To find y as a function of x, we need to solve the given differential equation:
4y'' - 8y' + 167y = 0
The characteristic equation is:
4r^2 - 8r + 167 = 0
Solving for r using the quadratic formula, we get:
r = (8 ± sqrt(8^2 - 4(4)(167))) / (2(4))
r = (8 ± sqrt(-2632)) / 8
Since the discriminant is negative, the roots are complex:
r = (4 ± sqrt(658)i) / 4
r1 = 1 + (sqrt(658)i) / 4
r2 = 1 - (sqrt(658)i) / 4
The general solution to the differential equation is:
y(x) = c1 e^(r1x) + c2 e^(r2x)
Using the initial conditions, we can solve for c1 and c2:
y(0) = 17 = c1 + c2
y'(0) = 11 = c1r1 + c2r2
y''(0) = 16 = c1r1^2 + c2r2^2
Solving this system of equations, we get:
c1 = (17 + 4sqrt(658)i) / 8
c2 = (17 - 4sqrt(658)i) / 8
Substituting these values into the general solution, we get:
y(x) = (17 + 4sqrt(658)i) / 8 e^[(1 + sqrt(658)i)x / 4] + (17 - 4sqrt(658)i) / 8 e^[(1 - sqrt(658)i)x / 4]
Simplifying this expression, we get:
y(x) = (17/4) cos(sqrt(658)x/4) + (1/4) sin(sqrt(658)x/4)
Therefore, y as a function of x is:
y(x) = (17/4) cos(sqrt(658)x/4) + (1/4) sin(sqrt(658)x/4)
And y(10) = (17/4) cos(sqrt(658)5/2) + (1/4) sin(sqrt(658)5/2) = -3.67.
Hi! To solve the given differential equation, we can use the given initial conditions:
Given: y''(x) - 8y'(x) + 16y(x) = 0, y(0) = 17, y'(0) = 11, y''(0) = 16, y'''(0) = 0.
We can solve the given homogeneous linear differential equation with constant coefficients by finding the characteristic equation:
r^2 - 8r + 16 = 0
This equation factors as (r - 4)^2 = 0, which has a repeated root r = 4. The general solution of the differential equation is:
y(x) = (C1 + C2 * x) * e^(4x)
Now we can use the initial conditions to find the constants C1 and C2:
1. y(0) = 17: (C1 + C2 * 0) * e^(4 * 0) = 17, so C1 = 17.
2. y'(x) = (C2 + 4 * (C1 + C2 * x)) * e^(4x), y'(0) = 11: (C2 + 4 * (17 + C2 * 0)) * e^(4 * 0) = 11. This simplifies to C2 + 68 = 11, so C2 = -57.
Therefore, the particular solution is:
y(x) = (17 - 57x) * e^(4x)
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Solve the system of equations algebraically: y = -x2 + 2x + 4 and y = 4 - x.
So:
\(\begin{gathered} y=\text{ 4 -0} \\ y=4 \\ \\ y=4\text{ - 3} \\ y=\text{ 1} \end{gathered}\)Then, the points are (3,1) and (0,4)
Question Progress
Homework Progress
y is directly proportional to x.
When y = 30, x = 6
Work out an equation connecting y and x.
Answer:
y=5x
Step-by-step explanation:
y=kx since they're directly proportional
30=k(6)
K=5
So y=5x
help me with this question please
Answer:
N+1
Step-by-step explanation:
It begins with = 2
then n+1=3
then n+2=4 and so on it is n+1
Make x the subject of these equations.
a(x + b) = c
X =
Answer:
x = \(\frac{c-ab}{a}\)
Step-by-step explanation:
a(x + b) = c ← distribute parenthesis on left side
ax + ab = c ( subtract ab from both sides )
ax = c - ab ( divide both sides by a )
x = \(\frac{c-ab}{a}\)
Answer:
Just expand and solve for x :)
SOMEONE ANSWER QUICK!!
Steven bought 4 pizzas to share with his family. Together, they ate 2 7/12 pizzas on Friday and another 2/3 of a pizza on Saturday. How much pizza is left??
Answer:
3/4 pizza is left. If you want an explanation, ask me ;>
Passes through the point of intersection of x-y=0 and x + y = 0 and (2, 2) find the equation of a straight line
The equation of the line is x-y=0
What is point of intersection?
A point of intersection is a point where two lines intersect.
We are given the two equations as x-y=0 and x+y=0
The point of intersection can be given by finding the coordinates of which will satisfy both the equation
Now the equation can be solved by
The point of intersection is (0,0)
We have to find the equation of the line passing through the point (0,0),(2,2)
This can be done by
\(\frac{y-0}{0-2}=\frac{x-0}{0-2}\)
\(\frac{-y}{2}=\frac{-x}{2}\)
\(x-y=0\)
Hence the equation of the line passing through the point of intersection of x-y=0 and x+ y=0 and (2,2) The equation of the line is x-y=0
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Does the table represent a proportional relationship?
O Proportional
O Not Proportional
Answer:
Not proportional
Step-by-step explanation:
1/5 = 0.2
2/8 = 0.25
6/18 = 0.33
etc...
Im trying to plot a slope function on a graph
Answer:
Graphing from slope
Step-by-step explanation:
To graph a linear equation in slope-intercept form, we can use the information given by that form. For example, y=2x+3 tells us that the slope of the line is 2 and the y-intercept is at (0,3). This gives us one point the line goes through, and the direction we should continue from that point to draw the entire line.
What is the product of −2 1/4 and −4 1/2?
Enter your answer as a mixed number, in simplified form, in the box.
Answer:
10 1/8
Step-by-step explanation:
-2 1/4 * -4 1/2
~Turn into improper fractions
-9/4 * -9/2
~Multiply both numerators and denominators
81/8
~Turn into a mixed number
10 1/8
Best of Luck!
Answer:
10 1/8
Step-by-step explanation:
What is the Next number in this series 7 11 19 35?
Answer:
67
Step-by-step explanation:
we have a gap between 1st and 2nd terms of 4. a gap between 2nd and 3rd of 8. 16 for next gap. the gap doubles every time.
so we expect gap between 4th and 5th terms to be 2 X 16 = 32.
35 + 32 = 67. that is the next number in the sequence.
4. Radix sort the following list of integers in base 10 (smallest at top, largest at bottom). Show the resulting order after each run of counting sort. First sort Second sort Third sort Original list 483 525 582 143 645 522 5. What will be the time complexity when using Quick sort to sort the following array, A: 4,4,4,4,4,4,4,4. (explain your answer) 6. Given an input array A = {12, 8, 7, 4, 2, 6, 11), what is the resulting sequence of numbers in A after making a call to Partition (A, 1, 7)
To radix sort the given list of integers in base 10, we can perform multiple passes of counting sort based on the digits from right to left. Here's the step-by-step process:
First sort:
Original list: 483 525 582 143 645 522
Counting sort based on the least significant digit (unit place):
143 522 483 582 645 525
Second sort:
Original list: 143 522 483 582 645 525
Counting sort based on the tens place:
143 522 525 582 645 483
Third sort:
Original list: 143 522 525 582 645 483
Counting sort based on the hundreds place:
143 483 522 525 582 645
The final sorted list is: 143 483 522 525 582 645
The time complexity of Quick sort depends on the partitioning scheme and the initial ordering of the elements. In the worst case scenario, when the array is already sorted or contains equal elements, Quick sort has a time complexity of O(n^2). This is because in each recursive call, the pivot chosen will always be the smallest or largest element, resulting in uneven partitioning.
In the given array A = {12, 8, 7, 4, 2, 6, 11}, making a call to Partition(A, 1, 7) means partitioning the array from the first element to the seventh element. The resulting sequence of numbers in A after the partition operation will depend on the chosen pivot. Since the pivot index is not specified, it is not possible to determine the exact resulting sequence without knowing the pivot selection mechanism.
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melanie uses up pencils at an incredible rate, 14 pencils every 4/9 of an hour. How many pencils does she use up per hour? Show your work
ANSWER
Melanie uses 31 and a half pencils per hour
EXPLANATION
If she uses 14 pencils in 4/9 of an hour, we want to find how many pencils does she use in 1 hour:
\(1\times(14\colon\frac{4}{9})=14\colon\frac{4}{9}=14\times\frac{9}{4}=\frac{126}{4}=\frac{63}{2}=31\frac{1}{2}\)An Austrian study was completed to determine if untrained sea lions and sea lionesses could follow various experimenter-given cues when given a choice of two objects. One experimenter-given cue was to point at one of the objects. One sea lioness, named Zwerg, successfully chose the pointed-at object 37 times out of 48 trials. Does this result show that Zwerg can correctly follow this type of direction by an experimenter more than 50% of the time?ââ
Using the z-distribution, it is found that since the test statistic is greater than the critical value for the right-tailed test, this result shows that Zwerg can correctly follow this type of direction by an experimenter more than 50% of the time.
What are the hypothesis?At the null hypothesis, it is tested if Zwerg cannot correctly follow this type of direction by an experimenter more than 50% of the time, that is:\(H_0: p \leq 0.5\)
At the alternative hypothesis, it is tested if Zwerg can correctly follow this type of direction by an experimenter more than 50% of the time, that is:\(H_1: p > 0.5\)
Test statisticThe test statistic is given by:
\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)
In which:
\(\overline{p}\) is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.For this problem, the parameters are:
\(n = 48, \overline{p} = \frac{37}{48} = 0.7708, p = 0.5\)
The value of the test statistic is:
\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)
\(z = \frac{0.7708 - 0.5}{\sqrt{\frac{0.5(0.5)}{48}}}\)
\(z = 3.75\)
Considering a right-tailed test, as we are testing if the proportion is greater than a value, with a significance level of 0.05, the critical value for the z-distribution is \(z^{\ast} = 1.645\).
Since the test statistic is greater than the critical value for the right-tailed test, this result shows that Zwerg can correctly follow this type of direction by an experimenter more than 50% of the time.
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17. Segment MN is drawn in the coordinate plane. Point M has coordinates (13,9) and the midpoint of MN is the point (4.4). What are the
coordinates of point N?
(-9.4)
(-5, -1)
(1,3)
(8.5, 6.5)
The required coordinate of the point N is (-5, -1). Option b is correct.
Given that,
Segment MN is drawn in the coordinate plane. Point M has coordinates (13,9) and the midpoint of MN is the point (4.4). What are the coordinates of point N to be determined.
Coordinate, is represented as the values on the x - axis and y - axis of the graph
Let the coordinate of point N is (x, y).
Here, point M has coordinates (13,9) and the midpoint of MN is the point (4.4).
The Coordinate of the midpoint is given as,
(4 = (x + 13)/2, 4 = (y + 9 )/2)
(x = 8 - 13, y = 8 - 9)
(x = -5 , y = -1 )
Coordinate of point N is (x, y) = (-5, -1)
Thus, the required coordinate of the point N is (-5, -1).
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Two sides of a triangle are 7 cm and 4 cm. Which measure could NOT be a length of the third side?
Length should be less than 11 cm and also greater than 3 cm.
What are the properties of the triangle?A triangle's (of all varieties) total sum of angles is 180°. The length of a triangle's two longest sides added together is longer than the third side. Similarly to this, the length of the third side of a triangle third side is shorter than the difference between its two sides.
Given Two sides of a triangle are 7 cm and 4 cm. From the properties of the triangle its third side should not be greater than the sum of its two sides and the third side should not be less than the subtraction of the two sides.
Therefore this triangle's third side would be greater than 3 and less than 11 cm.
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b.The branch manager wants to improve the service and suggests dispatching buses every 0.5 minute. She argues that this will reduce the average traveling time (a round trip) to 3.5 minutes. Is she correct? (Enter "Yes" or "No" in the following blank). c. Following the branch manager's suggestion (dispatch busses every 0.5 min), what will the average traveling time be? average travelling time____ (mins) (enter the numbers only)
(b) No, The branch manager's argument that dispatching buses every 0.5 minutes will reduce the average traveling time (a round trip) to 3.5 minutes is not correct.
To calculate the average time, we need to consider the time it takes for the bus to travel to the airport and back, as well as the time spent waiting for the bus.
If buses are dispatched every 3 minutes, and the average traveling time (a round trip) is 21 minutes, it means that passengers spend 18 minutes waiting for the bus (21 minutes - 3 minutes of traveling time).
If buses are dispatched every 0.5 minutes, the waiting time will be significantly reduced. However, the traveling time remains the same at 21 minutes for a round trip.
Therefore, the average traveling time will not be reduced to 3.5 minutes but will remain at 21 minutes (assuming the traveling time remains constant).
(c) The average traveling time, following the branch manager's suggestion of dispatching buses every 0.5 minutes, would still be 21 minutes.
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Complete question:
The Avis Company is a car rental company and is located three miles from the Los Angeles airport (LAX). Avis is dispatching a bus from its offices to the airport every 3 minutes. The average traveling time (a round trip) is 21 minutes.
(a) The branch manager wants to improve the service and suggests dispatching buses every 0.5 minute. She argues that this will reduce the average traveling time (a round trip) to 3.5 minutes. Is she correct? (Enter "Yes" or "No" in the following blank).
c. Following the branch manager's suggestion (dispatch busses every 0.5 min), what will the average traveling time be? average travelling time ____(mins) (enter the numbers only)
What is the correct order of the steps used to derive the identity? 4, 3, 5, 1, 2 4, 5, 3, 1, 2 3, 4, 5, 1, 2 3, 4, 1, 5, 2
The correct order of the steps used to derive the identity is (A.) 4, 3, 5, 1, 2.
What is the way to determine the correct order of the steps?The trigonometry identity is given as: tan(2x)
When the tangent formula is applied, we have: Tan (2x) = Sin (2x)/Cos (2x)......................(4)
Expand Sin (2x) and Cost 2x)
Tan (2x) = 2 Sin (x) Cos (x)/Cos (x) - Sin²(x)..........................(3)
It can be inferred therefore that the list that obeys the above order is:
Option (a) 4, 3, 5, 1, 2.
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Full Question:²
What is the correct order of the steps used to derive the identity?
A.) 4, 3, 5, 1, 2
B.) 4, 5, 3, 1, 2,
C.) 3, 4, 5, 1, 2
D.) 3, 4, 1, 5, 2
what is the value of x in the equation 3^(2x-1)=27?
Answer:
x=2
Explanation:
Given the equation:
\(3^{2x-1}=27\)To solve for x, begin by writing 27 as a power of 3.
\(3^{2x-1}=3^3\)Next, since both sides of the equation have the same base, 3, it follows from the law of indices that:
\(\begin{gathered} a^x=a^y\implies x=y \\ \text{Therefore:} \\ 3^{2x-1}=3^3\implies2x-1=3 \end{gathered}\)We then solve the resulting equation for x.
\(\begin{gathered} 2x-1=3 \\ \text{Add 1 to both sides} \\ 2x-1+1=3+1 \\ 2x=4 \\ \text{Divide both sides by 2} \\ \frac{2x}{2}=\frac{4}{2} \\ x=2 \end{gathered}\)The value of x in the equation is 2.
What is the intermediate step in the form (x + a)2 = b as a result of completing the
square for the following equation?
x2 + 34 = 10x
Answer:
So the intermediate step in question is (x - 10)² = 66
Step-by-step explanation:
Let's find out:
x² + 34 = 10x
x² - 10x = -34
x² - 20x + 100 = 66
(x - 10)² = 66
x - 10 = ± √66
x = 10 ± √66
x ≈ 18.12, 1.88
Answer:
(x-5)^2=
(x−5)
2
=
\,\,-9
−9
Step-by-step explanation:
.
Each year a certain amount of money is deposited in an account which pays an annual interest rate of r so that at the end of each
year the balance in the account is multiplied by a growth factor of x = 1 + r. $1,000 is deposited at the start of the first year, an
additional $300 is deposited at the start of the next year, and $500 at the start of the following year.
Write an expression for the value of the account at the end of three years in terms of the growth factor x.
The polynomial expression which represents the value of the account at the end of three years is 1000x³ + 300x² + 500x
Interest earned per year, x = 1 + r
First year :
deposit = $1000Year end balance = 1000 × x = 1000x
Second year :
Initial balance = 1000x + 300Year end balance = (1000x + 300)x = 1000x² + 300x
Third year :
Initial balance = 1000x² + 300x + 500Year end balance = (1000x² + 300x + 500)x = 1000x³ + 300x² + 500x
Therefore, the expression which represents the value of the account at the end of three years is 1000x³ + 300x² + 500
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On Saturday, Casey earns $15 babysitting. On Sunday, she receives $68 for her birthday. Casey purchases a belt for $11.50, a sweater for $23.24, and a pair of jeans for $29.99. She deposits the remaining money into her savings account. If Casey had a balance of $37.23 in her savings account before making her deposit, how much money does she currently have in her savings account?
Answer:
55.50
Step-by-step explanation:
Lauryn wants to analyze the weights of
the dogs for people that own that animal
in her class. She records the following
weights in a class survey:
28, 61, 17, 42, 37, 37, 22, 40, 13, 14, 33,
41, 25
What is the median of the data?
Answer: 33
If you put all the numbers In order from least to greatest and find the middle number you'll get the answer
Please solve with explanation
12. Determine whether the given number belongs
to each set.
Whole
Integers
Rational
Numbers
Numbers
-34
Answer:
-34 is an integer and a rational number
Step-by-step explanation:
whole numbers do not include negative numbers
(20 points) Two players have to simultaneously decide how much to contribute to the provision of a public good. If Player 1 contributes x and Player 2 contributes y, then the payoff to Player 1 is 2(x+y+xy)-x² and payoff to Player 2 is 2(x+y+xy)-2y². (a) (10 points) Find and draw the best response functions of both players. (b) (10 points) Find the Nash equilibrium of this game.
(a) The best response functions for both players are:
Player 1's best response function: x = 1 - y
Player 2's best response function: y = 1 - x
(b) The Nash equilibrium of this game is when both players contribute half of the maximum possible contribution, which is 0.5.
To find the best response functions, we need to determine the strategies that maximize the payoffs for each player given the other player's strategy.
For Player 1, the payoff function is 2(x + y + xy) - x². To find the best response, we maximize this function with respect to x while assuming y is fixed. Taking the derivative of the payoff function with respect to x and setting it to zero, we get:
∂(2(x + y + xy) - x²)/∂x = 2 + 2y - 2x = 0
Simplifying this equation, we find:
2x = 2 + 2y
x = 1 + y
x = 1 - y (rearranging the equation)
This is the best response function for Player 1.
Similarly, for Player 2, the payoff function is 2(x + y + xy) - 2y². Maximizing this function with respect to y while assuming x is fixed, we differentiate and set it to zero:
∂(2(x + y + xy) - 2y²)/∂y = 2 + 2x - 4y = 0
Simplifying the equation, we find:
2y = 2 + 2x
y = 1 + x
y = 1 - x (rearranging the equation)
This is the best response function for Player 2.
To find the Nash equilibrium, we need to find the values of x and y where both best response functions intersect. Solving the simultaneous equations x = 1 - y and y = 1 - x, we find the Nash equilibrium point at x = y = 0.5.
The best response functions for both players in this game are Player 1's best response function: x = 1 - y and Player 2's best response function: y = 1 - x. The Nash equilibrium occurs when both players contribute half of the maximum possible contribution, which is x = y = 0.5.
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Assume a businessman has 6 suits and 7 ties. He is planning to take 3 suits and 2 ties with him on his next business trip. How many possibilities of selection does he have?
The businessman has the number possible combinations of suits are 420 and ties to take on his next business trip.
The businessman has 6 suits and 7 ties, meaning he has 42 possible combinations of suits and ties if he were to take all of them. Since he is only taking 3 suits and 2 ties, he would need to calculate the combinations of 3 suits from the 6 available and the combinations of 2 ties from the 7 available. The calculation for the number of combinations of 3 suits from 6 is 6C3, which is equal to 20. The calculation for the number of combinations of 2 ties from 7 is 7C2, which is equal to 21. Since there are 20 possibilities of suits and 21 possibilities of ties, the total number of combinations of suits and ties he can take on his next trip is 20 x 21, which is equal to 420.
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My daughter created this account and i need help canceling. she has already graduated from high school and services are no longer needed.
To cancel the account, contact customer support and provide necessary details. Verify ownership, request cancellation, follow instructions, and keep confirmation of cancellation.
1. Contact customer support: Reach out to the customer support team of the service provider through their official channels. Look for their contact information on their website or in the account settings section.
2. Provide necessary details: When contacting customer support, explain the situation and provide any required information, such as the account username, email address, or any other identifying details associated with the account.
3. Verify ownership: The customer support team may ask for verification to ensure that you are the rightful owner of the account. Be prepared to provide any necessary documents or proof of ownership.
4. Request cancellation: Clearly state your intention to cancel the account and ask the customer support representative to assist you with the process. They will guide you through the necessary steps to close the account.
5. Follow instructions: Carefully follow any instructions provided by the customer support representative to complete the cancellation process. This may involve confirming your decision through an email or clicking on a cancellation link.
6. Confirmation of cancellation: After completing the cancellation steps, you should receive a confirmation email or notification from the service provider indicating that the account has been successfully canceled. Keep this confirmation for future reference.
Remember to keep any relevant documentation or communication related to the cancellation process in case you need it for reference or to resolve any potential issues that may arise.
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Please help show work
A 144
B 118
C 72
D 108
Answer:
D 108
Step-by-step explanation:
D + A = 180
72 + A = 180
A = 108
What is the area of the composite figure?
Units Cubed? Units Squared? Units?
The area of the figure is 825 and its unit is units squared
How determine area of the composite figure and its unit?The given figure is a trapezium. Area of trapezium(A) = 1/2(a+b)h
Considering the labelling on the image attached:
The distance h spans from -15 to 18. Thus h = 18 - (-15) = 18+15 = 33 units
The distance a spans from -15 to 6. Thus a = 6 - (-15) = 6 +15 = 21 units
The distance b span from -15 to 18. Thus b = 24 - (-15) = 18+15 = 39 units
Note: each square of the graph is 3. You can also get the distance by counting number of squares and then multiply by 3.
Now, Area(A) = 1/2(21+39) x 33
= 1/2(50) x 33
= 25 x 33 = 825 squared units
Therefore, the area of the composite figure is 825 and the unit is units squared
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simplify
x^4 * x
What would be the simplified answer
Answer: The simplified answer will be: x^5
Step-by-step explanation:
x4x
=x4*x1
=(x*x*x*x)*(x)
=x*x*x*x*x
=x^5
Answer:
x⁵
General Formulas and Concepts:
Algebra I
Exponential Property [Multiplying]: \(\displaystyle b^m \cdot b^n = b^{m + n}\)Step-by-step explanation:
Step 1: Define
Identify
x⁴ · x
Step 2: Simplify
Exponential Rule [Multiplying]: \(\displaystyle x^4 \cdot x = x^{4 + 1}\)Add: \(\displaystyle x^4 \cdot x = x^5\)