After considering the given data we conclude that
a) r = -2 + i and r = -2 - i value generated after solving the auxiliary equation
b)[tex]y_c = c_1e^{(-2t)} cos(t) + c_2e^{(-2t)} sin(t)[/tex] complementary solution
c) general solution to the nonhomogeneous equation is [tex]y = y_c + Y_p = c_1e^{(-2t)} cos(t) + c_2e^{(-2t)} sin(t) + (1/26)e^{(-21)} .[/tex]
d) initial value problem is [tex]y(t) = e^{(-2t)} (cos(t) + 2sin(t))/2 + (1/26)e^{(-21)} .[/tex]
To determine the position of the body at time t, we can apply the given differential equation to solve for y(t). To do this, we can follow the steps below:
(a) the characteristic (auxiliary) equation is
The characteristic equation is obtained by setting the coefficients of the differential equation to zero, which gives us the equation [tex]r^2 + 4r + 5 = 0.[/tex]Solving this quadratic equation, we get r = -2 + i and r = -2 - i.
(b) evaluate the complementary solution, yc, to the corresponding homogeneous equation, [tex]y" + 4y' + 5y = 0.[/tex]
The complementary solution is given by[tex]y_c = c_1e^{(-2t)} cos(t) + c_2e^{(-2t)} sin(t),[/tex]where [tex]c_1[/tex] and [tex]c_2[/tex] are constants determined by the initial conditions.
(c) Calculate a particular solution, Yp, to the nonhomogeneous differential equation, [tex]Y" + 4y' + 5y = e^{(-21)}[/tex]. Hence state the general solution to the nonhomogeneous equation as [tex]y = y_c + y_p.[/tex]
To describe a particular solution, we can use the method of undetermined coefficients and guess a solution of the form [tex]Yp = Ae^{(-21)}[/tex], where A is a constant to be determined.
Staging this into the differential equation, we get A = 1/26. Therefore, the particular solution is [tex]Y_p = (1/26)e^{(-21)}[/tex]. The general solution to the nonhomogeneous equation is [tex]y = y_c + Y_p = c_1e^{(-2t)} cos(t) + c_2e^{(-2t)} sin(t) + (1/26)e^{(-21)}[/tex]
(d) Solve the initial value problem if the initial position of the body is 1 m and its initial velocity is zero.
Applying the initial conditions, we can solve for the constants [tex]c_1[/tex] and [tex]c_2[/tex] in the complementary solution. Since the initial velocity is zero, we have [tex]y'(0) = -2c_1 + c_2 = 0[/tex], which gives us [tex]c_2 = 2c_1.[/tex]
Applying the initial position, we have [tex]y(0) = c_1 = 1[/tex], which gives us [tex]c_2 = 2.[/tex]Therefore, the solution to the initial value problem is [tex]y(t) = e^{(-2t)} (cos(t) + 2sin(t))/2 + (1/26)e^{(-21)}[/tex]
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Brainlest for correct awnser :D
Answer:
24 inches
Step-by-step explanation:
Please hurry I need this now !!!
1.What is the positive solution to this equation?
x2 – 12 = -11x
a. -12
b. 12
C. -1
d. 1
Answer:
b. 12
Step-by-step explanation:
Answer:
either a or d because they are both correct.
Step-by-step explanation:
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.)
an = ln(8n² + 9) − ln(n² + 9)
The limit of the sequence as n approaches infinity is ln(8). The sequence converges, and the limit is ln(8).
To determine whether the sequence given by an = ln(8n² + 9) − ln(n² + 9) converges or diverges, we can examine the behavior of the terms as n approaches infinity.
Taking the limit as n approaches infinity, we have:
lim(n→∞) ln(8n² + 9) − ln(n² + 9)
We can simplify this expression using logarithmic properties. The natural logarithm of a quotient is equal to the difference of the logarithms:
= lim(n→∞) ln[(8n² + 9)/(n² + 9)]
Now, let's analyze the behavior of the numerator and denominator as n approaches infinity:
As n becomes larger and larger, the higher-order terms dominate. In this case, the leading term in both the numerator and denominator is n².
In the numerator, 8n² dominates, and in the denominator, n² dominates. Therefore, as n approaches infinity, the ratio (8n² + 9)/(n² + 9) approaches 8.
Taking the natural logarithm of 8, we have ln(8).
Therefore, the limit of the sequence as n approaches infinity is ln(8).
Hence, the sequence converges, and the limit is ln(8).
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okay last one . help
8. Somebody said the answer is letter A. I Don't Know the answer
Which properties of equality justify steps c and f?
A. Addition Property of Equality; Division Property of Equality
B. Multiplication Property of Equality; Division Property of Equality
C. Subtraction Property of Equality; Multiplication Property of Equality
D. Addition Property of Equality; Subtraction Property of Equality
Answer:
D. Addition Property of Equality; Subtraction Property of Equality
Step-by-step explanation:
Answer:
Option C and B
Step-by-step explanation:
In the question step C is 23 + 11 = -11 +(-4x) + 11
which is in the form of a + b = c + a
In step C we have added 11 on both the sides to eliminate 11 from right side of the equation.
property which signifies this step is
Addition property of equality :
In step 'f' expression is
\frac{34}{-4}=\frac{-4x}{-4}
In this step equation has been divided by -4 on both the sides to eliminate 4 from the numerator.
In this step division property of equality has been applied.
Therefore Option C and B are the correct options.
pls pls pls, I beg you to how to put a link I want you to answer this correctly without a link please answer this correctly I beg you
Answer:
1. −51,−41,−38,13,41,50
2. $140 each pair of shoes costs $20 (80 divided by 4). 20 times 7 is 140
3. 5x +6y+1
4. 5+15(n) or using instead of using n for hours use h so, 5+15(h)
5. cylinder
Answer/Step-by-step explanation:
-51, -41, -38, 13, 41, 50
140
5x + 6y + 1
5 + 15h
Cube.
1. Five more than the product of 4 and m a. 4+m+5 b. 4m+5 c.5m+4N
Answer:
b. 4m+5
Step-by-step explanation:
Answer:
Step-by-step explanation:
(b − 7)(b + 3). SOLUTION: 4. (4n + 3)(n + 9). SOLUTION: 5. (8h − 1)(2h − 3) ... (m. 2. − 5m + 4)(m. 2. + 7m − 3). SOLUTION: 28. (x. 2. + 5x − 1)(5x. 2. − 6x + 1) ... The value of x must be greater than 4. If x = 4 ... c. SYMBOLIC For a sum of the form a + b, write an expression for the square of the sum. ... Then, for five days,.
Find the Median of the following set of data. (Round to the
nearest tenths place.)
1,1,3,0, 7, 2,0, 3, 1, 6, 8, 1
PLEASE HELP ASAP
Answer:
12
Step-by-step explanation:
put the numbers in least to greatest. so that would be 0,0,1,1,1,1,2,3,3,6,7,8, then find the one or two. in this case it is two. the medians in the one in the middle
What is the volume of a sphere with a radius of 60.5 ft, rounded to the nearest tenth
of a cubic foot?
Answer:
If rounded to the nearest tenth of a cubic foot, would be: 927587.2
Step-by-step explanation:
The equation of finding the equation of the volume of a sphere is "4π[tex]\frac{radius^{3} }{3}[/tex]"
If values are inserted in for radius as 60.5, the answer will be 927587.2 when rounded to the nearest tenths.
Hope this helps!
A sandwich shop sells sandwiches for $3.50 each, including tax. The shop received a total of $80.50 from the sales of sandwiches one afternoon. Which equation can be used to determine the number of sandwiches, x, sold by the sandwich shop that afternoon? A. 3.50 + x = 80.50 C. 3.50x = 80.50 B. 3.50 + 80.50 = x D. 3.50 ÷ x = 80.50
Find the volume of the composite shape to the right to the nearest while number
10-3(x+9-10x)
Whats the answer
Five Number Summary for Percent Obese by State Computer output giving descriptive statistics for the percent of the population that is obese for each of the SOUS states, from the USStates dataset, is given in the table below. Variable Mean StDev Minimum Q Median Qs Maximum Obese 50 31.43 3.82 23.0 28.6 30.9 34.4 39.5 N Click here for the dataset associated with this question, (a) What is the five number summary? The five number summary is :
The five number summary for the percent of the population that is obese among the SOUS states are Minimum: 23.0, First Quartile (Q1): 28.6, Median: 30.9, Third Quartile (Q3): 34.4, Maximum: 39.5
The five number summary provides a concise summary of the distribution of a dataset, consisting of five key values: minimum, first quartile (Q1), median, third quartile (Q3), and maximum. Let's explain each part using the given information:
Minimum: The minimum value represents the smallest observed value in the dataset. In this case, the minimum value is 23.0. It indicates that the lowest recorded percentage of obesity among the SOUS states is 23.0%.
First Quartile (Q1): The first quartile is the value that divides the dataset into the lower 25% of the data. It represents the 25th percentile of the data. In the table, the first quartile (Q1) is given as 28.6. This means that 25% of the SOUS states have a percentage of obesity lower than or equal to 28.6%.
Median: The median, also known as the second quartile or the 50th percentile, is the middle value of the dataset when it is sorted in ascending order. It represents the point that splits the data into two equal halves. In the table, the median is given as 30.9. This implies that 50% of the SOUS states have a percentage of obesity lower than or equal to 30.9%.
Third Quartile (Q3): The third quartile is the value that divides the dataset into the upper 25% of the data. It represents the 75th percentile of the data. In the table, the third quartile (Q3) is provided as 34.4. This means that 75% of the SOUS states have a percentage of obesity lower than or equal to 34.4%.
Maximum: The maximum value represents the largest observed value in the dataset. In this case, the maximum value is 39.5. It indicates that the highest recorded percentage of obesity among the SOUS states is 39.5%.
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what is the equation to 9x+3° 84°
Answer:
the solution to this equation is x = 9°
Step-by-step explanation:
9x + 3 = 84
9x = 84 - 3
9x = 81
x = 81 / 9
x = 9°
HURRY HELP ASAPPP Question 23 of 25
If WXYZ is a square, which statements must be true? Check all that apply.
A. WXYZ is a trapezoid.
B. Wis a right angle.
C. WXYZ is a rhombus.
D. WXXY
E. WXYZ is a rectangle.
OF. WXYZ
WX is perpendicular to XY, W is congruent to X, W is supplementary to X, WXYZ is a rhombus, and WX is parallel to YZ and this can be determined by using the properties of a square.
What is quadrilateral?A quadrilateral is a polygon with four sides four angles and four vertices. Whenever we name a quadrilateral, we need to keep in mind the order of the vertices.
Given that, WXYZ is square.
The properties of a square are given below:
All sides are equal in length.
The two consecutive sides are perpendicular.
Opposite sides are parallel to each other.
All the interior angles are 90 degrees.
The diagonals bisect one another.
The area of the square whose sides are 'a' is .
The perimeter of the square whose sides are 'a' is 4a.
Diagonal are equal.
Therefore, the correct statements about the square WXYZ are A), B), C), D), and F).
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what number is b in algebra
Answer:
I could be any number.
But it couldn't just be a 'b' it could be other letters. The letters is just a grown up way of saying a missing number. Its like saying:
10+b=11..
11-b=10..
therefore b=1
Does that make sense
It can also mean in the quadratic formula b
Step-by-step explanation:
In algebra, the variable "b" represents an unknown or variable number.
It is used to denote a quantity that can vary or take on different values. The purpose of using variables in algebraic equations is to generalize mathematical relationships and solve problems with unknown quantities. By assigning the letter "b" to a variable, we can manipulate and solve equations using algebraic operations, such as addition, subtraction, multiplication, and division.
The value of "b" can be determined through various methods, such as solving equations, simplifying expressions, or applying mathematical principles. The flexibility of variables like "b" allows us to solve a wide range of problems and analyze mathematical relationships without relying on specific numerical values.
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Kyle is building a model out of cardboard, as shown below. He needs to construct the top and sides of each section of the model but not the bottom. How many surfaces will Kyle need to find the area of in order to determine how much cardboard he will need? A. 17 B. 14 C. 8 D. 3
Answer:
The answer is B
Step-by-step explanation:
Answer: its B i did the quiz lol
Step-by-step explanation:
Which of the following would be the FIRST step to take when solving the given equation? -11n - 1 = 87
A) Divide both sides of the equation by 11
B) Subtract 11 from both sides of the equation
C) Subtract 1 both sides of the equation
D) Add 1 to both sides of the equation
Answer:
D) Add 1 to both sides of the equation
Step-by-step explanation:
-11n - 1 = 87
-11n = 87 + 1
(3, 3 3 ) (i) find polar coordinates (r, ) of the point, where r > 0 and 0 ≤ < 2. (r, ) = (ii) find polar coordinates (r, ) of the point, where r < 0 and 0 ≤ < 2. (r, ) =
(i) the polar coordinates of the point are (6, π/6).
(ii) the polar coordinates of the point are (-6, π/6).
The Cartesian coordinates of the point are given as (3√3, 3). We need to find the polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π and also where r < 0 and 0 ≤ θ < 2π.
To find the polar coordinates (r, θ) of the point, we use the following formulas:
r = √(x² + y²)
θ = tan⁻¹(y/x)
where x and y are the Cartesian coordinates of the point.
(i). For r > 0 and 0 ≤ θ < 2π, we have:
x = 3√3
y = 3
Using the above formulas, we get:
r = √((3√3)² + 3²) = √(27 + 9) = √36 = 6
θ = tan⁻¹(3/3√3) = tan⁻¹(1/√3) = π/6
Therefore, the polar coordinates of the point are (6, π/6).
b. For r < 0 and 0 ≤ θ < 2π, we have:
x = 3√3
y = 3
Using the above formulas, we get:
r = -√((3√3)² + 3²) = -√(27 + 9) = -√36 = -6
θ = tan⁻¹(3/3√3) = tan⁻¹(1/√3) = π/6
Therefore, the polar coordinates of the point are (-6, π/6).
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Given question is incomplete the complete question is incomplete
The Cartesian Coordinates Of A Point Are Given.
(3√3,3)
(i) Find Polar Coordinates (r, θ) Of The Point, Where r>0 And 0≤θ<2π.
(ii) Find Polar Coordinates (r, θ) Of The Point, Where r<0 And 0≤θ<2π.
Each lap around the track is 400 meters. How many meters does someone run if they run 5 laps?
Answer:
2000 meters
Step-by-step explanation:
400×5=2000
Why does the moon goes through phases?
A.
The moon rotates around its axis.
B.
The moon revolves around Earth.
C.
Earth rotates around its axis.
D.
Earth revolves around the sun.
It is because the moon revolves around Earth.
Hope it helps you...
SIGNS. *
If 2(3.8x – 10) - 2 = -1.2x(3 - 6) + 3x, what does
equal?
A5.5
B-5.5
C22
D-22
im not smart enough lol
WILL GIVE BRAINLIEST PLEASE HELP ASAP, BEST ANSWER GETES BRAINLIEST. NOT A SCAM AND ITS NOT CAP WHAT SO EVER
Answer:
A. 60 + x = 90
Step-by-step explanation:
Complementary angles add up to 90 degrees so
60 + x = 90
Answer:
The answer is A: 60 + x = 90
Step-by-step explanation:
Complimentary angles are two angles that add up to 90, so the equation 60 + x = 90 is what you need to use to find the complimentary angle. I hope this helps :)
Define the following matrix norm for an n x n real matrix B: || B||M. = sup {||Bx|lo : X ER", ||$||20 = 1}. Show that || B||M. = max = max {Bijl {3B41 } 1
The matrix norm for an n x n real matrix B is ||B||M = max{|Bij|}
First, we will prove that ||B||M ≤ max{|Bij|}. Let's assume k is the index that achieves the maximum value, i.e., max{|Bij|} = |Bkj|. Consider the vector x = (0, 0, ..., 0, 1, 0, ..., 0)T, where the 1 is in the k-th position. Then, ||x||2 = 1. Now, let's calculate ||Bx||M:
||Bx||M = sup{||Bx||2 : ||x||2 = 1}
= sup{√((Bx)T(Bx)) : ||x||2 = 1}
= sup{√(xTBTBx) : ||x||2 = 1}
= sup{√(xTBTBx) : ||x||2 = 1, xk = 1}
≤ √((BTB)kk) (using the fact that xTBTBx is a scalar and sup{scalar} = scalar)
= √(|Bkj|²)
= |Bkj|
= max{|Bij|}
Therefore, we have shown that ||B||M ≤ max{|Bij|}.
Now, let's prove the reverse inequality: max{|Bij|} ≤ ||B||M. Consider the vector x = (x1, x2, ..., xn)T, where xi = 1 for the index i that achieves the maximum absolute value of Bij, and xi = 0 for all other indices. Then, ||x||2 = 1. Now, let's calculate ||Bx||M:
||Bx||M = sup{||Bx||2 : ||x||2 = 1}
= sup{√((Bx)T(Bx)) : ||x||2 = 1}
= sup{√(xTBTBx) : ||x||2 = 1}
= sup{√(xTBTBx) : ||x||2 = 1, xi = 1 for some i}
≥ √((BTB)ii) (using the fact that xTBTBx is a scalar and sup{scalar} = scalar)
= sqrt(|Bij|²)
= |Bij|
= max{|Bij|}
Therefore, we have shown that max{|Bij|} ≤ ||B||M.
Combining both inequalities, we conclude that ||B||M = max{|Bij|}.
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let and be two integers with 0≤<≤100 . suppose you approximate (≤100≤) by ∑=−11! . what is the largest possible error you could make?
The largest possible error you could make in the given approximation is [tex]1 / (10^11 * 11!)[/tex]
To approximate the value of [tex]e^x[/tex] using the series expansion, we can use the formula:
[tex]e^x[/tex] ≈ ∑ [tex](x^n)/n![/tex]
In this case, we have:
x = -1/10
To find the largest possible error in the approximation, we can consider the next term in the series that we are neglecting:
1 / (10^11 * 11!) = [tex]|x^(n+1) / (n+1)!|[/tex]
For the given approximation, n = 10 (since we are using terms up to n = 10).
Substituting the values, we have:
[tex]|Error|[/tex] = [tex]|(-1/10)^(10+1) / (10+1)!|[/tex]
|Error| =[tex]|(-1/10)^11 / 11!|[/tex]
|Error| =[tex]1 / (10^11 * 11!)[/tex]
Since the value of n is fixed at 10, the largest possible error occurs when x is at its maximum value within the given range (0 ≤ x ≤ 100).
In this case, the maximum value of |Error| would be obtained by using the maximum value of x = 100 in the formula.
|Error| = [tex]1 / (10^11 * 11!)[/tex]
Therefore, the largest possible error you could make in the given approximation is [tex]1 / (10^11 * 11!)[/tex].
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Preventive medicine services are based on which of the following criteria?
A) Documentation of history, physical examination, and
medical decision making.
B) Age of the patient
C) Amount of time spent with the patient
D) The final diagnosis for the visit
Preventive medicine services are primarily based on documentation of history, physical examination, and medical decision making.
The correct answer is A) Documentation of history, physical examination, and medical decision making. Preventive medicine services focus on preventing or identifying potential health issues before they become more serious. To determine the appropriate preventive measures, healthcare professionals assess various factors. Among these, documentation of the patient's medical history is crucial to understand their individual health risks and needs.
Physical examination allows for a comprehensive assessment of the patient's current health status, identifying any existing conditions or potential areas of concern. Medical decision making refers to the process by which healthcare providers use the gathered information to determine appropriate preventive measures and interventions. Factors like the patient's age, time spent with the patient, and the final diagnosis may be relevant to specific aspects of healthcare but are not the primary criteria for preventive medicine services.
The focus lies on comprehensive documentation and medical decision making to promote and maintain optimal health.
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You purchase a new flat screen TV for $878.99. You are charged sales tax at a rate of 6%. What is your total balance due when you go to pay for the TV?
Answer:
Sales tax: $52.74
■ Cost/Price before ST: $878.99
■ Total Cost/Price including ST: $931.73
Step-by-step explanation:
help pleaseeee !!! will b marked brainliest!!!!!!
Answer:
I think it's the first one
Answer:
to my knowledge I would pick A
I need help with the Pythagorean Theorem
Answer:
8.4 I think
Step-by-step explanation:
Please don't hate me if I am wrong
consider trapezoid lmno. what information would verify that lmno is an isosceles trapezoid? check all that apply.
a. LN ≅ MO
b. LN ≅ ON
c. LO ≅ MN
d. ∠l ≅ ∠n
e. ∠l ≅ ∠m
An isosceles trapezoid LMNO has the side LO is congruent to side MN, the diagonal LN is congruent to diagonal MO, and the angle L is congruent to angle M. Hence correct options are a), c), and e)
Given :
Trapezoid LMNO.
The following are the conditions that show any trapezoid is an isosceles trapezoid:
Condition 1 -- Both the legs are of the same length.
Condition 2 -- The base angles are of the same measure.
Condition 3 -- Diagonals are of the same length.
So, the given trapezoid LMNO is an isosceles trapezoid when:
The side LO is congruent to side MN.
The diagonal LN is congruent to diagonal MO.
The angle L is congruent to angle M.
Therefore, the correct option is a), c), and e).
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