Find the general solution of the given higher-order differential equation. 16 d 4y dx4 + 48 d2y dx2 + 36y = 0
Answers
The general solution of the given higher-order differential equation 16(d^4y/dx^4) + 48(d^2y/dx^2) + 36y = 0 is y(x) = C1*cos((√3/√2)x) + C2*sin((√3/√2)x).
To find the general solution of the given higher-order differential equation, 16(d^4y/dx^4) + 48(d^2y/dx^2) + 36y = 0, follow these steps:
1. Replace the given equation with its characteristic equation. The characteristic equation is formed by replacing each derivative with the variable r raised to the power of the derivative order:
16r^4 + 48r^2 + 36 = 0
2. Solve for the roots of the characteristic equation. This equation is a quadratic equation in r^2, so let's set z = r^2:
16z^2 + 48z + 36 = 0
3. Factor the quadratic equation:
4(4z^2 + 12z + 9) = 0
4(2z + 3)^2 = 0
4. Solve for z:
(2z + 3) = 0
z = -3/2
5. Recall that z = r^2, so we now have:
r^2 = -3/2
6. Solve for r:
r = ±√(-3/2)
r = ±(√3/√2)i
7. Since the roots are complex, the general solution of the differential equation will be in the form:
y(x) = e^(αx)(C1*cos(βx) + C2*sin(βx)) + e^(−αx)(C3*cos(βx) + C4*sin(βx))
8. In our case, α = 0 and β = (√3/√2). So the general solution is:
y(x) = C1*cos((√3/√2)x) + C2*sin((√3/√2)x)
This is the general solution of the given higher-order differential equation.
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Related Questions
one day, a downtown hotel in san jose had to walk a guest to another hotel. the room rate for another hotel in downtown was $150. it cost $15 for the guest to take an uber to another hotel. the overbooked hotel also gave the guest a gift card of $25. how much is the cost of walking this guest? group of answer choices $150 $180 $190 $160
Answers
The cost of walking this guest is $190.
The cost of walking the guest can be calculated by adding up the expenses incurred by the hotel.
The guest was walked to another hotel that charged a room rate of $150. Therefore, the hotel incurred a cost of $150 for the room.
In addition to the room cost, the hotel also paid for the guest's Uber ride to the new hotel, which was $15.
Furthermore, the overbooked hotel gave the guest a gift card worth $25. Although the gift card does not directly represent an expense, it can be considered as an opportunity cost for the hotel, as they could have used that money to cover other costs.
Therefore, the total cost incurred by the hotel for walking the guest is:
$150 (room cost) + $15 (Uber cost) + $25 (gift card cost) = $190
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Determine whether the relation is a function. Give the domain and range for the relation. \[ \{(4,9),(4,10),(4,11)\} \] The domain of the relation is (Use a comma to separate aniswers as needed.)
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The given relation is not a function because it has multiple outputs for a single input. The domain of the relation is {4}, and the range is {9, 10, 11}.
The given relation is not a function because it has multiple outputs (range values) for a single input (domain value). In this case, the input value 4 is associated with three different output values: 9, 10, and 11.
According to the definition of a function, each input value should have only one corresponding output value.
The domain of the relation is {4} because it contains the unique input value present in the relation. The range of the relation is {9, 10, 11} since these are the distinct output values associated with the input value 4.
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let s be a set with n elements and let a and b be distinct elements of s. how many relations r are there on s such that
(a) (a, b) ϵ R?
b) (a; b) ∉ S?
(c) no ordered pair in R has a as its first element?
(d) at least one ordered pair in R has a as its first element?
(e) no ordered pair in R has a as its first element or b as its second element?
Answers
The number of relations according to given condition are (a) \(2^{(n^2 - n)\) , (b) \(2^{(n^2 - n)\) , (c) \(2^{((n - 1) * n)\) , (d) \(2^{(n^2 - n){ - 2^{((n - 1) * n)\) and (e) \(2^{((n - 1) * (n - 1))\).
What is a relation?
In mathematics, a relation is a set of ordered pairs that establishes a connection or association between elements from different sets.
(a) For the relation R to contain the ordered pair (a, b), there are two possibilities: either (a, b) is in R or it is not in R. This means that there are \(2^{(n^2 - n)\) total relations that satisfy this condition. The exponent \((n^2 - n)\)represents the total number of possible ordered pairs in the set S excluding (a, a) pairs.
(b) For the relation R to exclude the ordered pair (a, b), we need to consider all possible pairs (x, y) where x and y are distinct elements in S. The total number of such pairs is \((n^2 - n)\). For each pair, there are two possibilities: either (x, y) is in R or it is not in R. Hence, there are \(2^{(n^2 - n)\) total relations that satisfy this condition.
(c) For no ordered pair in R to have a as its first element, we need to consider all possible pairs (x, y) where x is any element in S except for a. The total number of such pairs is (n - 1) * n since there are (n - 1) choices for the first element and n choices for the second element. For each pair, there are two possibilities: either (x, y) is in R or it is not in R. Therefore, there are \(2^{((n - 1) * n)\) total relations that satisfy this condition.
(d) To have at least one ordered pair in R with a as its first element, we can exclude the case where no ordered pair in R has a as its first element. Hence, the total number of relations satisfying this condition is \(2^{(n^2 - n)} - 2^{((n - 1) * n)\)
(e) To have no ordered pair in R with a as its first element or b as its second element, we need to consider all possible pairs (x, y) where x is any element in S except for a, and y is any element in S except for b. The total number of such pairs is (n - 1) * (n - 1). For each pair, there are two possibilities: either (x, y) is in R or it is not in R. Therefore, there are \(2^{((n - 1) * (n - 1))\) total relations that satisfy this condition.
Note: The above calculations assume that a relation can contain both (a, a) and (b, b) pairs, as the conditions specified for a and b to be distinct elements of S.
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Define a relation R between elements in Z:a∈Z has the relation R to b∈Z, denoted by aRb, if a+b is divisible by 3 . (a) Is (3,7) in the subset of relation R ? How about (4,8) ? (b) Is the relation R a function relation? Why or why not? (c) Is the relation R an equivalence relation? Why or why not?
Answers
(3,7) is in the subset of relation R, but (4,8) is not. The relation R is not a function relation because 0 has three corresponding elements in the range (-3, 0, 3). Finally, the relation R is not an equivalence relation because it is not transitive.
Is (3,7) in the subset of relation R ? How about (4,8) ?a) Yes, (3,7) is in the subset of relation R because 3+7 = 10 which is divisible by 3.b) No, (4,8) is not in the subset of relation R because 4+8 = 12 which is divisible by 3.(b) Is the relation R a function relation?
Why or why not?The relation R is not a function relation because for a function relation, each element in the domain must have exactly one corresponding element in the range.
In this case, for example, 0 has three corresponding elements in the range (-3, 0, 3) and hence it is not a function relation.(c) Is the relation R an equivalence relation? Why or why not?.
No, the relation R is not an equivalence relation because to be an equivalence relation, a relation must be reflexive, symmetric, and transitive. While R is reflexive and symmetric,
it is not transitive.For example, if a=1, b=2, and c=4, aRb and bRc since 1+2=3 and 2+4=6 are both divisible by 3. However, aRc is not true because 1+4=5 is not divisible by 3, which violates the transitive property. Hence, R is not an equivalence relation.
(3,7) is in the subset of relation R, but (4,8) is not. The relation R is not a function relation because 0 has three corresponding elements in the range (-3, 0, 3). Finally, the relation R is not an equivalence relation because it is not transitive.
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Six times a number is greater than 20 more than that number. What are the possible values of that number?
n<4
n>4
n>20/7
n<20/7
Answers
Answer:
here
Step-by-step explanation:
n>4
hope it helps you
In 25 words or fewer, describe one thing the Fed can do to help
businesses.
Answers
The equation of a line in the point-slope form is show below
y - 9 = 1/5 (x -2)
What is the slope of this line?
A. 2
B. 1/9
C. 5
D. 1/5
Answers
Answer:
i tride so hard i dont know but i wish you luck but i think its A
Step-by-step explanation:
Answer:
Its not A thats all i know
Step-by-step explanation:
A study of a population of 1,500 moths revealed that 15 out of every 75 moths in the population have gray stripes on their wings. Based on the results of this study, how many moths in the population have gray stripes on their wings?
Answers
Answer: 300 moths
Step-by-step explanation:
Since 15 out of every 75 moths in the population have gray stripes on their wings, this means the fraction of moths that have gray stripes on their wings is 15/75 = 1/5.
Therefore, out of 1500 moths, the number of moths in the population that have gray stripes on their wings would be calculated as:
= 1/5 × 1500
= 300 moths
a farmer is making a circular pen for his sheep. he has 213.52 yards of fencing to use. what should the diameter of the circle pen be?
Answers
The diameter of the circle pen for the sheep of the farmer is 68 yards.
Explain the term circumference of the circle?The distance along a circle's perimeter is referred to as its circumference. In other words, the circumference of a circle is equal to the length of a straight line formed by opening up the circle.The space around a circle is known as its circumference. By calculating the distance required to walk around the globe, we may determine the size of the earth's circumference.The total length of the fencing used for the preparation of the fencing for sheep is 213.52 yards.
Thus,
circumference = 213.52 yards
The formula for the calculation of the circumference of circle is,
circumference = 2πr,
In which,
π = 3.14 and radius r.
Thus,
213.52 = 2πr
r = 213.52 / 2π
r = 34
Diameter = 2 x radius
Diameter = 2 x 34
Diameter = 68 yards.
Thus, the diameter of the circle pen for the sheep of the farmer is 68 yards.
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Select the correct answer What is this expression in simplified form? (V22) (5V2)
Answers
Answer:
A
Step-by-step explanation:
\(\sqrt{22}\) · 5\(\sqrt{2}\) = 5 \(\sqrt{44}\) = 5 \(\sqrt{4}\)·\(\sqrt{11}\) = 10\(\sqrt{11}\)
How far can a person run in 16min if they run 20 per hour
Answers
The person can run 5.33 miles (distance) in 16 minutes (time) if they run 20 per hour (speed).
What is the interaction between distance, time, and speed?Distance is the length of one point to the next.
Time refers to the hours or minutes consumed in making a displacement.
Speed shows the rate of the change in displacement resulting from the interaction of distance with time.
Speed measures the ratio of distance to time.
Thus, the person can run 5.33 miles (distance) in 16 minutes (time) if they run 20 per hour (speed).
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Help match them with the answer I would really appreciate it
Answers
Answer:
Graph 1 goes with the equation \(y = \frac{1}{2}x - 7\)
Graph 2 goes to the equation y = \(-\frac{3}{4}x + 9\)
Graph 3 goes to the equation y = x + 10
Compute a formula for dy/dx for the curve parametrized by: x=t^3−2ty=6t^2−t
Answers
The formula for \(dy/dx\) for the given parametric curve is \((12t - 1)/(3t^2 - 2t)\) for the curve \(x = t^3 - 2t\) and \(y = 6t^2 - t\).
To compute the formula for dy/dx, we can use the chain rule.
First, we need to find the derivatives of x and y with respect to t.
The derivative of \(x = t^3 - 2t\) is \(dx/dt = 3t^2 - 2\).
The derivative of \(y = 6t^2 - t\) is \(dy/dt = 12t - 1\).
Then, we can calculate \(dy/dx\) by dividing the derivative of y by the derivative of x.
\(dy/dx = (dy/dt)/(dx/dt)\\dy/dx = (12t - 1)/(3t^2 - 2t)\).
This formula gives us the rate of change of y with respect to x at any point on the curve parametrized by the given equations.
Therefore, the formula for \(dy/dx\) for the given parametric curve is \((12t - 1)/(3t^2 - 2t)\) for the curve \(x = t^3 - 2t\) and \(y = 6t^2 - t\)
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given the following information, n = 49, = 50, s = 7 h0: μ > 52 ha: μ < 52 the test statistic is
Answers
The test statistic by the given values is t = -2.
What is Test Statistic?Test statistic is a value calculated from a statistical test of hypothesis. It describes the closeness of the observed data with the expected distribution under the null hypothesis.
Test statistic can be calculated from the formula,
t = (xₐ - μ) / (s/√n)
where xₐ is the sample mean, μ is the population mean, s is the standard deviation and n is the sample size.
Given,
n = 49, xₐ = 50, s = 7
Since null and alternate hypothesis are given, μ = 52.
So the test statistic,
t = (50 - 52) / (7/√49)
= -2 / (7/7)
= -2
Hence the test statistic is -2.
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Speedy Sue, driving at 33.0 m/s, enters a one-lane tunnel. She then observes a slow-moving van 175 m ahead traveling at 5.40 m/s. Sue applies her brakes but can accelerate only at −1.90 m/s
2
because the road is wet. Will there be a collision? Yes No If yas, determine how far into the tunnel and at what time the collision occurs. If no, determine the distance of closest approach between Sue's icar and the van. (If no, enter " 0 " for the time.) distance Your responwedidfers from the correct answer by more than 10\%, Double chack your calculations, m times ox 5 Need Holp?
Answers
Yes, there will be a collision between Speedy Sue's car and the slow-moving van in the tunnel. The collision will occur at a distance of approximately 146.5 meters into the tunnel, and the time of the collision will be around 7.72 seconds.
To determine whether there will be a collision, we need to calculate the time it takes for Speedy Sue to reach the van and compare it with the time it takes for the van to exit the tunnel.
First, we calculate the time it takes for Sue to reach the van. The relative velocity between Sue and the van is (33.0 m/s - 5.40 m/s) = 27.6 m/s. Using the formula time = distance / velocity, the time it takes for Sue to reach the van is approximately 175 m / 27.6 m/s ≈ 6.34 seconds.
Next, we calculate the time it takes for the van to exit the tunnel. The distance the van needs to travel to exit the tunnel is the sum of the distance from its initial position to the end of the tunnel and the distance Sue needs to travel to reach the end of the tunnel. The total distance is 175 m + 175 m = 350 m. The velocity of the van is 5.40 m/s. Using the formula time = distance / velocity, the time it takes for the van to exit the tunnel is approximately 350 m / 5.40 m/s ≈ 64.81 seconds.
Since 6.34 seconds is less than 64.81 seconds, Sue will collide with the van before it exits the tunnel. To determine the distance into the tunnel where the collision occurs, we subtract the distance Sue travels in 6.34 seconds from the initial distance between Sue and the van. The distance Sue travels is (33.0 m/s - 1.90 m/s^2 * 6.34 s^2 / 2) * 6.34 s ≈ 146.5 meters.
Therefore, the collision between Sue's car and the van will occur at a distance of approximately 146.5 meters into the tunnel, and the time of the collision will be around 7.72 seconds.
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what is 2x2x2x2x2x4x0
Answers
Answer:
0.
Step-by-step explanation:
Can someone help me pls
Answers
Answer:
D
Step-by-step explanation:
Answer:
That’s prolly D
Step-by-step explanation:
Other stuff don’t make sense
Fill in the missing fraction: Do not reduce your answer. What is 10/12 plus blank equals 16/12
Answers
Answer:
The missing fraction is 6/12
(you can further simplify this but the question requires that you don't do that)
Step-by-step explanation:
To add fractions easily, their denominators should have the same value, so the denominator should be 12,
Then, to get 16 in the numerator, we need to find a number that on adding to 10, gives 16, or,
10 + x = 16
x = 16 - 10
x = 6
So, the numerator should be 6
so we get the fraction, 6/12
We can also solve it in an alternate way,
\(10/12 + x = 16/12\\x = 16/12 - 10/12\\x = (16-10)/12\\x = 6/12\)
Neighbor A can put up three 8 foot sections of wood fencing in two hours.
Neighbor B can put up 15 feet of chain link fencing each hour.
Neighbor C can put up 1 yard of vinyl fencing in half an hour.
Which neighbor's fencing project will take the least amount of time to complete?
Which neighbor's fencing project will take the most amount of time to complete?
Neighbor A can put up three 8 foot sections of wood fencing in two hours.
Neighbor B can put up 15 feet of chain link fencing each hour.
Neighbor C can put up 1 yard of vinyl fencing in half an hour.
Which neighbor's fencing project will take the least amount of time to complete?
Which neighbor's fencing project will take the most amount of time to complete?
Answers
Answer:
most is neighbor b
Step-by-step explanation:
1 yard is 3 feet
Answer:
Which neighbor's fencing project will take the least amount of time to complete? Neighbor B
Which neighbor's fencing project will take the most amount of time to complete? Neighbor C
Item 48 A couple has 5 children, all sons. If the woman gives birth to a sixth child, what is the probability that the sixth child will be a son
Answers
The probability that the sixth child will be a son is 50%. Each child, regardless of gender, has an equal chance of being born.
What is the probability that the sixth child will be a son?The probability of having a son as the sixth child can be calculated using the binomial formula. The binomial formula is used to calculate the probability of an event occurring after a certain number of trials, given the probability of success in each trial.In this case, the probability of having a son is the same for each trial (or birth), which is 0.5 (since the odds of having a boy or a girl are equal).Therefore, the probability of having a son as the sixth child can be calculated as follows:P(son) = (5 choose 6) x (0.5^6) = 0.015625
The binomial formula is used to calculate the probability of an event occurring after a certain number of trials, given the probability of success in each trial. In this case, the probability of having a son is the same for each trial (or birth), which is 0.5 (since the odds of having a boy or a girl are equal).Therefore, the probability of having a son as the sixth child can be calculated using the binomial formula as follows: P(son) = (5 choose 6) x (0.5^6) = 0.015625.
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look at pic I need help!!!! :(
Answers
Answer: x=12
Step-by-step explanation:
5x-15=2x+21(AIA)
3x-15=21
3x=36
x=12
1. the expected value of a random variable can be thought of as a long run average.'
Answers
Yes it is correct that the expected value of a random variable can be interpreted as a long-run average.
The expected value of a random variable is a concept used in probability theory and statistics. It is a way to summarize the average behavior or central tendency of the random variable.
To understand why the expected value represents the average value that the random variable would take in the long run, consider a simple example. Let's say we have a fair six-sided die, and we want to find the expected value of the outcomes when rolling the die.
The possible outcomes when rolling the die are numbers from 1 to 6, each with a probability of 1/6. The expected value is calculated by multiplying each outcome by its corresponding probability and summing them up.
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If EG = 10 and EF = 4, then
FG = [?]
E
F
G
Answers
Answer:
Step-by-step explanation:
It's 6
can anyone help plz thanks if u help
Answers
Answer:
68.04 cm^3
Step-by-step explanation:
The volume of the prism is given by
V = Bh
where B is the area of the base and h is the height
B - area of the triangle
B = 1/2 bh = 1/2 (5.4) (3.6) = 9.72
The volume is
V = 9.72*7
68.04 cm^3
if the margin of error in an interval estimate of μ is 4.6, the interval estimate equals _____.
Answers
If the margin of error is 4.6, the interval estimate would be the point estimate plus or minus 4.6.
In statistical estimation, the margin of error represents the maximum amount by which the point estimate may deviate from the true population parameter. It provides a measure of the precision or uncertainty associated with the estimate. When constructing a confidence interval, the margin of error is used to determine the range within which the true parameter is likely to fall.
To obtain the interval estimate, we add and subtract the margin of error from the point estimate. Let's denote the point estimate as x bar. Therefore, the interval estimate can be expressed as X bar ± 4.6, where ± denotes the range above and below the point estimate.
In summary, if the margin of error in an interval estimate of μ is 4.6, the interval estimate is given by the point estimate plus or minus 4.6. This range captures the likely range of values for the true population parameter μ.
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What is the complement to Angle 1 if it measures 63 degrees
Answers
Answer:
27º
Step-by-step explanation:
complementary angle is equal to 90º
90 - 63 = 27
solve the inequality
x+19<_-5
Answers
Answer:
x≤−24
Step-by-step explanation:
x+19−19≤−5−19 ( subtracting 19 from both sides )
( 19 cancels out -5-19=-24 )
leaves you with
x≤−24
pls, help! (NO LINKS!)
Thank you!
Answers
Answer:
18÷25 =0.72 convert proper fraction to decimal ,divide the numerator by the denominator.
3-0.72=3.72. add this decimal number to the whole number .final answer is 3.72
Use the 30-60-90 Triangle Theorem to find the length of the hypotenuse.
a = 8m
b = 8 √(3)
Answers
Answer
Step-by-step explanation:
What is the slope of the function y = -5/4x+1
Answers
Answer:-5/4
Step-by-step explanation:
the slope is the number next to the letter X.