The solutions of the differential equation y" - 6y' + 8y = 0 are [tex]y=3e^{2x}[/tex]
and [tex]y = Ce^{4x}[/tex]. So option D II and III only is correct.
A differential equation is an equation including dependent variables and their derivatives concerning independent variables.
Given the equation is y" - 6y' + 8y = 0. This can be written as [tex]\frac{d^2y}{dx^2}-6\frac{dy}{dx}+8y=0[/tex].
Now, let's substitute d/dx = m, and we get,
[tex]\begin{aligned}(m^2-6m+8)y&=0\\m^2-6m+8&=0\\m^2-(4+2)m+8&=0\\m^2-4m-2m+8&=0\\m(m-4)-2(m-4)&=0\\(m-4)(m-2)&=0\\m&=2,4\end{aligned}[/tex]
Then, the general solution will be written as [tex]y(x)=C_1e^{2x}+C_2e^{4x}[/tex]. Then, [tex]y_1=C_1e^{2x}[/tex] and [tex]y_2=C_2e^{4x}[/tex]. Hence, the solution of a given ODE is always this y₁ or y₂ or the combination of these. Therefore, (I) cannot be possible.
Now let's consider (II) and put [tex]y'=6e^{2x}[/tex] and [tex]y"=12e^{2x}[/tex] in the given equation. We get,
[tex]\begin{aligned}12e^{2x}-36e^{2x}+24e^{2x}&=0\\36e^{2x}-36e^{2x}&=0\\0&=0\end{aligned}[/tex]
Hence, (II) is the solution of the given equation and is possible.
Now let's consider (III) and put C₁=0 and we get, [tex]y(x)=C_2e^{4x}=Ce^{4x}[/tex]when C₂=C. Hence, (III) is possible.
Therefore, the correct option is D II and III only.
The complete question is -
Of the following, which are solutions to the differential equation y" - 6y' +8y=0?
I. y = 2 sin(4x)
II. [tex]y=3e^{2x}[/tex]
III. [tex]y = Ce^{4x}[/tex], where C is a constant.
A) I only B) Il only C) Ill only D) II and III only
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Determine whether the given value of the variable is a solution of the equation
Answer:
1. No
2. Yes
3. No
Step-by-step explanation:
1.
We know that c = 7, so we plug it in to prove if the equation is true.
[tex]7+8=15[/tex]
The variable is not a solution.
2.
We know a = 30, so we plug it in to prove if the equation is true.
[tex]30-4=26[/tex]
The variable is a solution.
3.
We know y = 4.1, so we plug it in to prove if the equation is true.
[tex]12.6-4.1=8.5[/tex]
The variable is not a solution.
2017, 1.20. 1ST
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A pole 5 feet tall is used to support a guy wire for a tower, which runs from the tower
to a metal stake in the ground. After placing the pole, Liam measures the distance
from the pole to the stake and from the pole to the tower, as shown in the diagram
below. Find the length of the guy wire, to the nearest foot.
Spr
Answer:
(Diagram is not to scale.)
5 ft
9 ft-
4 ft
ft
Submit Answe
The length of the wire is given as follows:
21 ft.
What are similar triangles?Similar triangles are triangles that share these two features presented as follows:
Congruent angle measures.Proportional side lengths.From the similar triangles, the proportional relationship to obtain the height of the tower is given as follows:
4/5 = 13/h
4h = 13 x 5
h = 13 x 5/4
h = 16.25.
Applying the Pythagorean Theorem, the length of the wire is given as follows:
l² = 16.25² + 13²
l = sqrt(16.25² + 13²)
l = 21 ft.
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Directions: Solve for.x. Round all answers to the nearest tenth.
11
X
31°
X =
The solution is, The value of x is 21.4.
What is right-angle triangle?A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangle triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and other angles of the right triangle.
here, we have,
The height of the right-angle triangle is 11. The hypotenuse of the right-angle triangle is x.
The measure of the angle opposite to height is 31°.
The sine of an angle is the ratio of height to the hypotenuse.
Therefore,
sin 31° = height/hypotenuse
sin 31° = 11/x
Multiply x with both sides:
x sin 31° = 11
Divide sin 31° with both sides:
x = 11/ sin 31°
x = 21.35
x ≈ 21.4 units
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What is the result 3 x 6 ?
Answer:
Step-by-step explanation:
3*6=18
what is functional residual capacity ?
Functional residual capacity (FRC) is the volume of air that remains in the lungs after a normal exhalation.
functional residual capacity (FRC) is the volume of air that remaining parts in the lungs after a typical exhalation when the muscles of breath are loose. It is the equilibrium point between the outward flexible force of the chest wall and the internal versatile backlash of the lungs. At FRC, there is no air development and the tensions in the lungs and the climate are equivalent.
FRC is a significant estimation in pneumonic capability tests and can be utilized to analyze different respiratory circumstances like obstructive lung illnesses, prohibitive lung sicknesses, and neuromuscular illnesses that influence the respiratory framework.
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Jess travels 196km to visit her cousins. She leaves home at 8:00am and arrives there are
11:15am. Calculate her average speed in km per hour to the nearst whole number.
please help because i need help if anyone can help with this
Question 5
A box-and-whisker plot is shown below:
Correctly label each part of the plot.
1. 0
2. 5
3. 10
4. 15
5. 20
6. 25
7. 30
8. 35
9. 40
10. 45
11. 50
Maximum
First Quartile (Q1)
Second Quartile (Median)
Minimum
Third Quartile (Q3)
Answer:4
Step-by-step explanation:
Need answers fast❗️
Answer: 22 degrees !
Step-by-step explanation: angle ABD is a right, 90 degree angle. angle ABC is a 68 degree angle. CBD is left, so you would do 90-68 to find it, which equals 22 :)
mark is earning money by mowing lawns over the summer. The function y=40x represents the total nunber of dollars Mark earns, y, depending on the number of lawns he mows, x. what is true about the function
The true statement about the function y = 40x is that it is a linear function
How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
y = 40x
The given function is y = 40x, which represents the total number of dollars Mark earns depending on the number of lawns he mows.
Here are some properties of the function:
The function is a linear function, which means that it has a constant rate of change. For every additional lawn mowed, Mark earns an additional $40.The function has a slope of 40, which is the coefficient of x. This means that for every additional lawn mowed, the total earnings increase by $40.The y-intercept of the function is 0, which means that if Mark doesn't mow any lawns, he doesn't earn any money.Read more about linear relation at
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Find the value of x
73°
109°
Answer:
x = 88
Step-by-step explanation:
To find the value of x, we know that the sum of a quadrilateral's exterior angles are 360. We can use this information to create an algebraic expression and solve for x.
[tex]x+73+90+109=360[/tex]
Add like terms
[tex]x+272=360\\[/tex]
Subtract 272 on both sides
[tex]x=88[/tex]
To prove our work, we can add up all the angle measures and see if they add up to 360.
[tex]88+73+90+109=360[/tex]
So, our work is correct.
A family of 6 is going to the fair. They have a coupon for $1.50 off each ticket. After the discount on each ticket, they pay $46.50 for all 6 tickets tickets
If it helps, use the sketch pad to draw a diagram that represents this situation.
Write an algebraic equation to represent this situation where x represents the original price of each ticket before the $1.50 discount was taken.
Answer:
$9.25
Step-by-step explanation:
Let x be the original price of each ticket before the discount was taken. The discount is $1.50 off each ticket, so the price they actually paid for each ticket is x - 1.50. Since there are 6 tickets, the total price they paid for all 6 tickets is:
6(x - 1.50)
We know from the problem that the total price they paid for all 6 tickets was $46.50, so we can set up the following equation:
6(x - 1.50) = 46.50
Simplifying this equation, we get:
6x - 9 = 46.50
Adding 9 to both sides, we get:
6x = 55.50
Dividing both sides by 6, we get:
x = 9.25
Therefore, the original price of each ticket was $9.25.
Answer:
9.25$
Step-by-step explanation:
Let x be the original price of each ticket before the discount was taken. The discount is $1.50 off each ticket, so the price they actually paid for each ticket is x - 1.50. Since there are 6 tickets, the total price they paid for all 6 tickets is:
6(x - 1.50)
We know from the problem that the total price they paid for all 6 tickets was $46.50, so we can set up the following equation:
6(x - 1.50) = 46.50
Simplifying this equation, we get:
6x - 9 = 46.50
Adding 9 to both sides, we get:
6x = 55.50
Dividing both sides by 6, we get:
x = 9.25
Therefore, the original price of each ticket was $9.25.
Please Brainliest
Find the length of the missing side
Answer: The missing side is 8
Step-by-step explanation: I hope this helps!
how to convert 4m to cm?
As per the unit conversion process, 4 meters is equal to 400 centimeters.
Unit conversion is a process of changing a given value from one unit of measurement to another. For example, converting meters to centimeters, or grams to kilograms. This skill is essential in science, engineering, and everyday life. In this article, we will learn how to convert 4 meters to centimeters.
First, we need to know the conversion factor between meters and centimeters. Since there are 100 centimeters in one meter, the conversion factor is 100 cm/m.
To convert 4 meters to centimeters, we need to multiply 4 meters by the conversion factor of 100 cm/m. This will give us the equivalent value in centimeters.
4 meters x 100 cm/m = 400 centimeters
It is essential to understand the conversion factor and the units of measurement involved in unit conversion. By doing so, we can accurately and efficiently convert values from one unit to another.
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A random sample of 12 four-year-old red pine trees was selected and the diameter (in inches) of each tree's main stem was measured.
The resulting observations are as follows: 11.3, 10.7, 12.4, 15.2, 10.1, 12.1, 16.2, 10.5, 11.4, 11.0, 10.7, and 12.0
Find the point estimate that can be used to estimate the true population mean.
s = 3.24
X= 11.97
X= 1.73
S = 14.02
The point estimate that can be used to estimate the true mean population is 11.97 inches.
To find the point estimate that can be used to estimate the true population mean, we need to take the sample mean of the given observations. The formula for the sample mean is:
Mod(X)= (Σx) / n
where Mod(X) is the sample mean, Σx is the sum of all the observations, and n is the size.
Using the given observations, we can calculate the sample mean as follows:
Mod(X) = (11.3 + 10.7 + 12.4 + 15.2 + 10.1 + 12.1 + 16.2 + 10.5 + 11.4 + 11.0 + 10.7 + 12.0) / 12
Mod(X) = 11.97
Therefore, the point estimate that can be used to estimate the true mean population is 11.97 inches.
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how many different ways can 3 people from england, 2 people from california and 4 people from mexico randomly sit down in adjacent seats at a concert so that all californians sit together and all people from mexico sit together
The different ways that the people from can randomly sit down in adjacent seats is 138240 ways
How to calculate the valueCombinations are also referred to as selections. Combinations implies the selection of things from a given set of things. In this case, we intend to select the objects. This can be illustrated by nCr
There are 2 people from California, so they can be arranged in 2! = 2 ways.
There are 4 people from Mexico, so they can be arranged in 4! = 24 ways.
Now we can treat the group of Californians and the group of Mexicans as a single block of 6 people (2 Californians and 4 Mexicans), which we can arrange with the 3 people from England. There are 3 + 1 = 4 blocks of 6 people that we can form (one for each possible position of the block), and within each block, there are 6! ways to arrange the people.
Therefore, the total number of arrangements that satisfy the given conditions is:
= 2! * 4! * 4 * 6! = 2 * 24 * 4 * 720
= 138,240 ways
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What do we mean by "LiFE"?
*
1 point
Taking choices that benefit the world on a microeconomic or macroecomomic level.
Taking choices that benefit the environment, whether on an individual, national or international level.
Striving towards establishing inclusive and resilient forums that are broad-minded.
Establishing close connections with other nations to benefit global communities and address major societal issues like gender discrimination and marginalisation.
Taking choices that benefit the world on a microeconomic or macroecomomic level.
Taking choices that benefit the environment, whether on an individual, national or international level.
Striving towards establishing inclusive and resilient forums that are broad-minded.
Establishing close connections with other nations to benefit global communities and address major societal issues like gender discrimination and marginalisation.
how many feet in acre
Answer:
43,560ft
Step-by-step explanation:
What are units?A unit can be used for measurement, and is commonly found in mathematics to describe length, size, etc.
1 Acre = 43,560 feetTherefore, for every 1 acre it is equivalent to 43,560 feet.
It is assumed that approximately 15% of adults in the U.S. are left-handed. Consider the probability that among 100 adults selected in the U.S., there are at least 30 who are left-handed. Given that the adults surveyed were selected without replacement, can the probability be found by using the binomial probability formula with x counting the number who are left-handed? Who or why not?A. no; since np<5, the normal distribution should not be usedB. As the probability of success increases, the probability distribution for a binomial variable becomes bell shaped.C. Yes, because the 100 adults represent less than 5% of the U.S. adult population, the trials can be treated as independent.D. No, because the probability of smoking is different for people who earn over $75,000 per year, the events are not independent.
The correct answer is A. no; since np<5, the normal distribution should not be used. This is because np<5, which violates the condition for using the normal distribution approximation to the binomial distribution. In this case, np=15 which is less than 5, and therefore, the binomial distribution should be used. If np is greater than or equal to 5, a normal approximation to the binomial distribution can be used.
The binomial distribution can be used to model the probability of a certain number of successes in a fixed number of independent trials, where the probability of success in each trial is the same. However, if the number of trials is large and the probability of success is small, the binomial distribution can be approximated by a normal distribution.
In this case, we have
n = 100 trials and p = 0.15
probability of success in each trial.
Therefore, np = 15, which is less than 5. According to the rule of thumb, if np < 5 or n(1-p) < 5, the normal distribution approximation is not valid, and the binomial distribution should be used.
Since the probability of success is small (0.15), and the number of trials is relatively large (100), we could use a normal approximation to the binomial distribution. However, since np < 5, we cannot use the binomial probability formula directly. Instead, we would need to use a continuity correction and the standard normal distribution to estimate the probability. Therefore, option A is the correct answer.
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What is the conversion of 3/2 as a decimal ?
The conversion of 3/2 as a decimal is 1.5.
To convert a fraction to a decimal, you can divide the numerator (the top number) by the denominator (the bottom number) using long division, a calculator, or by using a decimal equivalent chart. It's important to note that some fractions have repeating decimals or do not terminate, such as 1/3 or 7/11. In those cases, the decimal representation is either an infinite non-repeating decimal or a repeating decimal.
To convert a fraction to a decimal, you simply divide the numerator (the top number) by the denominator (the bottom number).
So, to convert 3/2 to a decimal, we can perform the following division:
3 ÷ 2 = 1.5
Therefore, 3/2 as a decimal is equal to 1.5.
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what is 4pm in military time
As per military time, 4pm would be 1600 hours or 16:00. We can deduce this by also seeing the 24 hour clock.
A day is divided into 24 equal-length segments and runs from midnight to midnight on the modern 24-hour clock, also known as military time in the United States.
Many nations use a 12-hour clock or a 24-hour/12-hour time combination, especially those that speak English as their primary language. Some professions favor using the 24-hour clock in nations where the twelve-hour clock is most prevalent.
A 24-hour clock is used in military time instead of a 12-hour clock to measure time. To convert from the 12-hour clock to military time, just add 12 to any time that is after noon. For example, 1 PM would be 13:00 in military time. To convert from military time to a 12-hour clock, just deduct 12 from any time that is after 12 PM (noon).
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[square] is a number that can be divided exactly by six.
When it is divided by five, four is the number left over.
Which of these could [square] stand for?
PLSS I NEED THIS NOW
The number [square] can divided exactly by six. and when [square] is divided by five, four is the number left over is:
12, 42, 72 o 102
Which of these could [square] stand for?The number [square] can be represented as 6x, where x is any positive integer, since it can be divided exactly by six. When [square] is divided by five, four is the number left over. Therefore, we can write the equation:
6x = 5y + 4
Where y is any positive integer. We can rearrange the equation to solve for x:
6x - 4 = 5y
2x - 2 = (5/3)y
2x - 2 = (5/3)(3x/5)
2x - 2 = (15/15)x
2x - 2 = x
x = 2
Therefore, the smallest possible value for [square] is 6(2) = 12. The next smallest possible value for [square] would be 6(2 + 5) = 42, since adding multiples of 5 to x will still satisfy the equation. The possible values for [square] are 12, 42, 72, 102, etc.
The possible values for [square] that are listed in the question are not provided, but the correct answer will be one of the numbers listed above.
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Benny the tiger, eats 12.5 pounds of meat per day. Each pound of meat costs $3.10. Jasmine prefers hay and alfalfa. She eats 200 pounds a day.Which animal cost more to feed each day? Show how you know
Answer:
Benny the tiger costs more to feed each day because he eats 12.5 pounds of meat per day, which costs $38.75 ($3.10 x 12.5). Jasmine eats 200 pounds of hay and alfalfa, which costs $0.00, since hay and alfalfa are not typically purchased with money. Therefore, Benny the tiger costs more to feed each day.
25 points. Please show working out!
Answer:
20 millilitres of oil
Step-by-step explanation:
You need to first find how much goes into 1 litre of oil and to do that we divide the two numbers
80/2 = 40
Now we know that for every 1 litre we need 40 millitres
Since .5 is half of 1 we just need to take half of 40
half of 40 = 20
20 millilitres of oil
how to convert 205 lbs to kg?
205 lbs is approximately equal to 92.9864 kg ( rounded to four decimal places )
The conversion factor to convert lbs to kilogram is 0.453592
1 lbs = 0.453592 kg
The conversion is the process of changing the unit of one quantity to another units
The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing
The mass in kg = The mass in lbs × conversion factor
Substitute the values in the equation
1 lbs = 0.453592 kg
205 lbs = 0.453592 × 205
Multiply the numbers
= 92.9864 kg ( rounded to four decimal places )
Therefore, 205 lbs is 92.9864 kg
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What number is shown by Point K on the number line?
The number line has numbers from 337 to 387 in increments of 5. Point K is between 367 and 377.
Thus, the value displayed by Point K is roughly 373.
What is the name of the numerical line?A number line in mathematics is a continuous straight line with numerals spaced equally apart along that line. Some stories will have a defined beginning and conclusion. We refer to these as closed number lines.
The distance between 367 and 377 can be split into five equal portions because the number line has 5 increments. Two components make up each section.
So, starting at 367, we must move 2 units to the right for each component until we reach Point K in order to determine the number represented by Point K.
We arrive at 369 by adding 2 units to the right of 367. From 369, we deduct another 2 units to arrive at 371. Following the same pattern, we arrive at 373, 375, and ultimately 377.
Point K is closest to 373 because it lies between 373 and 375. Thus, the value displayed by Point K is roughly 373.
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A circle has diameter 6 cm. Calculate the area of the circle. Give the units of your answer.
Answer: 9pi cm squared
Step-by-step explanation:
The radius is diameter divided by 2, so radius = 3cm.
Now, the equation for area is pi * r^2
3 squared is 9, so the area is 9pi cm squared.
Jasmine,an adult elephant, costs $21.80 per day to feed. Jasmine's calf, Siri, costs $16.60 per day to feed. So far sponsors have given $1,152.00 for these two elephants. How many days of food will this money buy? Write an equation and solve.
Answer:
Equation: 1,152.00 = 21.80x + 16.60y
21.80x + 16.60y = 1,152.00
x = 52 days
y = 69 days
This money will buy 121 days of food for Jasmine and Siri.
The radius of a circle is 6 inches. What is the area of a sector bounded by a central angle measuring 120°
Knowing that a circle has a radius of 6 inches, the area of a sector with a central angle of 120º is 12π square inches.
The area of a sector can be found using the formula:
Area of sector = (Central angle/360°) × π × r²
Where "central angle" is the angle of the sector in degrees and "r" is the radius of the circle.
In this case, the central angle is 120° and the radius is 6 inches. Plugging these values into the formula, we get:
Area of sector = (120°/360°) × π × 6²
Area of sector = (1/3) × π × 36
Area of sector = 12π square inches
Therefore, the area of the sector bounded by a central angle measuring 120° in a circle with a radius of 6 inches is 12π square inches.
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a statistical technique that would allow a researcher to cluster such traits as being talkative, social, and adventurous with extroversion is called:________
Cluster Analysis is a statistical technique that is used to group a set of objects into clusters such that objects within the same cluster are similar to one another and objects in different clusters are dissimilar. This technique can be used to group traits such as being talkative, social, and adventurous with extroversion.
The cluster analysis is performed by assigning each trait to a group, or cluster, based on the similarity of the traits. For example, if two traits are very similar, they may be grouped together. The cluster analysis uses various algorithms to determine which traits should be grouped together. These algorithms can be based on Euclidean distance, correlation, or other measures of similarity. Once the clusters have been created, the researcher can then analyze the clusters to see how they are related to extroversion. For example, the researcher may find that traits such as talkativeness and socialness are strongly correlated with extroversion, while adventurousness is only weakly correlated. This allows the researcher to identify which traits are most strongly associated with extroversion.
Overall, Cluster Analysis is a powerful statistical technique that can be used to group traits such as being talkative, social, and adventurous with extroversion. This technique can help researchers understand the relationship between various traits and extroversion and can be used to develop better intervention strategies for individuals who exhibit certain personality traits.
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what is definition of sampling error
Sampling error refers to the difference between the results of a sample and the true characteristics of the population from which the sample was drawn.
In statistics, sampling error is a measure of the degree of uncertainty that arises when estimating the characteristics of a population based on a sample of that population. This error occurs due to the fact that it is not feasible to collect data from every individual in a population, so researchers must rely on samples.
Sampling error can arise from various sources, including biases in the sample selection process, variability in the characteristics of the population, and random chance. Understanding and quantifying sampling errors are important in order to assess the validity and reliability of statistical estimates and to draw accurate conclusions from data.
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