find f(s). (4t 1) (t 1)

To find (4t^2) (t 1), we need to take the Laplace transform of the given function. For (4t^2) (t 1), f(s) = 0.Using the linearity property of the Laplace transform, we can split the function into two terms: (4t^2) (t 1) = (4t^2) - (4t^2)(1)Let's calculate each term separately: (4t^2):Using the power rule of the Laplace transform, we have: (4t^2) = 4 * (t^2)Applying the power rule again, we get: (t^2) = 2! / s^(2+1) = 2! / s^3 = 2 / s^3Therefore, (4t^2) = 4 * (2 / s^3) = 8 / s^3. (4t^2)(1):Using the property of the Laplace transform of a constant, we have: (4t^2)(1) = 4 * (t^2)(1)Again, applying the property of the Laplace transform of a constant, we get: (t^2)(1) = 1 * (t^2) = 1 * (2 / s^3) = 2 / s^3Therefore, (4t^2)(1) = 4 * (2 / s^3) = 8 / s^3.Now, we can combine the two terms: (4t^2) (t 1) = (4t^2) - (4t^2)(1) = 8 / s^3 - 8 / s^3 = 0.Hence, f(s) = 0.To learn more about Laplace transform visit : https://brainly.com/question/29583725#SPJ11

Mathematics High School

find f(s). ℒ (4t 1) (t − 1)

Answers

Answer 1

To find ℒ (4t^2) (t − 1), we need to take the Laplace transform of the given function. For ℒ (4t^2) (t − 1), f(s) = 0.

Using the linearity property of the Laplace transform, we can split the function into two terms:

ℒ (4t^2) (t − 1) = ℒ (4t^2) - ℒ (4t^2)(1)

Let's calculate each term separately:

ℒ (4t^2):

Using the power rule of the Laplace transform, we have:

ℒ (4t^2) = 4 * ℒ (t^2)

Applying the power rule again, we get:

ℒ (t^2) = 2! / s^(2+1) = 2! / s^3 = 2 / s^3

Therefore, ℒ (4t^2) = 4 * (2 / s^3) = 8 / s^3.

ℒ (4t^2)(1):

Using the property of the Laplace transform of a constant, we have:

ℒ (4t^2)(1) = 4 * ℒ (t^2)(1)

Again, applying the property of the Laplace transform of a constant, we get:

ℒ (t^2)(1) = 1 * ℒ (t^2) = 1 * (2 / s^3) = 2 / s^3

Therefore, ℒ (4t^2)(1) = 4 * (2 / s^3) = 8 / s^3.

Now, we can combine the two terms:

ℒ (4t^2) (t − 1) = ℒ (4t^2) - ℒ (4t^2)(1) = 8 / s^3 - 8 / s^3 = 0.

Hence, f(s) = 0.

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Related Questions

The area of a container is 3.01×10^6cm^2. What would the area of the container be in m^2? ENTER NUMERIC VALUE ONLY USING 3 SIG FIGS .. NO UNITS OR SCIENTIFIC NOTATION! Question 8 2 pts The volume of a container is 2.73×10^−7m^3. What would the volume of the container be in mm^3? ENTER NUMERIC VALUE ONLY USING 3 SIG FIGS - NO UNITS OR SCIENTIFIC NOTATION!

Answers

The area of the container in m² is 30.1.The volume of the container in mm³ is 27,300.

To convert the area of the container from cm² to m², to divide the given value by 10,000, as there are 10,000 cm² in 1 m².

Area in m² = Area in cm² / 10,000

Area in m² = 3.01 × 10³ cm² / 10,000

= 301 × 10² cm² / 10,000

= 30.1 m²

To convert the volume of the container from m³ to mm³, to multiply the given value by 1,000,000,000, as there are 1,000,000,000 mm³ in 1 m³.

Volume in mm³ = Volume in m³ × 1,000,000,000

Volume in mm³ = 2.73 × 10²(-7) m³ × 1,000,000,000

= 273 × 10²(-7) m³ × 1,000,000,000

= 273 × 10²(-7) × 10³ m³

= 273 × 10²(2) mm³

= 27,300 mm³

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Exam score =7. 78+(0. 05* Reading speed) +(5. 77* comprehension) what exam score would you expect students to achieve if they have a reading speed of 150w. P. M and a comprehension score of 7?

Answers

The value of exam score is 55.67 using basic mathematical concept like addition and multiplication.

Given Exam score in terms of an equation where Reading speed and comprehension are variables.

let's first try to understand what is an equation.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration,

2x - 5 = 13.

2x - 5 and 13 are expressions in this case.

These two expressions are joined together by the equal sign "=".

Here in our question

Exam score = 7.78 + 0.05*Reading Speed + 5.77*comprehension.

Reading speed is 150 wpm

comprehension = 7.

Put these values in equation.

Exam score = 7.78 + 0.05*150 + 5.77*7 = 55.67

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How many like terms are in the expression? 14x- 14y +7 - x + z + 2x
A.0
B.2
C.3
D.5

Answers

Answer:

Step-by-step explanation:

14y, 7, x, z, 2x are the terms in this equation. A term is separated by signs (like + or-)

given r={a,b,c,d} and f={b→c, ca→d, bd→a, ba→d, cd→b} when computing a minimal cover, if you process the functional dependencies in order, which is the first one that is found to be redundant?

Answers

The first functional dependency found to be redundant in the minimal cover is "bd→a".

To compute the minimal cover, follow these steps:

1. Make each functional dependency (FD) singleton on the right side.
2. Remove extraneous attributes in FDs.
3. Eliminate redundant FDs.

In this case, the given FDs are already singleton on the right side. For step 2, we simplify the FDs:
- ca→d becomes c→d (removing extraneous attribute 'a')
- ba→d remains the same

Now, for step 3, we check for redundancy:
- b→c is not redundant
- c→d is not redundant
- bd→a is redundant because b→c and ba→d imply bd→a (using transitivity)
- ba→d is not redundant
- cd→b is not redundant

So, the first redundant FD is "bd→a".

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4(t²-5t) + 3u³ when t=4 and u=5?

ASAP

Answers

The answer to this equation will be 359

Answer: 359

Step-by-step explanation:

4(t²-5t) + 3u³ plug in the t and u

= 4[4²-5(4)] + 3(5)³

= 359

PLEASE ACCTUALY HELP :<

Point A has the coordinates (-2,-4). Point A is reflected across the x-axis to create point 'A'. What are the coordinates of point "A"? Enter your answer in the space below.

Answers

Answer:

(-2, 4)

Step-by-step explanation:

Hopes this helps!

There are y narts to this question. Yiu war be anked to movide fint 1 answer in each part. In our dataset we obsenve thiee variables that we strangly befieve do not have a relabonhip with wages, but that are correlated with the endoeenour variable riciuct. These variables mee dixt, which denotes the distance between the wroticer's viliage and the closest school, wralh yofene. Which is a dummin variable that takes the value of 1 if the worker regularly brushes hiv/her teeth ithe eovemment provides a free toothbrunh to each citizen and we believe that more educated people tend to brush their teeth more offen, and library, which is a dummy variable that takes the value of 1 if the worker has access to a library in his/her viliage. We estimafe our regression model using TSIS We want to test if our instruments satisfy the relevance requirement. In the 1 st stage of TSLS we estimate the following equation: edue =π0+π1 diat +π2 aralhygiene +π1 hitrary +π4 erper +NH What is the null hypothesis to test for instruments' relevance? A) H0:π1=π2=π3=π4=0. B) H0:π1=π2=π3=0. C) H0:π2=π3=π4=0. D) H0:π2=0 or π3=0 or π4=0. E) HD:π1=0 or π2=0 or π3=0. F) H0:π1=0 or π2=0 or π3=0 or π4=0. Answer:

Answers

The null hypothesis to test for instruments' relevance is option D) H0:π2=0 or π3=0 or π4=0.In order to test the relevance of the instrument, the first stage equation's null hypothesis should be stated as: H0: π2 = 0 or π3 = 0 or π4 = 0.The relevance requirement will be fulfilled if we can refute the null hypothesis.

The null hypothesis will not be rejected if the F-statistic is less than 10.0. However, if the F-statistic is greater than 10.0, the null hypothesis will be rejected, indicating that the variables are relevant and that the instrument satisfies the relevance requirement.In summary, to test for instruments' relevance in TSLS, the null hypothesis of the first stage equation is stated as H0: π2 = 0 or π3 = 0 or π4 = 0.

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What are 3 ways to solve inequalities?

Answers

We can solve the Inequalities by Isolating the variables that are present in the given Inequality.

What are Inequalities:

In mathematics, an inequality is a connection between two values or mathematical equations that results in an unequal comparison.

The signs that we use in Inequalities are less than( < ), less than or equal to ( ≤ ), greater than ( > ), greater than or equal to ( ≥ ), and not equal to (≠) sign.

Solving Inequalities:

Lets us consider we have inequality 3x + 2 + x ≥ 10

We can solve the above inequality as given below

Here we will solve the inequality by Isolating the variable

Step - 1

Add x term and constant terms

=> 4x + 2 ≥ 10 [ here 3x + x = 4x ]

Step - 2

Bring out x terms at one side, and constant terms at another side by doing required operations like adding

=> 4x + 2 ≥ 10 [ here we will subtract 2 from both sides ]

=> 4x + 2 - 2 ≥ 10 - 2

=> 4x ≥ 8

Step - 3

Now isolate the variable to get the solution

=> 4x/4 ≥ 8/4 [ here divided by 4 ]

=> x ≥ 2

Therefore, the required solution is x ≥ 2

Therefore,

We can solve the Inequalities by Isolating the variables that are present in the given Inequality.

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b) Express 0.6363......as a rational number in its lowest term.

Answers

Answer:

$\frac{7}{11}$

Step-by-step explanation:

We require 2 equations with the repeating digits (63) placed after the decimal point.

let x = 0.636363..... (1) multiply both sides by 100

100x = 63.6363... (2)

Subtract (1) from (2) thus eliminating the repeating digits

99x = 63 ( divide both sides by 99 )

x = $\frac{63}{99}$ = $\frac{7}{11}$ ← in simplest form

What is the quotient of StartFraction 6 Over 7 EndFraction and StartFraction 3 Over 14 EndFraction?
(A) 1/4
(B) 2
(C) 3 1/3
(D) 4

Answers

Answer:

The correct answer is (D) 4

Step-by-step explanation:

Hopes this helps!

Answer:

(D) 4

Step-by-step explanation:

6/7

3/14

6/7

14/3

6 × 14

7 × 3

84/21

84 ÷ 21

21 ÷ 21

= 4

5x=5y=1
15x-15y=-15 solve using substitution

Answers

Step-by-step explanation:

Step1

Make y the subject of the formula from equation 2

-15y/-15=-15-15x/-15

Y=15+15/15..............3

Substitute equ..... 3 to equ.... 1

5x-5(15+15/15)=1

5x-1(15+15/3)=1

3*5x-1*3(15+15/3)=1*3

15x-1(15+15)=3

15x-15-15pp=3

15x-30=3

15x=3+30

15x/15=33/15

x=2.2

From equation.....

5x-5y=1

5(2.2)-5y=1

11-5y=1

-5y=1-11

-5y/-5=10/-5

Y=-2

PROVE

FROM EQUATION ONE

5X-5Y=1

5(2.2)-5(-2)=1

11-10=1

1=1

SO Y=-2 AND X=2.2

As a estimation we are told £3 is €4. Convert £25.50 to euros €

Answers

Answer:

£34

Step-by-step explanation:

→ Find how euros is in a pound

£3 = €4

£1 = €1.33

→ Multiply the euro by 25.50

1.33333 × 25.50 = £34

Answer:

€34

Step-by-step explanation:

First you'll want to find out how much £1 is.

Since we know £3 is equal to €4 we can:

divide £3 by 3 = £1divide €4 by 3 = €1.33

So, £1 = €1.33

With this in mind, we can find out what £25.50 is:

£1 x 25.50 = £25.50€1.33 x 25.50 = €34

Therefore, £25.50 = €34

On a number line -1 2/3 (negative one and two-thirds) would be placed between what 2 integers? *

Answers

-2 and -1 is the answer

which number has a value between -8.423 and -8.395 number line

Answers

The number between -8.423 and -8.395 will be - 8 2/5.

Good luck

About 7% of the population has a particular genetic mutation. 200 people are randomly selected.Find the mean for the number of people with the genetic mutation in such groups of 200.

Answers

The mean of 200 people with the genetic mutation will be 14.

In the question,

we are given that 7% of the population has a particular genetic mutation.

that is a probability of genetic mutation

P=7%

7%=7/100

number of people (n) = 200

mean = np (from binomial distribution)

=200*7/100

=200*0.07

=14

thus the mean of 200 people with the genetic mutation will be 14.

what is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

what is binomial distribution?

In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each containing its own Boolean-valued results: "success or failure".

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The following 5 keys are for the following 5 locked padlocks. Each key opens one and only one padlock. Different keys open different padlocks. What is the least number of trials needed to guarantee that you will open all 5 padlocks?

Answers

$ {5}^{5} $

is the answer.

how many packages of diapers can you buy with 40$ if one packages cost 8$. this is a one step equation

Answers

In order to determine how many packages of diapers you can buy, it is only necessary to divide the total money you have, between the price of each package.

You have:

available money = 40$

package cost = 8$

Then, you calculate the quotient between available money and package cost:

$\frac{40}{8}=5$

Hence, you can buy 5 packages of diapers with 40$

4r + 9s + r+ r+ r+ r+r

Answers

Answer:

9 + 9

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Have a great day, be safe and healthy

Thank u

find an equation for the hyperbola that satisfies the following conditions. vertices (−3,−4) and (−1,−4); foci 10 units apart .

Answers

The equation of the hyperbola centered at (-2, -4) with vertices at (-3, -4) and (-1, -4) and foci 10 units apart is ((x+2)^2)/(1/4) - ((y+4)^2)/(124/4) = 1, or equivalently, (x+2)^2/0.25 - (y+4)^2/31 = 1.

The center of the hyperbola is the midpoint of the segment between the vertices, which is ((-3-1)/2, (-4-4)/2) = (-2, -4). Since the foci are 10 units apart, the distance from the center to each focus is c = 10/2 = 5. The distance between the vertices is 2a, where a is the distance from the center to each vertex, so a = |-3 - (-2)|/2 = 1/2. The distance between each focus and vertex is b, where b^2 = c^2 - a^2, so b = sqrt(5^2 - (1/2)^2) = sqrt(124)/2. The equation of the hyperbola centered at (-2, -4) with vertices at (-3, -4) and (-1, -4) and foci 10 units apart is ((x+2)^2)/(1/4) - ((y+4)^2)/(124/4) = 1, or equivalently, (x+2)^2/0.25 - (y+4)^2/31 = 1.

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Lennox owns a big apple orchard. She ships her apples to various markets using a fleet of trucks. Every week, each truck goes on 333 trips, and for each trip Lennox gets 300300300 dollars. On a single trip, a truck delivers 505050 packs, and each pack contains 121212 kilograms of apples. Overall, Lennox sells 450045004500 dollars worth of apples in a week. How much does Lennox get for a single kilogram of apples? Dollars per kilogram

Answers

Using proportions, it is found that Lennox gets 2.5 dollars per kilogram.

During each week:

The truck goes on 3 trips.In each trip, 50 packs are delivered.Each pack contains 12 kilograms of apples.

Hence, the amount of kilograms delivered each week are:

$A = 3(50)(12) = 1800$

He sells 4500 dollars each week(1800 kilograms), hence, the amount of dollars per kg is:

$D = \frac{4500}{1800} = 2.5$

Lennox gets 2.5 dollars per kilogram.

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Answer:0.50

Step-by-step explanation:

the incomplete table above shows the results of a study in which doctors gave patients experiencing back pain either a drug or a sugar pill. three times as many patients were cured from the drug than from the sugar pill. for every 2 patients cured by the sugar pill, 5 patients were not cured by the sugar pill. according to the results, if a patient is given a sugar pill, what is the probability that the person will be cured of back pain?

Answers

The probability that the person will be cured of back pain is 2/7.

The probability that a person will be cured of back pain after being given a sugar pill can be determined by using the given information in the question. According to the question, for every 2 patients cured by the sugar pill, 5 patients were not cured by the sugar pill. This means that out of a total of 2 + 5 = 7 patients given the sugar pill, only 2 were cured. Therefore, the probability of a patient being cured of back pain after being given a sugar pill is 2/7.

To calculate the probability, we can use the formula:

P(cured) = number of patients cured / total number of patients

Plugging in the given values, we get:

P(cured) = 2 / 7

Therefore, the probability that a patient will be cured of back pain after being given a sugar pill is 2/7.

In conclusion, according to the results of the study, if a patient is given a sugar pill, the probability that the person will be cured of back pain is 2/7.

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When you have two or more numbers, written in scientific notation, with the same exponent, how do you know which
number is the biggest and which is the smallest?

Answers

Yes you know me and 3x the key.

What is m∠EQD, in degrees?

Answers

Answer:52

Step-by-step explanation:

104 / 2 = 52 and a inscribed angle is half of a central angle.

Given 12 consecutive integers, how many ways can three of these integers be selected to give a sum which divides by 4.

Disclaimer: A lot of points to be given, Full explanation required. Not only answer.

Answers

$\\ \rm\longmapsto ^nC_r=\dfrac{n!}{r!(n-r)!}$

$\\ \rm\longmapsto ^{12}C_3$

$\\ \rm\longmapsto \dfrac{12!}{3!(12-3)!}$

$\\ \rm\longmapsto \dfrac{12!}{3!(9!)}$

$\\ \rm\longmapsto \dfrac{12(11)(10)(9!)}{3!(9!)}$

cancel 9!

$\\ \rm\longmapsto \dfrac{12(11)(10)}{3!}$

$\\ \rm\longmapsto \dfrac{1320}{3(2)(1)}$

$\\ \rm\longmapsto \dfrac{1320}{6}$

$\\ \rm\longmapsto 220$

In a ∆ABC, if ∆A= 72° and ∆B = 63°, find ∆C..

Answers

Answer:

C is 45!

Explanation:

72+63=135

180-135=45

15. Describe the three general steps
for producing a recombinant DNA (rDNA) vector, state how rDNA can
be introduced into cells, and discuss the clinical applications of
rDNA.

Answers

Producing rDNA involves isolating and cleaving DNA, inserting fragments into a vector, and transforming host cells. rDNA can be introduced via transformation, transfection, or viral vectors. Clinical applications include protein production, gene therapy, vaccines, and diagnostics.

Producing a recombinant DNA (rDNA) vector involves several general steps. Here are the three main steps involved in the process:

Isolation and Cleavage of DNA:

The first step is to isolate the desired DNA fragments from the source organism. This can be done using various techniques such as PCR (Polymerase Chain Reaction) or restriction enzyme digestion. Restriction enzymes are enzymes that cut DNA at specific recognition sites. By using the appropriate restriction enzymes, the desired DNA fragment and a vector DNA can be cut at specific sites. The vector is usually a plasmid, which is a small circular DNA molecule.

Insertion of DNA Fragments into the Vector:

Once the DNA fragments and vector have been cut, they are mixed together and joined through a process called ligation. DNA ligase is used to catalyze the formation of covalent bonds between the ends of the DNA fragments and the vector. This creates a recombinant DNA molecule containing the desired DNA fragment within the vector. The recombinant DNA molecule is then introduced into host cells for replication.

Transformation of Host Cells:

The recombinant DNA molecules need to be introduced into host cells to produce multiple copies of the recombinant DNA. This is typically done using a process called transformation. Host cells, such as bacteria or yeast, are treated in a way that makes them more receptive to taking up the recombinant DNA. Methods for transformation include heat shock, electroporation, or using chemical agents. Once the host cells have taken up the recombinant DNA, they can be grown in culture to produce large quantities of the desired DNA fragment.

Introduction of rDNA into Cells:

Recombinant DNA can be introduced into cells using various methods, depending on the type of cells being targeted. Some common techniques include:

Transformation: As mentioned earlier, host cells, such as bacteria or yeast, can be treated to make them receptive to taking up the recombinant DNA. This can be achieved by exposing the cells to heat shock, electroporation, or using chemical agents.

Transfection: This method is used for introducing rDNA into eukaryotic cells, including animal cells. It involves the use of techniques such as calcium phosphate precipitation, liposome-mediated transfection, or electroporation.

Viral Vectors: Certain viruses, such as retroviruses, adenoviruses, or lentiviruses, can be modified to carry the recombinant DNA. These viral vectors can then infect target cells and deliver the rDNA into the host genome.

Clinical Applications of rDNA:

Recombinant DNA technology has revolutionized biomedical research and has led to numerous clinical applications. Some important applications include:

Production of Therapeutic Proteins: rDNA technology allows for the production of large quantities of therapeutic proteins, such as insulin, growth factors, clotting factors, and monoclonal antibodies. These proteins can be used to treat various diseases, including diabetes, cancer, and genetic disorders.

Gene Therapy: rDNA vectors can be used to deliver functional copies of genes into target cells to correct genetic defects. This holds promise for the treatment of inherited diseases caused by single gene mutations, such as cystic fibrosis and muscular dystrophy.

Vaccine Development: Recombinant DNA technology has been instrumental in the development of vaccines. By expressing specific antigens from pathogens, recombinant vaccines can be created to stimulate an immune response without causing disease.

Diagnostic Tools: Recombinant DNA techniques are used to produce specific DNA or RNA probes for diagnostic purposes. These probes can detect the presence of specific genes or mutations associated with diseases, aiding in early detection and personalized medicine.

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Someone please help!

Answers

Answer: b yes

Step-by-step explanation: the unit rate will be 48

Answer:

Step-by-step explanation:

yes, the proportional ratio is y/x=k

156/3.25=48

204/4.25=48

252/5.25=48

the ratio is 48

You are tasked with sorting the rods. What does RB likely stand for?
A. Rejected Bins
B. Requisite Bins
C. Red Bins
D. Rolling Bins
E. Rod Bins
A Report Content Errors