The homogeneous linear ODE
[tex]y^{(4)} + y''' + y'' = 0[/tex]
has characteristic equation
[tex]r^4 + r^3 + r^2 = r^2 (r^2 + r + 1) = 0[/tex]
with a double root at [tex]r=0[/tex] and two complex roots
[tex]r^2 + r + 1 = 0 \implies r = -\dfrac{1 \pm i\,\sqrt3}2[/tex]
Hence the characteristic solution is
[tex]y = C_1 e^{0x} + C_2x e^{0x} + C_3 e^{((-1/2)-i(\sqrt3/2))x} + C_4 e^{((-1/2)+i(\sqrt3/2))x}[/tex]
[tex]y = C_1 + C_2x \\\\ ~~~~~~~~~~ + C_3 e^{-x/2} \left(\cos\left(\dfrac{\sqrt3}2x\right) - i\, \sin\left(\dfrac{\sqrt3}2x\right)\right) \\\\ ~~~~~~~~~~ + C_4 e^{-x/2} \left(\cos\left(\dfrac{\sqrt3}2x\right) + i\,\sin\left(\dfrac{\sqrt3}2x\right)\right)[/tex]
[tex]y = C_1 + C_2x + C_3 e^{-x/2} \cos\left(\dfrac{\sqrt3}2x\right) + C_4 e^{-x/2} \sin\left(\dfrac{\sqrt3}2x\right)[/tex]
draw a translation of triangle ABC that is 2 units down and 3 units to the left
Answer: If there is a drawing then try copy that exact drawing but move it 2 units or squares down and 3 units or squares to the left
Step-by-step explanation:
Initial estimates of the probabilities of events are known as _____ probabilities.
Initial estimates of the probabilities of events are known as Prior Probabilities.
Prior Probabilities can be defined as the probability of the event before the event takes place.
For Example ,Let there be three wells X,Y,Z with water in it . it is given that one of the wells have the water that is fit for drinking. So the prior probability that Well Z can have drinking water is 1/3 i.e. 0.333 .
Therefore , the Initial estimates of the probabilities of events are known as Prior Probabilities.
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. The width of a rectangular plot of land is one- quarter of its length. If the perimeter is 360 m, find: a. The length of the land.
Answer:144
Step-by-step explanation: so if the width is a quarter of the length, then there are 4 parts to both length sides, plus another 2 parts ( one for each width side), 10parts total. 360/10=36, so 1 part equals 36 for the width, which multiplied by 4 is 144
What is the simplified form of this expression 4(2x-5y)-3x
Answer:
5x - 20y
Step-by-step explanation:
4(2x - 5y) - 3x ← multiply each term in the parenthesis by 4
= 8x - 20y - 3x ← collect like terms
= 8x - 3x - 20y
= 5x - 20y
Answer:
5x - 20y
Step-by-step explanation:
Hello!
Distribute the terms outside of the parenthesis to the terms inside.
Simplify4(2x - 5y) - 3x4(2x) +4(-5y) - 3x8x - 20y - 3x5x - 20yThe simplified expression is 5x - 20y.
Simplify (c4)−5
please please helpppp
Answer: Reformatting the input :
Changes made to your input should not affect the solution:
(1): "c5" was replaced by "c^5". 1 more similar replacement(s).
STEP
1
:
c4
Simplify ——
c5
Dividing exponential expressions :
1.1 c4 divided by c5 = c(4 - 5) = c(-1) = 1/c1 = 1/c
Final result :
1
—
c
Step-by-step explanation: hope this helps
1.
Write the numbers of dots in the next three steps of
this pattern:
3
6
10
15
2. What i
Answ
Answer:
your answer is 21
Step-by-step explanation:
The gap between 3 and 6 is 3 the gap between 6 and 10 is 4 the gap between 10 and 15 is 5 so your answer will be 6 more than 15 which is 21
your welcome
Solve for t.
|-3t - 1| - 3 = 3
Answer:
32028464937583748374
I GIVE BRAINLIEST FOR ALL QUESTIONS
The lengths of the sides of a triangle are 3, 4, 5. Can the triangle be a right triangle?
yes
no
Answer: No.
Step-by-step explanation: The sides are all different. Therefore, it cannot be a right angle.
(i think)
Answer:
Yes.
Step-by-step explanation:
By converse of Pythagoras' Theorem,
[tex]5 {}^{2} = 4 {}^{2} + 3 {}^{2} [/tex]
25 = 16 + 9
Therefore, the triangle is a right-angled triangle.
Hope this helped! ^^
Question 3 (1 point)
What is the correct solution for the following addition, reported to the correct
number of significant digits? Assume all numbers are measurements.
3001+ 20.3 +0.009
a) 3021
b) 3021.3
c) 3021.309
d) 3021.30
Answer:
I think it's C but I'm not 100% sure
Use the Angle Addition Postulate to find the measure of the unknown angle.
Answer:
Hey there!
Step-by-step explanation:
This is ur answer....
60 + 120 = 180DEF = 180Hope it helps!
Brainliest pls!
Follow me!
Play equation 19+0.15p= c gives the cost c in dollars that a store charges to deliver an appliance that weighs p pounds. use the equation and a table to find the weight of an appliance that cost $37 to deliver.
The appliance weighs ?? pounds.
Using the protractor tool on the right, choose the image that represents an angle measuring 55°.
Answer:
I think it's C.
Step-by-step explanation:
hope you get it right
A direct, consistent relationship between the independent variable and the dependent variable?
A direct, consistent relationship between the independent variable and the dependent variable is called "dose-response relationship."
What is a dose-response relationship?The effect on an organism and, more specifically, the risk of a defined outcome caused by a set quantity of an agent or level of exposure.
Some key features regarding the dose-response relationship are-
A dose-response relationship is considered the strongest proof for a causal relationship between exposure and outcome. Even in the absence of a dose-response relationship, the possibility of a causal relationship can not be discounted. Time can have a significant impact on dose-response relationships. For example, when examining the relationship between exposure and outcome, the time to response can be impacted by a latent period between outcome and exposure. If the effects have been measured too shortly after the exposed, no effect is seen, even if the exposure is the cause of the outcome.To know more about dose-response relationship, here
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In a students School, out of 4000 40% are & Boys. find the Percantage of girls Also find the no of girls. answer please
For the given question;
The total number of school students = 4000.
Percentage student of boys; 40%.
Thus the percentage of girls; 100 - 40 = 60
Thus, the total percentage of girls are 60%.
For finding the number of girls find the 60% of the total school students.
= 60% of 4000
= 60% × 4000
= (60×4000)/100
= 60×40
= 2400
Thus, the number of school girls are 2400.
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one of the subsets of set n and set g is a Ø true or false?
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
An empty set is subset of each and every possible set, as it has no elements in it, which is why the given statement is " True "
The 3-sigma limits for a process whose distribution conforms to the normal distribution includes _______ of the observed values, in the long run.
The 3-sigma limits for a process whose distribution conforms to the normal distribution include 99.74% of the observed values, in the long run. This means that if you have a process that is normally distributed, then, in the long run, 99.74% of the values will fall within three standard deviations of the mean.
This is an important concept to understand because it can be used to help control a process. For example, if you know that 99.74% of the values will fall within three standard deviations of the mean, then you can set up control limits that correspond to those values. This can help you ensure that your process stays within the desired range.
Understanding the 3-sigma limits can help you better control your process and ensure that it produces the desired results.
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Carls weight w is 76. 12kg tanya says that w ≥ 76.12 is tanya correct
Answer:
Step-by-step explanation:
If Carl weighs 76.12kg, and Tanya says w (weight) is ≥ 76.12 kg (greater than or equal to), Carl is equal to 76.12, meaning Tanya is Correct.
In a school election there were four candidates: Tom, Rebecca, Olly and Wendy.
540 students voted in the election.
5% of the votes were for Tom
of the votes were for Rebecca
The ratio of the number of votes for Olly to the number of votes to Wendy was 1:2
How many votes were for Wendy?
5% of votes were for Tom: 27
2/9 of the votes were for Rebecca: 114
213 votes are for Wendy
Use structure find the perimeter of equilateral triangle klm given the vertices k(-2, 1) and m(10, 6).
Perimeter of the equilateral triangle KLM with vertices K(-2 ,1) and M (10,6) is equal to 39 units.
As given in the question,
Coordinates of vertices K(-2,1) and M(10,6)
KM = [tex]\sqrt{ (10-(-2)^{2} +(6-1)^{2} }[/tex]
= [tex]\sqrt{12^{2}+5^{2} }[/tex]
= 13units
In equilateral triangle KL = LM = KM = 13 units
Perimeter of equilateral triangle KLM = 13 +13 +13
= 39 units
Therefore, perimeter of the equilateral triangle KLM with vertices K(-2 ,1) and M (10,6) is equal to 39 units.
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Given that f(x)=x^2+4x-32f(x)=x
2
+4x−32 and g(x)=x-4g(x)=x−4, find (f+g)(x)(f+g)(x) and express the result in standard form
Answer: So after solving and simplifying terms equation is[tex]x^4+10x^3-47x^2-360x+1296[/tex]
Step-by-step explanation: Given we have two equations f(x) =[tex]x^{2} +4x-32[/tex] and g(x) = [tex]x-4[/tex]
we have been asked to find ( f +g)(x) that is f(x)+g(x)
So first we add them [tex]x^{2} +4x-32 + x-4[/tex]
So we have an equation that is: [tex]x^{2} +5x-36[/tex]
Then we need to multiply both
[tex](x^2+5x-36)(x^2+5x-36)[/tex]
So we get[tex]\left(x^2+5x-36\right)^2[/tex]
Distribute parentheses
[tex]x^2x^2+x^2\cdot \:5x+x^2\left(-36\right)+5xx^2+5x\cdot \:5x+5x\left(-36\right)-36x^2-36\cdot \:5x-36\left(-36\right)[/tex]
On simplifying
[tex]x^4+10x^3-47x^2-360x+1296[/tex]
So standard form of result is [tex]x^4+10x^3-47x^2-360x+1296[/tex] .
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This figure is composed of a parallelogram and a trapezoid.
32 cm
26 cm
40 cm
T
16 cm
1
What is the area of the figure in square centimeters?
Answer:
944cm²
Step-by-step explanation:
Area = Area of parallelogram + Area of trapezoid
Area of parallelogram= l× b= 16×26= 416cm²
Area of trapezoid= h/2(a+b)
where a=26cm, b=40cm, h=16cm
Area of trapezoid= 16/2(26+40)=8(66)=528cm²
Area= 416+528=944cm²
hat is the domain of the given function? {(3, –2), (6, 1), (–1, 4), (5, 9), (–4, 0)} {x | x = –4, –1, 3, 5, 6} {y | y = –2, 0, 1, 4, 9} {x | x = –4, –2, –1, 0, 1, 3, 4, 5, 6, 9} {y | y = –4, –2, –1, 0, 1, 3, 4, 5, 6, 9}
Option 1, {x | x = –4, –1, 3, 5, 6} is the domain of the given function.
For any function, domain is the set of all input values that are accepted by the given function. For example, if there is a function, say f(x) = x + 2, then all the values of x will make up the domain of f(x).
Here, we are given a function {(3, –2), (6, 1), (–1, 4), (5, 9), (–4, 0)}
In this case, all the input values = all the x values
and all the output values = all the y values
Thus, the domain of the given function will be a set containing the following x values-
3, 6, -1, 5, -4
Arranging these values in the ascending order we get,
-4, -1, 3, 5, 6
Therefore, the domain of the function can be represented as {x | x = –4, –1, 3, 5, 6}.
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Modeling real life the average distance from earth to the sun is 92.95 million miles. the actual distance varies from the average by up to 1.55 million miles. write and solve an absolute value equation to find the minimum and maximum distance from earth to the sun.
The minimum and maximum distance from the earth to the sun are 91.4 and 94.5 million miles respectively.
What is absolute value?Absolute values are the value of any digit without considering the sign.
So all negative values will be considered positive for absolute value.
For example, the absolute value of -2 will be 2 and the absolute value of -7 will be 7.
Given that,
The average distance from the earth to the sun is 92.95 million miles.
Actual is varies by 1.55 million miles.
Minimum value = | 92.95 - 1.55 | = 91.4 million mile
Maximum value = | 92.95 +1.55 | = 94.5 million mile
Hence "The minimum and maximum distance from the earth to the sun are 91.4 and 94.5 million miles respectively".
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Loren already knows that he will have $500,000 when he retires. If he sets up a payoutannuity for 30 years in an account paying 10% interest, how much could the annuity provideeach month?
The annuity could pay $221.19 per month.
ANNUITY FORMULA: [tex]P_t=\frac{d\left[\left(1+\frac{s}{n}\right)^{n t}-1\right]}{\frac{s}{n}}[/tex]
Where,
[tex]P_t[/tex] is the account balance after t years.The regular deposit (the amount you deposit each year or month) is denoted by d.r denotes the annual interest rate in decimal form.n represents the number of compounding periods in a year.t consider the number of years.So,
Loren anticipates having $500,000 when he retires.
[tex]P_t[/tex] = $500,000He establishes a 30-year payout annuity at a 10%interest.
t = 30 years r = (10/100) = 0.1Each month, the annuity could provide
n = 2In the formula, replace the above values as follows:
500,000 [tex]=\frac{d\left[\left(1+\frac{1.1}{12}\right)^{(12)(30)}-1\right]}{\frac{11-1}{12}}[/tex]500,000 [tex]=\frac{d\left[(1.00833333)^{300}-1\right]}{0.00833333}[/tex]500,000 = d [2260.487925]Now, divide both sides by: 2260.487925
d = $221.19Therefore, the annuity could pay $221.19 per month.
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Write the equation of a circle in STANDARD FORM given that the center lies at
(-13, 13) on the graph and the circle has a radius of 4.
The equation of the circle in the standard form is:
(x + 13)² + (y - 13)² = 4².
What is defined as the equation of the circle?The equation for a circle with (h, k) center and radius r is as follows:(x - h)² + (y - k)² = r².This is the equation's standard form. And thereby, if we learn the coordinates of the circle's center and radius, we can quickly find its equation.For the given question;
The centre of the circle lies at (-13, 13).
Thus, (h. k) = (-13, 13).
The radius 'r' of the circle is 4 units.
Put the values in the standard form.
(x - (-13))² + (y - 13)² = 4²
(x + 13)² + (y - 13)² = 4² is the (standard form)
Therefore, the equation of the circle with radius 4 in the standard form is represented as: (x + 13)² + (y - 13)² = 4²
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6. You just had surgery on your knee. As part of rehabilitation your physical
therapist wants you to walk 1 minute on day 1 and double your time every day. How
many minutes will you be walking on day 7?
64 minutes
Step-by-step explanation:
1x2=2 it day one
2x2=4 it day two
and more
32x2=64 it day 7
t = 1,000 + 18h
in the equation above, T represents Brittany's total take home pay, in dollars...
Answer:
c. 55
Step-by-step explanation:
because if you divide the numbers you'll get this
If p = 2 3 , point b has a weight of 2, and point c has a weight of 4, find the weight of point a.
A fixed point Weight is the ideal weight for our bodies in order to function optimally and feel their best.
What are weighted points?"The set point is established over time," Harrison explains. "It's a complicated thing, but it appears to be your body's attempt to regulate itself, which results in a certain weight."
Even if set point theory is correct, it is possible to lose weight and keep it off. Avoiding fad diets and gradually losing weight may change your set point. It may allow your body to adjust to your new eating habits. You may be more successful if you seek the assistance of a therapist or a dietitian.
A fixed point Weight is the ideal weight for our bodies in order to function optimally and feel their best. It is the weight that our bodies can easily maintain—no micromanaging, counting calories, weighing food, and so on.
The point of weight A has been given in the figure.
The complete question is;
If p = 2/3, point b has a weight of 2, and point C has a weight of 4, find the weight of point A.
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A manufacturer determines that the cost of making a computer component is $4.252525........ Write the repeating decimal cost as a fraction and as a mixed number.
The fraction is $[tex]\frac{421}{99}[/tex] and the mixed fraction is $4 [tex]\frac{25}{99}[/tex]
The cost of manufacturing computer components is $4.25252525
To find the repeating decimal; cost as a fraction
Since we have two digits repeating decimal place, we multiply 100 and shift two digits
⇒$4.252525×100=$425.252525{using operation multiplication}
Now subtract the original number from this
⇒$425.252525-$4.252525=$421.00000 {using operation subtraction}
Now,
100×(fraction)-(fraction)=$421.00000 {using operation subtraction}
99(fraction)=$421.00000{ using operation division}
The Fraction=$[tex]\frac{421}{99}[/tex]
The mixed fraction is $4 [tex]\frac{25}{99}[/tex]
Therefore, The fraction is $[tex]\frac{421}{99}[/tex] , and the mixed fraction is $4 [tex]\frac{25}{99}[/tex]
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What is the equation in slope-intercept form of the line that passes through the points (12, -34) and (10, -28)?
Answer:
[tex]y=-2x+2[/tex]
Step-by-step explanation:
1) Determine Slope
[tex]\frac{y_2-y_1}{x_2-x1}[/tex] = [tex]\frac{-28-(-34)}{10-12}[/tex] = [tex]\frac{6}{-2}[/tex] = -3
2) Use point slope form to create equation
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-(-28)=-3(x-10)[/tex]
[tex]y+28=-2x+30[/tex]
[tex]y=-2x+2[/tex]
