Answers
Correct option is E, The roots of Auxiliary equation are √6 and -√6.
The solution of an nth-order differential equation or difference equation depends on an algebraic equation of degree n called the characteristic equation (or auxiliary equation) in mathematics.
The auxiliary equation, however, lacks true roots. Consider the simple harmonic equation y + y = 0, which has solutions and was given that name because of how it relates to the vibration of a musical tone. Y2(t) = cos t and Y1(t) = sin t. r2 + 1 = 0 is the auxiliary equation for the straightforward harmonic equation.
The Auxiliary form of the given equation is m² - 6 = 0
Using identity a² - b² = (a - b) (a + b),
⇒ The equation becomes (m - √6)(m+√6) = 0
⇒ either m = √6 or m = -√6
Hence, The roots of Auxiliary equation are √6 and -√6.
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Related Questions
A rectangle is 6 meters long and 4 meters wide. What is the area
of the rectangle?
Answers
Answer:
the rectangles area is 24 meters
Step-by-step explanation:
area = length x width
length is 6 using the words long and width is 4
Answer:
area = 24 cm²
Step-by-step explanation:
The area of a rectangle can be found using the formula:
[tex]\boxed {area = length \times width}[/tex].
Substituting the values into the equation:
[tex]area = 6 \space\ cm\times 4 \space\ cm[/tex]
⇒ [tex]\bf 24 \space\ cm^2[/tex]
Find the sum of the geometric series given a1=−1, r=2, and n=7
A. -127
B. -116
C. 1
D. -118
Answers
Answer:
A
Step-by-step explanation:
the sum to n terms of a geometric series is
[tex]S_{n}[/tex] = [tex]\frac{a_{1}(r^{n}-1) }{r-1}[/tex] , then for n = 7
S₇ = [tex]\frac{-1(2^{7}-1) }{2-1}[/tex] = [tex]\frac{-1(128-1)}{1}[/tex] = - 1 (127) = - 127
The sum of three consecutive integers is -15.
If 1 is added to each integer, what is the product.
of the three resulting integers?
Answers
The board of education has decreed that a maximum student teacher ratio in a classroom be 18:1
If the current school has 235 total students then what is the minimum number if teachers that must be working in your school ?
Answers
Answer:
235÷18=
how many classes of 18 students for each teacher
Step-by-step explanation:
Membership selection. A town council has members, Democrats and Republicans.
(A)
If the president and vice-president are selected at random, what is the probability that they are both Democrats?
(B)
If a 3-person committee is selected at random, what is the probability that Republicans make up the majority?
The probability that they are both Democrats is approximately
enter your response here.
(Type a decimal. Round to three decimal places.)
Answers
Using the hypergeometric distribution, the probabilities are given as follows:
a) 0.2 = 20%.
b) 0.5539 = 55.39%.
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.Researching this problem on the internet, it is found that the council has 15 members, of which 7 are Democrats and 8 are Republicans.
Item a:
The parameters are:
N = 15, n = 2, k = 7.
The probability is P(X = 2), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,15,2,7) = \frac{C_{7,2}C_{8,0}}{C_{15,2}} = 0.2[/tex]
Item b:
At most one Democrat, with n = 3, hence:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]
In which:
[tex]P(X = 0) = h(0,15,3,7) = \frac{C_{3,0}C_{8,3}}{C_{15,3}} = 0.1231[/tex]
[tex]P(X = 1) = h(1,15,3,7) = \frac{C_{3,1}C_{8,2}}{C_{15,3}} = 0.4308[/tex]
Then:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.1231 + 0.4308 = 0.5539[/tex]
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The following table shows Jace's earnings based on the number of hours that he works.
Number of hours 111 222 333
Jace's Earnings \$20$20dollar sign, 20 \$30$30dollar sign, 30 \$40$40dollar sign, 40
Are Jace's earnings proportional to the number of hours that he works?
Answers
Answer:
no
Step-by-step explanation:
because no
Fill in the blank
Timothy runs a public transportation service in his town. He has learned from his accountant that his organization is a liable to a special kind of tax. Which tax would Timothy have to pay from his organization?
Timothy would have to pay the _______ tax for his transportation service.
Answers
Answer:
road
Step-by-step explanation:
Given the drawing, what would the value of x need to be in order
for it to be true that m ||n?
4x + 18
m
7x-21
Be sure to show all calculations and algebraic steps in your re-
sponse.
Hint: What must be true about alternate exterior angles in order
for lines to be parallel?
Answers
[tex]4x + 18 = 7x - 21 \\ 18 + 21 = 7x - 4x \\ 39 = 3x \\ x = \frac{39}{3} = 13 [/tex]
solve the system of equations. y=3x+2 y=x^2-4+2
Answers
The solutions to the system of equations are (4, 15) and (-1,-1)
How to solve the system of equations?The system of equations is given as:
y=3x+2
y=x^2-4+2
Substitute y=3x+2 in y=x^2-4+2
3x + 2=x^2-4+2
Simplify
x^2 - 3x - 4 = 0
Expand
x^2 + x - 4x - 4x = 0
Factorize
x(x + 1) - 4(x + 1) = 0
This gives
(x - 4)(x + 1) = 0
Solve for x
x = 4 and x = -1
Substitute these values in y=3x+2
y = 3(4)+2 = 15
y = 3(-1)+2 = -1
Hence, the solutions to the system of equations are (4, 15) and (-1,-1)
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PLEASE help me with this question, and preferably leave your handwritten answer
(Easier for me to understand) but typed is also ok :)
Help is greatly appreciated!!
Answers
Using a system of equations, it is found that there were 100 students at the bus stop.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Number of boys in the bus stop.Variable y: Number of girls in the bus stop.Considering the first paragraph, the equation is:
[tex]\frac{x}{y - 25} = \frac{3}{2}[/tex]
Considering the second paragraph, the equation is:
y - 25 = x - 15.
Hence:
y = x + 10.
Replacing on the first equation:
[tex]\frac{x}{x - 15} = \frac{3}{2}[/tex]
3x - 45 = 2x
x = 45.
y = x + 10 = 55.
The total number was:
45 + 55 = 100.
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An agriculture company is testing a new product that is designed to make plants grow taller. This can be thought of as a hypothesis test with the following hypotheses.
H0: The product does not change the height of the plant.
Ha: The product makes the plant grow taller.
Is the following an example of a type I or type II error?
The sample suggests that the product does not change the height of the plant, but it actually does make the plant grow taller.
Answers
It is an example of Type I error.
About Type I error
The rejection of a null hypothesis (H0) when it is actually true is a Type I error. It is represented by the following condition,
Failure to reject a null hypothesis when it is true that it is false which is a Type II error.
How is this an example of Type I error?
The given case's hypothesis is described as follows:
H₀: The product has no effect on the plant's height.
Hₐ: The substance causes the plant to enlarge.
The sample claims that the product causes the plant to grow taller, however in reality, it has no effect on the plant's height.
Therefore, the sample recommends rejecting the null hypothesis even though it is true. Consequently, a result, this error is a Type I error.
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If the solutions of f(x)=0 are -1 and 2
then find the solutions of f(x/2)=0
Answers
Answer: -2 and 4
Step-by-step explanation:
Let [tex]t=x/2[/tex].
[tex]f(t)=0 \longrightarrow t=-1, 2\\\\\therefore x=-2, 4[/tex]
question in the picture below
Answers
The doubling time after 4 and 7 years is 400 months and 700 months respectively
How to determine the doubling timeThe formula for finding doubling time is given as;
Doubling time = [tex]t \frac{In 2}{In 1 + \frac{r}{100} }[/tex]
Where t = time = 4 and 7 years
r = rate
For 4 years, we have
Doubling time = [tex]4 * \frac{In 2}{In ( 1 + \frac{0.7}{100}) }[/tex]
⇒ [tex]4 * \frac{In 2}{In 1. 0074}[/tex]
⇒ [tex]4 * \frac{0. 6931}{0. 0074}[/tex]
⇒ [tex]4[/tex] × [tex]93. 66[/tex]
⇒ 374. 65
⇒ 400 months in the nearest hundredth
For 7 years
⇒ [tex]7[/tex] × [tex]93. 66[/tex]
⇒ [tex]655. 62[/tex]
⇒ 700 months in the nearest hundredth
Thus, the doubling time after 4 and 7 years is 400 months and 700 months respectively
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There are 20 students in Mrs. Tanya's class and 24 kids in Mrs. Olga's class. The students need to be placed on teams of equal size with students from only their own class. What's the largest size of a team?
Answers
The largest size of a team according to the task content is; 20 kids.
What is the largest size of a team?It follows from the task content that the population is; 20 students in Mrs. Tanya's class and 24 kids in Mrs. Olga's class.
However, since, the team forming condition states that students be placed on teams of equal size with students from only their own class.
It therefore follows that the largest size of a team is 20 as only 20 students are in Mrs. Tanya's class hence leaving 4 kids in Mrs. Olga's class without a team.
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19) Write the scientific notation of 1
Answers
Answer:
1.0 x 10^0
Step-by-step explanation:
The above works because 10^0 = 1, and 1 x 1 = 1.
Brainliest, please :)
Anyone know the answer please teach me
Answers
Answer: Look at step by step
Step-by-step explanation:
(a) There are 119 stocks that increased in price out of 246 stocks so the probability of selecting a stock that is increased in price is 119/246 = 48.37%
(b) There are 112 stocks where it pays dividends so the probability so the probability of selecting a stock that pays dividends is 112/246 = 45.53%
(c) There are 49 stocks which satisfy the question so the probability is 49/246 = 19.92%
(e) There are 34 stocks which increase in price and pay dividends out of the 119 stocks that increase in price so the probability is 34/119 = 28.57%
(f) Using the same logic as (e), the probability is 85/134 = 63.43%
(g) From the requirements, we see that 49 stocks don't satisfy the requirements, so the probability is (246-49)/246 = 80.08%
Mike, Luke, and Alex each own a white hat marked with the first letter of their name. Winter owns a plain red hat, which is not marked with any letter.
How many ways can the four people wear these four hats so each person is wearing a different hat, and no one is wearing a hat marked with the first letter of their name?
Answers
Answer:switch mikes Luke’s and Alex in between each other and let winter keep her own
Step-by-step explanation:
log a^x² - 9log a³√x simplify
Answers
Answer:
log(a^x^2-27(radicalx))
Step-by-step explanation:
Assuming you have written your question correctly, this is it.
Name the figure below in two different ways.
Y
Symbol:
and
M
A
Answers
The line segment in the figure can be named as: IYM and MYI.
How to Name a Line Segment?If we have three points on a line segment, the point on the middle will be the alphabet in the center when naming the line, while the alphabets of both endpoints can be written either at the beginning or ending.
Given the figure above, Y will be at the center. The endpoints are I and M. Therefore, the line segment can be named as: IYM and MYI.
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A new plasma TV was marked down 20%. The new sale price of the TV was $380. What is the TV’s regular selling price?
Answers
x=regular selling price
X×80/100=380
= X×8/10=380
= 8X=380×10=3800
X=3800/8
X=475
the regular selling price is 475
Before the 20% discount, the TV's regular selling price was $475 as per the concept of percentage.
Let's denote the regular selling price of the plasma TV as "x". When the TV was marked down by 20%, the sale price became $380.
To find the regular selling price, we can set up an equation using the information given:
Sale Price = Regular Selling Price - (Discount Percentage × Regular Selling Price)
$380 = x - (0.20x)
Now, let's solve for "x" (the regular selling price):
$380 = x - 0.20x
$380 = 0.80x
To isolate "x," we divide both sides of the equation by 0.80:
x = $380 / 0.80
x = $475
The regular selling price of the plasma TV is $475.
Therefore, before the 20% discount, the TV's regular selling price was $475. After the discount, the sale price was reduced to $380, which is 20% less than the regular price.
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Otto builds and sells model cars. He made a graph to compare the number of days to the number of model cars. Three of the points form a proportional relationship, but one does not. Which point does not fit in the proportional relationship? Coordinate plane with Number of Days on the x-axis and Number of Model Cars on the y axis. 4 points are plotted in the plane: 2, 1; 4, 2; 6, 2; and 8, 4. A (2, 1) B (4, 2) C (6, 2) D (8, 4)
\
Need HELP ASAP
Answers
Answer:
I have attached a really rough graph!!
Step-by-step explanation:
The point that does not fit in the proportional relationship is (6,2) when we plot the other three points and join the points they will give us a staright line but the point (6,2) isnt lying on that staright line.. Therefore, it does not fit in the proportional relationship!
Answer:
(6,2)
Step-by-step explanation:
the domain of f(x)= logb x is the set of all real numbers true or false pls need now
Answers
Answer: False
Step-by-step explanation:
The only number that makes this impossible to solve is x = 0
Determine whether the relationship is linear, quadratic, or neither by completing each table. Be sure to give
a reason for your choice.
Answers
The 1st table represents a linear as well as the quadratic relationship, the 2nd table represents neither and the 3rd table also represents neither relationship.
Why do the given tables have the above relationship?The first table is having linear as well as quadratic because the 1st table has its first difference equal as well as the second difference is also equal i.e., why it is linear and quadratic respectively.The second table is having neither because 1st difference is not equal to each other as well as 2nd the difference is also not equal.The third table is having neither because 1st difference is not equal to each other as well as 2nd the difference is also not equal to each other. Therefore, the 3rd table is neither.Hence, the 1st table represents a linear as well as a quadratic relationship, the 2nd table represents neither and the 3rd table also represents neither relationship.
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Given the coordinates below, what is the midpoint of AB?
A(-6, -10)
B(2,5)
Answers
Given :
[tex] \: [/tex]
A(-6, -10)B( 2, 5)
[tex] \: [/tex]
[tex] \gray{ \frak{The \: given \: two \: \: points \: are(x_{1 },y_{1})=(−6 , -10)and(x_{ 2 },y_{2} )=( 2,5 )\:}}[/tex]
[tex] \: [/tex]
Let's solve by using midpoint formula :
[tex] \: [/tex]
[tex] \bf \boxed{\color{red}\frak{Midpoint \: \: Formula : {( \: x ,\:y \: ) = }( \frak{ \frac{x_{1 } + y_{1}}{2} , \frac{x_{2 } + y_{2}}{2} )}}}[/tex]
[tex] \: [/tex]
[tex] \large \gray{ \frak{( \: x ,\:y \: ) = }( \frak{ \frac{ -6 + 2}{2} , \frac{ - 10 + 5}{2} )}}[/tex]
[tex] \: [/tex]
[tex] \: \large \gray{ \frak{( \: x ,\:y \: ) = }( \frak{ \frac{ -4}{2} , \frac{ - 5}{2} )}}[/tex]
[tex] \: [/tex]
[tex]\large \gray{ \frak{( \: x ,\:y \: ) = }( \frak{ \cancel\frac{ -4}{2} , \cancel\frac{ - 5}{2} )}}[/tex]
[tex] \: \: [/tex]
[tex] \underline{ \boxed{ \large \red{ \frak{option \: d }( \frak{ - 2, - 2.5)}}}}✓[/tex]
Hope Helps! :)
The RLX Company just paid a dividend of $2.85 per share on its stock. The dividends are expected to grow at a constant rate of 4.5 percent per year, indefinitely. Assume investors require a return of 10 percent on this stock. What is the current price?
Answers
The current stock price is $54.15.
Given that RLX Company just paid a dividend of $2.85 per share on its stock and dividends are expected to grow at a constant rate of 4.5 percent per year, indefinitely.
Stock valuation alludes to the valuation of the natural worth per portion of an organization's stock which can help the organization in deciding its reasonable worth in case of twisting up or consolidation. One of the models used to esteem the stock cost is the profit development model. It expects the cost of the stock to be the current worth representing things to come profits of the stock accepted to develop at a consistent rate.
Dividend (D0) = $2.85
Growth rate (g) = 4.5%
Required return (r) = 10%
Firstly, we have to calculate the value of the current stock price.
The current stock price can be calculated by using the dividend growing model.
[tex]\begin{aligned}\text{Current stock price}&=\frac{D_{0}\times(1+g)}{r-g}\\ &=\frac{2.85\times (1+0.045)}{0.10-0.045}\\ &=\frac{2.85\times 1.045}{0.055}\\ &=\frac{2.97825}{0.055}\\ &=54.15\end[/tex]
Hence, the current stock price when dividend of $2.85 are expected to grow at a constant rate of 4.5 percent per year, indefinitely is $54.15.
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Solution for the attached question below
Answers
The solution to the question is 265.
What is the logarithm of a number?Logarithm of a number A is the exponent or power or index n, a given number called the base B would be raised to give the number A.
So n is the logarithm of A to base B.
Analysis:
log 2( log2(x-9)) = 3
log2(x-9) = [tex]2^{3}[/tex]
log2(x-9) = 8
x-9 = [tex]2^{8}[/tex]
x-9 = 256
x = 256 + 9
x = 265
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Write an equation of the line that passes through the point (4, –5) with slope 2.
answers:
A. y−4=2(x+5)
B. y+5=−2(x−4)
C. y−4=−2(x+5)
D. y+5=2(x−4)
Answers
Answer:
D. y+5=2(x−4)
Step-by-step explanation:
The point-slope form of the equation of a line is useful for writing an equation for a line through a given point with a given slope.
Point-slope formThe point-slope form of the equation of a line is ...
y -k = m(x -h) . . . . . . line through point (h, k) with slope m
ApplicationWe want a line through point (h, k) = (4, -5) with slope m = 2. Putting these numbers into the form gives ...
y -(-5) = 2(x -4)
y +5 = 2(x -4) . . . . . . simplifying the signs
HELPP WILL GIVE BRAINLIEST
which graph represents the function f(x) = sqrt(x) + 3
Answers
Answer:
the real answer is 2 I hope that
Your last five customer interactions lasted 2, 3, 6, 8, and 4 minutes."
Employee: "That means I've averaged __________ minutes across those 5 interactions."
Answers
Answer:
4.6 minutes
Step-by-step explanation:
Average = the sum of the numbers/ the number of numbers
Plug in the numbers: 2+3+6+8+4/5 = 23/5 = 4.6 minutes
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 7.9 years, and standard deviation of 0.9 years.
If you randomly purchase one item, what is the probability it will last longer than 9 years?
Answers
If you randomly purchase one item, the probability it will last longer than 9 years is; 11.12%
How to find the probability from z-score?
The formula for Z-score is;
z = (x' - µ)/σ
where;
x' = sample mean
µ = population mean
σ = standard deviation
Thus;
z = (9 - 7.9)/0.9
z = 1.22
From online p-value from z-score calculator, we have;
probability = 0.1112 = 11.12%
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