Find the general solution of the given higher-order differential equation. y''' + 3y'' + 3y' + y = 0
Answer:
[tex]y(x)=c_1e^{-x}+c_2xe^{-x}+c_3x^2e^{-x}[/tex]
Step-by-step explanation:
We can determine the characteristic equation all we have to do is:
let y' = m, hence y" = m², y'" = m³
Therefore, the higher-order differential equation becomes:
m³ + 3m² + 3m + 1 = 0
(m + 1)(m² + 2m + 1) = 0
(m + 1)(m + 1)(m + 1) = 0
(m + 1)³ = 0
m = -1, -1, -1
Therefore the general solution is given as:
[tex]y(x)=c_1e^{-x}+c_2xe^{-x}+c_3x^2e^{-x}[/tex]
[tex]c_1,c_2,c_3\ are\ constants.[/tex]
What is the missing expression that would make the left-hand-side of the equation equal to the right-hand-side?
[tex]\frac{???}{x-2}/\frac{x^{2}-1 }{x^{2} -4x+4} =\frac{5(x-2)}{x-1}[/tex]
Given:
The equation is
[tex]\dfrac{???}{x-2}/\dfrac{x^2-1}{x^2-4x+4}=\dfrac{5(x-2)}{x-1}[/tex]
To find:
The missing value.
Solution:
Let the missing value be k.
[tex]\dfrac{k}{x-2}/\dfrac{x^2-1}{x^2-4x+4}=\dfrac{5(x-2)}{x-1}[/tex]
[tex]\dfrac{k}{x-2}\times \dfrac{x^2-2(x)(2)+2^2}{x^2-1^2}=\dfrac{5(x-2)}{x-1}[/tex]
Using the formulae [tex](a-b)^2=a^2-2ab+b^2[/tex] and [tex](a-b)(a+b)=a^2-b^2[/tex].
[tex]\dfrac{k}{x-2}\times \dfrac{(x-2)^2}{(x-1)(x+1)}=\dfrac{5(x-2)}{x-1}[/tex]
[tex]\dfrac{k(x-2)}{(x-1)(x+1)}=\dfrac{5(x-2)}{x-1}[/tex]
Cancel out the common factors from both sides.
[tex]\dfrac{k}{x+1}=5[/tex]
Multiply both sides by (x+1).
[tex]k=5(x+1)[/tex]
Therefore, the missing value is 5(x+1).
In a basketball game, LeBron and Shaq combined to score 72 points. If LeBron scored three times as many points as Shaq, how many points did each player score?
Answer:
Lebron = 24
Shaq = 0
Step-by-step explanation:
x = LeBron
y = Shaq
3(24) + 0 = 72
To multiply two numbers using scientific notation, you would ____ the exponents.
Answer:
add
Step-by-step explanation:
Answer:
Add
Step-by-step explanation:
To multiply numbers written in scientific notation, first multiply the coefficients and then add the exponents.
See if that helps.
Can an opposite and an absolute value of an integer be the same?
Yes and opposite and an absolute value of an integer will be the same.
4+(8/(8-7)+6-12)x10)
The answer is 24, hopes this helps!
Analyzing a System
Solve the system of inequalities.
x² - gpg
v> 2
Which describe the solution set of the given system?
Check all that apply
The solution set is unbounded.
The point (1, 0) is in the solution set.
There is one point of intersection of the boundary
curves
The boundaries of the overlapping region are in the
solution set.
The boundary curves intersect at approximately
(-3,0).
Answer:
A, C, E
Step-by-step explanation:
took the assignment on edge
Answer:
a , c and e
Step-by-step explanation:
got it right on edg ^u^
find the slope and y-intercept of the line
y = -4x-5
Answer:
The slope is -4
The y-int is -5
Step-by-step explanation:
The slope intercept form is structured as:
y= mx + b
Being m is the slope and b is the y-intercept.
Which statement best describes the graph of 2c - 5y=-25 and the graph of y= +5?
Answer:
To easily compare the two linear equations just by looking at the equation, let's rearrange this into the slope-intercept formula: y = mx + b, where m is the slope and b is the y-intercept.
2x - 5y = -25
(-5y = -25x - 2x)-1
5y = 25/5 +2x/5
y = (2/5)x + 5
Thus, the slope is 2/5 and the y-intercept is 5.
y=52x + 5
The slope is 52 and the y-intercept is 5.
Thus, we can say that the two linear equations have the same y-intercept. This is the point in the y=-axis in which the two lines intersect. They must intersect at (0,5).
Step-by-step explanation:
Please help.. I’m stuck on this question
Answer: The answer is 1
Step-by-step explanation: The distance between -7 and -3 is 4 then half the distance in between -7 and -3 is going to be -5 because we just clarified that the distance between -7 and -3 is 4 so we did 4/2 and got 2 so we can figure out whats the distance between each point. Now that we figured that out we can determine what value the blue dot is if the value between each point is 2 then we can make out what the rest of the points on the line. If we from -3 to the blue point that would be 1.
What is a single discount rate and how does it apply to chain discounts?
Answer:
Single discount rates are one off discounts which are given by seller on certain products with certain conditions which most be met for it to apply such conditions can be for buyers who pay in cash, buyers who buy in bulks e.g buy 10 get one free, or for every 5 bought you get a 5% discount e.t.c.
This is related to chain discount because its also a series of discount which is allowed for list price of products or services.
quanto é (a+b) elevado a 3 --(b-c) elevado a 3???
Vamos escrever.
(a.b)³. b.(b.c)² =
a³.b³.b. b².c² =
a³b^6.c² ( forma simplificada)
some please help with this!!
Answer:
h. x=11
i. x=4 1/6 (1/6 is a fraction)
k. x=-8
l. x= 3 1/2 (1/2 is a fractio)
Step-by-step explanation:
Un bombardeo pica, formando ángulo de 53o con la vertical, y abandona una bomba a una altura de 2400 pies. Se observa que el proyectil llega al suelo 5 segundos después de
890 g of copper is mixed with 100 g of zinc to form brass. The density of copper is 8.9 g/cm³ and the density of zinc is 7.1 g / cm ³ .
a ) What is the volume of copper and zinc used to make the brass ?
b ) Calculate the density of the brass .
Density ρ is equal to mass m per unit volume v, or
ρ = m / v
Solve for volume:
v = m / ρ
(a) 890 g of copper, which has a density of 8.9 g/cm³, has a volume of
v = (890 g) / (8.9 g/cm³) = 100 cm³
100 g of zinc, with density 7.1 g/cm³, has a volume of
v = (100 g) / (7.1 g/cm³) ≈ 14.08 cm³
(b) The density of brass is then
ρ = (890 g + 100 g) / (100 cm³ + 14.08 cm³) ≈ 8.68 g/cm³
Plot point F so that △ABC ≅ △FGH. Identify a sequence of rigid motions that maps △ABC onto △FGH and use a theorem to complete the explanation of why the triangles are congruent.
Answer:
Step-by-step explanation:
Point F is plotted at (5, 4)
Translate ΔABC so that point B maps to point G.
B(1, -1) → G(0, 3)
Rule for the translation,
(x, y) → [x - 1, y + 4]
By this rule,
Point C will map the point,
C(-1, -2) → C'[(-1 - 1), (-2 + 4)]
→ C'(-2, 2)
A(-4, 0) → A'[(-4 - 1), (0 + 4)]
→ A'(-5, 4)
Now reflect these points across y-axis.
Rule for the reflection across y-axis,
(x, y) → (-x, y)
Points after reflection will be,
A'(-5, 4) → F(5, 4)
B'(0, 3) → G(0, 3)
C'(-2, 2) → H(2, 2)
Distance formula,
d = [tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
AB = [tex]\sqrt{(1+4)^2+(-1-0)^2}[/tex] = [tex]\sqrt{26}[/tex]
BC = [tex]\sqrt{(-2+1)^2+(-1-1)^2}[/tex] = [tex]\sqrt{5}[/tex]
CA = [tex]\sqrt{(-4+1)^2+(-2-0)^2}[/tex] = [tex]\sqrt{13}[/tex]
FG = [tex]\sqrt{(5-0)^2+(4-3)^2} =\sqrt{26}[/tex]
GH = [tex]\sqrt{(2-0)^2+(2-3)^2}=\sqrt{5}[/tex]
HF = [tex]\sqrt{(4-2)^2+(5-2)^2}=\sqrt{13}[/tex]
AB ≅ FG, BC ≅ GH, CA ≅ HF
By the SSS property Triangle congruence theorem, ΔABC ≅ ΔFGH
What is the perimeter of the composite figure? Round to the nearest tenth
Answer:
123.8 units
Step-by-step explanation:
The vertices of the polygon has been labelled ABCDEF, as shown in the diagram attached below.
Perimeter of the Polygon = [tex] \overline{AB} + \overline{BC} + \overline{CD} + \overline{DE} + \overline{EF} + \overline{FA} [/tex]
[tex] \overline{AB} [/tex] = |-12 - 24| = |-36| = 36 units
[tex] \overline{BC} [/tex]: calculate the distance between B(24, 16) and C(15, 3) using the distance formula.
[tex] \overline{BC} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
[tex] \overline{BC} = \sqrt{(24 - 15)^2 + (16 - 3)^2} [/tex]
[tex] \overline{BC} = \sqrt{(9)^2 + (13)^2} [/tex]
[tex] \overline{BC} = \sqrt{81 + 169} = \sqrt{250} [/tex]
[tex] \overline{BC} = 15.8 units [/tex]
[tex] \overline{CD} [/tex] = |6 - 15| = |-9| = 9 units
[tex] \overline{DE} [/tex] = |3 -(-12)| = |-15| = 15 units
[tex] \overline{EF} [/tex] = |-12 - 6| = |-18| = 18 units
[tex] \overline{FA} [/tex] = |18 -(-12)| = 30 units
Perimeter = 36 + 15.8 + 9 + 15 + 18 + 30 = 123.8 units
Mason made 3/4 of a pound of trail mix. If he puts 3/8 of a pound into each bag, how many bags can Mason fill?
A. half of a bag
B. 3 bags
C. 4 bags
D. 2 bags
Answer:
3/4^ 8/3= 24/12= 2 so d.2bags
Was this helpful?
Does the following road sign have rotational symmetry?
Yes
No
Answer:
YES
Step-by-step explanation:
ITS JUST YES
Graph. f(x) = |2x+2| - 1
Answer:
I included the graph for you, hope this helps!
Step-by-step explanation:
Which is the quotient and remainder, written as partial fractions, of 2x^3-x^2+x+5/x^2+3x+2
it's C
Answer: thank yuu
Step-by-step explanation:
Write an equation in slope-intercept form of the line that passes through (4, 6) and (9,2)
Answer:
m=0
b=-9
Step-by-step explanation:
Slope is equal to the change in
y
over the change in
x
, or rise over run.
m
=
change in y
change in x
The change in
x
is equal to the difference in x-coordinates (also called run), and the change in
y
is equal to the difference in y-coordinates (also called rise).
m
=
y
2
−
y
1
x
2
−
x
1
Substitute in the values of
x
and
y
into the equation to find the slope.
m
=
−
9
−
(
−
9
)
2
−
(
−
4
)
The equation of the line is equal to y=-5x/4 +c
What is the slope-intercept form of a line?The slope-intercept form of a line is represented by y=mx+c where m=slope and c is the y-intercept of the line
Given here: The given line passes through (4,6) and (9,2)
We know the slope intercept form is given by
y=mx+c
putting (4,6) in the equation we get
6=4m+c
Again substituting (9,2) in the equation we get
2=9m+c
Thus solving this two equations we get the value of m=-5/4 and c=11
Hence, The equation of the line is equal to y=-5x/4 +c
Learn more about the slope intercept form here:
https://brainly.com/question/29146348
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The integrity of financial statement presentations and disclosures is enhanced when
a) The financial statements are audited by a CPA.
b) The financial statements are prepared in an environment that includes a strong system of internal control.
c) The financial statement preparers have the appropriate education and experience necessary.
d) All of the above.
Answer:
All of the above
Step-by-step explanation:
In this question, we want to select which of the options can enhance the integrity of financial statements preparations and disclosure.
The correct answer is the last option which is all of the above
The last option is correct because each of the individual options above it will enhance the integrity.
A financial statement with integrity is one which is audited by the CPA, prepared in an environment with strict interval control and overall the people who are in charge of preparing it are experienced people
Jon reads 23 pages per hour. In all. How many hours of reading will Jon have to do this
week in order to have read a total of 46 pages?
Answer:
he would have to read 3.307692308 hour
Step-by-step explanation:
Ace Heating and Air Conditioning Service finds that the amount of time a repairman needs to fix a furnace is uniformly distributed from 5 and 9 hours. . Let x = the time needed to fix a furnace.
Required:
a. What is the probability that it takes the repairman more than 7 hours to fix a furnace?
b. Find the probability that a randomly selected furnace repair requires less than 3 hours.
c. Find the 30th percentile of furnace repair times.
d. The longest 25% of repair furnace repairs take at least how long? (In other words: Find the minimum time for the longest 25% of repair times.) What percentile does this represent?
e. Find the mean and standard deviation
Answer:
a
[tex]P(X > 7) = 0.5[/tex]
b
[tex]P(X < 3) = -0.5[/tex]
c
[tex]x = 6.2 \ hours[/tex]
d
[tex]x_1 = 8 \ hours[/tex]
e
Mean [tex]\mu = 7[/tex]
Standard deviation [tex]s \approx 1.1547[/tex]
Step-by-step explanation:
From the question we are told that
The amount of time a repairman needs to fix a furnace is uniformly distributed from 5 and 9 hours
Generally the probability that it takes the repairman more than 7 hours to fix a furnace is mathematically represented as
[tex]P(X > 7) = \frac{9- 7}{9-5}[/tex]
=>[tex]P(X > 7) = 0.5[/tex]
Generally the probability that a randomly selected furnace repair requires less than 3 hours. is mathematically represented as
[tex]P(X < 3) = \frac{3 -5}{9-5}[/tex]
=>[tex]P(X < 3) = -0.5[/tex]
Generally the 30th percentile of furnace repair times is mathematically represented as
[tex]30^{th} \ percentile = \frac{x - 5}{9-5}[/tex]
=> [tex]0.3 = \frac{x - 5}{9-5}[/tex]
=> [tex]x = 6.2 \ hours[/tex]
Generally the time taken for the longest 25% of furnace repair is mathematically evaluated as
[tex]75^{th} \ percentile = \frac{x_1 - 5}{9-5}[/tex]
Here making use of the [tex]75^{th}[/tex] because we are considering duration that fall with the top [tex]25^{th}[/tex]
=> [tex]0.75 = \frac{x_1 - 5}{9-5}[/tex]
=> [tex]x_1 = 8 \ hours[/tex]
Generally the mean is mathematically represented as
[tex]\mu = \frac{5 + 9 }{2}[/tex]
=> [tex]\mu = 7[/tex]
Generally the standard deviation is mathematically represented as
[tex]s = \sqrt{ \frac{(9- 5)^2}{12} }[/tex]
=> [tex]s \approx 1.1547[/tex]
Algebra II
Find the product (multiply).
answer:
Answer:
3 m^3 - 26 m^2 + 45 m - 70
Step-by-step explanation:
Applying distributive property we get:
3 m^3 - 5 m^2 + 10 m - 21 m^2 + 35m - 70
combining like terms:
3 m^3 - 26 m^2 + 45 m - 70
Susan has two pieces of ribbon, one 18 inches long and the other 12 inches long. To decorate an album, she wants to cut them up to produce many pieces of ribbon that are all of the same length, with no ribbon left over. What is the greatest length, in inches, that she can make them? PLEASE HURRY IM TAKING A TIMED TEST!!
Answer:
I'm pretty sure its 12 inches
Step-by-step explanation:
(8,3) (5,6) what is slope??
Answer:
-1
Step-by-step explanation:
List 5 significant advances in architecture Eastern Indians made
Answer:
Primarily, the Indian temple architecture has been classified into three broad types, namely; Nagara or the northern style, Vesara or mixed style, and the Dravida which is the southern style. All these styles carry their unique regional influences and lineages.
Step-by-step explanation:
A music website sold 68 single songs and 40 albums today. The number of single downloads has been increasing by 12 each day. The number of album downloads has been decreasing by 2 each day. If these trends continue, in how many days will the number of single downloads be 5 times the number of album downloads?
Answer:
In 66 days will the number of single downloads be 5 times the number of album downloads
Step-by-step explanation:
For the music website, we know 68 single songs and 40 albums were sold today.
The number of single downloads increases by 12 each day. This means that in t days, there will be:
68 + 12t single downloads
The number of album downloads increases by 2 each day. In t days, there will be:
40 + 2t
We need to find when the following condition is met:
68 + 12t = 5(40 + 2t)
Operating:
68 + 12t = 200 + 10t
Rearranging:
12t - 10t = 200 - 68
2t = 132
Solving:
t=132 / 2
t = 66 days
In 66 days will the number of single downloads be 5 times the number of album downloads