calc 3 iiiiiiiiiiiiiiiiiiiiiiiiiiii

Calc 3 Iiiiiiiiiiiiiiiiiiiiiiiiiiii

Answers

Answer 1

Take the Laplace transform of both sides:

L[y'' - 4y' + 8y] = L[δ(t - 1)]

I'll denote the Laplace transform of y = y(t) by Y = Y(s). Solve for Y :

(s²Y - s y(0) - y'(0)) - 4 (sY - y(0)) + 8Y = exp(-s) L[δ(t)]

s²Y - 4sY + 8Y = exp(-s)

(s² - 4s + 8) Y = exp(-s)

Y = exp(-s) / (s² - 4s + 8)

and complete the square in the denominator,

Y = exp(-s) / ((s - 2)^2 + 4)

Recall that

L⁻¹[F(s - c)] = exp(ct) f(t)

In order to apply this property, we multiply Y by exp(2)/exp(2), so that

Y = exp(-2) • exp(-s) exp(2) / ((s - 2)² + 4)

Y = exp(-2) • exp(-s + 2) / ((s - 2)² + 4)

Y = exp(-2) • exp(-(s - 2)) / ((s - 2)² + 4)

Then taking the inverse transform, we have

L⁻¹[Y] = exp(-2) L⁻¹[exp(-(s - 2)) / ((s - 2)² + 4)]

L⁻¹[Y] = exp(-2) exp(2t) L⁻¹[exp(-s) / (s² + 4)]

L⁻¹[Y] = exp(2t - 2) L⁻¹[exp(-s) / (s² + 4)]

Next, we recall another property,

L⁻¹[exp(-cs) F(s)] = u(t - c) f(t - c)

where F is the Laplace transform of f, and u(t) is the unit step function

[tex]u(t) = \begin{cases}1 & \text{if }t \ge 0 \\ 0 & \text{if }t < 0\end{cases}[/tex]

To apply this property, we first identify c = 1 and F(s) = 1/(s² + 4), whose inverse transform is

L⁻¹[F(s)] = 1/2 L⁻¹[2/(s² + 2²)] = 1/2 sin(2t)

Then we find

L⁻¹[Y] = exp(2t - 2) u(t - 1) • 1/2 sin(2 (t - 1))

and so we end up with

y = 1/2 exp(2t - 2) u(t - 1) sin(2t - 2)


Related Questions

Ms. McCullough bought a bunch of bananas. If she ate 2/8
the bananas and Mrs. Byrd ate 1/4, what fraction of bananas
remains?

Answers

Answer:

1/2

Step-by-step explanation:

that's the answer because 2/8-1/4 is 1/2

Three times the difference “2x minus 1” is the opposite of 9 times x. Solve for x.

Answers

Answer:

x = 1/5 - first box

Step-by-step explanation:

Let's interpret this by using what I call the "isolated-x method."

First, we can simplify whatever's being affected in the parentheses.

#1: 3 times (2x) is equal to 6x

#2: 3 times (- 1 | equal to -1) results in -3, or + -3

So now we're working with 6x - 3 = -9x.

Now, we'll add a positive 9x to the -9x, since it can be hugely helpful to have one side result in 0.

Now we're working with 15x (6x + our new 9x) - 3 = 0

Since we have "whole like terms" we can now easily add 3 to each side.

Now we're working with 15x = 3 (0 + our new 3)

We can finish by dividing each side by 3.

15x = 3 now turns into 5x = 1.

To get from 5 to 1 you can multiply 5 by its "multiplicative inverse," also known as 1/5.

Therefore, x = 1/5

Hopefully this helped a bunch! Tell me if you need any further assistance...

( :

A scale model of a bicycle has a scale of 1 : 25. The real bicycle has a length of 1.75 m. What is the length of the model in cm?​

Answers

Answer:

It's 7 I just did this question today and got it right

Find the product. Simplify your answer.
(m+2)(3m+2)

Answers

there you go the answer is in the picture

3m^2+2m+6m+4
3m^2+8m+4

In the past, Marcie's father rode his bike 108 miles in 7.5 hours. Her mother rode the same distance in 8 hours. Marcie plans to ride her bike 108 miles at a steady rate of 18 mph for y hours. Will she match her father or mothers time? Use the equation 108÷y=18 to justify your answer.​

Answers

Using the speed - distance relationship, Marcie's time will be 6 hours. Hence, she'll match her parents time.

Recall :

Speed = distance / time

To obtain Marcie's time :

18 = 108 / y

We can solve for y thus :

y × 18 = 108

y = 108 / 18

y = 6 hours

Since, Marcie's will cover the same distance in 6 hours, the she'll match and surpass her parents time.

Learn more : https://brainly.com/question/25449918

Strawberries cost $3.00 per pound. For each question
a.
How many pounds of strawberries can you buy for $1.00?
b.
How many pounds of strawberries can you buy for $11.0

Answers

Answer:

A. 1/3 pound

B. 11/3 or 3.666666667

Step-by-step explanation:

:)

The area of a rectangle is 24 square inches. Determine both dimensions if the length is 6 inches less than three times the width

Answers

Answer:

width is 4 inches

length is 6 inches

Step-by-step explanation:

the length is 6 inches less than three times the width

l = 3w - 6

a = l * w

a = (3w - 6)w

a = 3w^2 - 6w

area of the rectangle is 24 square inches

3w^2 - 6w = 24

subtract 24 from both sides

3w^2 - 6w - 24 = 0

Divide both sides by 3

w^2  - 2w - 8 = 0

Factor

(w - 4)(w + 2) = 0

w = {-2, 4}

disregard the negative root since measurement must be positive

w = 4

l = 3w - 6

l = 3(4) - 6

l = 6

In the penny game exercise, why do you think it takes longer for one person to flip five batches of two pennies then one batch of ten pennies

Answers

It takes longer for one person to flip five batches of two pennies than one batch of ten pennies, mainly for a simple reason: although 5 x 2 is equal to 10, that is, it will take the same time to flip the coins, 5 batches is greater than 1 batch, which will take longer to manipulate each of these, increasing the total time.

Learn more about maths in https://brainly.com/question/21477139

Alvin’s family used 18.5 gallons of gas to drive 518 miles. How many miles did they drive per gallon of gas?

Please help me

Answers

Answer:

the answer is 1.2

Step-by-step explanation:

The number of miles Alvin’s family drive per gallon of gas is 28 miles.

Given that, Alvin’s family used 18.5 gallons of gas to drive 518 miles.

What is the unitary method?

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Number of miles drive per gallon of gas = Total number of miles ÷ Total number of gallons

= 518 ÷ 18.5

= 28 miles

Hence, the number of miles Alvin’s family drive per gallon of gas is 28 miles.

To learn more about the unitary method visit:

brainly.com/question/22056199.

#SPJ2

Are the two ratios that make up a proportion
always, sometimes, or never equivalent

Answers

Answer:

Always

Step-by-step explanation:

In mathematics, when we say that two ratios form a proportion, we mean that the two ratios are equal.

Ex: Ratios and Proportions - Proportions - In Depth. A proportion is simply a statement that two ratios are equal. It can be written in two ways: as two equal fractions a/b = c/d; or using a colon, a:b = c:d. The following proportion is read as "twenty is to twenty-five as four is to five."

A proportion is two ratios which have been set equal to each other; a proportion is an equation that can be solved. When I say that a proportion is two ratios that are equal to each other, I mean this in the sense of two fractions being equal to each other. For instance, 105 equals 21 .

The two ratios sometimes that make up a proportion.

What is Proportional?

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

We know that;

Two ratios that make up a proportion when both ratios are equal to each other.

And, When two ratios are not equal then it cannot make a proportion.

Hence, The two ratios sometimes that make up a proportion.

Learn more about the proportion visit:

https://brainly.com/question/1496357

#SPJ2

solve the equation 5/x+3 + 4/x+2 = 2

Answers

Answer:

5 + 4 = 9

x × x = X2

3 + 2 = 5

9/x + 5 = 2

Answer:

5/x+3+4/x+2=2

=9/x+5=2

9/x=-3

Multiply both sides by x

9= -3x

Divide by -3

Answer x=  -3

Hope this helps

WILL GIVE BRAINLIEST ‼️ The graph represents the piecewise function:

Answers

Answer:

[tex]f(x) = \left \{ {{x + 3} \quad \text{if} \ -3 \leq x < -1\atop {5} \quad \text{if} \ -1 \leq x \leq1} \right.[/tex]

Step-by-step explanation:

You can find the first function if you know the general form of a line:

[tex]y = mx + b[/tex]

where [tex]m[/tex] is the slope and [tex]b[/tex] the intercept point with the [tex]y[/tex]-axis.

So in the first case the slope is 1 because the next formula

[tex]m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2-0}{-1+3} = 1[/tex]

And you can find the interception point if extend the line, then in our case is  3.

So the function is:

[tex]f(x) = x + 5[/tex]

In the other case is constant function that's mean that the function has the next form

[tex]f(x) = k[/tex]

Where [tex]k[/tex] is a constant.

So you only have to observe what is the value for each point in the interval, in this occasion is 5.

So the final answer is:

[tex]f(x) = \left \{ {{x + 3} \quad \text{if} \ -3 \leq x < -1\atop {5} \quad \text{if} \ -1 \leq x \leq1} \right.[/tex]

dur rn help pls ))))))))))

Answers

I believe it is a because I had a question just like that in 8th grade

A secured loan would most likely be used to pay for

A. college
B. a car
C. groceries
D. a phone

Answers

Obviously a phone and grocers :) Just kidding it’s probably college

A secured loan would most likely be used to pay for a car, the correct option is B.

We are given that;

The four options

Now,

A secured loan is a loan that is backed up by collateral pledged by the borrower, such as a car or property.

The lender can sell the collateral to cover repayment of the loan if the borrower defaults.

Car, since it is a common type of collateral for secured loans.

College, groceries and a phone are less likely to be used as collateral for secured loans, since they are either intangible, perishable or low-value assets.

Therefore, by loan the answer will be car.

Learn more about loan payment here:

https://brainly.com/question/4234016

#SPJ2

Does anyone know this?

Answers

Answer:

I think 7.6 i remember i had something like this  

Step-by-step explanation:

Please help I do not understand thanks

Answers

I don’t think I can help you with this, but I hope you have a nice day and figure it out!

help me due today it is math

Answers

Yes I need to know and find the digit that makes 1258 divisible by 9

Answer:

2

Step-by-step explanation:

sum of digits=1+2+5+8=16

smallest term to be added to make it divisible by 9 is 2

∵16+2=18÷9=2

A package contains 12 ounces of cereal .If you use 1 portion of this cereal which is 1 1/3 how much would be left in the cereal box?

Answers

To answer this question, you would need to divide the total amount of cereal in the box by the serving size.

This would be 12 2/3 divided by 1 1/3.

We can write each mixed number as an improper fraction first before we divide:12 2/3 = 38/3 and 1 1/3 = 4/3

Now divide 38/3 by 4/3. Recall that dividing by a fraction is accomplished by multiplying by the reciprocal of the divisor: 38/3 * 3/4 = 114/12 = 38/4 OR 19/2

Also, 19/2 is equivalent to 9 and 1/2. There would be 9 and 1/2 servings in the box of cereal.

Hope this helps

-----------------------------

Answers

Answer:

thanks for tha points

Step-by-step explanation:

From a group of 15 men and 12 women, how many ways can you select a group of 2?
Answer:

Answers

The total number of ways this can be done together is 105 × 66 = 6930

This is a combination question question it has to do with selection.

In order to group 2 men from 15 men, this can be expressed using the combination formula as shown;

15C2 = 15!/(15-2)!2!

15C2 = 15!/13!2!

15C2 = 15×14/2

15C2 = 105 ways

Similarly in order to group 2 women from 12 men, this can be expressed using the combination formula as shown;

12C2 = 12!/(12-2)!2!

12C2 = 12!/10!2!

12C2 = 12×11/2

12C2 = 66 ways

The total number of ways this can be done together is 105 × 66 = 6930

Learn more about combination here: https://brainly.com/question/14492965

write the value of the underlined digit in words 6,302,450? 3 being the underlined number.

Answers

Answer:

Three hundred thousand

Step-by-step explanation:

Hope this helps

Please helpppp I will mark you branliest pleaseee

Answers

Answer:

no

Step-by-step explanation:

the ratios shown in this table are not proportionate. You will also never get (0,0) in this table.

What is 3.59 rounded to the nearest whole number?

Answers

Answer:

its 4 ezy

Step-by-step explanation:

please mark as brainlists

-2.875 greater than or less than -2 7/8

Answers

Answer:

They are both the same.

Step-by-step explanation:

-2.875

7/8 = 0.875 thus -2 7/8 is equal to -2.875

if there was a group of ten people the probability of them being born on the same day of the same year is 1, true or false and why

Answers

Answer:

True

Step-by-step explanation:

For instance, twins are born on the same day but imagine ten people instead of two being born on the same day.

solve for x and y then find the measure of each angle ​

Answers

Step-by-step explanation:

∵ MP is a straight line.

∴ ∠MNQ + ∠PNQ = 180°

[tex](3y + 8)° + (3y + 22)° = 180° \\ 3y + 8 + 3y + 22 = 180 \\ 6y + 30 = 180 \\ 6y = 150 \\ y = 25[/tex]

∵ MP is a straight line.

∴ ∠MNR + ∠PNR = 180°

[tex](2x + 5)° + (3x - 55)° = 180° \\ 2x + 5 + 3x - 55 = 180 \\ 5x - 50 = 180 \\ 5x = 230 \\ x = 46[/tex]

A fire is sighted due west of lookout A. The bearing of the fire from lookout B, 8.6 miles due south of A, is N 42°26'W. How far is the fire from B (to the nearest tenth of a mile)? 7) A)13.7 mi B)11.7 mi C)12.7 mi D)14.7 mi

Answers

Answer:

11.7 miles

Step-by-step explanation:

I hope this helped!


Problem example: For the given sequence: -2,2,6,10,14,18
Write a recursive formula to find the nth term: a = an-1+4
Write a explicit formula to find the nth term: a = -2 + 4(n-1)
What is the 64th term in the sequence?

Answers

Answer:

250

Step-by-step explanation:

You can take the explicit formula and simply substitute the n value with 64:

-2 + 4 * (64 - 1)

-2 + 4 * (63)

-2 + 252

250

what is the distance between the coordinates (9, -2) and (9, 8) show your work on a coordinate grid pleas help mee

Answers

Answer:

10

Formular for finding distance between two points; (x2-x1)² + (y2-y1)² (all square root)

X1=9

X2=9

Y1=-2

Y2=8

Distance= (9-9)²+(-2-8)² (all square root)

=(0)²+(-10)² (all square root)

=0 + 100 (square root)

=100 square root

=10

20 feel from the ground i need a ladder placed 15 feet from the house what is the length

Answers

Answer:

helooo

Step-by-p explanation:

Other Questions
PLS HELP CHEMWhat is the temperature, in Celsius, of 20.8 g of carbon dioxide (CO2) in a 575 mL container under 1.5 atm of pressure? El texto literario utiliza un tipo de lenguaje que persigue un cierto fin esttico para captar el inters del lector, por lo tanto, utiliza la funcin: Pls solve this, its math And only if you know the answer pls What type of cell is shown above? A. prokaryotic B. plant C. eukaryotic D. animal The sum of two numbers is 91 the difference of the two numbers is 67 what are the two numbers let x be the larger number and y be the smaller number 50 points for the answers to this question 67 is 0.12% of what number? Explain why might it be a good idea to go into business with someone who has a very different personality than you please help me w my khan academy Paragraph 71. What is the purpose of the last paragraph? How do youknow? What words or phrases insinuate this purpose? Need help ASAP, Im going somewhere! Reuben Garza just graduated from high school and had begun a five year apprenticeship as a machinist. His starting wage ... https://brainly.com/question/25586250 orFind the slope of the line y = 95x 95. how old was winter the dolphin when she passed away Complete each series with the next logical word1. Vendredi, samedi, ___2. Le matin, L'apres-midi, ___3. Hier, aujourd'hui, ____4. Lundi, mercredi, ___5. mardi, jeudi some macromolecules are polymers. what is a polymer Finding it hard. Id love some help and the answers. Thanks 22. They don't______ the grammar point before. A. look as though they study B. sound as if to study C. appear like they were studying D. seem to have studied Select the correct answer from each drop-down menu.The graph of g(x) is shown.The graph of h(x) = g(x + 5) has and . Biology cell division What are the answers to this chart Which number line shows the solution set for StartAbsoluteValue d EndAbsoluteValue greater-than 3?A number line going from negative 4 to positive 4. Closed circles are at negative 3 and positive 3. Everything to the left of negative 3 and right of positive 3 is shaded.A number line going from negative 4 to positive 4. Open circles are at negative 3 and positive 3. Everything between the points is shaded.A number line going from negative 4 to positive 4. Closed circles are at negative 3 and positive 3. Everything between the points is shaded.A number line going from negative 4 to positive 4. Open circles are at negative 3 and positive 3. Everything to the left of negative 3 and to the right of positive 3 is shaded.