The correct form of a particular solution of the differential equation y" + 4y = cos (2x) is y_p = A cos (2x) + B sin (2x).
The complementary function of the differential equation is y_c = C_1 cos (2x) + C_2 sin (2x), where C_1 and C_2 are constants determined by the initial conditions.
To find the particular solution, we assume that y_p has the same form as the forcing function, which is cos (2x). Since the equation is linear, we can superimpose the particular solution on top of the complementary function, so we have:
y_p = A cos (2x) + B sin (2x)
Taking the first and second derivatives of y_p, we get:
y'_p = -2A sin (2x) + 2B cos (2x)
y''_p = -4A cos (2x) - 4B sin (2x)
Substituting these expressions into the differential equation, we have:
(-4A cos (2x) - 4B sin (2x)) + 4(A cos (2x) + B sin (2x)) = cos (2x)
Simplifying, we get:
(4B - 4A) sin (2x) + (4A + 4B) cos (2x) = cos (2x)
We can solve for A and B by equating coefficients of sin (2x) and cos (2x) on both sides of the equation. This leads to:
A = 0
B = 1/4
Therefore, the particular solution is y_p = A cos (2x) + B sin (2x) = 1/4 sin (2x).
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which equation represents a proportional relationship A. y=4x B. 5x+2 C. y= 7 D. y= 3x²
Answer:
The answer is A) \(y=4x\)
Step-by-step explanation:
This is because y directly corresponds to x, if x is 1, then y = 4, if x is 2, then y = 8 and so on.
A Web music store offers two versions of a popular song. The size of the standard version is 2.8 megabytes (MB). The size of the high-quality version is 4.5 MB. Yesterday, the high-quality version was downloaded four times as often as the standard version. The total size downloaded for the two versions was 4784 MB.How many downloads of the standard version were there?
There were 644 downloads of the standard version
Explanation:Let x represent the standard version's download size
Then high quality's download size will be (4784 - x)
The high quality was downloaded 4 times, so 4 * 4.5 = 18 mb
Then the equation for the ratios below is correct
\(\frac{2.8}{18}=\frac{x}{4784-x}\)Solving for x
\(\begin{gathered} 18x=2.8(4784-x) \\ 18x=13395.2-2.8x \\ 18x+2.8x=13395.2 \\ 20.8x=13395.2 \\ x=\frac{13395.2}{20.8}=644 \end{gathered}\)There were 644 downloads of the standard version
Albert is traveling 40mph in his car. After 5 hours, how far will he have traveled
Answer:
I believe he traveled 200 miles
Step-by-step explanation:
Multiply 40 by 5
please solve this simultaneous equation
Answer:
b6 2hich method
Step-by-step explanation:
I solv3 this
Walkway Over the Hudson, a bridge that crosses the Hudson River in Poughkeepsie, is 2.063
kilometers long. Anping Bridge, which was built in China 850 years ago, is 2.07 kilometers long.
a. What is the total span of both bridges?
Show your thinking
b. How much longer is the Anping Bridge
than the Walkway Over the Hudson?
Answer: 4.126 km
Step-by-step explanation:
First, We have to find total span of both bridges
As Question indicates 'total' ,that is, we have to find bridge length in total ( You can join Bridges to have better understanding)
Now, Walkway over hundson Bridge length= 2.063 km
Amping bridge length= 2.07 km
So, Total span of both bridges = 2.063+2.07 = 4.133 km
b) Now Leah wanna walk across and back on walkway over hudson ,that is, she wanna return to starting point from where she walk forth
So,that means, she walk double distance of length of walkway over hudson
So, total distance = 2× 2.063
= 4.126 km
hope this helps,
Plzzs give brainliest if you like my answer.
elsa and her husband are each starting a saving plan. Elsa will initially set aside 750 and then add $165 every month to the savings. The amount (in dollars saved this way is given by the function A = 750 + 165N where is the number of months she has been saving Her husband will not set an initial amount aside but will add $385 to the savings every month. The amount B (in dollars) saved using this plan is given by the function B = 385N Let be total amount (in dollars) saved using both plans combined. Write an equation relating to N. Simplify your answer as much as possible
Solution
T = A + B
=> T = 750 + 165N + 385N
=> T = 750 + 550N
What is the effect of k on f(x)=g(5x) where g(x) is a piecewise function? Explain.
Answer:
g(x) will be dilated horizontally to get f(x)
Step-by-step explanation:
Given
f(x) = g(kx) --> the correct equation
Required
The effect of k
The given equation is an illustration of horizontal dilation.
If |k| is greater than 0, then the function will be compressed.
However, if |k| is between 0 and 1 (exclusive), then the function will be stretched.
Take for instance:
f(x) = g(x/5)
In the above function, g(x) will be stretched by 5 units
Another instance is:
f(x) = g(x/0.5)
In the above function, g(x) will be stretched by 0.5 units
A car has an initial velocity of 10 m/s and final velocity of 43 m/s. The time taken
to reach the final velocity was 3 seconds. What is the acceleration of the car?
Hint: Acceleration (in terms of velocity) = (final velocity - initial velocity)/(time) *
Answer:
160 m/s
Step-by-step explanation:
vi= 10m/s
a= 5om/s*2
t=3 second
vf=?
frist step: find s(distance)
s=vit+1/2 at*2=10m/s x3s +0.5 x50m/s*2 (3s)*2 =30m+225m=255m
second : find vf
s=(vf+vi)/2 xt
vf=2s/t- vi=2(255m)/3s -10 m/s=170 m/s-10m/s=160m/s
Therefore , the final velocity of the car is 160m/s
Which choice most effectively sets up the list of
examples that follows in the next sentence?
A) NO CHANGE
B) garnered national publicity for the agency.
C) generated a steady stream of new technology.
D) made a lot of money for the agency
The choice that most effectively makes up the list of examples is to generate a steady stream of new technologies. Option C is correct.
Given the passage is shown in the attached images.
It most effectively creates the list of examples of new technologies listed in the following sentence:
"Communication satellites, invisible dental appliances and wireless tools."
Options other than C that are A, B and D are incorrect because they say "international cooperation", "national publicity" and "money for the agency", respectively; However, the following sentence lists examples of Technology.
Therefore, the selection that most effectively forms the list of examples that follows in the next sentence of the given passage will generate a steady stream of new technology.
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x²-5x-14/2x³-13x²-7x
Answer:
\( \frac{(x - 7)(x + 2)}{x(2 {x}^{2} -13x - 7) } \\ \frac{(x - 7)(x + 2)}{x(x - 7)(2x + 1)} \\ \frac{(x + 2)}{x(2x + 1)} \)
The Jayden family eats at a restaurant that is having a 15% discount promotion. Their meal costs $78.40 before the discount, and they leave a 20% tip. If the tip applies to the cost of the meal before the discount, what is the total cost of the meal? Round your intermediate calculations and answer to the nearest cent.
Answer:
$ 80.22
Step-by-step explanation
Assumed 20% tip is on the discounted meal.The cost of the meal is $78.65
The cost of the meal after discount (15%)is 78.65(1−0.15)≈$ 66.85
Tip (20%) is : 66.85⋅0.2$13.37
Total cost of the meal is
66.85+13.37≈$80.22 [Ans]
Jack works after school. each day he is paid a set amount, plus an hourly wage. Which is the reasonable domain for the function f(x)=10x+8
Answer:
x>-⅘ OR x<-⅘ (Can I have brainliest ;-;)
Step-by-step explanation:
1) Find x-int:
0=10x+8
-8=10x (÷10)
-⅘=x
x(-⅘;0)
2) Domain:
x>-⅘x<-⅘3) Choose 1 of those, since i cant see the graph i cant say which domain would fit the graph
we used an algorithm that computes the median of 5 and showed that it works in a worst-case linear time. 1. repeat the problem using the median of 3 and argue that it does not work in linear time. 2. repeat the problem using the median of 7 and show that it works in a linear time. 1
The median of 3 algorithm does not work in linear time when computing the median of 5. It requires additional comparisons and rearrangements, resulting in a higher time complexity than linear. The median of 7 algorithm works in linear time when computing the median of 5. It allows for efficient selection of the median by utilizing a larger set of elements, ensuring linear time complexity.
To illustrate this, let's consider the scenario of finding the median of 5 using the median of 3 approach. We start by selecting three elements and finding their median, let's say it's element A. Then we compare element A with the remaining two elements. If A is greater than both of them, it becomes the median. Otherwise, we need to consider another pair of elements and repeat the process. This additional step introduces more comparisons and operations, making the algorithm more complex than a linear time algorithm. When using the median of 7 to compute the median of 5, it works in linear time. The median of 7 algorithm selects the median element from a set of seven elements, which can be done in linear time. By applying this algorithm to find the median of 5, we select a subset of five elements and determine their median using the median of 7 algorithm. This approach ensures that we find the median of 5 in a linear time complexity.
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Please help me find the relationship and value
Mark and Gary had a basketball game Saturday. Mark had three times as many rebounds as Gary. If together they had 28 rebounds, how many rebounds did Mark have?
Answer: 19
Step-by-step explanation:
What is the output of the following code fragment?
int x=0;
while( x < 5)
cout << x << endl;
x ++;
cout << x << endl;
The output of the following code fragment
int x=0;
while( x < 5)
cout << x << endl;
x ++;
cout << x << endl; will be 0, 1, 2, 3, 4, 5.
The code initializes the variable x to 0, and then enters a while loop that will execute as long as x is less than 5. During each iteration of the loop, the value of x is output to the console using the cout statement, followed by a new line character.
After the cout statement, x is incremented by 1 using the x++ statement. This process is repeated until x is equal to 5, at which point the loop terminates. Finally, the value of x is output to the console using the cout statement, followed by a new line character, giving the output of 5.
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can someone help me with this question please
the answer isn't 28 btw
Answer:
Use Pythagorean.
The triangles have sides 2, 5 and c.
\(c^2= 2^2+5^2\)\(c^2=29\)\(c=\sqrt{29}\)Help Please!!!!!!!!!!!!!
Answer:
Answer vary:
(a)
*Laila is not wearing tennis shoes.
*It is not the case that Laila is wearing tennis shoes.
(b)
*Jassim is in Germany
Step-by-step explanation:
honestly in my opinion that’s my answer. to be honest either could be wrong but I’m fairly confident in part a but b I’m sorta confident.
(a) what you need to do is focus on the word negations and then you’ll see easily what the answers are. and that’s how I got the answers I got.
meaning of negations : the contradiction or denial of something
(b) so on part b your looking for the conclusion of the sentence and as the sentence explains “If Jassim’s spouse is happy, then Jassim is in Germany.” and for me I came to the conclusion of that answer.
giving brainliest!! thanks in advance!
Answer:
55,000 Step-by-step explanation:thats my answer thank you for the nice questionWhich value is a solution for the equation tan x/2 = -1?
A. 5pi/4
B. 7pi/4
C. 3pi/4
D. 3pi/2
Answer:
D
Step-by-step explanation:
What we have to do is to find the arc tan
x/2 = arc tan (-1)
tan is negative on the 4th and second quadrant
arc tan (-1) = 135 or 315
pi is 180 degrees
so we have;
135 is 3 pi/4
multiplied by the 2
= 6 pi/4 which is 3 pi/2
315 is 7 pi/4 which is same as 7 pi/2 when we multiply by 2
Answer:
the answer is d
Which of the following is true of newborn reflexes?
Reflexes do not appear until the third week of life.
Newborns have control over their reflexes.
These reflexes become involuntary over time.
Abnormalities in the reflexes can indicate brain damage.
Among the provided statements, only the statement "Abnormalities in the reflexes can indicate brain damage" is true of newborn reflexes:
Newborn reflexes are automatic, involuntary movements or actions that are exhibited by infants in response to certain stimuli. These reflexes are typically present from birth and serve as important indicators of neurological development and overall health.
Abnormalities or deviations from the expected patterns of newborn reflexes can suggest underlying neurological issues or brain damage.
For example, the absence, asymmetry, or persistence of certain reflexes beyond the expected timeframe can be signs of potential neurological problems that require further evaluation and medical attention.
However, the other statements provided in the options are not accurate:
- Reflexes do not appear until the third week of life: This statement is false. Newborn reflexes are present from birth or shortly after birth, and they can be observed in the early days of a baby's life.
- Newborns have control over their reflexes: This statement is false. Newborn reflexes are instinctual and involuntary responses that occur without conscious control from the infant. As the baby grows and develops, they gain more control over their movements and their reflexes become integrated into voluntary actions.
- These reflexes become involuntary over time: This statement is false. Newborn reflexes are already involuntary from the start. They are not intentionally controlled by the baby and are automatic responses triggered by specific stimuli.
It's important to note that the presence or absence of specific newborn reflexes and their developmental patterns can vary among individuals, but deviations from the norm may indicate potential health concerns and should be addressed by medical professionals.
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a culture initially contains 2000 bacteria. if the number of bacteria doubles every 3 hours, how many bacteria will be in the culture at the end of 14 hours?
By using the unitary method and dividing the time into equal intervals, the number of bacteria doubled every 3 hours, the final total of 32,000 bacteria after 14 hours.
Unitary method involves dividing the time interval into equal parts, and calculating the growth for each unit of time before adding them all up to get the total growth.
To start, let's divide the 14 hours into 3 hour intervals. We have
=> 14 hours / 3 hours = 4 intervals.
Next, we need to calculate the growth in each 3 hour interval. Since the number of bacteria doubles every 3 hours, we can find the growth by multiplying the initial number of bacteria by 2.
Starting with the first interval, we have 2000 bacteria * 2 = 4000 bacteria.
We can now repeat this calculation for each interval, multiplying the previous total by 2 each time.
For the second interval, we have 4000 bacteria * 2 = 8000 bacteria.
For the third interval, we have 8000 bacteria * 2 = 16,000 bacteria.
Finally, for the fourth interval, we have 16,000 bacteria * 2 = 32,000 bacteria.
So, at the end of 14 hours, there will be 32,000 bacteria in the culture.
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the magazine mass marketing company has received 15 entries in its latest sweepstakes. they know that the probability of receiving a magazine subscription order with an entry form is 0.5 . what is the probability that less than a third of the entry forms will include an order? round your answer to four decimal places.
The probability that less than a third of the entry forms will include an order is 0.3760.
To solve this problem, we need to use the binomial distribution, which is a probability distribution that describes the number of successes in a fixed number of independent trials. In this case, we want to find the probability that less than a third of the 15 entries will include an order, given that the probability of receiving an order with an entry form is 0.5.
Let X be the random variable that represents the number of entries with an order out of the 15 total entries. Then X follows a binomial distribution with parameters n=15 and p=0.5. The probability of less than a third of the entries having an order is equivalent to the probability of X being less than or equal to 5, since 5 is one third of 15.
Using a binomial probability table or calculator, we can find that the probability of X being less than or equal to 5 is 0.3760, rounded to four decimal places.
In summary, we used the binomial distribution to model the number of entries with an order, and found the probability that less than a third of the entries will include an order. We obtained a probability of 0.3760, which represents the likelihood of observing 5 or fewer entries with an order out of the 15 total entries.
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Bobby has $27 to spend on ice cream for the month. The ice cream he likes is two dollars each how many ice cream‘s can he buy this month
?
The volume of box A is 60, and the volume of box B is half the volume of box A. What is the height of box B, a?
Answer: The box measurements are as follows: Box A: height = 5 inches, length = 18 inches, width = 10. Box B: height = 8 inches, length = 10 inches, ..
Step-by-step explanation:
A classic rock radio station claims to play and average of 50 minutes of music every hour. However, it seems like every time you turn to this station, there is a commercial playing. To investigate their claim, you randomly selected 12 different hours during the next week and recorded the number of minutes of music played during each of the 12 hours. Here are the number of minutes of music in each of these hours: 44 49 45 51 49 53 49 44 47 50 46 48 Is there evidence that the mean number of hours of music played each hour is less than what the radio station advertises? Interpret the p-value in the context of the problem. If an error has been committed, explain which type of error it could be.
So the convincing evidence that the radio station plays less than
\(50\ min\ of\ music\ per\ hour\). Here we have to see graph and chart.
How to get convincing evidence that radio station play less?Parameter of Interest, \(\mu = the\ true\ average\ number \ minutes\ of\ music \ played\ every \ hour.\)
Null Hypothesis, \(H_{o} : \mu = 50\)
Alternative Hypothesis, \(H_{a} : \mu < 50\)
\(Conditions\ of\ test :\)
\(Random :\) A random sample of \(hours\) was selected.
\(Independent:\) There are more than \(10(12) = 120\ hours\) of music played during the week.
\(Normal:\) We do not know if the population distribution of the music \(times\) is approximately Normal and we don’t have a large (big) sample size, so we will graph the data and look for any departures from Normality.
Level of Significance, \(\alpha = 0.05\ Significance\ level\)
\(n = 12, df = 11, \bar x = 47.9, S_{x} = 2.81\)
1- var Stats:
\(\bar x= 47.9166\) , \(\Sigma\ x = 575\), \(\Sigma\ x^{2} = 27639\), \(Sx = 2.81096\), \(\sigma x = 2.69129\)
\(t = \frac{\bar x- \mu_{o}}{ \frac{S_{x} }{\sqrt{n} } }\)
\(t = \frac{47.9- 50}{ \frac{2.81 }{\sqrt{12} } }\)
\(= - 2.59\)
T test :
\(\mu < 50, t = -2.5674, p=.013, \bar x = 47.9166, S_{x} = 2.81, n = 12\)
P-value (Use correct probability notation.) \(P-value = P(t < -2.59) = 0.0126\)
Since the \(P-value(.013)\) is less than \(\alpha =.05\), we reject the null hypothesis.
There is convincing evidence(proof) that the radio station plays less than \(50\ min\ of\ music\ per\ hour\).
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Given the graph of the function f(x), find each of the following.
† y
a. f(-4) 2
b.
f(0) O
C.
f (2) -1
d. f (5) -1
Answer:
a) 2 ; b) 0; c) -2 ; d) -1
Step-by-step explanation:
a) f(-4)=2 ;
b) f(0)=0;
c) f(2)= -2 ;
d) f(5)= -1
2. Aqueous cleaners are
parts cleaning agents.
Answer:
water based
Step-by-step explanation:
trust
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
x2 + (y – 3)2 = 36
x2 + (y – 5)2 = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x2 + (y + 8)2 = 36
(A) x2 + (y – 3)² = 36, is the equation that represents circles with a diameter of 12 units and a center on the y-axis.
What are equations?In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.So, the standard form for calculating the equation of a circle is as follows:
(x-a)² + (y-b)² = b = r²
Where;
(a, b) is the circle's center.The radius of the circle is denoted by r.Information:
diameter = 12 unitsradius = 12/2 = 6 unitsIf the center is on the y-axis, it will be at (0, 3).
By substituting into the formula, we get (x-0)² + (y-3)² = 6² is equivalent to
x²+ (y-3)² = 36Therefore, the equation that represents circles with a diameter of 12 units and a center on the y-axis is (A) (A) x2 + (y – 3)² = 36.
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The correct question is given below:
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
a. x2 + (y – 3)2 = 36
b. x2 + (y – 5)2 = 6
c. (x – 4)² + y² = 36
d. (x + 6)² + y² = 144
e. x2 + (y + 8)2 = 36
1. Statistics from Cornell’s Northeast Regional Climate Center indicate that Ithaca, NY, gets an average of 35.4" of rain each year, with a standard deviation of 4.2". Assume that a Normal model applies. (Problem from Intro Stats by De Veaux, Velleman, Bock – 3rd Edition)
a. During what percentage of years does Ithaca get more than 40" of rain?
b. Less than how much rain falls in the driest 20% of all years?
c. A Cornell University student is in Ithaca for 4 years. Let represent the mean amount of rain for those 4 years. Describe the sampling distribution model of this sample mean, Be sure to check assumptions and conditions.
d. What’s the probability that those 4 years average less than 30" of rain?
Probability is a measure of the likelihood or chance of an event occurring.
a. To find the percentage of years where Ithaca gets more than 40" of rain, we need to calculate the z-score for this value and then use a standard normal table to find the percentage. The z-score is:
z = (40 - 35.4) / 4.2 = 1.33
From a standard normal table, we find that the percentage of values above z = 1.33 is approximately 9.87%. Therefore, during about 9.87% of years, Ithaca gets more than 40" of rain.
b. To find the value of rainfall corresponding to the driest 20% of years, we need to calculate the z-score for the 20th percentile and then convert it back to rainfall units. The z-score is:
z = invNorm(0.20) = -0.84
where invNorm is the inverse normal function. Therefore,
-0.84 = (x - 35.4) / 4.2
Solving for x, we get:
x = 32.2"
So less than 32.2" of rain falls in the driest 20% of all years.
c. Since the sample size n = 4 is small and the population standard deviation is unknown, we need to use the t-distribution to describe the sampling distribution model of the sample mean. However, since the sample size is small, we also need to assume that the population follows a normal distribution.
Under these assumptions, the sampling distribution of the sample mean is approximately normal with a mean of μ = 35.4" and a standard error of σ/√n = 4.2/√4 = 2.1". Therefore, the sampling distribution of the sample mean is:
t(3, 35.4, 2.1)
where t denotes the t-distribution, 3 is the degrees of freedom (n - 1), 35.4 is the mean, and 2.1 is the standard error.
d. To find the probability that the 4-year average is less than 30", we need to calculate the z-score for this value and then use the t-distribution with 3 degrees of freedom to find the probability. The z-score is:
z = (30 - 35.4) / (4.2 / √4) = -2.57
Using a t-table or calculator with 3 degrees of freedom, we find that the probability of a t-value less than -2.57 is approximately 0.041. Therefore, the probability that those 4 years average less than 30" of rain is approximately 0.041 or 4.1%.
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