Answer:
x=(y+2b)/3m
Step-by-step explanation:
y+2b=3mx
(y+2b)/3m=x
Find the general solution of y''' + 9y'' + y' − 111y = 0 if it is known that y1 = e−6x cos(x) is one solution.
Answer:
[tex]\mathbf{y(x) = \dfrac{(c_1 + c_2) \ cos (x)}{e^{6x} }+ \dfrac{i(c_1 -c_2) \ sin (x)}{e^{6x}}+ c_3e^{3\ x}}[/tex]
Step-by-step explanation:
The objective of this question is to solve:
[tex]\dfrac{dy(x)}{dx}+ 9\dfrac{d^2y(dx)}{dx^2}+\dfrac{d^3y(x)}{dx^3}-111y(x) = 0 :[/tex]
Suppose the general solution is proportional to [tex]e^{\lambda x}[/tex] for [tex]\lambda[/tex] is constant; Then:
Let's replace [tex]y(x) = e^{\lambda\ x}[/tex] into the above equation:
i.e.
[tex]\dfrac{d^3}{dx^3}(e ^{\lambda x} )+ 9 \dfrac{d^2}{dx^2}(e ^{\lambda x} ) + \dfrac{d}{dx}(e ^{\lambda x} )- 111 \ e ^{\lambda x} = 0[/tex]
To Replace:
[tex]\dfrac{d^3}{dx^3}(e ^{\lambda x} )[/tex] with [tex]\lambda^3 e ^{\lambda x }[/tex]
[tex]\dfrac{d^2}{dx^2}(e ^{\lambda x} ) \ with \ \lambda^2 e^{\lambda\ x}[/tex]
[tex]\dfrac{d}{dx}(e ^{\lambda x} ) \ with \ \lambda e ^{\lambda \ x}[/tex]
Thus;
[tex]\lambda^3 e ^{\lambda x }[/tex] + [tex]9 \lambda^2 e^{\lambda\ x}[/tex] + [tex]\lambda e ^{\lambda \ x}[/tex] - 111 [tex]e ^{\lambda \ x}[/tex] = 0
[tex]e ^{\lambda \ x} (\lambda ^3 + 9 \lambda ^2 + \lambda - 111 )= 0[/tex]
∴
In as much as [tex]e^{ \lambda x}\neq 0[/tex] for any finite [tex]\lambda[/tex]; Then:
[tex]\lambda ^3 + 9 \lambda ^2 + 111 = 0[/tex]
By Factorization:
[tex](\lambda - 3) ( \lambda ^2 + 12 \lambda + 37) = 0[/tex]
[tex]\lambda = -6 + i \ or\ \lambda = -6 - i \ or \ \lambda = 3[/tex]
However;
The root [tex]\lambda = -6 \pm i[/tex] yield;
[tex]y_1 = (x) = c_1 e ^ {(-6+i)x}[/tex]
[tex]y_2 (x) = c_2e^{(-6-i)x}[/tex]
The root [tex]\lambda = 3[/tex] yield;
[tex]y_3(x) = c_3 e^{3x}[/tex]
∴
The general solution is:
[tex]y(x) = y_1(x) + y_2(x) + y_3(x) = \dfrac{c_1}{c^{(6-i)}x}+\dfrac{c_2}{c^{(6+i)}x}+ c_3e^{3x}[/tex]
Using Euler's Identity ;
[tex]e^{\alpha+i \beta} = e^\alpha \ cos (\beta ) + i \ e^\alpha \ sin ( \beta)[/tex]
[tex]y(x) = c_1 ( \dfrac{cos (x) }{e^{6x}}+ \dfrac{i \ sin x }{e^{6x} }) + c_2 ( \dfrac{cos (x)}{e^{6x}}- \dfrac{-i \ sin (x)}{e^{6x}})+c_3 e^{3x}[/tex]
[tex]\mathbf{y(x) = \dfrac{(c_1 + c_2) \ cos (x)}{e^{6x} }+ \dfrac{i(c_1 -c_2) \ sin (x)}{e^{6x}}+ c_3e^{3\ x}}[/tex]
3/4x-4=5/6
Rewrite so it doesn’t have any fraction
1079 divided by 4 Yeah Also whoever helps thank you :D
Answer:
269.75
Hope this helps:)
Step-by-step explanation:
Whats the answers please
Answer: D,C,B
Step-by-step explanation:These are the answers
Drag the operator to the correct location on the image. Which operation results in a trinomial?
Answer:
-
Step-by-step explanation:
I took the test
The correct operator that enters a circle is a subtraction sign.
Given the expressions
[tex](4x^5-8x) ()(3x^2-8x+9)[/tex]
We need to know which sign goes into the bracket that will give a trinomial when simplified.
A trinomial is a function containing 3-terms.
Using the subtraction sign.
[tex](4x^5-8x) - (3x^2-8x+9)[/tex]
Expand
[tex]= 4x^5-8x - 3x^2+8x-9\\= 4x^5-3x^2-8x+8x-9\\=4x^5-3x^2+0-9\\=4x^5-3x^2-9[/tex]
Since the resulting term is a trinomial (3 terms), hence the correct operator that enters a circle is a subtraction sign.
Learn more here: https://brainly.com/question/1320408
3252614683754629158741032465x93756356872264881+432757232878247-3243566=
Answer:
bout 7
Step-by-step explanation:
Answer:3.049533e+44 to be exact
Step-by-step explanation:
Please Solve Brainliest and 10 points!
Answer:
x=20°
Step-by-step explanation:
statements:1.) m<DOB = m<DOE + m<BOE (or m<EOB)
2.) m<DOB = 90°+x
3.) m<AOC = m<DOB
4.) 110° = 90° + x
5.) x = 20°
reasons:1.) given
2.) substitution
3.) vertical/reflexive
4.) substitution
5.) algebra
Is anyone willing to answer this question I can’t do it
Answer:
Not 100% sure on this make sure you double check
Step-by-step explanation:
X- 10
Y- 10
Slope- (-1)
like I said this could be wrong
how do you solve 1/2x=6
Answer:
x=12
Step-by-step explanation:
multiply 2 from both sides to isolate x
then u should end up with 1x=12
Christina's ice cream parlor sold 60 vanilla cones on the first day of summer. If the goal is to increase the number of vanilla cones sold each day by 4, how many will be sold 20 days later?
1280 cones because you would add 60 +4 and multiply by 20, and would get 1280 cones.
Select all the conditions for which it is possible to construct a triangle. A.A triangle with angle measures , , and B.A triangle with side lengths 3 cm, 7 cm, and 11 cm C.A triangle with side lengths 6 in, 13 in, and 12 in D.A triangle with side lengths 8 cm and 5 cm and a angle E.A triangle with angle measures and , and a 9 cm side length
Answer:
As
Step-by-step explanation:
Aaa
Nicole buys candy that costs $4 per pound. She will spend more than $28 on candy. What are the possible numbers of pounds she will buy?
Enter the correct answer in the box. Write the sum of √28x^6 + 4√7x^6 in simplest form, if x ≠ 0.
Answer:
21.97025026/250
Math To Do, i-Ready X G isabella belongs to a fitness club X + student/dashboard/home sabella belongs to a fitness club. She paid an initial fee of $50 when she joined and also pays $10 per month. Since becoming a member of the fitness club, Isabella has paid a total of $240. Use the drop-down menus to complete the statements about the length of time that Isabella has been a member of the fitness club. Click the arrows to choose an answer from each menu.
The equation Choose can be used to determine the value of the number of months Isabella has been a member of the fitness club. She has been a member of the fitness club for Choose months.
Answer: 19 months
Step-by-step explanation:
given data:
amount paid initially when joining the club = $50.
monthly payments made = $10.
total amount paid since joining the club = $240.
Solution:
= 10X + 50 = 240
collect like terms
= 10X = 240 – 50
10X = 190
divide both sides by 10
10X/10 = 190/10
X = 19
isabella has been a member of the club for 19 months.
Select three ratios that are equivalent to 11:1.
Choose 3 answers:
1:11
22:2
55:5
9:99
Answer:
22:2, 55:5, 1:11
Step-by-step explanation:
Answer:
22:2 55:5 and no others
Step-by-step explanation:
find the value of x
I have to show the work
Answer:
x = 39
Step-by-step explanation:
A circle is made up of 360 degrees
235+ 54+ x+32 = 360
Combine like terms
x+321=360
Subtract 321 from each side
x+321-321 = 360-321
x = 39
Factorise fully
-12a - 16
please do quick, first to answer marked brainiest!!
Answer:
-4( 3a+4)
Step-by-step explanation:
-12a - 16
-4*3a -4*4
Factor out a -4
-4( 3a+4)
4x = 7y + 5 what is the slope
Step-by-step explanation:
7y=4x-5
y=(4/7)x-5/7
slope is equal to m where m is
y=mx+b
in this case m is 4/7
so slope =4/7
he is reading a novel into passive voiceWhat is the simplified form of the expression? 5 + 3(2)
Answer:
The answer is 11
hence 5 + 6 = 11
Answer:
hi
Step-by-step explanation:
[tex]5 + 3(2) = 11[/tex]
probably…
simplify 12x⁵y² ÷ 3x²y
Answer:
f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)
Step-by-step explanation:
Could you answer this please a lot of points to you
Answer:
Step-by-step explanation:
13/16 dived by 5/6 = 9/40
7 dived by 1/6 = 42
2 1/5 dived by 1 1/3 = 1 13/20
2 1/7 dived by 3/28 = 20
Write the equation of the line parallel to the given line and through the given
point. y=2x - 8 through (3.10)
Answer:
y-2x -8
Step-by-step explanation:
your jus gonna right it back because it's parallel which means it's the same thing.
Write an equation to find the nth term of each sequence.
7, 13, 19, 25....
Answer:
6n+1
Step-by-step explanation:
n=term#
PLEASE HELP!!! ILL GIVE BRANLIEST *EXTRA POINTS* dont skip :((
Answer:
-3.21
Step-by-step explanation:
If you pay close attention the numbers are 5 points away from each other, so after -3.2 is -3.21! Hope that helped love :)
pleas help me ill give brainleyest
Answer:
11.8% Decrease
Step-by-step explanation:
I googles it i am sorry if it's not right
Click to review the online content. Then answer the question(s) below, using complete sentences. Scroll down to view additional questions
Online Content Site 1
What are some of the ways citizens can participate in ggovernment? (Site 1) This is a change to online content
Answer:
paying taxes, voting , serving a public office, and obeying the law.
Which graph indicates decreasing speed?
A. Graph c
B Graph A
c graph F
d graph
What is a possible third side to a triangle with side lengths of 13 and 4?
The possible third side to a triangle is 12.
Given that,
The side length is 13 and 4.We need to find the third side length.
Based on the above information, the calculation is as follows:
Here we use the pythagoras theorem.
[tex]= \sqrt{13^2 - 4^2} \\\\= \sqrt{169-16} \\\\= \sqrt{153}[/tex]
= 12.37
= 12
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324 soldiers queued up such that the number of queues is equal to the number of soldiers in each queue. find the number of queues
The value of a share of stock in an electronics company increased by 2/3 % during one week. If the value of a share of stock was $141 at the beginning of the week, estimate the increase in value of a share of stock at the end of the week.
Answer:
An increase of $0.94
Step-by-step explanation: