I'm going to assume that you mean to say that i = √(-1) is a root of the auxiliary equation. That is, if the Cauchy-Euler DE is
x ²y'' + axy' + by = 0
then the auxiliary equation obtained by substituting y = xᵐ is
x ² (m (m - 1) xᵐ ⁻ ²) + ax (m xᵐ ⁻ ¹) + bxᵐ = 0
which reduces to
m (m - 1) + am + b = 0
or
m ² + (a - 1) m + b = 0
By the fundamental theorem of algebra, we can write the quadratic in terms of its roots r₁ and r₂,
(m - r₁) (m - r₂) = 0
Given that one root is the imaginary unit i, and the coefficients of the aux. equation are real, it follows that the other root is -i, because complex roots must occur with their conjugates. So we have as our aux. equation,
(m - i ) (m + i ) = 0
or
m ² + 1 = 0
Then a - 1 = 0 and b = 1, so that the given root and general solution correspond to the DE,
x ²y'' + xy' + y = 0
i would like some help please i am stuck
Answer: -2(d) is the answer.
Step-by-step explanation:
x1 = 3
y1 = -5
x2 = -2
y2 = 5
slope (m) = rise/run = (y2 - y1)/(x2-x1)
=(5-(-5))/(-2-3)
= 10/-5
= -2
Which of the following expressions are equivalent?
I. 5a6
II. 30a
III. a6 + a6 + a6 + a6 + a6
IV. 6a5
Answer:
5а⁶=а⁶+а⁶+а⁶+а⁶+а⁶
~~~~~~~~
Derive the explicit rule for the pattern: 3, 0, - 3, - 6, - 9, ...
Answer:
Step-by-step explanation:
a1 = 3
d = -3
an = a1 + (n - 1)*d
an = a1 + (n - 1)*-3
Try it
Let n = 5
a5 = 3 + (5 - 1)*-3
a5 = 3 + 4*-3
a5 = 3 - 12
a5 = - 9 which is exactly what it should be.
The interesting one to try is n = 2
a2 = a1 + (2 - 1)*-3
a3 = 3 + 1(-3)
a3 = 3 - 3
a3 =0
Which is exactly what the second term is. It's interesting because you would never guess that 0 is what you get.
***URGENT***
PLEASE HELP ME ASAP, ITS DUE TODAY!!!
............................................................
T is the point on AB such that AT:TB = 5: 1. Show that ot is parallel to the vector a + 2b.
Step-by-step explanation:
SO, OT is parallel to the vector a+2b
The lengths of the parallel sides of
a trapezium are 12cm and 26cm
If Its area is 228cm square Find the
perpendicular distance between the
Parallel sides
Answer:
12 cm
Step-by-step explanation:
12+26/2 ×x =228
19x =228
X=12cm
I need to know this answe ASAP
Answer:
The function is always increasing
Step-by-step explanation:
To be increasing, the y value needs to be getting bigger as x gets bigger
This is true for all values of x
The function is increasing for all values of x
Which graph represents the function f(x) = x-2?
Answer:
click in photo
nejdjjd
nxndjdbbdjf
lấy x=0 ta có y= -2 => A(0;-2)
lấy y=0 ta có x=2 => B(2;0)
nối 2 điểm A và B ta có đồ thị:
Convert the improper fraction to a whole or mixed number. (Enter your answer as a simplified mixed number.)
25
7
If total sales are $54000 your food service total is 42% of your total sales what is your dollar target for food service
Answer:
Your dollar target for food service is $22,680
Step-by-step explanation:
It is given in the question that total sales are = $54,000
your food service is 42% of your total sales = 42% × $54,000
= × 54,000
= 0.42 × 54,000
= $22,680
Write a linear equation in point-slope form for the line that goes through (1, -3) and (3,9).
A. y+3 = -6(x-1)
B. y- 9 = 6(x - 3)
C. y- 9 = 2(x-3)
D. y + 3 = 6(x-1)
The product of two positive integer numbers is 70 and the sum of the same two numbers is 17. Find the
numbers.
Answer:
7 and 10
Step-by-step explanation:
7 * 10 = 70
7 + 10 = 17
Answer:
10 and 7
Step-by-step explanation:
call them a and b, respectively
so a*b=70 -> b=70/a
a+b=17 ->a+70/a=17 ->a=10 b =7
Bridgette bought 1 pack of white T-shirts and 5 packs of blue T-shirts for her basketball team. The white T-shirts come in packs of 2, and the blue T-shirts come in packs of 6. How many T-shirts did Bridgette buy in all?
Work Shown:
1 pack of white = 2 shirts = A
1 pack of blue = 6 shirts
5 packs of blue = 5*6 = 30 shirts = B
A+B = 2 white shirts + 30 blue shirts = 32 shirts total
Answer:
32 T-shirts in total
Step-by-step explanation:
1 white has 2
1 blue has 6
1*2=2 white T
5*6=30 blue T
30+2=32
In an accelerated failure test, components are operated under extreme conditions so that a substantial number will fail in a rather short time. In such a test involving two types of microchips, 580 chips manufactured by an existing process were tested, and 125 of them failed. Then, 780 chips manufactured by a new process were tested, and 130 of them failed. Find a 90% confidence interval for the difference between the proportions of failures for chips manufactured by the two processes. (Round the final answers to four decimal places.) The 90% confidence interval is
Answer:
The 90% confidence interval is (0.0131, 0.0845).
Step-by-step explanation:
Before finding the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Old process:
125 out of 580, so:
[tex]p_O = \frac{125}{580} = 0.2155[/tex]
[tex]s_O = \sqrt{\frac{0.2155*0.7845}{580}} = 0.0171[/tex]
New process:
130 out of 780. So
[tex]p_N = \frac{130}{780} = 0.1667[/tex]
[tex]s_N = \sqrt{\frac{0.1667*0.8333}{780}} = 0.0133[/tex]
Distribution of the difference:
[tex]p = p_O - p_N = 0.2155 - 0.1667 = 0.0488[/tex]
[tex]s = \sqrt{s_O^2+s_N^2} = \sqrt{0.0171^2 + 0.0133^2} = 0.0217[/tex]
Confidence interval:
[tex]p \pm zs[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower bound of the interval is:
[tex]p - zs = 0.0488 - 1.645*0.0217 = 0.0131[/tex]
The upper bound of the interval is:
[tex]p + zs = 0.0488 + 1.645*0.0217 = 0.0845[/tex]
The 90% confidence interval is (0.0131, 0.0845).
PLEASEE HELP ME ASAPPP (geometry)
Answer:AE=EC và BF=FC => EF là đường trung bình của tam giác ABC
=> EF // và bằng 1/2 AB
=> AB = 16
Step-by-step explanation:
Answer:
AB=16
Step-by-step explanation:
Midsegment Theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long.
The mid-segment of a triangle, which joins the midpoints of two sides of a triangle, is parallel to the third side of the triangle and half the length of that third side of the triangle.
AD=DB
AD+DB=AB=2EF
AB=2×8=16
Solve for x
-3x = -15
A) x = -45
B) x = 5
C) x = -5
C-x=-5
Step-by-step explanation:
-3x=-15
or,-3x x =-15
or, x=-15÷3
therefore, x=-5
I need help ASAP pleasee
Answer:
The answer is 4 1/2
Step-by-step explanation:
Because A to C is 2 1/4 so all you have to do add 2 1/4 + 2 1/4 which will equal 4 1/2
Which equation can she use as statement 5? 60:x = 48:(48 + 36) 60 + x = 48 + 36 60 − x = 48 − 36 60:(60 + x) = 48:(48 + 36)
1
What is the perimeter of a rectangle
whose length is 5 feet and whose width
is 3.5 feet?
O 8.5 ft.
O 16.5 ft.
O 17 ft.
O 17.5 ft.
Answer:
17ft
Step-by-step explanation:
5*2 + 3.5*2=17
What is 1/8+1/4 whats the answer
What are the solutions of this quadratic equation?
4x2 + 3 = 4x + 2
Answer:
A. x = 1/2
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
Terms/CoefficientsFactoringStandard Form: ax² + bx + c = 0Solving quadraticsStep-by-step explanation:
Step 1: Define
Identify
4x² + 3 = 4x + 2
Step 2: Solve for x
[Equality Property] Rewrite in standard form: 4x² - 4x + 1 = 0Factor: (2x - 1)² = 0Solve: x = 1/2Natalie Jenny, Steve and Jatin paid $12 for their taxi. They shared this equally between them. What fraction did each pay?
Answer:
1/4
Step-by-step explanation:
12/4= 3
Each paid $3 but as a fraction 3/12=1/4
Answer:
[tex] \frac{1}{4} [/tex]
Step-by-step
12÷4=3
3/12=1/4-each pay this fraction
Using a directrix of y = 5 and a focus of (4, 1), what quadratic function is created?
HELP PLS
Answer:
(x-4)^2=-8(y-3)
This is a parabola.
Step-by-step explanation:
Since the directrix is horizontal, the parabola faces up or down. Since the focus is below the directix it faces down. This means p will be negative in the equation (x-h)^2=4p(y-k).
p also tells us the half the distance between the focus and the directrix. The distance between 1 and 5 is 4, so p=-2.
The vertex is half way point between focus (4,1) and directrix y=5.
So the vertex is (4, [1+5]/2 )= (4 ,6/2)=(4,3). This is (h,k) in our equation.
(x-h)^2=4p(y-k)
(x-4)^2=4×-2(y-3)
(x-4)^2=-8(y-3)
Please help!! Given the recursive formula shown, what are the first 4 terms of the sequence?
Answer:
C
Step-by-step explanation:
the fibrin definition tells us that the first term of the sequence a1 = 6
so, B is out.
and for every following term we always add 7 to every previous term to create the next one.
so, when I add 7 to 6, what is my second term in the sequence ? 7+6 = 13
not 42, not -7
therefore, only C is correct.
and 13+7 = 20
and 20+7 = 27
it all fits
11
find the number of ways of forming
an executive Committee of four in a
social club consisting of 15 members,
If a particular man must be in
the comittee
There are 365 ways of forming an executive Committee of four in a social club consisting of 15 members
Understanding Permutation and CombinationIf a particular man must be in the committee, we can choose the remaining 3 members from the remaining 14 members. The number of ways to choose 3 members from 14 is given by the combination:
14Cr3 = [tex]\frac{14!}{3! 11!}[/tex] = [tex]\frac{14x13x12}{3x2x1}[/tex] = 364
Therefore, there are 364 ways of forming an executive committee of four in a social club consisting of 15 members, if a particular man must be in the committee.
Learn more about combination here:
https://brainly.com/question/28065038
#SPJ1
Convert 15,000 meters to centimeters.
15,000 centimeters
150,000 centimeters
15,000,000 centimeters
1,500,000 centimeters
Answer:
1500000
Step-by-step explanation:
1 metre = 100 cm
15000metre =15000*100
=1500000
PLEASEEEEEE HELPPPPPPPPP
what are the zeros for this?
f(x) = 2x^2 + 6x + 2
Answer:
-3/2 ±1/2 sqrt(5) = x
Step-by-step explanation:
f(x) = 2x^2 + 6x + 2
Set the function equal to 0
0 = 2x^2 + 6x + 2
Factor out 2
0 = 2(x^2 + 3x + 1)
Divide by 2
0 = (x^2 + 3x + 1)
Subtract 1 from each side
-1 = x^2 +3x
Complete the square by dividing the x coefficient by 2 and then squaring
(3/2)^2 = 9/4
-1 +9/4 = x^2 +3x+9/4
-4/4+9/4 = (x+3/2) ^2
5/4 = (x+3/2) ^2
Taking the square root of each side
± sqrt(5/4) = sqrt( (x+3/2) ^2)
±1/2 sqrt(5) = (x+3/2)
Subtract 3/2 from each side
-3/2 ±1/2 sqrt(5) = x
Jim, Katrina, Larry, and Jim have all been invited to a dinner party. They arrive randomly and each person arrives at a different time.
a. In how many ways can they arrive?
b. In how many ways can Jim arrive first and Kim last?
c. Find the probability that Jim will arrive first and Kim last.
a.___ (Type an integer)
b.___ (Type an integer.)
c.___ (Type a fraction. Simplify your answer)
Answer:
24
6
1/12
Step-by-step explanation:
a) This is a counting problem 4*3*2*1 = 24 different ways.
b) 1 * 2 * 1 * 1 = 2 ways
This is one you should try.
Jim Kat Larry Kim
Jim Larry Kat Kim
You can't get another way.
c)
There are 2 ways that Jim can arrive first and Kim Last shown in b
2/24 = 1/12
What is the area of the trapezoid?
Answer:
A=a+b
2
Step-by-step explanation:
To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2.
find the missing length indicated
Answer:
Step-by-step explanation:
192
Answer:
Step-by-step explanation:
can somboby help me please
Answer:
x = 8
Step-by-step explanation:
The question had specified that x is equal to 8.
x=8
explanationsplease mark this answer as brainlist
