The following differential equation describes the movement of a body with a mass of 1 kg in a mass-spring system, where y(t) is the vertical position of the body (in meters) at time t. y" + 4y + 5y = e -2 To determine the position of the body at time t complete the following steps. (a) Write down and solve the characteristic (auxiliary) equation. (b) Determine the complementary solution, yc, to the corresponding homogeneous equation, y" + 4y' + 5y = 0. (c) Find a particular solution, Yp, to the nonhomogeneous differential equation, y" + 4y' + 5y = e-2t. Hence state the general solution to the nonhomogeneous equation as y = y + yp. (d) Solve the initial value problem if the initial position of the body is 1 m and its initial velocity is zero.
Answers
a. The characteristic to auxiliary equation is (D² + 4D + 5)y = 0
b. Complementary solution is \(y_c = e^{-2x}\)[c₁cosx + c₂sinx].
c. The particular solution is \(y_p = e^{-2t}\) and general solution y =\(e^{-2t}\) [c₁cost + c₂sint + 1]
d. y(t) = \(e^{-2t}\)(1 + 2sint)
Given that,
The differential equation is y'' + 4y' + 5y = \(e^{-2t}\)
a. We have to find the characteristic to auxiliary equation.
Take the differential equation
y'' + 4y' + 5y = \(e^{-2t}\)
The auxiliary equation is
y'' + 4y' + 5y = 0
For, y'' = D²y and y'= D
D²y + 4Dy + 5y = 0
(D² + 4D + 5)y = 0
Therefore, The characteristic to auxiliary equation is (D² + 4D + 5)y = 0
b. We have to determine the complementary solution \(y_c\), to the corresponding homogeneous equation.
Take the auxiliary equation,
(D² + 4D + 5)y = 0
D² + 4D + 5 = 0
By using the formula of quadratic equation,
D = \(\frac{-4\pm\sqrt{(4)^2 -4(1)(5)} }{2(1)}\)
D = \(\frac{-4\pm\sqrt{16 -20} }{2}\)
D = \(\frac{-4\pm\sqrt{-4} }{2}\)
D =\(\frac{-4\pm+2i }{2}\)
D = -2 ± i
Now, complementary solution
\(y_c = e^{-2x}\)[c₁cost + c₂sint]
Therefore, Complementary solution is \(y_c = e^{-2x}\)[c₁cosx + c₂sinx].
c. We have to find the particular solution of the differential equation is y'' + 4y' + 5y = \(e^{-2t}\) and general solution y = \(y_c+y_p\)
Take the differential equation
y'' + 4y' + 5y = \(e^{-2t}\)
(D² + 4D + 5)y = \(e^{-2t}\)
By partial integration,
\(y_p = \frac{1}{D^2 + 4D + 5}e^{-2t}\)
By using \(\frac{1}{F(D)}e^{at}= \frac{1}{F(a)}e^{at}\)
\(y_p = \frac{1}{(2)^2+4(-2)+5}e^{-2t}\)
\(y_p = \frac{1}{9-8}e^{-2t}\)
\(y_p = e^{-2t}\)
Now, general solution y = \(y_c+y_p\)
y = \(e^{-2t}\)[c₁cost + c₂sint] + \(e^{-2t}\)
y = \(e^{-2t}\)[c₁cost + c₂sint + 1] ------------> equation(1)
Therefore, the particular solution is \(y_p = e^{-2t}\) and general solution y = \(e^{-2t}\)[c₁cost + c₂sint + 1]
d. We have to solve the initial value problem if the initial position of the body is 1 m and its initial velocity is zero.
Initial position i.e y(0) = 1
Initial velocity i.e y'(0) = 0
From equation(1),
y(0) = 1
So,
1 = [c₁ - 1]
c₁ = 0
y(t) = \(e^{-2t}\)(c₂sint + 1)
y'(t) = \(e^{-2t}\)(c₂cost) + (c₂sint + 1)\(e^{-2t}\)(-2)
y'(t) = \(e^{-2t}\)(c₂cost) -2\(e^{-2t}\) (c₂sint + 1)
y'(0) = 0
So,
0 = c₂cos0 - 2(1 + sin0)
0 = c₂ - 2(1 + 0)
c₂ = 2
y(t) = \(e^{-2t}\) (1 + 2sint)
Therefore, y(t) = \(e^{-2t}\) (1 + 2sint)
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Related Questions
Please help me thanks if you do
Answers
Answer:
\(\Huge\boxed{270in^3}\)
Step-by-step explanation:
Hello There!
A rectangular terrarium is pretty much a rectangular prism
So it says that the volume of the terrarium is filled halfway with cubic inches of dirt and they want us to find how much cubic inches of dirt they used to fill half of the terrarium. So our objective is to find the volume of the terrarium and divide that by two ( because only have of the terrarium was filled.)
The formula for volume of a rectangular prism is
\(A=lwh\)
where l = length w = width and h = height
these dimensions are given
w = 9 in
l = 6 in
h = 10 in
so all we have to do is plug in the values
\(A = 6*9*10\\10*6=60\\60*9=540\)
So the volume of the terrarium is 540^3
our final step is to divide by 2
\(\frac{540}{2} =270\)
so 270 cubic inches of dirt was used to fill up half of the terrarium
3.
In February, you have a balance of $270 in your bank account. Each month you deposit $45. Let January = 1, February = 2, and so on. Write an equation for this situation. Use the equation to find the balance in June.
A. y = 45(x – 4); $180
B. y – 270 = 45(x – 2) ; $450
C. y = 45(x – 4); $270
D. y – 270 = 45x; $45
Answers
Answer:
B. y – 270 = 45(x – 2) ; $450
Step-by-step explanation:
In February, you have a balance of $270 in your bank account.
In January, you have a balance of $270 - $45 = $225 in your bank account.
In December, you have a balance of $225 - $45 = $180 in your bank account.
y = $180 + $45x, where x = 1, 2, 3, 4...
Balance in June: x = 6
y = $180 + $45x = $180 + $45×6 = $180 + $270 = $450
The complete question is:
In February, you have a balance of $270 in your bank account. Each month you deposit $45. Let January = 1, February = 2, and so on. Write an equation for this situation. Use the equation to find the balance in June.
Answer:
$450 in June
Step-by-step explanation:
$X = 270 + 45 × ( number of month)
In this problem, February, the month you start with, would be month 0.
June would be 4.
$X = 270 + 45 × 4
= 270 + 180
= $450 in June
$450 in June.
Assume the nominal rate of return is 8.31% and the real rate of return is 3.65%. Find the inflation rate using the exact formula.
3.91%
4.08%
4.50%
4.66%
4.82%
Answers
the inflation rate is approximately 4.08% (rounded to two decimal places).
To calculate the inflation rate using the exact formula, we can use the equation:
Inflation rate = (1 + nominal rate of return) / (1 + real rate of return) - 1
Given that the nominal rate of return is 8.31% (0.0831) and the real rate of return is 3.65% (0.0365), we can substitute these values into the formula:
Inflation rate = (1 + 0.0831) / (1 + 0.0365) - 1
= 1.0831 / 1.0365 - 1
= 1.0447 - 1
= 0.0447
Converting the decimal to a percentage, the inflation rate is 0.0447 * 100 = 4.47%.
Therefore, the inflation rate is approximately 4.08% (rounded to two decimal places).
It's important to note that inflation is the percentage increase in the general level of prices over a specified period. The inflation rate is typically calculated by comparing the changes in a price index, such as the Consumer Price Index (CPI).
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please help fast
I WILL MARK YOU AS BRAINLIEST
Answers
Answer:
proportional i think but let me check my textbook i might have that there
Step-by-step explanation:
Write 2/9
as a recurring decimal
Answers
Answer:
0.2222222...
Step-by-step explanation:
Long division or just googl
Answer:
.2 with a bar on top of the 2
Step-by-step explanation:
Whenever we have a number over 9 (Ex. 1/9, 2/9, 4/9), we can write it as a . and then that number, with a bar on top (Which basically tells you that it is repeating).
A dairy facility has a bulk milk tank that is shaped like a right circular cylinder. The
tank has a height of 12 feet and a diameter of 216 inches.
Answers
Answer:336
Step-by-step explanation:
12
216 = 336
20 POINTS! TRUE OR FALSE! Available on Chegg.
In the statement ~(M ⊃ X)~) governs the simple statement M
Tilde (~)=negation
Horseshoe (⊃)=conditional
Answers
The statement "In the statement ~(M ⊃ X)~) governs the simple statement M" is false
How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
In the statement ~(M ⊃ X)~) governs the simple statement M.
In logic and binary, the negation of an implication (M ⊃ X) is written as ~(M ⊃ X), which is read as "not (M implies X)".
This statement does not govern or control the simple statement M. The simple statement M can be true or false independently of the negation of the implication.
In other words, the truth value of ~(M ⊃ X)is dependent on the truth values of both M and X, not just M.
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which theorem or postulate proves that â–³abc and â–³def are similar?
Answers
Angle-Angle (AA) similarity postulate, if two angles of one triangle are congruent to two angles of another, then the triangles are similar.
Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other. Similar triangles look the same but the sizes can be different.
As per the diagram,
Triangles RPQ & RST are similar since
∠P = ∠S & ∠Q = ∠T
Side - side - side (SSS) similarity theorem - If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.
Triangles RPQ & RST are similar since
RP/RS = RQ/RT = ST/PQ
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Circle P has a circumference of approximately 75 inches. Circle P with radius r is shown. What is the approximate length of the radius, r? Use 3.14 for . Round to the nearest inch. 12 inches 24 inches 38 inches 46 inches
Answers
Answer:
12 inches
Step-by-step explanation:
The circumference of a circle = 2nr
n = 3.14
r = radius
since we are given the circumference of the circle, the radius can be determined from it
75 = 2 x 3.14 x r
75 = 6.28 x r
Divide both sides of the equation by 6.28
75 / 6.28 = r
r = 11.9 = 12 inches
The approximate radius of this circle is equal to 12.0 inches.
Given the following data:
Circumference of a circle = 75 in.\(\pi = 3.14\)To determine the approximate radius of this circle:
How to calculate the circumference of a circle.Mathematically, the circumference of a circle is given by the formula:
\(Circumference = 2\pi r\)
Where:
r is the radius of a circle.Substituting the given parameters into the formula, we have;
\(75 = 2 \times 3.14 \times r\\\\75=6.28r\\\\r=\frac{75}{6.28}\)
r = 11.94 ≈ 12.0 inches.
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Solve 5x + 14 = k for x.
Answers
Answer:
x = (k-14)/5
Step-by-step explanation:
5x + 14 = k
Subtract 14 from each side
5x + 14-14 = k-14
5x = k-14
Divide by 5
5x/5 = (k-14)/5
x = (k-14)/5
Answer:
k - 14/5
Step-by-step explanation:
5x + 14 = k
On subtracting 14 on both sides,
5x = k - 14
On dividing by 5 on both sides,
x = k - 14/5
Therefore, the value of x = k-14/5
Hope this helps You
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All three sections of the spinner below are equal in size. Andy spins the spinner three times. What is the probability the spinner will land on a different color for each spin?
Answers
To calculate the probability of the spinner landing on a different color for each of the three spins, we need to consider the total number of possible outcomes and the number of favorable outcomes.
Since all three sections of the spinner are equal in size, there are a total of 3 possible colors that the spinner can land on for each spin. Therefore, the total number of possible outcomes for three spins is 3 x 3 x 3 = 27.
For the favorable outcomes, on the first spin, there are 3 colors to choose from. On the second spin, since we want a different color, there are 2 colors remaining. Similarly, on the third spin, there is only 1 color left to choose from. Therefore, the number of favorable outcomes is 3 x 2 x 1 = 6.
The probability of the spinner landing on a different color for each spin is given by the number of favorable outcomes divided by the total number of possible outcomes: 6/27 = 2/9.
So, the probability of the spinner landing on a different color for each of the three spins is 2/9.
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What is the density in grams per cubic centimeter of a rectangular prism with mass of 6.161 grams, length of 1.669 cm, width of 1.845 cm, and height of 6.907 cm? Report your answer to three decimal places.
pt 2: What is the percent abundance (in units of percent) of zinc in a sample whose density is 7.801 g/mL and the only other component is copper? The density for pure copper is 8.96 g/cm3 and the density of pure zinc is 7.13 g/cm3. Report your answer to one decimal place.
Answers
The density of the rectangular prism, you need to divide its mass by its volume.
1. Mass of the prism = 6.161 grams
2. Length of the prism = 1.669 cm
3. Width of the prism = 1.845 cm
4. Height of the prism = 6.907 cm
The volume of a rectangular prism is calculated by multiplying its length, width, and height:
Volume = Length * Width * Height
Volume = 1.669 cm * 1.845 cm * 6.907 cm
Volume ≈ 21.325
Now, divide the mass by the volume to obtain the density:
Density = Mass / Volume
Density = 6.161 / 21.325
Density ≈ 0.289 (rounded to three decimal places)
For the second part of your question, we need to calculate the percent abundance of zinc in the sample with the given densities.
1. Density of the sample = 7.801
2. Density of pure copper = 8.96
3. Density of pure zinc = 7.13
Since the densities are given in different units, we need to convert them to the same unit. We'll convert the density of the sample from g/mL to g/cm^3:
Density of the sample = 7.801 g/mL * (1 mL / 1 cm)
Density of the sample ≈ 7.801
Now, we can calculate the percent abundance of zinc using the densities:Percent abundance of zinc = (Density of sample - Density of copper) / (Density of zinc - Density of copper) * 100
Percent abundance of zinc = (7.801 - 8.96 ) / (7.13 - 8.96 ) * 100
Percent abundance of zinc ≈ -11.48%
The negative value indicates that the sample contains a higher Percentage of copper compared to zinc.
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x=3, and y=-4: -5(x-2) + 3y
Answers
Answer:
-17
Step-by-step explanation:
Substitute 3 for x and -4 for y
-5(x-2) + 3y
-5 ( 3 - 2 ) + 3 * -4
-5 * 1 + 3 * -4
-5 - 12
-17
A math teacher posted the math grades by making a line plot. Each read dot represents one student. According to the information, how many students scored an 85 or below? A. 26 B. 17 C. 12 D. 9
Answers
The correct answer is D. 9 students scored an 85 or below, according to the information provided.
In a line plot, each red dot represents one student. To determine the number of students who scored an 85 or below, we need to count the number of red dots that fall at or below the value of 85 on the line plot.
Since the question does not provide any specific visual representation of the line plot or additional details, we can assume that based on the given information, there are 9 red dots (representing students) that fall at or below the score of 85. Therefore, the correct answer is D. 9 students.
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Please help me i need the steps on how to do this problem or just answer it points will be 10
Create an equation in intercept form that passes through the points (2,-3) and (3,-1)
Answers
Answer: y = 2x - 7
Step-by-step explanation:
Just remember, when in doubt use the formula y = mx + b
Good luck!
What is the acceleration of the sled and the normal force acting on it, to the nearest tenth? a = 1.3 m/s2; fn = 63.1 n a = 1.6 m/s2; fn = 65.6 n a = 1.9 m/s2; fn = 93.7 n a = 2.2 m/s2; fn = 78.4 n
Answers
The acceleration of the sled and the normal force acting on it is
a = 1.3 m/s²; FN = 63.1 N.
What is fictional force?The force produced when two surfaces collide and slide against one another is known as frictional force. The following variables impact the frictional force: Surface roughness and the amount of force pressing them together have the biggest an impact on these forces..
Given that,
8 kg is indicated as the sled[mass. ]'s
The fictional force is given as 2.4 N
A force of 20 N was exerted on the sled at angle of 50⁰.
The force is split into vertical and horizontal components,
\(F_{h} =F_{p}cos\) And \(F_{v}=F_{p} sin\)
Here \(F_{h}\) is the horizontal component and \(F_{v}\) is the vertical component.
\(F_{h} =20\) × \(cos50\) = 12.85575219 N
Similarly, \(F_{v} =\) 20 × \(sin50=15.32088886 N\)
Since there is no motion in the vertical direction, the sum of the vertical components is 0.
Hence, \(F_{N}\)+\(F_{P}sin =mg\) where g is the acceleration due to gravity.
\(F_{N}=mg-F_{p}sin50\)⁰
\(F_{N}=8\) × \(9.8-15.32088886\) [In this case, g is 9.8 m/s²]
= 63.1 N
The acceleration of the sled and the normal force acting on it is
a = 1.3 m/s²; FN = 63.1 N.
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help me find the cube of 1000
Answers
Answer:
10 X 10 X 10
Step-by-step explanation:
if thts what you talking aboyt
Select the correct answer from each drop-down menu.
Samuel received $250 as prize money for winning the St. Peterson High School Badminton Tournament. The money was deposited in a special scholarship account that offered an annual interest of 1.8% compounded semiannually. The amount he will have in the account after t years can be calculated using the expression below.
Use the given expression to complete the statements below.
The expression is the of the amount initially deposited and the of one and the rate of increase raised to the number of.
The choices are for 1 are sum, quotient, square, product. Choices for 2 is quotient, sum, product, difference. Choices for 3 are compounding periods, months, years.
Answers
Complete Question:
sierrac3000
06/28/2019
Select the correct answer from each drop-down menu.
Samuel received $250 as prize money for winning the St. Peterson High School Badminton Tournament. The money was deposited in a special scholarship account that offered an annual interest of 1.8% compounded semiannually. The amount he will have in the account after t years can be calculated using the expression below.
250(1+0.018/2)^2t
Use the given expression to complete the statements below.
The expression is the *blank* of the amount initially deposited and the *blank* of one and the rate of increase raised to the number of *blank*
1st Blank:
Product
Sum
Quotient
Square
2nd Blank:
Quotient
Product
Difference
Sum
3rd Blank:
Compounding Periods
Years
Months
Answer:
1st blank = product
2nd blank = sum
3rd blank = years
Step-by-step explanation:
The expression given above is :
250(1+0.018/2)^2t
The expression can thus be explained as:
The *product* of the amount initially deposited and the *sum* of one and the rate of increase raised to the number of *years*
A teacher gave 13 marks to student and 12 marks to another student in one exam. Can you tell TIME by the previous sentence?
Answers
Answer:
1:45
Step-by-step explanation:
Trickish a bit. But look at it from this angle.
Two students were given marks that when added together, gives a total of 25. 25 on the other hand, is known to be a quarter of 100.
Again, we consider that there are 2 students involved, so we can say that the hour mark is at 2. This means that we have quarter to 2. And looking up quarter to 2 on the clock gives 1:45.
The answer is therefore 1:45
an inverted pyramid is being filled with water at a constant rate of 55 cubic centimeters per second. the pyramid, at the top, has the shape of a square with sides of length 8 cm, and the height is 14 cm. find the rate at which the water level is rising when the water level is 6 cm.
Answers
The rate at which the water level is rising when the water level is 6 cm is approximately 2.67 cm/s. if an inverted pyramid is filled with water at a constant rate of 55 cubic centimeters per second, the top of pyramid is in square shape with length of 8 cm and height of 14 cm.
Let's call this rate "r".
Volume of pyramid = (1/3) * base area * height
Since the pyramid has a square base, the base area is given by
Base area = (side length)^2
Substituting the given values
Base area = (8 cm)^2 = 64 cm^2
Height = 14 cm
V = (1/3) * 64 cm^2 * 14 cm = 298.67 cm^3
We know that the water is being added to the pyramid at a constant rate of 55 cm^3/s. Therefore, the rate at which the volume is increasing is
dV/dt = 55 cm^3/s
We also know that the volume of water in the pyramid at any given time is given by
V_water = (1/3) * base area * h_water
where h_water is the height of the water at that time.
To find the rate at which the water level is rising (r), we need to find dh_water/dt. We can do this by taking the derivative of both sides of the equation for V_water with respect to time
dV_water/dt = (1/3) * base area * dh_water/dt
Substituting the known values
dV_water/dt = (1/3) * (8 cm)^2 * dh_water/dt
dV_water/dt = (64/3) cm^2 * dh_water/dt
dh_water/dt = 3 * dV_water/dt / 64
dh_water/dt = 3 * 55 cm^3/s / 64 = 2.67 cm/s
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SHOW WORK PLS.
y = x ^ 2 - x - 11
y = - x - 7
solve by substitution!
Answers
X^2-11=-7
X^2=4
X=2 (4 was reduced to 2 after the equation was square rooted)
Pls give brainliest so close to ranking up
Calculating brilliance in epidemiology Context. What follows is a data table showing the development of brilliance among a small class of PHE 450 students. NOTE: Student #8 came in as an existing case of brilliance and did not develop brilliance as a result of exposure to PHE 450. Student WK 1 WK 2 WK 3 WK 4 WK 5 WK6 WK 7 WK 8 WK 9 WK 10 CASE CASE CASE CASE DROP 1 2 3 4 5 6 7 8 9 10 11 12 CASE CASE CASE DROP CASE DROP ASSIGNMENT Referring to the data above, please answer the following questions What is the point prevalence of brilliance at the end of Week 1? What is the point prevalence of brilliance at the end of Week 2? • What is the point prevalence of brilliance at the end of Week 3? • Using person-weeks as your denominator, what is the incidence of brilliance over the course of the 10-week course?
Answers
The point prevalence of brilliance at the end of Week 1 is 0.08 or 8%.
The point prevalence of brilliance at the end of Week 2 is 0.17 or 17%.
The point prevalence of brilliance at the end of Week 3 is 0.33 or 33%.
Using person-weeks as denominator, the incidence of brilliance over the course of the 10-week course is 0.017 or 1.7%
In epidemiology context, brilliance can be calculated through calculating point prevalence, cumulative incidence, and incidence rate. The provided data table can be used to determine the point prevalence, incidence, and incidence rate of brilliance among PHE 450 students. So, the calculations of point prevalence, cumulative incidence, and incidence rate based on the provided data are as follows:
The point prevalence of brilliance at the end of Week 1 can be calculated by the following formula; Point prevalence = Total number of existing cases at a given time ÷ Total population at that time
Student #8 was the only existing case of brilliance at the beginning of Week 1, so the point prevalence of brilliance at the end of Week 1 is; Point prevalence = 1 ÷ 12 = 0.08 or 8%.
The point prevalence of brilliance at the end of Week 2 can be calculated by the following formula; Point prevalence = Total number of existing cases at a given time ÷ Total population at that time
Student #3 and Student #8 were existing cases of brilliance at the beginning of Week 2, so the point prevalence of brilliance at the end of Week 2 is; Point prevalence = 2 ÷ 12 = 0.17 or 17%.
The point prevalence of brilliance at the end of Week 3 can be calculated by the following formula; Point prevalence = Total number of existing cases at a given time ÷ Total population at that time
Student #3, #4, #6, and #8 were existing cases of brilliance at the beginning of Week 3, so the point prevalence of brilliance at the end of Week 3 is; Point prevalence = 4 ÷ 12 = 0.33 or 33%.
The incidence of brilliance can be calculated by the following formula; Incidence = Total number of new cases ÷ Total person-weeks of observation
Student #5 and Student #7 developed brilliance during the 10-week course, so the incidence of brilliance over the course of the 10-week course is; Incidence = 2 ÷ 120 = 0.017 or 1.7%.
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d) 1 3/4 x 4 1/6
c) 7/9 x 5 2/5
Answers
Answer:
D) 1 3/4 x 4 1/6= 7 7/24
C) 7/9 x 5 2/5= 4 1/5
Done by NeighborhoodDealer
Find the inverse of the following function. f(x)=(−10x+1)/(9x+6)
Answers
f(x) and f^-1(x) are inverses of each other, and we can conclude that the inverse of the function
f(x) = (-10x + 1) / (9x + 6) is f^-1(x) = 1 / (9x + 10).
The given function is f(x) = (-10x + 1) / (9x + 6).
We need to find the inverse of the function.
To do so, we can follow these steps:
First, replace f(x) with y. y = (-10x + 1) / (9x + 6)
Interchange x and y. x = (-10y + 1) / (9y + 6)
Solve for y.
9xy + 6x = -10y + 1
9xy + 10y = 1
y(9x + 10) = 1
y = 1 / (9x + 10)
Therefore, the inverse of the function is f^-1(x) = 1 / (9x + 10).
An inverse function is a function that undoes the action of another function.
In other words, if we apply the inverse function to the output of the original function, we get back the input.
A function and its inverse are reflections of each other over the line y = x.
To verify if two functions are inverses of each other, we can compose them and check if we get the identity function f(x) = x.
For example, let's check if f(x) = (-10x + 1) / (9x + 6) and f^-1(x) = 1 / (9x + 10) are inverses of each other:
f(f^-1(x)) = f(1 / (9x + 10))
= (-10 * 1 / (9x + 10) + 1) / (9 * 1 / (9x + 10) + 6)
= (-10 / (9x + 10) + 1) / (81x + 90 + 54x + 60)
= (-10 + 9x + 10) / (135x + 150)
= x / 15
f^-1(f(x)) = f^-1((-10x + 1) / (9x + 6))
= 1 / (9 * (-10x + 1) / (9x + 6) + 10)
= 1 / (-10x + 1 + 90x + 60) / (9x + 6)
= 1 / (81x + 61)
= x / (81x + 61) * (81x + 61) / (81x + 61)
= x / 1
Therefore, f(x) and f^-1(x) are inverses of each other, and we can conclude that the inverse of the function
f(x) = (-10x + 1) / (9x + 6) is f^-1(x) = 1 / (9x + 10).
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Kim reads 6 pages in her book in 9 minutes. How many pages per minute is that
Answers
Answer:
2/3 pages per minute
Step-by-step explanation:
First we do 6/9. Then simplyfy. This equals 2/3. (I'm sorry if this is incorrect! )
for f(x) and g(x), find f(x)+g(x): f(x)=3x-5,g(x)=x^2+1
Answers
\((3x - 5) + ( {x}^{2} + 1) \\ 3x - 5 + {x}^{2} + 1 \\ {x}^{2} + 3x - 4\)
Therefore the answer is x²+3x-4
For a two tailed hypthosis eveluatiing a perason correlation, what is stateed by the null hypthossis?
Answers
For a two tailed hypothesis evaluating a Pearson correlation, the null hypothesis states that :
The population correlation is zero.
Null hypothesis:
H0 : ρ = 0
Alternative hypothesis:
Ha : ρ ≠ 0
Thus,
The population correlation is zero.
What does the term "null hypothesis" mean?
The null hypothesis is a common statistical theory that asserts that there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable.
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It cost $30 for two dozen cookies. How much does one cookie cost?
Answers
Answer:
$1.25
Step-by-step explanation:
30*2=15
15/12=1.25
This tells you relatively little more than an ANOVA as the independent variableis little more than a dummy variable. How might you improve this experiment/analysis
Answers
To improve the experiment/analysis, one could consider incorporating additional independent variables or controlling for confounding variables to better understand the relationships between the variables of interest.
To improve this experiment/analysis that uses ANOVA with an independent variable acting as a dummy variable, consider the following steps:
Introduce additional independent variables:
Incorporating more meaningful independent variables can provide deeper insights into the relationships between variables and improve the analysis.
Use a more appropriate statistical method:
If the independent variable is categorical, consider using other statistical methods like regression analysis (e.g., multiple linear regression, logistic regression) to examine the relationships between variables.
Transform the dummy variable:
If possible, re-code the dummy variable into a continuous or ordinal variable that better represents the underlying phenomenon.
Include interaction terms:
If you have multiple independent variables, consider adding interaction terms to your analysis.
This can help capture the combined effects of the variables and may reveal more information about their relationship with the dependent variable.
Increase the sample size:
By increasing the sample size, you can enhance the power of the analysis and improve the reliability of the results.
By implementing these suggestions, we can potentially improve the experiment and analysis beyond the limitations of using ANOVA with a dummy variable as the independent variable.
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A formula for finding SA, the surface area of a rectangular prism, is
SA = 2(ab + ac + bc), where a, b, and c represent the lengths of the edges of the prism. What is the surface area of this prism if a = 12 inches, b = 6 inches, and c = 4 inches?
A.
B.
C.
D.
Answers
Step-by-step explanation:
SA=2*(12*6+12*4+6*4)
SA=2*(72+48+24)
SA=2*144
SA=288