Help me answer dis .

The solution to the initial-value problem is:

y(t) = (1/7)(1) + (6/7)(e^(-7t))

y(t) = 1/7 + (6/7)e^(-7t)

To solve the given initial-value problem using the Laplace transform, we'll take the Laplace transform of both sides of the differential equation, solve for Y(s), and then find the inverse Laplace transform to obtain the solution y(t).

Let's denote the Laplace transform of y(t) as Y(s) and the Laplace transform of y'(t) as Y'(s).

Taking the Laplace transform of the differential equation:

L[y''(t)] + 7L[y'(t)] = L[δ(t - 1)]

Using the properties of the Laplace transform and the derivative property, we have:

s²Y(s) - sy(0) - y'(0) + 7sY(s) = e^(-s)

Substituting the initial conditions y(0) = 0 and y'(0) = 1:

s²Y(s) - 0 - 1 + 7sY(s) = e^(-s)

Simplifying the equation:

(s² + 7s)Y(s) = 1 + e^(-s)

Y(s) = (1 + e^(-s)) / (s² + 7s)

Now, we need to express the right side of the equation in terms of standard Laplace transforms. We can rewrite (1 + e^(-s)) as (1 + e^(-s))/s^0:

Y(s) = (1/s^0 + e^(-s)/s^0) / (s² + 7s)

Using the Laplace transform pairs, the Laplace transform of 1/s^0 is 1, and the Laplace transform of e^(-s)/s^0 is 1/s:

Y(s) = (1 + 1/s) / (s² + 7s)

Now, we can use partial fraction decomposition to express Y(s) in a form that can be inverted using standard inverse Laplace transforms.

Y(s) = [(s + 1) / s(s + 7)]

Using partial fraction decomposition:

Y(s) = A/s + B/(s + 7)

To find the values of A and B, we'll multiply through by the denominators and equate the numerators:

(s + 1) = A(s + 7) + Bs

Expanding and equating coefficients:

s + 1 = As + 7A + Bs

By comparing the coefficients of the corresponding powers of s, we get:

A + B = 1 (coefficient of s)

7A = 1 (constant term)

From the second equation, A = 1/7. Substituting this back into the first equation, we find B = 6/7.

Therefore, the partial fraction decomposition is:

Y(s) = 1/7s + 6/7(s + 7)

Taking the inverse Laplace transform:

y(t) = (1/7)(L^(-1)[1/s]) + (6/7)(L^(-1)[1/(s + 7)])

Using the inverse Laplace transform pairs:

L^(-1)[1/s] = 1

L^(-1)[1/(s + 7)] = e^(-7t)

Therefore, the solution to the initial-value problem is:

y(t) = (1/7)(1) + (6/7)(e^(-7t))

y(t) = 1/7 + (6/7)e^(-7t)

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Answer:

Increase of 9.3%

Step-by-step explanation:

Hence, the percent increase in salary did Jerry receive is \(4.68\)%.

What is the percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

Here given that,

Jerry’s monthly salary was $\(3,050\) last year. This year his monthly salary is $\(3,350\).

His monthly salary in last year is $ \(3050\).

In this year his salary is $\(3350\).

So, the increase in salary is

\(3350-3050=300\)

And the overal salary is $ \(3050+3350=6400\)

So, the percent increase in salary did Jerry receive is

\(\frac{300}{6400}\) × \(100=4.68\)

Hence, the percent increase in salary did Jerry receive is \(4.68\)%.

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Answer:

((x)h)g

Step-by-step explanation:

Hope this helps and if this is wrong then please comment the right answer and I will edit it thanks :)

The ships will be approximately 28.9 miles apart after two hours.

The speed and bearing of two ships leaving from a harbor, we need to find how far apart they will be after two hours.Applying the formula of distance = speed × time. We can find the distance covered by each ship.Distance covered by the first ship in 2 hours = 12 × 2 = 24 miles.

Distance covered by the second ship in 2 hours = 8 × 2 = 16 miles.

To find the distance between the two ships, we need to use Pythagoras' theorem.

As per the question, one ship is traveling at S12°W while the other ship is traveling at N75°E.

This can be shown in the figure below:\(\(AB=24\) and \(BC=16\)\)

Now, we can find the distance between the two ships as:AC² = AB² + BC² = 24² + 16²= 576 + 256 = 832

The distance between the two ships after 2 hours will be approximately \(\sqrt{832}\) miles.

The distance between the two ships after 2 hours is approximately 28.9 miles (rounded to one decimal place).

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Answer:

i think c

Step-by-step explanation:

Answer:

440 minutes

Step-by-step explanation:

i just multiplied by 2

continuous is an experiment studies the number of tickets written each day by campus police for illegal parking by the university of akron students.

A continuous variable is a type of variable that can take on an infinite number of values within a defined range. The number of tickets written each day by campus police for illegal parking is an example of a continuous variable because there can be an infinite number of values that it can take on within a certain range (e.g. 0 tickets to 100 tickets).

Continuous variables are often used in scientific experiments to measure things like time, weight, height, and so on. These variables can take on any value within a specified range, and the values can be expressed to any level of precision. In contrast, a categorical or discrete variable is a type of variable that can only take on a limited number of values. For example, the number of days in a week (7 days) is a discrete variable because it can only take on 7 values.A continuous variable is a type of variable in statistics and mathematics that can take any value within a specific range or interval. This means that there is an infinite number of possible values that a continuous variable can assume. For example, the height of a person, the temperature of a room, or the time it takes to run a certain distance are all examples of continuous variables. Unlike discrete variables, which can only take specific, distinct values, continuous variables can take any value within a certain range.

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an experiment studies , the number of tickets written each day by campus police for illegal parking by the university of akron students. this variable is

Answer: The one on the left.

Step-by-step explanation:

There is no file, but the panda on the left is bigger.

I used Elimination method

x =3

y = 1/10

Hope it helps

Answer:

The correct answer is 9.5 ft

Step-by-step explanation:

got this correct on my test

The ratio of the volume of the first cube to the volume of the second cube is 1:27. The correct option is (C).

Let's represent the length of the edge of the first cube "n" and the length of the edge of the second cube "3n".

The volume of the first cube is:

V1 = n³

The volume of the second cube is:

V2 = (3n)³ = 27n³

To find the ratio of the volume of the first cube to the volume of the second cube, we divide V1 by V2:

V1/V2 = n³ / (27n³) = 1/27

Therefore, the required ratio is 1:27.

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The correct question is as follows:

One cube has edges n meters long. Another has edges 3n meters long. What is the ratio of the volume of the first cube to the volume of the

second cube?

A 1:3

B. 1:9

C. 1:27

D. 1:6

E. 1:81

Answer:

C.N x = ±√2, 0

Step-by-step explanation:

Basic Power Rule:

f(x) = cxⁿ

f’(x) = c·nxⁿ⁻¹

Critical numbers occur when f'(x) is equal to zero or undefined.

Step 1: Define function

f(x) = x⁴ - 4x²

Step 2: Find critical numbers

Answer:

3n + 21

Step-by-step explanation:

3(n + 7)

~Distribute

3n + 21

Best of Luck!

Answer:

The exact answer is 4\(\sqrt{2}\) or 5.7 rounded to the nearest tenth

Step-by-step explanation:

\(x^{2}\) + \(7^{2}\) = \(9^{2}\)

\(x^{2}\) + 49 = 81  Subtract 49 from both sides

\(x^{2}\) = 32

\(\sqrt{x^{2} }\) = \(\sqrt{32}\)

x = \(\sqrt{32}\) = \(\sqrt{2x2x2x2x2}\) = 4\(\sqrt{2}\)

Answer:

\(-5x+7\)

Step-by-step explanation:

Given: Two expressions are \((4x+1),(-9x+6)\)

To find: sum of the given expressions in simplest terms

Solution:

A variable is a term that takes various numerical values and a constant is a term that takes a fixed numerical value.

Consider \((4x+1)+(-9x+6)\)

Here, solve \((4x-9x),(1+6)\)

\(4x-9x=(4-9)x=-5x\\1+6=7\)

Therefore,

\((4x+1)+(-9x+6)=(4x-9x)+(1+6)=-5x+7\)

Answer:

14 feet

Step-by-step explanation:

Area= base x height

Height=area/base

182/13=14

The answer to part a) is that next year, in 2023, NCSSM will use approximately 55,485 sheets of paper. In part b), total of approximately 363,353 sheets of paper will be used from 2018 through the end of 2030.


a) To calculate the paper used in 2023, we start with the initial amount used in 2018, which is given as 60,000 sheets of paper. We then need to calculate the decrease in paper use over the years. The rate of decrease is given as 2.25%, which can be written as 0.0225 in decimal form. To find the paper used in 2023, we multiply the initial amount by (1 - rate of decrease)^5, since five years have passed from 2018 to 2023.

b) To calculate the total paper used from 2018 to 2030, we need to sum up the paper used for each year in that time period. We start with the initial amount used in 2018, which is 60,000 sheets. Then we calculate the paper used each year using the same formula as in part a), multiplying the initial amount by (1 - rate of decrease)^n, where n represents the number of years since 2018. We sum up these values for the years 2018 to 2030, which is a total of 13 years.

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The algebraic rule applied to one of the vertices is (x, y) → (-y, x)

From the question, we have the following parameters that can be used in our computation:

Triangle ABC and 270 degrees rotation counter clockwise

Assuming that vertex A is located on the coordinate plane, one of the rules applied to its coordinates would be (x, y) → (-y, x) for a counterclockwise rotation of 270° about the origin.

This means that the new coordinates of point A after the rotation would be (-y, x).

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The inequality represented in the graph attached is y ≥ (1/2)x + 3 and 3x - y > 2

An equation is an expression that shows the relationship between two or more numbers and variables.

Independent variables represent function inputs that do not depend on other values, while dependent variables represent function outputs that depends on other values.

The inequality represented in the graph attached is y ≥ (1/2)x + 3 and 3x - y > 2

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Step-by-step explanation:

11.

tan 30 = perpendicular / base = x/ 7

1/√3 = x/7

X= 7/√3

2.

cos 30 = 7/y

√3/2 = 7/y

y = 7×2/ √3

y= 14/√3

plz mark my answer as brainlist plzzzz.

hope this will be helpful to you ☺️.

Answer:

-4.23230, -4.232300, -4.2323000

Answer:

1) -4.23230 2)-4.232300 3)-4.2323000

Step-by-step explanation:

Where is my brainliest and my points :)

Answer:

1:2
2:4
3:6
4:8

Step-by-step explanation:

K=2

Answer:

See below

Step-by-step explanation:

● (7x^3 - 2x^2 -12) + (-3x^3 - 8x^2 +10x)

● 7x^3 - 2x^2 - 12- 3x^3 - 8x^2 + 10x

Combine like terms

● 7x^3 - 3x^3 -2x^2 - 8x^2 -12 + 10x

● 4x^3 - 10x^3 +10x -12

Answer:

Addition:::::4x^3-10x^2+10x-12

25 components are randomly chosen and tested; if there are no more than 3 defective components, the entire batch is accepted. The probability is it that the shipment will be accepted is 0.7323.

Given that,

An organization utilizes the following acceptance sampling strategy for ordering shipments of 600 machine parts: 25 components are randomly chosen and tested; if there are no more than 3 defective components, the entire batch is accepted. This specific component is known to have a 4% fault rate.

We have to find how probability is it that the shipment will be accepted.

By binomial we get,

Binomial Problem:

n = 25 ; p = 0.04

P(0<= p <= 2)

= 0.7323

Therefore, The probability is it that the shipment will be accepted is 0.7323.

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The length of the rectangle is 7y - 3

What is a Rectangle?

A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. The area of  a rectangle A = L×W

Where,

A = Area of the rectangle which is 7y^2 - 3y

L = Length  which is unknown

W = Width of the rectangle which is y

Substituting,

7y^2 - 3y = L × y

divide through by y

(7y^2 - 3y)/y = L

L = 7y - 3

Therefore the length of the rectangle is 7y - 3

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The sets of number to which - 2/5 belongs is a rational number.

If p and q are integers and q is not equal to 0, then the number is in the form of p/q and is said to be rational. Among the rational number examples are 1/3, 2/4, 1/5, 9/3, and so forth. A rational number is any number that can be expressed as a ratio (or fraction) of two integers.

P/Q is the format for rational numbers, where p and q are open-ended integers and q 0. Thus, natural numbers, whole numbers, integers, fractions of integers, and decimals are all examples of rational numbers.

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The smallest such whole number is 11 which is, Which is divided by 3, the remainder is 2, f it, divided by 4, the remainder is 3

Let the number be x

Here we have to find the whole number which is Divided by 3,4 the remainder is 2,3 respectively,

x+(3–2)= x +1 is multiple of 3

Div by 4 remainder is

3x+(4–3) = x+1 is multiple of 4

So LCM of 3,4 is 3×4 = 12

Hence,x=12 –1 =11

The smallest such whole number is 11 which is divided by 3, the remainder is 2, if it divided by 4, the remainder is 3.

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The expression that is equivalent to \((3a)^{-2}\) is \(\frac{1}{9a^{2} }\).

Given expression is \((3a)^{-2}\)

\(a^{-n} =\frac{1}{a^{n} }\)

So, the given expression \((3a)^{-2}\)can be written as \(\frac{1}{(3a)^{2} }\)

\(\frac{1}{(3a)^{2} }= \frac{1}{3a*3a} =\frac{1}{9a^{2} }\)

Therefore, the expression that is equivalent to \((3a)^{-2}\) is \(\frac{1}{9a^{2} }\).

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Answer:

A

Step-by-step explanation:

StartFraction 1 Over 9 a squared EndFraction or 1/9a^2 looks something like that :) hopefully it helps

Answer:

Hi

Step-by-step explanation:

How is your day??

Answer:

Hello

How are you doing??