Solve the separable differential equation dx/dt = x^2 + 1/49, and find the particular solution satisfying the initial condition x(0) = - 2. x(t) =

In summary, the Fourier coefficients for the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5 are:

c₀ = -3 (DC component)

cₙ = 0 for n ≠ 0 (other coefficients)

To find the Fourier coefficients of the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5, we can use the formula for Fourier series coefficients:

cn = (1/T) ∫[t₀-T/2, t₀+T/2] y(t) \(e^{(-i2\pi nt/T)}\) dt

where T is the period of the function and n is an integer.

In this case, the function y(t) is constant, y(t) = -3, and the period is T = 10 (since the interval -5 ≤ t ≤ 5 spans 10 units).

To find the Fourier coefficient c₀ (corresponding to the DC component or the average value of the function), we use the formula:

c₀ = (1/T) ∫[-T/2, T/2] y(t) dt

Substituting the given values:

c₀ = (1/10) ∫[-5, 5] (-3) dt

  = (-3/10) \([t]_{-5}^{5}\)

  = (-3/10) [5 - (-5)]

  = (-3/10) [10]

  = -3

Therefore, the DC component (c₀) of the Fourier series of y(t) is -3.

For the other coefficients (cₙ where n ≠ 0), we can calculate them using the formula:

cₙ = (1/T) ∫[-T/2, T/2] y(t)\(e^{(-i2\pi nt/T) }\)dt

Since y(t) is constant, the integral becomes:

cₙ = (1/T) ∫[-T/2, T/2] (-3) \(e^{(-i2\pi nt/T)}\) dt

  = (-3/T) ∫[-T/2, T/2] \(e^{(-i2\pi nt/T)}\) dt

The integral of e^(-i2πnt/T) over the interval [-T/2, T/2] evaluates to 0 when n ≠ 0. This is because the exponential function oscillates and integrates to zero over a symmetric interval.

all the coefficients cₙ for n ≠ 0 are zero.

To know more about function visit:

brainly.com/question/30721594

#SPJ11

Step-by-step explanation:

The answer is: c=2 d=2 . Because: c+3d=8 c=4d−6. Let's substitue c from the second equation to the first: 4d−6+3d=8⇒7d=14⇒d=2.

Answer:

theres no picture availible

Step-by-step explanation:

The item that is not an item in the income statement is b. Furniture & Fixture as it is considered a fixed asset and is reported on the balance sheet instead.

The income statement, also known as the profit and loss statement, provides a summary of a company's revenues, expenses, gains, and losses over a specific period. It helps to assess the financial performance of a business. The income statement typically includes various items such as revenues, cost of goods sold, operating expenses, interest income or expense, and other gains or losses.

a. Discount allowed is a revenue item that represents the discounts given to customers as an incentive for early payment or other reasons. It is usually reported as a deduction from sales revenue.

c. Furniture & Fixture is not typically included in the income statement. Instead, it is considered a non-operating or non-recurring item and is generally classified as a fixed asset on the balance sheet. Fixed assets represent long-term investments made by a company for its operations.

d. Discount received is also not an item in the income statement. It represents the discounts received by a company from its suppliers for early payment or other reasons. Similar to discount allowed, it is usually reported as a deduction from the respective expense account.

In summary, b. Furniture & Fixture is the item that is not included in the income statement. It is considered a fixed asset and is reported on the balance sheet instead.

To know more about fixed assets, refer here:

https://brainly.com/question/14392032#

#SPJ11

The difference between the two temperatures is mathematically given as

|81 - (-29)| Option C

This is further explained below.

Generally, the equation is  mathematically given as

h-l=d

Therefore

81-(-29)=d

81+29=d

d=110

In conclusion,, in magnitude form

|81 - (-29)|=|81 +29|=|110|=110

|81 - (-29)|

Option C is correct

Read more about temperature

https://brainly.com/question/11464844

#SPJ1

It is important to check for multicollinearity in a regression model and take steps to reduce it, such as removing one of the highly correlated independent variables or using regularization techniques.

Multicollinearity is a statistical phenomenon where two or more independent variables in a regression model are highly correlated with each other. This can cause problems in the regression model as it becomes difficult to distinguish the individual effects of the independent variables on the dependent variable.
When multicollinearity is present in a regression model, the p-values of the slopes of the independent variables are affected. The p-value measures the probability of obtaining a result as extreme or more extreme than the observed result, assuming that the null hypothesis is true. The null hypothesis in a regression model is that the slope of the independent variable is zero, meaning that there is no relationship between the independent variable and the dependent variable.
Multicollinearity can cause the standard errors of the slopes to increase, leading to inflated p-values. In other words, the significance of the relationship between the independent variable and the dependent variable may be underestimated. This is because the highly correlated independent variables are both trying to explain the same variation in the dependent variable, leading to an unreliable estimate of the effect of each independent variable on the dependent variable.
Therefore, it is important to check for multicollinearity in a regression model and take steps to reduce it, such as removing one of the highly correlated independent variables or using regularization techniques. This can help to ensure that the regression model produces reliable estimates of the effects of the independent variables on the dependent variable.

for more questions on multicollinearity

https://brainly.com/question/17216244

#SPJ11

Answer:

  4ab +10b

Step-by-step explanation:

Perhaps you want to simplify the expression.

  \((2.5ab+14b)-(-1.5ab+4b)=2.5ab+14b+1.5ab-4b\\\\=ab(2.5+1.5)+b(14-4)=\boxed{4ab+10b}\)

Answer: 4ab+10

Step-by-step explanation:

2.5ab+14b--1.5ab-4b

4ab+10

Answer:

The first one: 19/15a

second one: b²-4ac = D

Step-by-step explanation:

for first one: take LCM and solve

for second one: you square the expression on both sides then b²= D + 4ac, then when you take 4ac to the left hand side, it becomes b²-4ac= D

The output will be:

film_id
-------
997
996
995
994
993
992
991
990
989
988
... (and so on)
```

Step 1: Find the minimum film length (L) and the maximum rental duration (R) in the table film.

To find the minimum film length, we can use the MIN() function on the length column:

```
SELECT MIN(length) AS L FROM film;
```

To find the maximum rental duration, we can use the MAX() function on the rental_duration column:

```
SELECT MAX(rental_duration) AS R FROM film;
```

Step 2: Find all films that have length L or duration R or both.

To find all films with length L or duration R or both, we can use the WHERE clause with OR conditions:

```
SELECT film_id
FROM film
WHERE length = L OR rental_duration = R OR (length = L AND rental_duration = R)
ORDER BY film_id DESC;
```

Note that we use parentheses to group the last condition (length = L AND rental_duration = R) with the OR conditions.

Step 3: Order the results by film_id in descending order.

We add the ORDER BY clause at the end of the query to sort the results by film_id in descending order:

```
SELECT film_id
FROM film
WHERE length = L OR rental_duration = R OR (length = L AND rental_duration = R)
ORDER BY film_id DESC;
```

This will give us the expected output as follows:

```
film_id
-------
997
996
995
994
993
992
991
990
989
988
... (and so on)
```

Know more about length (L) here:

https://brainly.com/question/15161439

#SPJ11

An example of a randomized block design is fertilizers

The randomized block design is a type of experimental design where the subjects or objects are divided into blocks, and each block is randomly assigned to different treatments. This design is used to control for variables that could potentially affect the outcome of the study.

To illustrate the randomized block design, let's consider an example of a study examining the effect of different types of fertilizers on crop yield. In this study, we have four different types of fertilizers (treatments) and six different plots of land (blocks) that are different in soil type and exposure to sunlight.

To conduct the study using a randomized block design, we first randomly assign each plot of land to one of the four fertilizers. Then, we measure the crop yield for each plot of land and analyze the results.

To know more about randomized block design here

https://brainly.com/question/25295125

#SPJ4

Answer:

The volume of the solid bounded by the given equations is approximately 170.67 cubic units.

Step-by-step explanation:

To find the volume of the solid, we need to set up the double integral as follows:

V = ∫∫R (x + y) dA

where R is the region in the first octant bounded by the graph of x^2 + y^2 = 64.

Converting the equation of the boundary to polar coordinates, we have:

\(r^2 = x^2 + y^2 = 64\)

so r = 8.

The limits of integration for r are 0 to 8, and for θ are 0 to π/2, since we are only interested in the first octant.

Thus, the double integral is:

V = ∫0^(π/2) ∫0^8 (r cosθ + r sinθ) r dr dθ

\(= ∫0^(π/2) ∫0^8 r^2 cosθ dr dθ + ∫0^(π/2) ∫0^8 r^2 sinθ dr dθ\)

Evaluating each integral separately, we get:

\(V = (1/3)[r^3 cosθ]0^π/2 [0^8] + (1/3)[r^3 sinθ]0^π/2 [0^8]\)

\(= (1/3)[(8^3)(1) - (0^3)(1)] + (1/3)[(8^3)(0) - (0^3)(0)]\)

= (1/3)(512) + 0

= 170.67

Therefore, the volume of the solid bounded by the given equations is approximately 170.67 cubic units.

To know more about polar coordinates,, refer here:

https://brainly.com/question/11657509

#SPJ11

The total number of handshakes in the party is given as follows:

3 handshakes.

The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

For this problem, we have that the order does not matter, as João and Elisa shaking hands is the same outcome as Elisa and João shaking hands, which is the reason for the use of the combination formula.

Each handshake is composed by two people, and there are three people, hence the total number of handshakes in the party is given as follows:

C(3,2) = 3!/(2! x 1!) = 3.

More can be learned about the combination formula at https://brainly.com/question/11732255

#SPJ1

Answer:

A. -146

Step-by-step explanation

46th term = -11 + ( 46 -1) (-3)

= -11 + (45)(-3)

=-11 -135

= - 146

Answer:

14

Step-by-step explanation:

\(f(x)=x^2-8x+5\\f(-1)=(-1)^2-8(-1)+5\\f(-1)=1+8+5\\f(-1)=14\\\)

Answer:  B 9:21

Step-by-step explanation:

9 reduces to three and 21 reduced to 7

Answer:

If a rectangle

77ft

Step-by-step explanation:

Answer:17in

Step-by-step explanation:

Step-by-step explanation: x =9

don't know bro sorry for points comment below to talk

Answer:

7.3

Step-by-step explanation:

range is the difference between the smallest and biggest number in the list so you just subtract the lowest from the biggest 8.9-1.6 = 7.3

You can use the fact that whenever bases are same, the product of such quantities end up getting their exponents added.

The product result of given expression is \(^5\sqrt{(2x)^4}\)

Suppose you've got two values to multiply with each other and you have got both value's bases same, then the multiplication will end up with result being that base raised with sum of the exponents of both the initial values.

For example:

\(a^b \times ^c =a^{b+c}\)

You can convert the roots to powers. Then you can use the fact that the bases are same and thus the powers will add.

Remember that if you've got xth root, then the power would be 1/x.

For our case, it will go like this:

\(^5\sqrt{4x^2} \times ^5\sqrt{4x^2} = \: ^5\sqrt{(2x)^2} \times ^5\sqrt{(2x)^2} = {((2x)^2)}^{\frac{1}{5}} \times {((2x)^2)}^{\frac{1}{5}} = (2x)^{\frac{2}{5}} \times (2x)^{\frac{2}{5}}\\\\ ^5\sqrt{4x^2} \times ^5\sqrt{4x^2} = (2x)^{\frac{2}{5} + \frac{2}{5}} = (2x)^{\frac{4}{5}} = \: ^5\sqrt{(2x)^4}\)

Thus, the final product result will be written as \(^5\sqrt{(2x)^4}\)

Learn more about base and exponent here:

https://brainly.com/question/9047706

The z-scores will remain the same regardless of whether you use inches or centimetres for the height measurements.

The z-scores will not change if you convert the height measurements from inches to centimetres or vice versa. The z-score is a standard score representing the number of standard deviations, a value above or below the mean of a normal distribution.

The z-score is calculated using the formula z = (x - mean)/standard deviation, where x is the value being compared to the mean and standard deviation of the distribution.

Converting the height from inches to centimetres or vice versa will only change the units of measurement, but the relative position of a value within the distribution will remain unchanged.

Therefore, the z-scores will remain the same regardless of whether you use inches or centimetres for the height measurements.

To know more about z-scores, here

https://brainly.com/question/15016913

#SPJ4

Any number that can be written as a fraction and in which the numerator and denominator are both integers is referred to as a rational number. In other words, p/q can be used to represent a rational number when p and q are both integers and q is 0. It will be 0.25 and 0.5.

Hence, the  rational numbers will be 0.25 and 0.5.

To learn more about rational numbers refer to:

https://brainly.com/question/12088221

#SPJ10

Answer:

82.8

Step-by-step explanation:

In the above question, we are given the following information:

The equation for the line of best fit is given as y = -1.4x + 117.8, where

x is the "age in years"

y is the "typing speed. If you are 25 years of age, what is your typing speed?

This is calculated as:

y = -1.4x + 117.8

x = 25 years

y = -1.4(25) + 117.8

y = -35 + 117.8

y = 82.8

Hence, If you are 25 years of age, what is your typing speed is 82.8

Answer:

P V = N R T      ideal gas equation

V2 / V1 = T2 / T1       dividing equations

V2 = 397 cm^3 * (220 / 515) = 170 cm^3

Answer:

\(\displaystyle m=\frac{-2}{3}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Find points from graph

Point (-3, 1)

Point (3, -3)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Therefore , the solution of the given problem of angles comes out to be  Lines I and m can be inferred to be parallel by the Corresponding Angles Converse .

An angle is a shape in Euclidean geometry consisting of two rays, or sides of a circular, that split at the angle's apex and the angle's apex, which is in the middle. Where they are located, two rays can join to form an angle. Angle is another outcome of two entities interacting. They are known as dihedral angles.

Here,

The Corresponding Angles Converse states that if two parallels are intersected by a transversal such that a set of corresponding angles are congruent, then perhaps the two lines are parallel.

This can be used to demonstrate that lines I and m are parallel.

We can infer that 1 and 2 are corresponding angles because 1 2.

We can infer that they have the same measure because they are congruent.

Let's now think about the transversal line t. Lines I and m can be inferred to be parallel by the Corresponding Angles Converse because 1 and 2 are corresponding angles and t crosses both I and m.

We have thus demonstrated that I / m.

To know more about angles visit:

https://brainly.com/question/14569348

#SPJ1

Answer:

Hey there!

The reciprocal of a number, n, is 1/n.

Thus, the answer is n+7(1/n)

Let me know if this helps :)

option B correctly expresses the relationship between the value and the number of years, where the number of years is equal to the value divided by 12.53. The equation that correctly expresses the relationship between the two variables is option B: Number of years = value/12.53.

This equation is a straightforward representation of the relationship between the value and the number of years. It states that the number of years is equal to the value divided by 12.53.

To understand this equation, let's look at an example. If the value is 120, we can substitute this value into the equation to find the number of years. By dividing 120 by 12.53, we get approximately 9.59 years.

Therefore, if the value is 120, the corresponding number of years would be approximately 9.59.

In summary, option B correctly expresses the relationship between the value and the number of years, where the number of years is equal to the value divided by 12.53.

To Know more about  The relationship between the two variables Visit:

https://brainly.com/question/606076

#SPJ11

Answer:

$6.49

Step-by-step explanation:

Fruit=$1.99

Cheese tray=$4.50

1.99

+4.50

=$6.49