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The solution to the given initial value problem, y'' 2y' + 2y = δ(t-π), with y(0) = 4 and y'(0) = 2 is given by:  y(t) = 4 + 2t + e-t (1 + eπ-t)-1.


To arrive at this answer, we must use the definition of the Dirac delta function to solve the given equation. We know that δ(t-π) = 0 for all t ≠ π, and that it is an impulse at t = π. This means that the left side of the equation (y'' 2y' + 2y) is equal to 0 for all t ≠ π. This equation can be solved using the method of undetermined coefficients, and the general solution of this homogeneous equation is yh = c1et + c2e-t.

To solve for the particular solution of this equation, we use the given initial conditions of y(0) = 4 and y'(0) = 2. Using this information, we solve for the constants c1 and c2 in the general solution and the particular solution is yp = 4 + 2t + e-t (1 + eπ-t)-1. This is the solution to the given initial value problem.

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Step-by-step explanation:

simplify each term. think that's the answer

\( \huge \boxed{\mathbb{QUESTION} \downarrow}\)

\( \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}\)

\( \sf\frac { 1 } { 8 } \times 64 \\ \)

Multiply 1/8 and 64 to get 64/8.

\( \sf \: \frac{64}{8} \\ \)

Divide 64 by 8 to get 8.

\( = \boxed{ \boxed{\bf \: 8}}\)

Hey there!

1/8 × 64

= 64/8

= 8/1

= 8

Hope it helps ya!

Answer:

y = 4x

Hope that helps!

Step-by-step explanation:

Answer: Option 2 is correct Y= -2x+1/2

Step-by-step explanation:

The solution is Option 2.

The equation of line in the slope intercept form is y = -2x + 1/2

where m is the slope m = -2 and the y intercept is 1/2

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

The value of A is given by

y - 5/2 = -2 ( x + 1 )

Now , the slope intercept of the equation of line is given by

Equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

So , on simplifying the equation , we get

y - 5/2 = -2 ( x + 1 )

y - 5/2 = -2x - 2

Adding 5/2 on both sides of the equation , we get

y = -2x - 2 + 5/2

y = -2x + ( -4 + 5 ) / 2

y = -2x + 1/2

The slope of the equation A is m = -2

The y intercept of the equation A is 1/2

Hence , The equation of line in the slope intercept form is y = -2x + 1/2

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Answer:

9%

Step-by-step explanation:

Set up a ratio:

\(\frac{33}{100}\) = \(\frac{35.97}{x}\)

Cross multiply: 33x = 35.97 * 100

33x = 3597

Divide by 33: x = 109

That means the tax is 9%.

Answer:

Step-by-step explanation:

\(V=10^2\cdot7+\frac13\cdot10^2\cdot(18-7)=700+\frac13\cdot1100=700+366,(6)=1066,(6)\\\\V\approx1067\,cm^2\)

Using the given linear equation, we found the altitude of the plane at different time periods and the altitude of airplane at 5 and 30 minutes is found to be 250 feet and 0 feet respectively.

What is a linear equation?

A linear equation is one that has the highest degree of 1 possible. This indicates that there are no variables in a linear equation with exponents greater than 1. A linear equation's graph almost always takes the shape of a straight line.

The linear equation which shows the altitude of an airplane is as follows,

y = -10x + 300

where y = altitude (in feet)

           x = time of descend ( minutes)

a) when x = 0

     y = 300 feet

  when x = 5 minutes

    y = -10 * 5 + 300 = 250 feet

 when x = 8 minutes

   y = -10 * 8 + 300 = 220 feet

when x = 10 minutes

 y = -10 * 10 + 300 = 200 feet

when x = 30 minutes

y = -10 * 30 + 300 = 0 feet.

the table is as follows:

x (minutes)     0         5          8          10       30

y(feet)            300    250     220     200       0

b) From the above table, we can see that at 5 minutes the altitude is 250 feet and at 30 minutes, the altitude is 0 feet. There is a decrease in altitude, which suggests the plane is descending and finally landed when the time was 30 minutes.

Therefore using the given linear equation, we found the altitude of the plane at different time periods and discussed the altitude of airplane at 5 and 30 minutes.

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Answer:

3 buses are needed.

Step-by-step explanation:

If there are only 2 buses, it would be full, but there would still be 12 students without a bus. To take all students, you'd need 3 buses. 2 buses will be full, and the other bus would only have 12 students.

Answer:3 buses

Step-by-step explanation:

Because 50+50 is 100 which is two buses

But there are 12 students left so you need 1 more buses

Answer:

x = 30 degrees

Step-by-step explanation:

Okay so we start by noticing that the two pointed out vertices = 180 degrees. So we have the following equation.

(x + 12) + (3x + 48) = 180

If you combine them you get:

4x + 60 = 180

Subtract 60 from both sides..

4x = 120

Divide both sides by 4..

x = 30

And there's your answer!

Part A - The coordinates of their houses are A(0,0) and A’(-5,-5).

Part B - We have shown that triangles ZBC and TAB’ are congruent by ASA congruence criterion, since they have a pair of congruent angles (angle ZBC = angle TAB’), a pair of congruent sides (BC = B’C’), and a right angle (angle ZBC and angle TAB’).

Part 1:

As Zari’s house is located at point A, and each unit on the coordinate plane corresponds to one mile, we can represent the location of her house as (0,0).

Similarly, Taye’s house is located at point A’, which is at (-5,-5) on the coordinate plane.

Part 2:

To draw their routes, we need to add the distances they run to their starting points.

Zari’s route:

2 miles north takes her to point B(0,2)

4 miles east takes her to point C(4,2)

Returning home via the shortest route takes her to point A(0,0)

Taye’s route:

2 miles west takes him to point B’(-7,-5)

4 miles south takes him to point C’(-7,-9)

Returning home via the shortest route takes him to point A’(-5,-5)

Now, we need to prove that the two triangles formed by their routes are congruent. Let's call the triangles ZBC and TAB’, as shown in the diagram below:

Proof:

We will prove that triangles ZBC and TAB’ are congruent by the ASA (Angle-Side-Angle) congruence criterion.

First, we notice that angle ZBC is a right angle because Zari returns home via the shortest route, which is a straight line that intersects BC perpendicularly. Similarly, angle TAB’ is a right angle because Taye also returns home via the shortest route, which is a straight line that intersects B’C’ perpendicularly.

Secondly, we can see that angle BZC and angle B’C’A’ are congruent because they are vertically opposite angles.

Finally, we can observe that the two sides BC and B’C’ are congruent because they both represent a distance of 4 miles.

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Answer:

The answer is 20 feet.

Step-by-step explanation:

Answer:

20 ft

Step-by-step explanation:

5 : 2 :: x : 8

Product of means  = product of extremes

2*x = 5*8

  2x = 40

     x = 40/2

x = 20

Step-by-step explanation:

Let width of the rectangle be y

Length of rectangle = 3y + 12.1

Perimeter = 2(L + y) = 122.6

2 (4y + 12.1 ) = 122.6

8y + 24.2 = 122.6

y = 98.4 / 8

y (width) = 12.3

Length = 49

x = 1

2x + 8 = 10

2x = 10 - 8

2x = 2

x = 2 : 2

x = 1

Answer:

1

Step-by-step explanation:

\(2x + 8 = 10 \\ 2x = 10 - 8 \\ 2x = 2 \\ x = \frac{2}{2} \\ x = 1\)

Answer:

-2.5

Step-by-step explanation:

(-15+-12+8+9)/4= -2.5

In order to convert the given measurement of the bar high jump connection from meters to millimeters, we need to use the following conversion factor:1 meter = 1000 millimeters

Therefore, to convert 4/75 meters to millimeters, we need to multiply it by 1000.4/75 meters x 1000 = 53.333... millimeters. However, we cannot have a fractional value of millimeters since it is a unit of measurement that cannot be divided into smaller units.

Therefore, we need to round our answer to the nearest whole millimeter.Rounding 53.333... millimeters to the nearest whole millimeter gives us:53.333... ≈ 53 millimeters. Therefore, the length of the bar high jump connection must always be 53 millimeters.

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Answer: i got you my boi answer is x > -3

Step-by-step explanation:

Answer:

35.11 ft

Step-by-step explanation:

This given situation can be thought of as triangle \(\triangle PQR\) where PQ is the length of pole.

PR is the length of rope.

and QR is the distance of bottom of pole to the point of fastening of rope to the ground.

And \(\angle Q \neq 90^\circ\)

Given that:

PQ = 44 ft

PR = 51 ft

\(\angle R = 58^\circ\)

To find:

Side QR = ?

Solution:

We can apply Sine Rule here to find the unknown side.

Sine Rule:

\(\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}\)

Where  

a is the side opposite to \(\angle A\)

b is the side opposite to \(\angle B\)

c is the side opposite to \(\angle C\)

\(\dfrac{PR}{sinQ}=\dfrac{PQ}{sinR}\\\Rightarrow sin Q =\dfrac{PR}{PQ}\times sinR\\\Rightarrow sin Q =\dfrac{51}{44}\times sin58^\circ\\\Rightarrow \angle Q =79.41^\circ\)

Now,

\(\angle P +\angle Q +\angle R =180^\circ\\\Rightarrow \angle P +58^\circ+79.41^\circ=180^\circ\\\Rightarrow \angle P = 42.59^\circ\)

Let us use the Sine rule again:

\(\dfrac{QR}{sinP}=\dfrac{PQ}{sinR}\\\Rightarrow QR =\dfrac{sinP}{sinR}\times PQ\\\Rightarrow QR =\dfrac{sin42.59}{sin58}\times 44\\\Rightarrow QR = 35.11\ ft\)

So, the answer is 35.11 ft.

When the level of significance is 0.07, the corresponding confidence level is 93%.

The level of significance (α) in statistical hypothesis testing represents the probability of rejecting the null hypothesis when it is actually true. In contrast, the confidence level represents the degree of certainty or reliability we have in the estimated results from a statistical analysis.

The confidence level is calculated as the complement of the level of significance, subtracted from 1. In this case, if the level of significance is 0.07, we subtract it from 1 to find the confidence level:

Confidence level = 1 - level of significance

Confidence level = 1 - 0.07

Confidence level = 0.93 or 93%

Therefore, when the level of significance is 0.07, the corresponding confidence level is 93%. This means that we can be 93% confident that the estimated results from a statistical analysis will fall within the desired range, while allowing for a 7% chance of Type I error (rejecting the null hypothesis when it is true).

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Answer:

\(z = \frac{q}{2} \)

Step-by-step explanation:

\(z \infty q\)

\(z = kq\)

\(z = 2 \: and \: q = 1\)

\(2 = k1\)

\(k = \frac{2}{1} \)

\(z = \frac{1}{2} q\)

\(z = \frac{q}{2} \)

9514 1404 393

Answer:

  z = 2q

Step-by-step explanation:

The formula for direct variation is ...

  z = kq . . . . . k is the constant of proportionality

We can find k using the given values of z and q:

  k = z/q = 2/1 = 2

Then the equation connecting z and q is ...

  z = 2q

Answer:

59/110

Step-by-step explanation:

Based on these results, express the probability that the next person will purchase one or more costumes as a fraction in simplest form.

204 no costume, 209 exactly one costume, 27 more than one costume.

204+\color{steelblue}{209}+\color{steelblue}{27}=

204+209+27=

\,\,\color{indianred}{440}

440

There were a toal of 440 customers. 209+27=236 visitors purchased one or more costumes costumes.

Probability the next visitor will purchase one or more costumes:

\frac{\color{steelblue}{236}}{\color{indianred}{440}}=

440

236

​

=

\,\,\frac{59}{110}

110

59

​

The perimeter of the inside of the track is 444.44m

Based on the information given, the length will be 150m and the width is 46m.

The circumference will be:

=2πr

= (2 × 3.14 × 46/2)

= 144.44

The length will be:

= 2 × 150

= 300

The perimeter of the oval will be:

= 300 + 144.44

= 444.44m

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Step-by-step explanation:

(x² /x² + 7x + 6)÷(9x - 9/x² - 1)

(x²/(x + 1)(x + 6))×((x + 1)(x - 1)/9(x - 1))

(x²/(x + 6))×1/9

x²/9(x + 6)

Yes.

Using the distributive property 3(2x-12) = 6x-36

the distributive property: a(b+c) = ab+ac

3(2x-12) = 3.2x - 3.12 = 6x - 36

yes i agree

The total weight of the liquid that filled the hemispheric tank to the nearest full pounds is 66775 pounds.

An hemisphere is half of a sphere. Therefore,

volume = 2 / 3 πr³

where,

Therefore,

r = 7 feet

volume = 2 / 3 × 3.14 × 7³

volume = 2 / 3 × 3.14 × 343

volume = 2154.04 / 3

volume = 718.013333333

volume = 718.013

Therefore,

density = mass / volume

93 =  mass / 718.013

mass = 718.013 × 93

mass = 66775.24

mass ≈ 66775 pounds

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Answer:iuygafsg78t arsy9u E)AFI_0=W]O-W[IOUPDIOYfguvydagai8sw09dQI

Step-by-step explanation:

Answer:

look at the screenshot

Step-by-step explanation:

Answer:

Step-by-step explanation:

25- guaranteed

$14 on each table waited on

He waited on 17.

17x14= $238 tips

238+25= $263

1. Marques expects to earn $263 on 17 tables

2. He expects to make 25+14t per day.

Answer:

Option A will be your answer

Step-by-step explanation:

hope it helps

have a great day