6 + 4x + -4x
Combine like terms: 4x + -4x = 0
-6 + 0 = 6 + 4x + -4x
-6 = 6 + 4x + -4x
Combine like terms: 4x + -4x = 0
-6 = 6 + 0
-6 = 6
Solving
-6 = 6
A figure is made up of with seven X rodes and five Y rodes . If X= 3 and Y= 5 calculate the perimeter with the formula.
OPTIONS:
8
46
50
40
Answers
12 C 6 B F 8 B 20 a. What is the length of segment A'A? Type the answer in the box below. length of segment A'A = 18 b. What is the length of segment B'B? Type the answer in the box below. length of segment B'B = I
Answers
The length of the segment A'A is 18 units
The length of the segment B'B is 8 units
What is the length of segment A'A?From the question, we have the following parameters that can be used in our computation:
The similar triangle
Using the ratio of corresponding sides, we have
(AA' + 12)/20 = 12/8
So, we have
AA' + 12 = 20 * 12/8
AA' + 12 = 30
Evaluate
AA' = 18
What is the length of segment B'B?Here, we have
(BB' + 6)/20 = 6/8
So, we have
BB' + 6 = 20 * 6/8
BB' + 6 = 15
Evaluate
BB' = 8
Hence, the length is 8 units
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ſ x - 5y = -9( 4x + 4y = - 12Step 1 of 2: Determine if the point (-4,1) lies on both of the lines in the system of equations by substituting theordered pair into both equations.
Answers
Given:
\(\begin{gathered} x-5y=-9\ldots\ldots(1) \\ 4x+4y=-12\ldots\text{.}\mathrm{}(2) \end{gathered}\)The given point is (-4,1)
Let's check the ordered pair (-4,1) in the first equation
\(\begin{gathered} x-5y=-9 \\ (-4)-5(1)=-9 \\ -4-5=-9 \\ -9=-9 \end{gathered}\)Hence, (-4,1) is a solution of the first equation x-5y=-9.
Now, let's check (-4,1) in the second equation.
\(\begin{gathered} 4x+4y=-12 \\ 4(-4)+4(1)=-12 \\ -16+4=-12 \\ -12=-12 \end{gathered}\)So, (-4,1) is a solution of the second equation 4x+4y=-12.
Hence, (-4,1) is a solution of both equation in the system, then it is a solution to the overall system.
what is half way between 18x28 and 22x28
Answers
Answer: 160
Step-by-step explanation:
first workout the multiplication sums [22 x 28 = 616]
[18 x 28 = 505] then add 2 numbers together [616 + 505 = 1120]
then divide the answer by 2 [1160 / 2 = 160
A source of money that allows individuals to pay for goods and services later is called _____. (1- consumer credit, 2- earned income, 3- capital) an advantage of this source of money is that ____. (1- it can be used to shop online, 2- there are no interest charges, 3- there are no penalties for delayed payment) i need answers fast.
Answers
A source of money that allows individuals to pay for goods and services later is called consumer credit and an advantage of this source of money is that there are no interest charges.
Consumer credit, also known as consumer debt, enables the consumers to incur debt or borrow money and to defer repayment of that money over time. It allows consumers to buy goods without having to pay for them in cash at the time of purchase. Examples of consumer credit include credit cards, student loans, etc. Among the advantages of using consumer credit is that there is no interest charge to borrow the money for a certain period of time until the due date.
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Please help me, I’ll mark you as brainliest!!!!
Answers
Answer:
C)
Step-by-step explanation:
Subtract the FICA Tax:
45,000 - 3,440 = 41, 560
Subtract the State Income tax:
41, 560 - 1,800.00 = 39,760
Subtract the Federal Income tax:
39,760 - 3,700.00 = 36,060
Subtract the Med Insurance:
36,060 - 1,00.00 = 35,060
HP usually sells its laser printers at discounted prices and charges its customers much more when those customers buy consumables such as printer cartridges. What can we learn from this
Answers
HP's pricing strategy allows them to capture a larger customer base, create customer loyalty and long-term profitability.
HP uses the 'razor' and 'blade' model. Here, Laser printer is sold at a lower price while the consumables (printer cartridges) are sold at higher profit margins. This strategy aims to create a recurring revenue stream from the sales of consumables, which have higher profit margins compared to the initial printer sale.
By relying on the sales of consumables, HP diversifies its revenue streams. While printer sales may have lower profit margins, the higher profit margins from consumables help offset those costs and contribute to overall profitability. This reduces HP's reliance on a single revenue source and improves financial stability.
Therefore , HP is leaning towards a scheme which aims at long-term profitability.
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Zach bought 200 shares of Goshen stock years ago for $21.35 per share. He sold all 200 shares today for $43 per share. What was his gross capital gain?
Answers
Gross capital gain = (selling price - purchase price) x number of shares sold
The purchase price was $21.35 per share, and he bought 200 shares, so the total purchase price was:
Purchase price = $21.35 x 200 = $4,270
The selling price was $43 per share, and he sold all 200 shares, so the total selling price was:
Selling price = $43 x 200 = $8,600
Therefore, the gross capital gain is:
Gross capital gain = ($8,600 - $4,270) x 200 = $8,6600
So Zach's gross capital gain from selling his 200 shares of Goshen stock is $8,6600.
Answer: 8,600
Zach's gross capital gain can be calculated as follows:
Total proceeds from selling the stock = 200 shares x $43/share = $8,600
Total cost of buying the stock = 200 shares x $21.35/share = $4,270
Gross capital gain = Total proceeds - Total cost = $8,600 - $4,270 = $4,330
Therefore, Zach's gross capital gain from selling 200 shares of Goshen stock is $4,330.