The slope of the graphed line is . Which formulas represent the line that is graphed? Check all that apply.

The solution to the differential equation D²y(t) + 12 Dy(t) + 36y(t) = 2 \(e^{(-5t)}\), with initial conditions y(0) = 1 and Dy(0) = 0, is \(y(t) = (1 + 6t) e^{(-6t)}\).

To solve the given differential equation using the classical method, we can assume a solution of the form \(y(t) = e^{(rt)}\) and find the values of r that satisfy the equation. We then use these values of r to construct the general solution.

Using the classical method:

Substitute the assumed solution \(y(t) = e^{(rt)}\) into the differential equation:

D²y(t) + 12 Dy(t) + 36y(t) = \(2 e^{(-5t)}\)

This gives the characteristic equation r² + 12r + 36 = 0.

Solve the characteristic equation for r by factoring or using the quadratic formula:

r² + 12r + 36 = (r + 6)(r + 6)

= 0

The repeated root is r = -6.

Since we have a repeated root, the general solution is y(t) = (c₁ + c₂t) \(e^{(-6t)}\)

Taking the first derivative, we get Dy(t) = c₂ \(e^{(-6t)}\)- 6(c₁ + c₂t) e^(-6t).\(e^{(-6t)}\)

Using the initial conditions y(0) = 1 and Dy(0) = 0, we can solve for c₁ and c₂:

y(0) = c₁ = 1

Dy(0) = c₂ - 6c₁ = 0

c₂ - 6(1) = 0

c₂ = 6

The particular solution is y(t) = (1 + 6t) e^(-6t).

Using the Laplace transform method:

Take the Laplace transform of both sides of the differential equation:

L{D²y(t)} + 12L{Dy(t)} + 36L{y(t)} = 2L{e^(-5t)}

s²Y(s) - sy(0) - Dy(0) + 12sY(s) - y(0) + 36Y(s) = 2/(s + 5)

Substitute the initial conditions y(0) = 1 and Dy(0) = 0:

s²Y(s) - s - 0 + 12sY(s) - 1 + 36Y(s) = 2/(s + 5)

Rearrange the equation and solve for Y(s):

(s² + 12s + 36)Y(s) = s + 1 + 2/(s + 5)

Y(s) = (s + 1 + 2/(s + 5))/(s² + 12s + 36)

Perform partial fraction decomposition on Y(s) and find the inverse Laplace transform to obtain y(t):

\(y(t) = L^{(-1)}{Y(s)}\)

Simplifying further, the solution is:

\(y(t) = (1 + 6t) e^{(-6t)\)

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Answer:

Please refer to the attachment

Answer:

Step-by-step explanation:

the answer would be 5/4 i belive

The volume of the figure is 1, 005. 4 mi³

Note that the figure is a cylinder

The formula for volume of a cylinder is given as;

Volume = πr²h

Where

h = height = 5 mi

r = radius = 8mi

Substitute into the volume

Volume = 3. 142 × 8 × 8 × 5

Volume = 1,005. 4 mi³

Thus, the volume of the figure is 1, 005. 4 mi³

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Answer:

The value of e is -1 and f is -2.

Step-by-step explanation:

The steps are :

\(2e - 3f = 4 - - - (1)\)

\(2e - 5f = 8 - - - (2)\)

\(2e - 3f - 2e - ( - 5f) = 4 - 8\)

\(2f = - 4\)

\(f = - 4 \div 2\)

\(f = - 2\)

\(substitute \: f = - 2 \: into \: (1)\)

\(2e - 3( - 2) = 4\)

\(2e + 6 = 4\)

\(2e = 4 - 6\)

\(2e = - 2\)

\(e = - 2 \div 2\)

\(e = - 1\)

To solve this system of equations by addition, our first goal is to cancel

out one of the variables by adding the two equations together.

However, before we add, we need to cancel out a variable.

I would choose to cancel out the e's.

To do this, we need a 2e and a -2e and

here we have a 2e in both equations.

If we multiply the second equation by -1 however,

that will give us the -2e we are looking for.

So we have (-1)(2e - 3f) = (4)(-1).

So rewriting both equations, our first equation stays the same

but our second equation becomes -2e + 3f = -4.

Notice that every term in the second

equation has been multiplied by -1.

2e - 3f = 4

-2e + 5f = -8

Now when we add the equations together,

the e's cancel and we have 2f = -4 so f = -2.

To find e, plug -2 back in for f in the

first equation to get 2e - 3(-2) = 4.

Solving from here, e = -1.

Note that e comes before f in our final answer, (-1, -2).

To determine which variable should go first

in your answer, use alphabetical order.

Answer:

x = 5

Step-by-step explanation:

4x + 3 = 23

Subtract 3 from both sides;

4x = 20

Divide both sides by 4;

x = 5

Answer:

x=5

Step-by-step explanation:

4x+3=23

4x=23-3

4x=20

x=20/4

x=5

1. 1080°

2. 36°

3. 27 diagonals

4. 140°

5. 7 sides

1. The sum S of the interior angles of a polygon is given by;

S = (n-2) x 180°

Where;

n = number of sides of the polygon.

Therefore, to get the sum of the interior angles of a polygon having 8 sides, we substitute n = 8 into equation (i) as follows;

S = (8 - 2) x 180°

S = 6 x 180°

S = 1080°

Therefore, the sum of the interior angles of a polygon having 8 sides is 1080°

2. The sum of interior angles of a polygon is given by;

S = (n - 2) x 180°

For a polygon which is a regular decagon where the number of sides n = 10, the sum is;

S = (10 - 2) x 180°

S = 8 x 180°

S = 1440°

Since the decagon is regular, then each of its interior angles is given by;

1440° / 10

=> 144°

Now, since we know that the sum of the interior angle and exterior angle will give 180°, then;

The exterior angle of a regular decagon is;

180° - 144° = 36°

Therefore, the exterior angle of a regular decagon is 36°

3. The number of diagonals N of a polygon with n sides is given by;

N = \(\frac{1}{2} n(n-3)\)

So, for a nonagon which has 9 sides (i.e n = 9), the number of diagonals is;

N = \(\frac{1}{2}*9(9-3)\)

N = \(\frac{1}{2}*9(6)\)

N = 9(3)

N = 27

Therefore, a nonagon has 27 diagonals.

4. The sum of interior angles of a polygon is given by;

S = (n - 2) x 180°

For a polygon which is a nonagon where the number of sides n = 9, the sum is;

S = (9 - 2) x 180°

S = 7 x 180°

S = 1260°

Since the nonagon is regular, then each of its interior angles is given by;

1260° / 9

=> 140°

Therefore, the measure of each angle (interior angle) of a regular nonagon is 140°

5. The sum of the interior angles of a polygon is given by;

S = (n - 2) x 180°

So if the sum is 900, then to get the number of sides of the polygon, we substitute S = 900 into the equation;

900° = (n - 2) x 180°

Divide through by 180°

5 = (n - 2)

Solve for n;

n = 5 + 2

n = 7

Therefore, the regular polygon has 7 sides.

Answer:

Step-by-step explanation:

∠A and ∠B being complementary means  m∠A + m∠B = 90°

4x + 24 + 3x - 4 = 90

7x + 20 = 90

  7x = 70

   x = 10

m∠B = (3•10 - 4)° = 26°

Answer:

si es suma tiene que ser 12+15=27

-2x = 28 - 6x --------------------------> Given

-2x + 6x = 28 - 6x + 6x------------------------------>Addition property of equality

4x = 28 -----------------------------------------> Simplification

4x/4 = 28/4 --------------------------------->Division property of equality

x = 7 --------------------------------------->Simplification

To determine the sign of the sum of two integers when one integer is positive and the other is negative, we can follow a simple rule based on their magnitudes.

If the magnitude of the positive integer is greater than the magnitude of the negative integer, the sum will be positive. This is because the positive integer outweighs the negative integer, resulting in a positive value.

On the other hand, if the magnitude of the negative integer is greater than the magnitude of the positive integer, the sum will be negative. In this case, the negative integer dominates and determines the sign of the sum.

In both scenarios, the sign of the larger magnitude integer takes precedence and determines the sign of the sum. It is important to note that the sum will always have the sign of the integer with the larger magnitude, regardless of the specific values of the integers involved.

By considering the magnitudes of the integers, we can easily determine the sign of their sum when one integer is positive and the other is negative.

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Answer: 4/3

Step-by-step explanation:

Answer:slope = 4

i gotchu fam

Step-by-step explanation:

Unsigned whole numbers in binary are represented by a sequence of 1s, with the number of 1s equal to the value of the number itself.

In binary representation, numbers are expressed using only 0s and 1s. When dealing with unsigned whole numbers, the value of the number determines the length of the sequence of 1s used for its representation. For example, the decimal number 5 would be represented in binary as "11111" since it consists of five consecutive 1s. Similarly, the decimal number 10 would be represented as "1111111111" since it consists of ten consecutive 1s. This encoding scheme allows for a simple and efficient representation of positive whole numbers in binary.

Binary representation provides a concise and efficient way to represent numbers in computing systems. It is the foundation of digital communication and storage, enabling the manipulation and processing of numerical data. Understanding how numbers are encoded in binary is essential for working with computer systems, algorithms, and programming languages.

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Answer:

250

Step-by-step explanation:

....................

Answer:

75%

Step-by-step explanation:

54/72 = 0.75

Answer:

1a. first 7×9=63 Then substracting 16 we get 47 and 2-47= -45

Answer:

a.  - 77

b. 4

c. 5x-14

d. 14

Step-by-step explanation:

a. 2-(7*9)-16

=> 2-63-16

=>(-61) - 16

=> -77

b.64 / 4+(3*4)

=> 64 /  4+12

=> 64 / 16

=> 4

c. 3x+2(x-7)

=> 3x+2x - 14

=> 5x-14

d. 5 + 6^2/ 4

=> 5+ 36/4

=> 5+9

=> 14

The solution is, Lower class limit is 7,7+13=20...33,46,59,72 and,

Upper class limit is 7+13-1=19,32,45,58,71,84

Class limits represent the largest and smallest data values that an be included in the class. Class limits are actual data values. Class boundaries provide values that eliminate gaps between the classes in the frequency distribution. Class boundaries are one decimal place more accurate than the data.

here, we have,

We have that the Class Width is given as

7-19

20-32

33-45

46-58

59-71

72-84

Generally

Class width =12.67

Class width =13

Hence

Lower class limit is

7,7+13=20...33,46,59,72

Upper class limit is

7+13-1=19,32,45,58,71,84

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Answer:

GO WITH THE GUT. ITS D

Step-by-step explanation:

Answer:207

Step-by-step explanation: circumference = to 2πr or πd
substitute the diameter into the equation πd (22/7)(66) and you get 207.4285...

The correct answer is 138 students.

x = .24 * 575

x = 138 students

Therefore, the correct answer is 138 students.

Answer:

$1,700.

Step-by-step explanation:

Since Cándido normally pays $ 875 for bodily injury and property damage insurance, and his insurance company increases premiums by 150% for 1 accident, 200% for 2-3 accidents, and 250% for 4 accidents, to find his premium for the year after he has three accidents to the nearest dollar, the following calculation must be performed:

875 x 200 / 100 = X

875 x 2 = X

1,700 = X

Therefore, his premium for the year after he has three accidents is $1,700.

Answer:

premium = $ 875

increase 200%

875 * 200 / 100

=$1750

Step-by-step explanation:

The number of combinations of 6 boys and 20 girls that can exist among 26 children born in a hospital on a given day is 230,230.

]To calculate the number of combinations, we can use the concept of binomial coefficients. The formula for calculating the number of combinations is C(n, k) = n! / (k!(n-k)!), where n is the total number of objects and k is the number of objects we want to select.

In this case, we have 26 children in total, and we want to select 6 boys and 20 girls. Plugging these values into the formula, we get C(26, 6) = 26! / (6!(26-6)!) = 230,230. Therefore, there are 230,230 different combinations of 6 boys and 20 girls that can exist among the 26 children born in the hospital on that given day.

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The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day, 3 days a week is 0.653.

We have,
Vermont had 65.3% of respondents who said yes to exercising for at least 30 minutes a day, 3 days a week.

To find the sample proportion, you can convert the percentage to a decimal by dividing the percentage by 100.

Step 1:

Convert the percentage to a decimal.
65.3 / 100 = 0.653

Thus,
The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day, 3 days a week is 0.653.

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Differentiate both sides of

\(y = \dfrac{x\sqrt{a^2-x^2}}2 + \dfrac{a^2}2\sin^{-1}\left(\dfrac xa\right)\)

with respect to y ; by the product rule,

\(1 = \dfrac12\sqrt{a^2-x^2}\dfrac{\mathrm dx}{\mathrm dy} + \dfrac x2 \dfrac{\mathrm d}{\mathrm dy}\left[\sqrt{a^2-x^2}\right] + \dfrac{a^2}2\dfrac{\mathrm d}{\mathrm dy}\left[\sin^{-1}\left(\dfrac xa\right)\right]\)

Use the chain rule for the remaining derivatives.

\(\dfrac{\mathrm d}{\mathrm dy}\left[\sqrt{a^2-x^2}\right] = \dfrac1{2\sqrt{a^2-x^2}}\dfrac{\mathrm d}{\mathrm dy}\left[a^2-x^2\right] \\\\ = \dfrac{-2x}{2\sqrt{a^2-x^2}}\dfrac{\mathrm dx}{\mathrm dy} \\\\ = -\dfrac x{\sqrt{a^2-x^2}} \dfrac{\mathrm dx}{\mathrm dy}\)

Recall that

\(\dfrac{\mathrm d}{\mathrm dx}\left[\sin^{-1}(x)\right] = \dfrac1{\sqrt{1-x^2}}\)

Then

\(\dfrac{\mathrm d}{\mathrm dy}\left[\sin^{-1}\left(\dfrac xa\right)\right] = \dfrac1{\sqrt{1-\left(\frac xa\right)^2}}\dfrac{\mathrm d}{\mathrm dy}\left[\dfrac xa\right] \\\\ = \dfrac1{a\sqrt{1-\left(\frac xa\right)^2}}\dfrac{\mathrm dx}{\mathrm dy} \\\\ = \dfrac1{\sqrt{a^2}\sqrt{1-\left(\frac xa\right)^2}}\dfrac{\mathrm dx}{\mathrm dy} \\\\ = \dfrac1{\sqrt{a^2-x^2}}\dfrac{\mathrm dx}{\mathrm dy}\)

Putting everything together, we have

\(1 = \dfrac{\sqrt{a^2-x^2}}2\dfrac{\mathrm dx}{\mathrm dy} - \dfrac{x^2}{2\sqrt{a^2-x^2}}\dfrac{\mathrm dx}{\mathrm dy} + \dfrac{a^2}{2\sqrt{a^2-x^2}}\dfrac{\mathrm dx}{\mathrm dy}\)

\(1 = \left(\dfrac{\sqrt{a^2-x^2}}2+\dfrac{a^2-x^2}{2\sqrt{a^2-x^2}}\right)\dfrac{\mathrm dx}{\mathrm dy}\)

\(1 = \dfrac1{2\sqrt{a^2-x^2}}\bigg((a^2-x^2) + (a^2-x^2)\bigg)\dfrac{\mathrm dx}{\mathrm dy}\)

\(1 = \dfrac{2a^2-2x^2}{2\sqrt{a^2-x^2}}\dfrac{\mathrm dx}{\mathrm dy}\)

\(1 = \sqrt{a^2-x^2}\dfrac{\mathrm dx}{\mathrm dy}\)

\(\boxed{\dfrac{\mathrm dx}{\mathrm dy} = \dfrac1{\sqrt{a^2-x^2}}}\)

Answer:

rfgcc ft v crytrcvrcvhtfvyrfftv ffg

Step-by-step explanation:

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