Suppose that a fourth order differential equation has a solution y = - 3e^3x x sin(x). Find the initial conditions that this solution satisfies.
Answers
The initial conditions that the solution y = -3e^(3x)sin(x) satisfies are:
y(0) = 0, y'(0) = 3, y''(0) = -6, y'''(0) = 0, and y''''(0) = 18.
To find the initial conditions that the solution y = -3e^(3x)sin(x) satisfies, we need to differentiate it four times and then evaluate it at the initial time t = 0.
y = -3e^(3x)sin(x)
y' = -3e^(3x)sin(x) + 3e^(3x)cos(x)
y'' = -6e^(3x)cos(x)
y''' = 18e^(3x)sin(x)
y'''' = 18e^(3x)cos(x)
Now, evaluating these expressions at t = 0:
y(0) = -3e^(3*0)sin(0) = 0
y'(0) = -3e^(30)sin(0) + 3e^(30)cos(0) = 3
y''(0) = -6e^(3*0)cos(0) = -6
y'''(0) = 18e^(3*0)sin(0) = 0
y''''(0) = 18e^(3*0)cos(0) = 18
Therefore, the initial conditions that the solution y = -3e^(3x)sin(x) satisfies are:
y(0) = 0, y'(0) = 3, y''(0) = -6, y'''(0) = 0, and y''''(0) = 18.
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Related Questions
Dante drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 10 hours. When Dante drove home, there was no traffic and the trip only took 7 hours. If his average rate was 18 miles per hour faster on the trip home, how far away does Dante live from the mountains?Do not do any rounding.
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You know that:
- Last weekend his trip took 10 hours when he drove to the mountains.
- When he drove home, the trip took 7 hours.
- His average rate was 18 miles per hour faster on the trip home.
By definition, the distance can be calculated with this formula:
\(d=rt\)Where "d" is distance, "r" is rate, and "t" is time.
Then, you can set up the following equation to represent his trip to the mountains ("d" is in miles):
\(d=10r\)And you can set up the following equation to represent his trip home ("d" is in miles):
\(d=7(r+18)\)To find the value of "r", you need to make both equations equal to each other and solve for "r". Then, you get:
\(\begin{gathered} 10r=7(r+18) \\ 10r=7r+126 \\ 10r-7r=126 \\ \\ r=\frac{126}{3} \\ \\ r=42 \end{gathered}\)Knowing the value of "r", you can substitute it into the second equation:
\(\begin{gathered} d=7\mleft(r+18\mright) \\ d=(7)\mleft(42+18\mright) \end{gathered}\)Finally, evaluating, you get (Remember that "d" is in miles)
\(\begin{gathered} d=(7)(60) \\ d=420 \end{gathered}\)Therefore, the answer is:
\(420\text{ }miles\)Find all the terms in 4x power of 3 + x power of 2 + 3x + 6. Plsssss help you’ll make my day :(
Answers
We are given the following expression
there are 16 pounds in 1 pond. juan is mailing a package that weighs 96 ounces. he wants to know the weight of the package in pounds. complete the statement to describe how to convert ounces to pounds.
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Answer:
To find the weight in pounds, divide the number of ounces by the unit rate, 6 ounces per pound.
96 divided by 16 = 6
i dont understand the last one can anyone help
Answers
Answer:
the spaces between the bars are not equal.
Answer:
the spaces between the bars are not equal
Step-by-step explanation:
The value of y varies directly with x. When y = 85, x = 14. What is the value of y when x is 112?
Answers
Answer:
y = 679.952
Step-by-step explanation:
It is given that, the value of y varies directly with x.
y₁ = 85, x₁ = 14
\(y\propto x\\\\y=kx\\\\k=\dfrac{y}{x}\\\\k=\dfrac{85}{14}\\\\k=6.071\)
We need to find the value of y when x is 112.
\(y=k\times x\\\\=6.071\times 112\\\\y=679.952\)
So, the value of y is 679.952 when x is 112.
find teh exact value of sin 2x given that sec x = 3/2 and csc y = 3 and x and y are in quadrant 1
Answers
The exact value of \(sin 2x\) is \(4√5/9.\)
Given that \(sec x = 3/2 and csc y = 3\)where x and y are in the 2x = 2 sin x quadrant, we need to find the exact value of sin 2x.
In the first quadrant, we have the following values of the trigonometric ratios:\(cos x = 2/3 and sin y = 3/5\)
Also, we know that sin \(2x = 2 sin x cos x.\)
Now, we need to find sin x.
Having sec x = 3/2, we can use the Pythagorean identity
\(^2x + 1 = sec^2xtan^2x + 1 = (3/2)^2tan^2x + 1 = 9/4tan^2x = 9/4 - 1 = 5/4tan x = ± √(5/4) = ± √5/2\)
As x is in the first quadrant, it lies between 0° and 90°.
Therefore, x cannot be negative.
Hence ,\(tan x = √5/2sin x = tan x cos x = √5/2 * 2/3 = √5/3\)
Now, we can find sin 2x by using the value of sin x and cos x derived above sin \(2x = 2 sin x cos xsin 2x = 2 (√5/3) (2/3)sin 2x = 4√5/9\)
Therefore, the exact value of sin 2x is 4√5/9.
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A Lunar Rover carrying an astronaut wearing a space suit and backpack weighs 880 pounds 13 ounces. The astronaut wearing a space suit and backpack weighs 379 pounds 5 ounces. What is the weight of the Lunar Rover? lbs. oz.
Answers
The Lunar Rover therefore weighs **497 pounds 12 ounces**.
what is a lunar rover?A lunar rover, often known as a moon rover, is a space research spacecraft made to traverse around the moon's surface1. Three American crews from Apollo 15, 16, and 171 operated the Lunar Roving Vehicle during the Apollo Program. Other rovers, like the Chinese Yutus and the Soviet Lunokhods, were either completely or partially autonomous robots. The Soviet Union, the United States, and China were the three nations with active rovers on the Moon.
We need to deduct the astronaut's space suit and backpack weight from the overall weight of the Lunar Rover hauling the astronaut in order to determine the weight of the Lunar Rover.
The astronaut weighs 379 pounds 5 ounces while wearing a space suit and carrying a rucksack; the Lunar Rover itself weighs 880 pounds 13 ounces.
We must convert these two weights to a single unit in order to subtract them. We can convert both weights to ounces and then remove them because there are 16 ounces in every pound.
880 lbs. 13 oz. = (880× 16) + 13 = 14,033 oz.
379 lbs. 5 oz. = (379× 16) + 5 = 6,069 oz.
As a result, the Lunar Rover weighs 7,964 ounces, which is equal to (14,033 - 6,069) ounces.
We divide this by 16 to get the following in pounds and ounces:
7,964 / 16 = 497, leaving a 12 digit residue.
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Which of the following values are solutions to the inequality 4+2x\le 4?4+2x≤4?
\text{I.}\hspace{2px}0\hspace{20px}\text{II.}\hspace{2px}-4\hspace{20px}\text{III.}\hspace{2px}-3
I.0II.−4III.−3
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3. Triangle DEF with vertices D(0, 6), E(3, 5), and F(1, 1):
90° counterclockwise about the point (5,2)
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The vertices of the triangle DEF after the 90º counterclockwise rotation about the point (5,2) are given as follows:
D'(-11, -2), E'(-10, 1) and F'(-6, -3).
What are the rotation rules?The five more known rotation rules are given as follows:
90° clockwise rotation: (x,y) -> (y,-x)90° counterclockwise rotation: (x,y) -> (-y,x)180° clockwise and counterclockwise rotation: (x, y) -> (-x,-y)270° clockwise rotation: (x,y) -> (-y,x)270° counterclockwise rotation: (x,y) -> (y,-x)Considering the 90º counterclockwise rotation about the point (5,2), the rule is given as follows:
(x,y) -> (-y - 5, x - 2).
Hence the vertices are given as follows:
D'(-11, -2), E'(-10, 1) and F'(-6, -3).
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a person eating at a cafeteria must choose 3 of 19 vegetable on offer. calculate the number of elements in the sample space for this experiment
Answers
The number of elements in the sample space for this experiment is 969.
If a person eating at a cafeteria must choose 3 of 19 vegetables on offer, we can calculate the number of elements in the sample space, or the total number of possible outcomes, using the formula for combinations:
nCr = n! / [r!(n - r)!]
where n is the total number of items in the set and r is the number of items being chosen.
In this case, we have 19 vegetables and we want to choose 3 of them, so we can plug in n = 19 and r = 3:
19C3 = 19! / [3!(19 - 3)!]
= 19! / (3!)(16!)
= 969
Therefore, there are 969 possible combinations of 3 vegetables that a person can choose from a selection of 19 vegetables.
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Which of the following is equivalent to (4x?) ?
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4 TIMES I THINK
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Consider the points below. P(θ),−4,0),Q(5,1,−2),R(6,4,1) (a) Find a nonzero vector orthogonal to the plane through the points P,Q, and R. (b) Find the area of the triangle PQR.
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(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.
(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:
PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)
PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)
Taking the cross product of PQ and PR, we have:
n = PQ x PR = (9, 1, -2) x (10, 4, 1)
Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.
(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:
|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)
Evaluating the magnitude gives |n| = \(\sqrt\)(811).
The area of triangle PQR is then:
Area = |n| / 2 = \(\sqrt\)(811) / 2.
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Determine the truth value of each conditional statement. If true, explain your reasoning. If false, give a counterexample.If two angles are congruent, then they are vertical angles.
Answers
The truth value of the conditional statement is false, and the counterexample of this statement is corresponding angles
How to determine the truth value of the conditional statement?The conditional statement is given as:
If two angles are congruent, then they are vertical angles.
The above statement is false because not all congruent angles are vertical angles
A counterexample of this statement is a corresponding angle
i.e. corresponding angles are congruent angles, but they are not vertical angles
Hence, the truth value of the conditional statement is false, and the counterexample of this statement is a corresponding angle
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How do you calculate the required sample size for a desired ME (margin of error)?
Answers
Answer: Calculate
Step-by-step explanation: How to calculate the margin of error?
1. Get the population standard deviation (σ) and sample size (n).
2. Take the square root of your sample size and divide it into your population standard deviation.
3. Multiply the result by the z-score consistent with your desired confidence interval according to the following table:
Solve the quadratic F(x)=x^2+10x-1
Please explain.
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The solutions to the quadratic equation f(x) = x² + 10x - 1 are x = -5 + √26 and x = -5 - √26
To solve the quadratic equation f(x) = x² + 10x - 1
we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
For the given equation, a = 1, b = 10, and c = -1.
Substituting these values into the quadratic formula:
x = (-(10) ± √((10)² - 4(1)(-1))) / (2(1))
= (-10 ± √(100 + 4)) / 2
= (-10 ± √104) / 2
Simplifying further:
x = (-10 ± 2√26) / 2
= -5 ± √26
Therefore, the solutions to the quadratic equation f(x) = x² + 10x - 1 are:
x = -5 + √26 and x = -5 - √26
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6. What might be the opportunity cost of a large portion of your income going toward credit
card payments each month?
Answers
Calculate the length of x.
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The Length of x as shown in the right angled triangle is 8.48.
What is length?Length is the distance between two points.
To calculate the length of x in the right-angled triangle, we use the formula below
Formula:
a² = b²+c²........................... Equation 1(From Pythagoras theorem)From the diagram,
Given:
a = 11b = xc = 7Substitute these values into equation 1
11² = x²+7²x² = 121-49x² = 72x = √72x = 8.48Lear more about length here: https://brainly.com/question/2217700
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can you guys help me is real quick no link or bots...
Answers
I hope this helps you :)
Use De Morgan's laws to write negations for the statement. Sam is an orange belt and Kate is a red belt.
A. Sam is an orange belt or Kate a red belt.
B. Sam is not a red belt and Kate is not an orange belt.
C. Sam is not an orange belt and Kate is not a red belt.
D. Sam is not a red belt or Kate is not an orange belt.
E. Sam is not an orange belt or Kate is not a red belt.
Answers
Answer:
C. Same is not an orange belt and Kate is not a red belt.
Step-by-step explanation:
The negation for the statement is Sam is not an orange belt or Kate is not a red belt.
What is Negation of De- Morgan's Law?The negation of a conjunction is equivalent to the disjunction of the negation of the statements making up the conjunction. To negate an “and” statement, negate each part and change the “and” to “or”.
Given statement:
Sam is an orange belt and Kate is a red belt.
Now, to make the negation we have to consider the rule "To negate an “and” statement, negate each part and change the “and” to “or”."
So, the negation statement would be
Sam is not an orange belt or Kate is not a red belt.
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The tables represent the points earned in each game for a season by two football teams.
Eagles
3 24 14
27 10 13
10 21 24
17 27 7
40 37 55
Falcons
24 24 10
7 30 28
21 6 17
16 35 30
28 24 14
Which team had the best overall record for the season? Determine the best measure of center to compare, and explain your answer.
Eagles; they have a larger median value of 21 points
Falcons; they have a larger median value of 24 points
Eagles; they have a larger mean value of about 22 points
Falcons; they have a larger mean value of about 20.9 points
Answers
Falcons had a more effective overall record because of the higher median. Thus, the answer is option B.
The median is usually used for the comparison of two data sets instead of the mean, as it is not affected by outliers.
Compare the total points earned by each team.
The Eagles data set is given below:
3, 7, 10, 10, 13, 14, 17, 21, 24, 24, 27, 27, 37, 40, 55.
As the data set has an odd cardinality, the median is the middle element, therefore it is for:
21.
For the Falcons, we use the same approach and obtain a median about:
24.
Therefore, we can say that the Falcons had a more effective overall record because of the higher median and the best measure of center to compare would be mean.
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What is the equation of the line that passes through the point (8,1) and has a slope
Answer:
Answers
Answer:
x=1y
Step-by-step explanation:
there's no way of knowing the equation without 2 coordinate pairs or one coordinate pair and slope but you have none
#3 Mia has $50 on a gift card to her favorite *
coffee shop. Each time she visits the coffee
shop she spends $3.75 on her favorite drink.
Write an equation to represent the relationship
between n, the number of times she visits the
coffee shop, and b, the total balance on her
gift card
Answers
Which sequence of transformations will map figure Konto figure Kí?109876432Х10-9-8--5-4-3-2-11 +2 3 4 5 6 7 8 9 1010Reflection across X = 4, 180° rotation about the origin, and a translation of (x + 8, y)Reflection across X = 4, 180° rotation about the origin, and a translation of (x - 8, y)Reflection across y = 4, 180° rotation about the origin, and a translation of (x + 8, y)Reflection across y = 4, 180° rotation about the origin, and a translation of (x - 8, y)
Answers
Answer:
A
Explanation:
To determine which sequence of transformation will map figure K onto figure K', we test each of the options using the point (6,5) in Figure K.
Option A
Reflection across x=4, 180° rotation about the origin, and a translation of (x+8,y)
\(\left(6,5\right)\rightarrow(2,5)\rightarrow\left(-2,-5\right)\rightarrow(6,-5)\)Option B
Reflection across x=4, 180° rotation about the origin, and a translation of (x-8, y)
\(\left(6,5\right)\rightarrow(2,5)\rightarrow\left(-2,-5\right)\rightarrow(-10,-5)\)Option C
Reflection across y=4, 180° rotation about the origin, and a translation of (x+8,y)
\(\left(6,5\right)\rightarrow(6,3)\rightarrow\left(-6,-3\right)\rightarrow(2,-3)\)Option D
Reflection across y=4, 180° rotation about the origin, and a translation of (x-8,y)
\(\left(6,5\right)\rightarrow(6,3)\rightarrow\left(-6,-3\right)\rightarrow(-14,-3)\)We can see that Option A is the one which maps point (6,5) to (6,-5).
Therefore, it is the sequence of transformations will map figure K onto figure K'.
30 is 250% of what number? I will give brainliest!
Answers
\(30=2.5x \\ \\ 60=5x \\ \\ x=\boxed{12}\)
We will have 25%
Then multiple by 4
You will have 12
I answered 2. Am I right?
Answers
Answer:
Yes, I agree, the score of 2 was an outlier, outside of what is close to everyone else's score
Step-by-step explanation:
What is 2 1/5 × (−5 1/3)?
Write the answer as a mixed number in simplest form.
Giving brainliest to best answer.
Answers
Answer:
-11 11/15
Step-by-step explanation:
convert 2 1/5 to an improper fraction of: 11/5
convert -5 1/3 to an improper fraction of: -16/3
11/5 × -16/3 = -176/15
-176/15 = -11 11/15
solve the system of equations algebraically -5x+2y=4 2x+3y=6
Answers
(2x+3y=6).5
-10x+4y=8
10x+15y=30
[10x+(-10x)]+[15y+4y]=[30+8]
19y=38
y=38/19
y=2
2x+3y=6
2x+3(2)=6
2x=6-6=0
x=0
Step-by-step explanation:
-5x+2y= 4 <==== Multiply entire equation by -3 to get:
15x-6y = -12
2x+3y= 6 <==== Multiply entire equation by 2 to get :
4x+6y = 12 Add the two underlined equations to eliminate 'y'
19x = 0 so x = 0
sub in x = 0 into any of the equations to find: y = 2
(0,2)
Solve for g: g + 8 > 10
Answers
Given the inequality:
\(g+8>10\)Solve for g, subtract 8 from both sides
\(\begin{gathered} g+8-8>10-8 \\ \\ g>2 \end{gathered}\)so, the answer will be:
\(g=(2,\infty)\)What is the difference between (-5,-6) and (-3,-8)?
please provide steps and I will give Brainliest
Answers
d = √8
Step-by-step explanation:
d = √((x2 - x1)² + (y2 - y1)²)
points: (-5, -6) and (-3, -8) where the first point “(-5, -6)” = (x1, y1) and the second point “(-3, -8)” = (x2, y2)
d = √((-3 - -5)² + (-8 - -6)²)
d = √((2)² + (-2)²)
d = √(4 + 4)
d = √8
If the figure is a regular polygon, solve for x.
(7x + 31)
I need help with this
Answers
The value of x is approximately 72.71.
In a regular polygon, the sum of the interior angles is given by the formula:
Sum of interior angles = (n - 2) x 180°
where n is the number of sides of the polygon.
For a pentagon, n = 5.
Using the given information, we can set up an equation:
(7x + 31)° = (5 - 2) 180°
Simplifying:
7x + 31 = 3 (180)
7x + 31 = 540
7x = 540 - 31
7x = 509
x = 509 / 7
x ≈ 72.71
Therefore, x is approximately 72.71.
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The complete question:
If the figure is a regular polygon, solve for x.
The interior angle of the pentagon is (7x + 31)°.