4. Consider the initial value problem y+y = 3+2 cos 2r, y(0) = 0 (a) Find the solution of this problem and describe the behavior for large x.
Answers
The solution to the initial value problem y+y = 3+2cos(2r), y(0) = 0 is y(r) = 3/2 + cos(2r) - (3/2)cos(r). The behavior for large x tends towards a steady value
To solve the initial value problem, we can start by rewriting the equation as a first-order linear differential equation by introducing a new variable, v(r), such that v(r) = y(r) + y'(r).
Differentiating both sides of the equation with respect to r, we get v'(r) = 2cos(2r).
Integrating v'(r) with respect to r, we have v(r) = sin(2r) + C, where C is a constant.
Substituting y(r) + y'(r) back in for v(r), we have y(r) + y'(r) = sin(2r) + C.
To find C, we can use the initial condition y(0) = 0. Substituting r = 0 and y(0) = 0 into the equation, we get 0 + y'(0) = sin(0) + C, which gives us C = 0.
Therefore, the solution to the initial value problem is y(r) = 3/2 + cos(2r) - (3/2)cos(r).
Now, let's consider the behavior of the solution for large r (or x, since r and x are interchangeable in this context).
As r approaches infinity, the exponential term e^(-r) approaches zero. This means that the term Ce^(-r) becomes negligible compared to the other terms.
Therefore, the behavior of the solution for large x is primarily determined by the terms 3 + (1/2)sin(2r) - (1/4)cos(2r). The sin(2r) and cos(2r) terms oscillate between -1 and 1, but their coefficients (1/2 and -1/4, respectively) ensure that the amplitudes of the oscillations are limited.
Thus, for large x, the solution y approaches a steady value determined by the constant terms 3 - (1/4), which is approximately 2.75.
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Related Questions
Is this employee correct? please help and explain your thinking.
Answers
Answer: yes it is
Step-by-step explanation:
Find the value of X 6*6*6*6*6*6*6=6x
Answers
Answer:
46656
Step-by-step explanation:
6*6*6*6*6*6*6 = 6x
Multiply the terms.
279936 = 6x
Divide 6 into both sides.
279936/6 = 6x/6
= 46656
The solution of x for the expression 6 × 6 × 6 × 6 × 6 × 6 × 6 = 6ˣ is,
⇒ x = 7
We have to given that,
An expression to solve,
⇒ 6 × 6 × 6 × 6 × 6 × 6 × 6 = 6ˣ
We can write above expression into power as,
⇒ 6 × 6 × 6 × 6 × 6 × 6 × 6 = 6ˣ
Since, 6 repeats seven times.
⇒ 6⁷ = 6ˣ
By comparing, we get;
⇒ 7 = x
⇒ x = 7
Therefore, The solution of x for the expression 6 × 6 × 6 × 6 × 6 × 6 × 6 = 6ˣ is,
⇒ x = 7
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Substitution:
Y = 2x + 6
2x - y = 2
Answers
Answer:
no solution
-6 ≠ 2
Step-by-step explanation:
y = 2x + 6
2x - y = 2
substitute for y:
2x - (2x + 6) = 2
combine like terms:
-6 ≠ 2
The ize of a rectangle i 25 cm by 16 cm. A quare ha the ame area a the rectangle. Find the
perimeter of the quare
Answers
The square has a 48 centimeter perimeter.
To find the perimeter of the square, we need to calculate its side length. The area of a rectangle is given by its length multiplied by its width, so we can use the given measurements of the rectangle to calculate its area: 25 cm x 16 cm = 400 cm². The area of a square is given by the square of its side length, so we can use the area of the rectangle to calculate the side length of the square: √400 cm² = 20 cm.
Thus, the perimeter of the square is equal to 4 times its side length, or 4 x 20 cm = 80 cm.
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This equation models the height over time of a deep-water sensor.
h(t) = -4.9t^2 + 29.4t + 5.9
Rewrite the function in vertex form.
Answers
Answer:
h(t) = -4.9(t - 3)^2 + 50.
Step-by-step explanation:
h(t) = -4.9t^2 + 29.4t + 5.9
h(t) = -4.9(t^2 - 6t) + 5.9 Complete the square on t^2 - 6t:
h(t) = -4.9[ (t - 3)^2 - 9] + 5.9
h(t) = -4.9(t - 3)^2 + 44.1 + 5.9
h(t) = -4.9(t - 3)^2 + 50
The function in vertex form is: h(t) = -4.9(t - 3)² + 50
To rewrite the function in vertex form, we need to complete the square. The vertex form of a quadratic function is given by:
h(t) = a(t - h)² + k
where (h, k) represents the coordinates of the vertex.
We have,
h(t) = -4.9t² + 29.4t + 5.9
First, factor out the common factor -4.9 from the first two terms:
h(t) = -4.9(t² - 6t) + 5.9
So, h(t) = -4.9(t² - 6t + 9 - 9) + 5.9
h(t) = -4.9((t - 3)² - 9) + 5.9
Next, distribute -4.9:
h(t) = -4.9(t - 3)² + 44.1 + 5.9
h(t) = -4.9(t - 3)^2 + 50
Therefore, the function in vertex form is: h(t) = -4.9(t - 3)² + 50
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Find the area of this circle.
Use 3.14 to approximate .
A = πr²
14 ft
A = [?] ft²
Answers
The area of the circle, using 3.14 to approx. The area of this circle is 615.44\(ft^{2}\).
How to find the area of circle?The space a circle takes up in a two-dimensional plane is known as the area of the circle. Alternately, the area of the circle is the area included inside the circumference or perimeter of the circle. A = \(\pi r^{2}\), where r is the circle's radius, is the formula for calculating a circle's surface area.
The square unit—for instance, \(m^{2}, cm^{2}, in^{2}\) etc.—is the unit of area. In square units, the area of a circle is equal to \(\pi r^{2}\)or \(\frac{\pi d^{2} }{4}\)where (Pi) = \(\frac{22}{7}\) or 3.14. The ratio of a circle's circumference to its diameter is known as pi (π). This unique mathematical constant exists.
Area = \(\pi r^{2}\)
3.14×14×14 = 615.44\(ft^{2}\).
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What is the probability that a randomly chosen young adult has at least a high school education? which rule of probability did you use to find the answer?
Answers
The probability that a randomly chosen young adult has at least a high school education can be found using the rule of probability called the "complement rule".
To find the answer, we need to subtract the probability that a randomly chosen young adult does not have at least a high school education from 1. In other words:
Probability of having at least a high school education = 1 - Probability of not having at least a high school education.
By using this rule, we can calculate the probability.
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3253548cmid=308488 D Plant Stores Tracker... Which of the following forces is not driving renewable energy technologies? Select one: A. Concern for the environment B. Energy independence C. Inflation proof fuel costs D. Aggressive pursuit of higher quarterly corporate eamings E. Abundant resource Incorrect
Answers
The force that is not driving renewable energy technologies is D. Aggressive pursuit of higher quarterly corporate earnings.
Renewable energy is known for its great potential in providing environmental and social benefits. Below are explanations of the other forces driving renewable energy technologies:
A. Concern for the environment: The environment is a driving force behind renewable energy. The depletion of fossil fuels has contributed significantly to climate change. Renewable energy technologies can be a sustainable solution that can have a positive impact on the environment.
B. Energy independence: Renewable energy is a critical force in energy independence. By using renewable energy, countries can become more energy-independent and less dependent on imported fossil fuels.
C. Inflation proof fuel costs: Renewable energy is a force behind inflation proof fuel costs. Renewable energy is less susceptible to price volatility than traditional energy sources. Renewable energy resources are essentially infinite, so the costs remain constant and predictable.
E. Abundant resource: Renewable energy is a force behind the abundance of resources. Renewable energy sources are virtually limitless and available to the vast majority of countries. This abundance of resources has the potential to reshape the global economy and increase sustainable development opportunities.
The answer is D. Aggressive pursuit of higher quarterly corporate earnings.
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Andrea earns $32 washing 4 cars. At this rate, how much does Andrea earn washing 6 cars?
Andrea will earn $
washing cars.
Answers
Andrea earns a total of $48 for washing 6 cars at the rate.
What is cross multiplication?By using the cross multiplication approach, the denominator of the first term is multiplied by the numerator of the second term, and vice versa.
Using the cross multiplication method, we may determine the answer to a pair of linear equations. Using the mathematical rule of three, we may determine the answer based on proportions. The best illustration is cross multiplication, where we can write in a proportion to determine the values of unknown variables.
Given that,
$32 = 4 cars
$x = 6 cars
Using the method of cross multiplication:
x = 32(6) / 4
x = $48
Hence, Andrea earns a total of $48 for washing 6 cars at the rate.
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PLEASE HELP ILL GIVE BRAINLIEST!!
Answers
180 deg rotation about the origin and a translation 2 units left
Express 24 1/2 in simplest radical form.
Answers
Answer:
49/2
Step-by-step explanation:
The simplest radical form of the given expression will be √24.
How do convert the exponent into the simplest radical form?If the power of the variable "a" is b/c.
Then the simplest radical form of the expression will be
\(\rm \left ( a \right )^{\rm \frac{b}{c}} = \rm \sqrt[\rm c]{\rm a^b}\)
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ \((24)^{1/2}\)
If the power of the base is in half then it can be replaced by the square root.
Convert the expression into the simplest radical form. Then we have
⇒ \((24)^{1/2}\)
⇒ √24
The simplest radical form of the given expression will be √24.
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What would the cross sections be of a triangular prism cut diagonally NOT through the base?
A circle
B ellipse
C rectangle
D square
E trapezoid
F triangle
Answers
Answer:it might be (F)
Step-by-step explanation:
Tell me if I’m right or wrong
The ratio of juice to water is 1:5. How much
juice is needed to make 24 liters of punch?
Answers
Answer:
5.8 liters
Step-by-step explanation:
24 divided by 5 becomes 5.8
f(4) =
If g(x) = 2, x =
Answers
Sososos
Step-by-step explanation:
Identify the type of sampling used: random, systematic, convenience, stratified, or cluster. To estimate the percentage of defects in a recent manufacturing batch, a quality control manager at selects every th that comes off the assembly line starting with the until she obtains a sample of .
Answers
Complete question is;
Identify the type of sampling used: random, systematic, convenience, stratified, or cluster.
To estimate the percentage of defects in a recent manufacturing batch, a quality control manager at General Foods selects every 18th soup can that comes off the assembly line starting with the fifth until she obtains a sample of 40 soup cans
Answer:
Systematic Sample
Step-by-step explanation:
We are told that the quality control manager selects every 18th soup can that comes off the assembly line starting with the fifth until she obtains a sample of 40 soup cans.
Thus, the selection is from a large sample of produce.
This is synonymous with systematic sample because systematic sample can be defined as a type of probability sampling in which sample members from a larger population are selected according to a random starting point but with a set periodic interval.
This resonates with the statement in the question about selecting every 18th soup from the production assembly line.
8. The world's tallest
totem pole is in Alert
Bay, B.C., home of the
Nimpkish First Nation.
Twenty feet from the
base of the totem pole,
the angle of elevation
of the top of the pole
is 83.4º. How tall is
the totem pole to the
nearest foot?
Answers
Answer:
The height of the totem tree is approximately 172.8ft
Step-by-step explanation:
Hello,
To find the height of the totem pole, we need to use our date to make a pictorial representation so that we can know if the pole and base makes a right angle triangle with the angle of elevation.
See attached document for better illustration.
Let T represent the height of the pole.
Using trigonometric ratio,
SOHCAHTOA, we can use tangent since we have our adjacent and we're to solve for the opposite.
Tanθ = opposite/ adjacent
Opposite = T
Adjacent = 20ft
θ = 83.4°
Tan83.4 = T / 20
T = 20Tan83.4
T = 20 × 8.64
T = 172.8ft
The height of the totem tree is approximately 172.8ft
The product of a number and -7 is greater than 42
Answers
divide by -7
x < -6
Answer:
-7*x>42
Step-by-step explanation:
-7 times any negative number greater than 6 is equal to more than 42
What is the slope for theses two
Answers
Method: Forty-eight preschoolers (age range =3 years 6 months to 4 years 5 months; 24 boys, 24 girls) watched a video featuring two female actors seated side by side. On each of four trials, one actor announced her intention to hide a ball under one of four cups; the other agreed, covered her eyes, and turned around to face the back wall. The hider placed a small barrier in front of the cups so that the children could watch as she hid the ball but could not see the particular cup she baited. She announced that she had finished and removed the barrier. Both actors faced the camera throughout the rest of the trial. The children were randomly assigned to three conditions. In the point condition (n=16; mean age =3 years 11 months), the two actors simultaneously pointed to different cups. In the grasp condition ( n=16; mean age =4 years 0 months), they simultaneously grasped the tops of different cups. We used grasping as a comparison gesture because young children understand that it, like pointing, is intentional and object-directed (Woodward, 1999). However, it is not often used communicatively, and so may not be as likely as pointing to lead to the misattribution of knowledge. In the baseline condition ( n=16; mean age =3 years 11 months), the two actors simply sat with their hands in their laps. After the actors gestured (or not), the experimenter paused the video and asked, "Who knows where the ball is?" One actor hid the ball on the first and fourth trials; the other actor did so on the middle two trials. Results: Children in the grasp and baseline conditions selected the actor who hid the ball as the one who knew its location more frequently than would be expected by chance, ts (15)>3.74, ps <.01,ds>0.94; specifically, children in the grasp location selected that actor on 3.13(SD=1.20) of the 4 trials, and children in the baseline condition selected her on 3.25(SD=1.06) of the 4 trials. Children in the point condition performed at chance level, t(15)<1, selecting the hider on just 2.13(SD=1.25) trials. An analysis of variance revealed a significant effect of condition, E(2,45)=4.38,p=.018,η2=.16. Children in the point condition were less likely to select the hider than were children in the grasp or baseline condition (Tukey's honestly significant difference, ps<.05 ); performance did not differ between the latter two conditions. Seeing the two actors point may have led children in the point condition to assume that both were knowledgeable. But it is also possible that these children ignored the test question: Rather than indicating which pointer was knowledgeable, perhaps they reflexively indicated where they would search for the ball, which would also lead to chance performance (Palmquist, Burns, \& Jaswal, 2012; Povinelli \& deBlois, 1992). One reason to doubt this possibility is that the children tended to respond to the test question by pointing to an actor's face rather than one of the cups (72\% vs. 28% of trials). However, to investigate this possibility directly, we conducted a control study with 8 different children (mean age =3 years 9 months, range =3 years 6 months to 4 years 1 month; 5 boys, 3 girls). The procedure was the same as in the point condition, but after the actors pointed, the experimenter asked, "Who hid the ball?" If pointing automatically triggers a search response, even when the test question does not ask children to indicate where they would search, they should select the two pointers equally (as they did in the point condition) when this procedure is followed. In fact, however, the children correctly indicated the hider on 3.89(SD=0.35) of the 4 trials, more often than expected by chance, t(7)=15.00,p<.001,d=7.59. Thus, children do not automatically respond to pointing by
Answers
The study found that preschoolers in the grasp and baseline conditions recognized the actor who hid the ball as the one with knowledge of its location, suggesting that pointing gestures influenced their judgments.
In this study, 48 preschoolers participated, ranging in age from 3 years 6 months to 4 years 5 months, with an equal distribution of 24 boys and 24 girls. The children watched a video featuring two female actors seated side by side.
The actors engaged in a task where they hid a ball under one of four cups, while the other actor covered her eyes and turned around. A small barrier was placed in front of the cups, preventing the children from seeing the specific cup where the ball was hidden.
In the grasp condition, the actors simultaneously grasped the tops of different cups.
The baseline condition served as a comparison, where the actors simply sat with their hands in their laps. After the actors performed the gestures or remained in the baseline condition, the video was paused, and the children were asked, "Who knows where the ball is?"
The results showed that children in the grasp and baseline conditions selected the actor who hid the ball as the one who knew its location more frequently than would be expected by chance.
In contrast, children in the point condition performed at chance level, indicating the hider on just 2.13 out of 4 trials
An analysis of variance revealed a significant effect of condition, suggesting that the pointing gesture influenced the children's judgments.
The possibility that children in the point condition ignored the test question and instead reflexively indicated where they would search for the ball was considered.
The results showed that children correctly indicated the hider more often than expected by chance, indicating that they were not simply responding to the pointing gesture.
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Find the Area. Use 3.14 for pi
Answers
Answer: 36.56
Step-by-step explanation:
To solve the equation, first acknowledge that the radius of the quarter circle shown at the top of the figure is 4 cm, so the rectangle's dimensions are 4 by (10-4) or 4 by 6, meaning the area is 24 cm^2.
Then address the circle, with an area of pi * r^2.
pi * r^2
3.14 *(4)^2
3.14 * 16
50.24
Then, because the figure shows 1/4 of a circle, divide 50.24 by 4.
50.24/4
12.56
Then add 24 to 12.56 to get 36.56.
Hope it helps :) and let me know if you want me to elaborate.
What is the range of the function f(x) = 2x + 1 given the Domain D = {-1,0, 1, 2}?
R = {0, 1,3,5)
R= {-1,1,3,5)
R = {-5, -3,-1,1)
R = {0, 1,3,6}
Answers
Answer:
R= {-1,1,3,5)
Step-by-step explanation:
To find the range, use the domain values as the input and find the output for the function
Domain D = {-1,0, 1, 2}?
f(x) = 2x + 1
f(-1) = -2 +1 = -1
f(0) = 0 + 1=1
f(1) = 2 + 1 = 3
f(2) = 4 + 1 = 5
The range is { -1,1,3,5}
H
SSS
SAS
ASA
AAS
HL
cannot determine
Answers
Answer:
last answer
Step-by-step explanation:
Evaluate: 792.6 ÷ 10-4
remember it is not 10-4. it is 10 to the -4 power
Answers
Answer:
792600
Step-by-step explanation:
For this question you can add four zeroes to the back of 792.6 andmove the decimal to get you the answer, hope this helps
It's also good to know that if the exponent was positive the answer would be 0.07926
SOLUTION STEPS
10 ^−4/792.6
Calculate 10 to the power of −4 and get
10000
1
.
10000
1
792.6
Divide 792.6 by
10000
1
by multiplying 792.6 by the reciprocal of
10000
1
.
792.6×10000
Multiply 792.6 and 10000 to get 7926000.
7926000
hopefully i helped
There are 650 toothpicks in a regular-sized box. If a jumbo box is made by tripling all the dimensions of the regular-sized box, how many toothpicks will the jumbo box hold?
Answers
Answer: 1950 is how many it will hold.
Step-by-step explanation:
Can someone help me find the value of X I would really appreciate it ;)
Answers
Step-by-step explanation:
the similarity of the triangle:
x/18 = 8/12
=> 12x = 18×8
12x = 144
x = 12
Question 39 of 45What is the domain of the discrete function shown below?G(x) = ((9,10), (10,11), (11, 12),. (12, 13)}
Answers
The domain of the discrete function G(x) is {9, 10, 11, 12}.
The domain of a function refers to the set of all possible input values for which the function is defined.
In the case of the given discrete function G(x), we can determine its domain by examining the set of input values or x-values present in the function's ordered pairs.
Looking at the ordered pairs provided: ((9,10), (10,11), (11, 12), (12, 13)), we can observe that the x-values in these pairs are 9, 10, 11, and 12. Therefore, the domain of the function G(x) is the set {9, 10, 11, 12}, which includes these four values.
It's important to note that the domain of a discrete function consists of individual, isolated values rather than a continuous range.
Each x-value in the domain corresponds to a specific output or y-value, as indicated by the ordered pairs.
In this case, the function G(x) maps each x-value to the corresponding y-value in the pairs: 9 maps to 10, 10 maps to 11, 11 maps to 12, and 12 maps to 13.
To summarize, the domain of the given discrete function G(x) is {9, 10, 11, 12}, representing the set of possible input values for which the function is defined.
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Plz could u help me solve dis, I'll be grateful
Answers
Answer:
X= -3/4
or X=-0.75 if you want it in decimal form.
Step-by-step explanation:
Or in decimal form x=−0.75
Suku kedua belas dari barisan bilangan 8, 15, 24, 35, .... adalah ...
Answers
Pls help I inserted a picture
Answers
The inequality is 7<x<31.
What is inequality ?
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
The third side of any triangle must be more than the difference between the other two sides.
x>19-12
x>7 (or) 7<x
The third side of any triangle must be less than the sum of the other two sides.
x<19+12
x<31 (or) 31>x
Put them together.
7<x<31 (or) 31>x>7
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Use the distributive property to write an expression that is equivalent to: 3(x + 5)
Answers
Answer:
3x=15
Step-by-step explanation:
Here's what I found on google about the distributive property-
To “distribute” means to divide something or give a share or part of something. According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
Now for the math-
3(x+5)
distribute the numbers- 3(x)+3(5)
solve- 3*5=15
3x+15