-2( 3x - 1) = -6x - 1

The equation in integral form by taking the inverse Laplace transform: x(t) = L^-1((s^2 - 9s + 20)X(s)) + L^-1(F(s) + sx(0) + x'(0) - 8x(0)), where L^-1 represents the inverse Laplace transform.

To express the given initial value ordinary differential equation (ODE) using convolution notation with *, we can rewrite it as:

(x'' - 8x' + 12x) = f(t)

Taking the Laplace transform of both sides, we have:

s^2X(s) - sx(0) - x'(0) - 8(sX(s) - x(0)) + 12X(s) = F(s)

where X(s) is the Laplace transform of x(t), x'(0) is the initial condition of the derivative of x(t), x(0) is the initial condition of x(t), and F(s) is the Laplace transform of f(t).

Simplifying the equation, we get:

(s^2 - 8s + 12)X(s) - sx(0) - x'(0) + 8x(0) = F(s)

Now, let's express the left-hand side of the equation using convolution notation. Using the property that the Laplace transform of the derivative of a function f(t) is sF(s) - f(0), we can rewrite the equation as:

((s^2 - 8s + 12) - s + 8)X(s) = F(s) + sx(0) + x'(0) - 8x(0)

Simplifying further, we have:

(s^2 - 9s + 20)X(s) = F(s) + sx(0) + x'(0) - 8x(0)

Finally, we can express the equation in integral form by taking the inverse Laplace transform:

x(t) = L^-1((s^2 - 9s + 20)X(s)) + L^-1(F(s) + sx(0) + x'(0) - 8x(0))

where L^-1 represents the inverse Laplace transform.

To know more about  inverse Laplace transform refer here:

https://brainly.com/question/13263485#

#SPJ11

Comparing this with the left-hand side expression -V cosec^2θ - 3V^2cosec^2θcotθ, we can see that both sides are equal.

To prove the given equation, we will differentiate both sides with respect to θ and simplify the expression.

Differentiating V cotθ + V^3cosecθ with respect to θ:

d/dθ(V cotθ + V^3cosecθ) = d/dθ(V cotθ) + d/dθ(V^3cosecθ)

Applying the differentiation rules:

= V (-cosec^2θ) + 3V^2cosecθ(-cosecθcotθ)

= -V cosec^2θ - 3V^2cosec^2θcotθ

Now, we need to express the right-hand side of the original equation in terms of dV/dθ:

V cotθ + V^3cosecθ = V(cotθ + V^2cosecθ)

                      = V(cotθ + cotθV^2)

                      = Vcotθ(1 + V^2)

Taking the derivative of the right-hand side with respect to θ:

d/dθ(Vcotθ(1 + V^2)) = V(−cosec^2θ)(1 + V^2) + Vcotθ(0)

                           = -Vcosec^2θ(1 + V^2)

Comparing this with the left-hand side expression -V cosec^2θ - 3V^2cosec^2θcotθ, we can see that both sides are equal. Therefore, we have proved that dV/dθ = V cotθ + V^3cosecθ.

To know more about expression, refer here:

https://brainly.com/question/28170201#

#SPJ11

Answer:

Part A - i. 0.68 N ii. 1.88 N

Part B - The wagon will move slowly while being raised up off the ground.

Step-by-step explanation:

Part A: Suppose the direction of the force changes from a 48° angle with the floor to a 70° angle with the floor. Determine the effect on the horizontal and vertical components of the force. Give forces to the nearest hundredth of a unit.

Since the force of 2 N is exerted at this new angle of 70°,

i. the horizontal component u = 2cos70° = 0.684 N ≅ 0.68 N and its

ii. vertical component, v = 2sin70° = 1.879 N ≅ 1.88 N

Part B: What implications does this have for pulling the wagon? Explain.

Since we have a horizontal component of 0.68 N and a vertical component of 1.88 N, most of the force is used in raising the wagon off of the ground with less of it moving it forward. So, the wagon will move slowly while being raised up off the ground.

Answer:

It is plugging it the 36pye

Step-by-step explanation:

h = 36pye

what it wants you to do is plug that into all the numbers

so it be

2 x 36pye (you get it for the next one)

for the fraction ones it would

be divding 36pye by the number on the bottom

The mean number of students in the class is 2.4 siblings.

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = total sum of siblings / number of students

[(0 x 4) + ( 1 x 4) + ( 2 x 2) + ( 3 x 8) + ( 4 x 4) ] / ( 2 + 4 + 2 + 8 + 4)

= 48 / 20 = 2.4 siblings

To learn more about mean, please check: https://brainly.com/question/25842202

#SPJ1

The accumulated value of $8600 at 6.45% after 8 months (simple interest) is $8971.90.

To compute the accumulated value of $8600at 6.45% after 8 months (simple interest), we need to use the formula for simple interest, which is given by:

I = P × r × t

Where, I is the interest earned, P is the principal amount, r is the interest rate, and t is the time in years.

Here, we have t in months, so we need to convert it into years by dividing by 12.

So, t = 8/12 = 2/3 years.

Now, substituting the given values, we get:

I = 8600 × 6.45/100 × 2/3 = $371.90

Therefore, the accumulated value of $8600 at 6.45% after 8 months (simple interest) is $8600 + $371.90 = $8971.90.

Learn more about interest rate at:

https://brainly.com/question/23920675

#SPJ11

Answer:

The perimeter to the question is 30.

Step-by-step explanation:

.

[tex]3 + 3 + 3 + 3 + 9 + 9 \\ 6 + 6 + 18 \\ 12 + 18 \\ 30[/tex]

Answer:

Sample standard deviation = 3

Step-by-step explanation:

We can use the following steps to calculate the sample standard deviation for the given data set:

Step 1: First, calculate the mean of the data set by adding all the values and dividing by the total number of values:

(12 + 12 + 12 + 15 + 18 + 18 + 18) / 7 = 15.

Thus, the mean is 15.

Step 2: Next, subtract the mean from each value in the data set to get the deviation of each value from the mean.

(12 - 15) = -3

(15 - 15) = 0

(18 - 15) = 3

Thus, the deviations are -3, -3, -3 0, 3, 3, and 3.

Step 3:   Square each deviation:

(-3)^2 = 9

0^2 = 0

(3)^2 = 9

Thus, the squares of all our deviations are 9, 9, 9, 0, 9, 9, and 9.

Step 4:  Add up all the squared deviations:

9 + 9 + 9 + 0 + 9 + 9 + 9 = 54.

Thus, the sum of the squared deviations is 54.

Step 5:  Find the variance by dividing the sum of squared deviations by one less than the number of values in the data set:

54 / (7 - 1) = 9

54 / 6 = 9

Thus, the variance is 9

Step 6:   Finally, find the sample standard deviation by taking the square root of the variance:

√9 = 3

So, the sample standard deviation for this data set is 3.

Answer:

288 cm

Step-by-step explanation:

The formula to solve this polygon is: area = 1/2 x perimeter x apothem

To find the perimeter all you have to is find the sum of all sides together: 12+12+6+6+6+6= 48

Then the Apothem is, the "segment that joins the polygon's center to the midpoint of any side that is perpendicular to that side." To find this you find the point from the middle to the edge which is 12cm.

Then you plug in this information into the polygon. 1/2 x 48 x 12= 288!

The polygon is 288 cm!

Hope this helps! :) Please let me know if it does, and mark as brainliest!

Answer:

Subtract the y's: 7 - 2 = 5

Subtract the x's in the same order: 6 - 4 = 2

slope = (difference in y)/(difference in x) = 5/2

Answer: 5/2

To determine how many bow ties he can make, we need to convert the units of measurement and calculate the number of half-yard lengths in 18 feet.

To convert feet to yards, we need to divide the number of feet by 3, as there are 3 feet in a yard.

In this case, 18 feet is equal to 6 yards (18 feet ÷ 3).

Since Benjamin wants to make bow ties that are each half a yard long, we can calculate the number of bow ties he can make by dividing the total length of fabric (6 yards) by the length of each bow tie (0.5 yards).

Dividing 6 yards by 0.5 yards gives us a total of 12. Benjamin can make 12 half-yard long bow ties using the 18 feet of fabric he has.

Learn more about half-yard here:

https://brainly.com/question/29033686

#SPJ11

Answer:

Step-by-step explanation:   The graph of a quadratic function is a parabola whose axis of symmetry is parallel to the y -axis. The coefficients a,b, and c in the equation y=ax2+bx+c y = a x 2 + b x + c control various facets of what the parabola looks like when graphed.

Hope you like it.

Answer:

£6.05

Step-by-step explanation:

Multiply the number of coffees by the cost of coffee:

5 × 65p

325p

Multiply the number of teas by the cost of tea:

2 × £1.40

£2.80

Add the two answers together:

325p + £2.80

Convert p to £

£3.25 + £2.80

£6.05

Answer: add 3

Step-by-step explanation:

Answer:

This is your answer ☺️☺️

The national average for mathematics on a standardized test in 2011 was 518, with a standard deviation of approximately 48.

In statistics, the bell-shaped distribution is known as the normal distribution or the Gaussian distribution. It is characterized by its symmetry and the majority of the data falling within a certain range.

The national average score of 518 represents the central tendency of the distribution. This means that a large number of students scored around this average score.

The standard deviation of approximately 48 measures the variability or spread of the scores. It indicates how much the scores deviate from the average. In a normal distribution, about 68% of the data falls within one standard deviation of the mean.

By knowing the average score and the standard deviation, we can determine the proportion of students who scored above or below a certain score, as well as calculate percentiles and compare individual scores to the national average.

Understanding the characteristics of the distribution, such as the average and standard deviation, helps in interpreting and analyzing the scores, making meaningful comparisons, and identifying students' performance relative to the national average.

Learn more about Gaussian distribution here:

https://brainly.com/question/29734279

#SPJ11

a) In Quadrant 2, a sin(20) is equal to -sin(20).

b) In Quadrant 2, cos(2a) is equal to -cos(2a).

c) In Quadrant 2, tan(20) is equal to -tan(20).

In Quadrant 2, the angle 'a' is between 90 degrees and 180 degrees, or π/2 and π radians. Knowing that cos(a) is a negative value, we can determine the exact values for the given trigonometric expressions.

a) a sin(20) = -sin(20):

The sine function (sin) is positive in Quadrant 1 and negative in Quadrant 2. Therefore, the value of a sin(20) in Quadrant 2 is equal to the negative of sin(20). This means that the answer for a sin(20) is -sin(20).

b) cos(2a) = -cos(2a):

The cosine function (cos) is negative in Quadrant 2. Since we are given that a is in Quadrant 2, the angle 2a will also be in Quadrant 2. Therefore, cos(2a) in Quadrant 2 is equal to the negative of cos(2a). Thus, the answer for cos(2a) is -cos(2a).

c) tan(20) = -tan(20):

The tangent function (tan) is negative in Quadrant 2. Hence, the tangent of any angle in Quadrant 2 will be equal to the negative of its positive counterpart. Consequently, the answer for tan(20) in Quadrant 2 is -tan(20).

Learn more about Quadrant

brainly.com/question/29296837

#SPJ11

The value of variable h is,

⇒ h = 18

We have to given that,

A heptagon with angles are shown in figure.

Here, All the angles are,

⇒ 6h°, 132°, 146°, 146° , (6h + 10)° , (6h + 10)° , 146°, and 132°

We know that,

Sum of all the angles in a heptagon is, 900°

Hence, We get;

⇒ 6h° + 132° + 146° + 146° + (6h + 10)° + (6h + 10)° + 146° + 132° = 900°

Combine like terms,

⇒ 18h + 576 = 900

⇒ 18h = 900 - 576

⇒ 18h = 324

⇒ h = 18

Thus, The value of variable h is,

⇒ h = 18

Learn more about the angle visit:;

https://brainly.com/question/25716982

#SPJ1

Answer:

Choice D

Step-by-step explanation:

I believe that it is Choice D. Due to the fact that the moons orbit around Earth is inclined around 5 degrees, not allowing an eclipse to happen every New or Full Moon. Most of the time, the Sun, Earth, and Moon don't line up precisely enough to cause an eclipse.

Therefore, the value of c is 2/9.

The joint density of X and Y is given by f (x,y) = c(1/2) x² y², 1.

We are to calculate the value of c.

Step-by-step solution: It is given that joint density of X and Y is f (x,y) = c(1/2) x² y², 1.

The joint probability density function f(x, y) satisfies the following properties:f(x, y) ≥ 0 for all x and y.f(x, y) is continuous in x and y.∫∞−∞∫∞−∞f(x, y)dxdy = 1

From the given joint density function, we can compute marginal density of X and marginal density of Y by integrating over the other variable, as follows: P(X = x) = ∫ f(x, y) dy and P(Y = y) = ∫ f(x, y) dx

Let's calculate the marginal density of X.P(X = x) = ∫ f(x, y) dy∫ f(x, y) dy = c(1/2) x² ∫y² dy Limits of integration are from -1 to 1.P(X = x) = c(1/2) x² [(1/3) y³]1 and -1.∫ f(x, y) dy = c(1/2) x² [(1/3) (1³ - (-1)³)]P(X = x) = c(1/2) x² [(1/3) (1 - (-1))]P(X = x) = c(1/2) x² (2/3)P(X = x) = (1/3) c x²P(X = x) = 1,

integrating over all possible values of x, we obtain:1 = ∫ P(X = x) dx= ∫ (1/3) c x² dx Limits of integration are from -1 to 1.1 = (1/3) c [(1/3) x³]1 and -1.∫ P(X = x) dx = (1/3) c [(1/3) (1³ - (-1)³)]1 = (1/3) c [(1/3) (1 - (-1))]1 = (1/3) c (2)1/2 = (2/9) c2/9 = c

To Know more about probability density function visit:

https://brainly.com/question/31039386

#SPJ11

Answer:

Step-by-step explanation:

The joint density of X and Y is given by the function f (x,y) = c1/2x²y², 1. The value of c is 18.

We are required to find the value of c.

First, we need to know the definition of joint density.

A joint probability density function (PDF) is a statistical measure that describes the probability of two or more random variables occurring simultaneously in terms of their PDFs.

It's a measure of the probability of an event happening as a function of two variables, usually expressed as f(x,y).

So, in this problem, we have given the joint density of x and y is f(x,y) = c/2x²y², 1.

We can solve it by integrating it over the entire range.

The probability density function of X and Y can be found by integrating over the whole sample space.

[tex]$$\begin{aligned}&\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}f_{X,Y}(x,y)dxdy=1\\&\implies\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}f_{X,Y}(x,y)dxdy\\&=\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}c\frac{1}{2}x^2y^2dxdy=1\\&=\frac{c}{2}\int_{-\infty}^{\infty}x^2dx\int_{-\infty}^{\infty}y^2dy\\&=\frac{c}{2}\cdot \frac{1}{3}\cdot \frac{1}{3}=1\end{aligned}$$[/tex]

Hence, [tex]$$\implies c=\boxed{18}$$[/tex].

To know more about Probability density function, visit:

https://brainly.com/question/31039386

#SPJ11

To determine the normal and shear stresses at point D, which act perpendicular and parallel to the grains, respectively, we require additional information such as the applied forces or loadings at that point.

The given question mentions the need to determine the normal and shear stresses at point D, which act perpendicular and parallel to the grains, respectively. However, to accurately calculate these stresses, we need more information about the system under consideration. Key details include the applied forces or loadings on the system, the material properties, and the specific orientation and arrangement of the grains at point D.

Normal stress, also known as axial stress, refers to the force per unit area acting perpendicular to the surface. Shear stress, on the other hand, represents the force per unit area acting parallel to the surface. The magnitudes and directions of these stresses depend on the applied forces, the geometry of the system, and the material properties.

Learn more about perpendicular here:

https://brainly.com/question/11707949

#SPJ11

Answer:

slope = 5/3

y-intercept = (0,-3)

Step-by-step explanation:

Make the equation in slope-intercept form:

-5x+3y=-9

add 5x on both sides

3y=5x-9

divide by 3 on both sides

y=5/3x-3

slope = 5/3

y-intercept = (0,-3)

Complete question is;

Loretta is rolling an unfair 6 sided die with a single number between 1 and 6 on each face. She has a 70% chance of rolling a four. She is playing a game with a friend and knows that if she rolls a four on three of her next five rolls she will lose the game. She wants to determine the probability that she rolls a four on three of her next five rolls.

Which simulation design has an appropriate device and a correct trial?

A) Using a fair coin let heads represent rolling a four and tails represent not rolling a four. Flip the coin five times.

B) Using a table of random digits select a digit between 0 and 9. Let 0-6 represent rolling a four and 7-9 represent not rolling a four. Select five digits.

C) Roll a fair die with a single digit between 1 and 6 on each face. Let four represent rolling a four and 1-3 and 5 and 6 represent not rolling a four. Roll the die five times.

D) Using a table of random digits select a digit between 1 and 6, ignoring digits 0, 7, 8, and 9. Let 4 represent rolling a four and 1-3 and 5 and 6 represent not rolling a four Select five digits.

Answer:

B) Using a table of random digits, select a digit between 0 and 9. Let 0-6 represent rolling a four and 7-9 represent not rolling a four. Select five digits.

Step-by-step explanation:

Since she knows that if she rolls a four on three of her next five rolls she will lose the game, then the best simulation that she will roll a four on three of the next five rolls will be option B because it uses a table of random digits and doesn't ignore any number but is well ordered with 0-6 representing a four and 7-9 not rolling a four.

12,351,789

ignore this ------

12346789

+      5000

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

12351789

The real answer is B

Answer: 17.8% + $1.789.17 + $650 = 2439.348 or 2439

Step-by-step explanation: if you read the word problem it has a key word the key word is total.

Nash uses his credit card with a 17.8% APR, compounded monthly, to pay for a cruise totaling $1,789.17. He can pay $650 per month on the card. What will the total cost of this purchase be?

Answer:

I think 100

Step-by-step explanation:

Answer:

if you make 4 free throws for every 10 shots taken you would make 20 out of 50 free throws

Step-by-step explanation: