Transform the differential equation -3y" + 2y + y = t3
y(0) = -6 y' = 7 Into an algebraic equation by taking the Laplace transform of each side. ________ = 0 and Y =
Answers
An algebraic equation by taking the Laplace transform of each side is y(0) = -6 and y'(0) = 7.
To transform the given differential equation using the Laplace transform, we will apply the Laplace transform operator to each term in the equation and use the properties of the Laplace transform. The Laplace transform of a function y(t) is denoted as Y(s), where s is the complex variable.
Taking the Laplace transform of the given equation -3y" + 2y + y = t³, we get:
L[-3y"] + L[2y] + L[y] = L[t³]
Applying the properties of the Laplace transform, we have:
-3(s²Y(s) - sy(0) - y'(0)) + 2Y(s) + Y(s) = (3!)/s⁴
Simplifying the equation, we get:
-3s²Y(s) + 3sy(0) + 3y'(0) + 2Y(s) + Y(s) = 6/s⁴
Combining like terms, we have:
(-3s² + 2 + 1)Y(s) = 6/s⁴ - 3sy(0) - 3y'(0)
Simplifying further, we get:
(-3s² + 3)Y(s) = 6/s⁴ - 3sy(0) - 3y'(0)
Dividing both sides by (-3s² + 3), we obtain the algebraic equation:
Y(s) = [6/s⁴ - 3sy(0) - 3y'(0)] / (-3s² + 3)
To know more about algebraic equation:
https://brainly.com/question/29131718
#SPJ11
Related Questions
A study compared the effects of regular-fat cheese to an equal amount of reduced-fat cheese on LDL cholesterol levels. What is/are the dependent variable(s)?
a. regular fat cheese
b. LDL levels
c. reduced fat cheese
d. both a and b
e. both b and c
Answers
In the given study comparing the effects of regular-fat cheese to reduced-fat cheese on LDL cholesterol levels, the dependent variable(s) refers to the outcome(s) that are being measured or observed. In this case, the dependent variable in this study is: b. LDL levels
The dependent variable is the variable that is measured or observed to assess the effect of the independent variable(s). In this case, the study is comparing the effects of regular-fat cheese and reduced-fat cheese on LDL cholesterol levels.
LDL cholesterol levels are the outcome being measured to determine the impact of the different types of cheese on cholesterol. Therefore, option b, LDL levels, is the dependent variable in this study. Options a (regular fat cheese) and c (reduced fat cheese) are not the dependent variables but rather the independent variables, as they are the different conditions being compared to assess their effect on LDL levels.
Option d (both a and b) and option e (both b and c) are incorrect because regular-fat cheese (option a) is an independent variable, not a dependent variable.
To know more about dependent variable refer here:
https://brainly.com/question/1479694?#
#SPJ11
find the 55th term 17,22,27,32
Answers
We can see that the given sequence is an arithmetic sequence with a common difference of 5. To find the 55th term, we can use the formula for the nth term of an arithmetic sequence: an = a1 + (n - 1)d
where a1 is the first term, d is the common difference, and n is the term number.
Substituting the given values, we get:
(swear filter is bugging, so i needed to put a "-" in between the a and 55)
a-55- = 17 + (55 - 1)5
a-55- = 17 + 270
a-55- = 287
Therefore, the 55th term of the sequence 17, 22, 27, 32 is 287.
There are 12 eggs in a dozen. Write an algebraic expression for the number of eggs in d dozen.
Answers
Answer:
4d=48
Step-by-step explanation:
Your credit card has a baiance of \( \$ 3052.41 \). How many years will it take to pay the balance to 0 if the card has an annual interest rate of \( 18 \% \) and you will make payments of \( \$ 55 \)
Answers
It would take approximately 11.7 years to pay off the credit card balance of $3052.41 with a monthly payment of $55 and an annual interest rate of 18%.
To calculate the time it will take to pay off a credit card balance, we need to consider the interest rate, the balance, and the monthly payment. In your question, you mentioned an annual interest rate of 18% and a monthly payment of $55.
First, let's convert the annual interest rate to a monthly interest rate. We divide the annual interest rate by 12 (the number of months in a year) and convert it to a decimal:
Monthly interest rate = (18% / 12) / 100 = 0.015
Next, we can calculate the number of months it will take to pay off the balance. Let's assume there are no additional charges or fees added to the balance:
Balance = $3052.41
Monthly payment = $55
To determine the time in months, we'll use the formula:
Number of months = log((Monthly payment / Monthly interest rate) / (Monthly payment / Monthly interest rate - Balance))
Using this formula, the calculation would be:
Number of months = log((55 / 0.015) / (55 / 0.015 - 3052.41))
Calculating this equation gives us approximately 140.3 months.
Since we want to find the number of years, we divide the number of months by 12:
Number of years = 140.3 months / 12 months/year ≈ 11.7 years
Therefore, it would take approximately 11.7 years to pay off the credit card balance of $3052.41 with a monthly payment of $55 and an annual interest rate of 18%.
Learn more about interest rate here: https://brainly.com/question/27743950
#SPJ11
Calculate the surface area of a solid box in the shape of a cube with side length 11cm.ILL MARK U BRAINEST!!!
Answers
Answer:
11 x 11 = 121 121 x 6 = 726 cm
Step-by-step explanation:
Hope this helps
mrs patrick is employed by a clothing store.She recieves a 6% commission plus a small sallary. Last week she sold $8419 in clothing how much commission did mrs patrick receive
this is a story problem btw :)
Answers
Answer:
$505.40
Step-by-step explanation:
now wheres the answer to my question?
Answer:
630.babycrazy
Step-by-step explanation:
hmu on ig
The questions are in the picture below solve all.
Answers
Answer:
Step-by-step explanation:
1 is 28
2 is 24
3 is 7
4 is 9
Show that the frequency of small oscillations about the equilibrium position (using isentropic relations) is: PA n 20 L W where L is the height of the cylinder and W is the weight on the piston. Compare this result with the frequency of a simple pendulum. Justify the use of the isentropic relations
Answers
Using isentropic relations, the frequency of small oscillations about the equilibrium position in a system can be determined to be PA/(n20LW), where L is the height of the cylinder and W is the weight on the piston.
This frequency can be compared with the frequency of a simple pendulum. The use of isentropic relations is justified in this context because it assumes adiabatic and reversible processes, which are reasonable approximations for small oscillations where energy losses and external disturbances are minimal.
The frequency of small oscillations about the equilibrium position in a system can be determined using isentropic relations. For a system involving a cylinder and piston, with L being the height of the cylinder and W being the weight on the piston, the frequency is given by PA/(n20LW), where P is the pressure, A is the cross-sectional area, n is the number of moles of gas, and 20 is the molar heat capacity at constant volume.
This frequency can be compared to the frequency of a simple pendulum, which is given by 1/(2π√(L/g)), where L is the length of the pendulum and g is the acceleration due to gravity.
The use of isentropic relations is justified in this context because it assumes adiabatic and reversible processes, which are reasonable approximations for small oscillations where energy losses and external disturbances are minimal. In such conditions, the system behaves in a predictable manner, and the use of isentropic relations allows for accurate calculations of the frequency of small oscillations.
To learn more about weight click here:
brainly.com/question/31659519
#SPJ11
Define T in L(C2) by T(w,z)=(−z,w).
Find the generalized eigenspaces corresponding to the distinct eigenvalues of T.
I believe that once I have the eigenvalues, I know how to find the eigenspaces, but I'm not sure I'm looking for the eigenvalues correctly.
I know that if the eigenvalues are a,b corresponding to (w,0) and (0,z) respectively, then (ab)=1, since a(w)=−z implies ab(−z)=−z. But I think my whole approach to this is wrong and that I'm missing some very elementary idea.
Answers
T is the linear transformation described by T(w,z) in L(C2). This indicates that the linear transformation T changes two-dimensional vectors of the type (w,z) to (-z,w).
To get T's eigenvalues, solve the equation T(v) = v, where is the eigenvalue and v is the eigenvector. By solving this equation, we discover that T's eigenvalues are λ1 = -1 and λ2 = 1.
For each eigenvalue, the associated eigenspaces are the subspaces of C2 that are spanned by the eigenvectors of T. The eigenspace is the subspace covered by the eigenvector λ1= -1 is (1,0). The eigenspace is the subspace spanned by the eigenvector λ2= 1 is (0,1).
As a result, the subspaces covered by (1,0) and (1,1) are the generalized eigenspaces corresponding to the different eigenvalues of T. (0,1).
Learn more about eigenvalues here:
https://brainly.com/question/15423383
#SPJ4
a sphere is inscribed in a unit cube. a smaller cube is then inscribed within the sphere. what is the side length of the smaller cube?
Answers
Answer:10
Step-by-step explanation:
beausepppppp
The side length of the smaller cube inscribed within the sphere is approximately 0.7071.
To find the side length of the smaller cube inscribed within the sphere, which is inscribed in a unit cube, we can follow these steps:
Determine the diameter of the inscribed sphere.
Since the sphere is inscribed in the unit cube, its diameter will be equal to the side length of the unit cube. Therefore, the diameter of the inscribed sphere is 1.
Calculate the radius of the inscribed sphere.
The radius of the sphere is half of its diameter, so the radius is 0.5.
Apply the Pythagorean theorem to the smaller cube.
We can imagine a right triangle formed by half the side length of the smaller cube (let's call this length 's') and the sphere's radius (0.5) as the two shorter sides, and the diagonal of the smaller cube as the hypotenuse.
By applying the Pythagorean theorem, we get:
(s/2)^2 + (s/2)^2 = (0.5)^2
Solve for the side length 's' of the smaller cube.
Expanding the equation, we get:
2 * (s^2 / 4) = 0.25
(s^2 / 2) = 0.25
s^2 = 0.5
s = sqrt(0.5)
Express the side length 's' of the smaller cube.
The side length of the smaller cube, 's', is equal to the square root of 0.5, which can also be written as sqrt(0.5) or approximately 0.7071.
So, the side length of the smaller cube inscribed within the sphere is approximately 0.7071.
for more questions on cube
https://brainly.com/question/10421656
#SPJ11
10 more than the product of 2 and a number value
Answers
Answer:
10 + 2x
also,
2x + 10
Step-by-step explanation:
"a number value" is the unknown, so use a variable (letter) I used x, but could be almost any letter (avoid e and i, they have other math meanings)
"10 more than" means to add on 10. You can do that up front or at the end. Order is way more important for subtracting, so no worries here.
"product" means multiplying. So the "product of 2 and a number" is 2x.
So to translate this word phrase into an algebraic expression, you get:
10 + 2x
but also 2x + 10 is the same thing.
Find the value of x??????????
Answers
Answer:
x = 35
Step-by-step explanation:
Since the sum of angle measures is 180, you can set up this equation:
40 + 3x + x = 180
Combine like terms:
4x + 40 = 180
Subtract 40 from each side:
4x = 140
Divide each side by 4:
x = 35
troy organizes a samll party there are 30 glasses of drinks at the party 20 of which contain an orange flavored drink what is the probability that a randomly selected drink will be orange flavored
Answers
Answer:
66(2/3) %
Step-by-step explanation:
There are 30 possible outcomes because there are 30 cold drinks.
The Probability of orange flavored 20/30 = 2/3 = 0.6666....
66.6666....%= 66(2/3) %
Find the nth taylor polynomial for the function, centered at c. f(x) = ln(x), n = 4, c = 5
Answers
The nth taylor polynomial for the given function is
P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴
Given:
f(x) = ln(x)
n = 4
c = 3
nth Taylor polynomial for the function, centered at c
The Taylor series for f(x) = ln x centered at 5 is:
\(P_{n}(x)=f(c)+\frac{f^{'} (c)}{1!}(x-c)+ \frac{f^{''} (c)}{2!}(x-c)^{2} +\frac{f^{'''} (c)}{3!}(x-c)^{3}+.....+\frac{f^{n} (c)}{n!}(x-c)^{n}\)
Since, c = 5 so,
\(P_{4}(x)=f(5)+\frac{f^{'} (5)}{1!}(x-5)+ \frac{f^{''} (5)}{2!}(x-5)^{2} +\frac{f^{'''} (5)}{3!}(x-5)^{3}+.....+\frac{f^{n} (5)}{n!}(x-5)^{n}\)
Now
f(5) = ln 5
f'(x) = 1/x ⇒ f'(5) = 1/5
f''(x) = -1/x² ⇒ f''(5) = -1/5² = -1/25
f'''(x) = 2/x³ ⇒ f'''(5) = 2/5³ = 2/125
f''''(x) = -6/x⁴ ⇒ f (5) = -6/5⁴ = -6/625
So Taylor polynomial for n = 4 is:
P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴
Hence,
The nth taylor polynomial for the given function is
P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴
Find out more information about nth taylor polynomial here
https://brainly.com/question/28196765
#SPJ4
Algebra 2 Piece-wise functions!!
Answers
It's A.
1. The closed circle connects to the x≥1 function, so that rules out B and C.
2. The x≥1 piece has a positive slope on the graph, so that rules out D.
How do you dilate a line segment around a point?
Answers
You dilate a line segment around a point by following a simple procedure mentioned below that begins with identifying the center of a line segment.
Dilating a line segment around a point is a simple process. First, you need to identify the center of the line segment.
Then, use a ruler or other measuring device to measure the distance from the center of the line segment to each end point.
To dilate the line segment, multiply the measured distance by the desired scale factor. Finally, draw a new line segment connecting the two new end points.
This will give you the dilated line segment around the point you identified at the beginning.
To learn more about segment, click here:
https://brainly.com/question/280216
#SPJ4
FIND THE DEGREE OF THE TERM 7X^3
Answers
Answer: uh its just 3
the degree is the power of the exponent on the x term
Solve X
5x + 15 = 35
Answers
Answer:
x = 4
Step-by-step explanation:
5x + 15 = 35
subtract 15 from each side of the equation:
5x = 20
divide both sides by 5:
x = 4
-15 = -15
5x=20
— = —
5 5
x= 4
mr.floyd is laying grass squares in his backyard .He will cover the entire yard except for the vegetable garden.
15ft by 25ft
Garden 8ft by 8ft.
Answers
Answer:
Remain garden Area = 311 ft²
Step-by-step explanation:
Given:
Dimension of vegetable garden = 15 ft by 25 ft
Dimension of garden = 8 ft by 8 ft
Find:
Remain garden Area
Computation:
Remain garden Area = Area of vegetable garden - Area of Garden
Remain garden Area = [(15)(25)] - [(8)(8)]
Remain garden Area = 375 - 64
Remain garden Area = 311 ft²
Which graph shows a function where f(2) = 4
Answers
The that graph shows a function where f(2) = 4 is:
option 1
Which graph shows a function where f(2) = 4?We have to find a function where f(2)=4. It means the value of function is 4 at x=2.
In graph 1, the value of function is 4 at x=2, therefore option 1 is correct.
In graph 2, the value of function is -4 at x=2, therefore option 2 is incorrect.
In graph 3, the value of function is not shown in the graph at x=2, therefore option 3 is incorrect.
In graph 4, the value of function is not shown in the graph at x=2, therefore option 4 is incorrect.
Therefore, correct option is 1.
Learn more about function on:
brainly.com/question/1415456
#SPJ1
Complete Question
Check attached image
.........................................
Answers
Answer:
66 red marbles
Step-by-step explanation:
We can find how much 11/12 is by finding what 1/12 is.
72/1*11/12=792/12 which is 66 so 66 marbles.
brainliest?
STRUCTURE The students in Mrs. Mangione’s class attempt to guess the number of marbles in a jar to earn 2 extra credit points on their next exam. Suppose there are 1206 marbles in a jar and a student makes a guess of m marbles. Which expression represents the difference between the student's guess and the actual number of marbles. Select all that apply.
Answers
The expression that represents the difference between the student's guess and the actual number of marbles will be 1206 - 2m.
How to illustrate the information?When there are 1206 marbles in a jar and a student makes a guess of m marbles. The expression for the guesses will be:
= 2 × m
= 2m
The expression that represents the difference between the student's guess and the actual number of marbles will be:
= 1206 - 2m
= 2(603 - m)
Learn more about expressions on:
brainly.com/question/1280754
#SPJ1
A thousand dollars is left in bank savings account drawing 7% interest, compounded quarterly for 10 years. What is the balance at the end of that time? show work
Answers
Answer:
Step-by-step explanation:
p(1+r/n)nt
= 1000 (1 + 0.07/4) 4 x 10
1000 (1 + 0.0175) 40
1000(1.0175) 40
1000x 2.0015
= 2001.59
therefore the answer is 2001.59
Compound Interest can be defined as the interest that is compounded on a particular sum of money over a given period of time.
The balance at the end of that time is $2,001.60
The question wants us to find the balance at the end of that time which means we are to find the amount at the end of 10 years.
The formula for the compound interest is given as:
A = P(1 + r/n)^nt
Where:
A = Amount or the balance after time "t"
Principal(P) = $1,000
Interest rate(R) = 7%
Time(T) = 10 years
First, convert R as a percent to r as a decimal
r = R/100
r = 7/100
r = 0.07 rate per year
Then solve the equation for A
A = P(1 + r/n)^nt
A = 1,000.00(1 + 0.07/4)^(4 x 10)
A = 1,000.00(1 + 0.0175)^(40)
A = $2,001.60
Therefore, the balance at the end of that time is $2,001.60
To learn more, visit the link below:
https://brainly.com/question/24681193
Cali baked a box of brownies. she took some to school but left 2/3 at home for her brothers. her brother, todd, had eaten 1/4 of what she left. what portion of the entire pan did todd eat?
Answers
Answer:
1/6 pan
Step-by-step explanation:
You want to know the portion of the whole represented by 1/4 of 2/3.
Fraction of fractionTodd ate 1/4 of 2/3 of the pan of brownies. That fraction of the original whole amount is ...
(1/4)×(2/3) = (1·2)/(4·3) = 2/12 = 1/6
Todd ate 1/6 of the entire pan.
A line passes through the points (-6,4) and (-2,2). Which is the equation of the line?
A. y= -1/2x + 1
B. y= 1/2x + 7
C. y= -2x + -8
D. y= 2x + 16
Please Help ☺️
Answers
Answer:
Is A
Step-by-step explanation:
(2-4)/(-2--6) = -1/2
And the only answer that has -1/2 as the slope is A
f(x) = 5x2+2x2 - 90x - 36
find all zeros by factoring
Answers
Answer:
10x+4x-90x-36
14x-90x=36
76x=36
X=36/76
0.47 is the answer
Tommy is baking a cake. He knows that he needs 2/3 cups of flour to make 4 cakes. How many cups of flour will Tommy need to make 8 cakes?
Answers
HELP I WILL GIVE BRAINLIEST Which choice is equivalent to the quotient below the square root of 12 over 2 square root of 2
Answers
Answer to the question is D. \sqrt6/2
The quotient of the given expression is √6/2. Therefore, option D is the correct answer.
The given expression is √12/2√2.
We need to find the equivalent quotient to the given expression.
What are surds?In Mathematics, surds are the values in the square roots that cannot be further simplified into whole numbers or integers. Surds are irrational numbers.
Now, √12/2√2
We can write √12 as √4×3
Then, we get 2√3/2√2
Further, rationalise the denominator
A fraction whose denominator is a surd can be simplified by making the denominator rational. This process is called rationalising the denominator.
That is √3×√2/√2×√2=√6/2
Therefore, option D is the correct answer.
To learn more about the surds visit:
https://brainly.com/question/24700530.
#SPJ2
How many significant figures would this calculation have if it were completed: \[ (9.04-8.23+21.954+81.0) \times 3.1416 \]
A) 3 B)4 C)5 D)6
Answers
The calculation \((9.04-8.23+21.954+81.0) \times 3.1416\) would have 4 significant figures.
To determine the number of significant figures in a calculation, we follow the rules for significant figures:
1. Addition and subtraction: The result should have the same number of decimal places as the measurement with the fewest decimal places.
2. Multiplication and division: The result should have the same number of significant figures as the measurement with the fewest significant figures.
Let's break down the calculation step by step:
\(9.04-8.23+21.954+81.0\) yields \(104.764\).
Now, multiplying this result by \(3.1416\) gives \(329.5719744\).
The measurement with the fewest significant figures in the calculation is \(3.1416\), which has 5 significant figures.
According to the rule for multiplication and division, the result should have the same number of significant figures as the measurement with the fewest significant figures. Hence, the result, \(329.5719744\), will be rounded to 4 significant figures.
Therefore, the calculation \((9.04-8.23+21.954+81.0) \times 3.1416\) would have 4 significant figures.
Learn more about significant figures here : brainly.com/question/29153641
#SPJ11
Random sampling is to ________ as random assignment is to ________.
Answers
It should be noted random sampling is to survey as random assignment is to experiment.
What is random sampling?Random sampling can be regarded as kind of sampling technique whereby each of the sample posses equal probability of being chosen.
Therefore, random sampling is to survey.
Learn more about random sampling at:
https://brainly.com/question/13336365