PLEASE HELP!!!!!!!!!!

The first three nonzero terms of two linearly independent solutions about x = 0 can be obtained by Taylor expanding the solutions in terms of the exponent r and truncating the series to the desired order.

To determine if x = 0 is a regular singular point of the differential equation xy'' + y = 0, we substitute y = x^r into the equation and solve for the exponent r. Differentiating y twice with respect to x, we have y'' = r(r - 1)x^(r - 2). Substituting these expressions into the differential equation, we get \(x(x^r)(r(r - 1)x^(r - 2)) + x^r = 0\). Simplifying, we obtain r(r - 1) + 1 = 0, which yields r^2 - r + 1 = 0. Solving this quadratic equation, we find that the exponents at the singular point x = 0 are complex and given by r = (1 ± i√3)/2.

To find the first three nonzero terms of two linearly independent solutions about x = 0, we can use the Taylor series expansion. Let's consider the solution y1(x) corresponding to the exponent r = (1 + i√3)/2. Expanding y1(x) as a series around x = 0, we have y1(x) =\(x^r = x^((1 +\)i√3)/2) = x^(1/2) *\(x^(i√3/2\)). Using the binomial series expansion and Euler's formula, we can write \(x^(1/2) and x^(i√3/2)\) as infinite series.

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Answer:

19.741

Step-by-step explanation:

When subtracting decimals line up the decimals and then add 0s to the end to make it work. SO instead of

21.25

-1.509

___________

It would be

21.250

- 1.509

______________

Solve the subtraction problem like you normally would. THen drop the decimal down so it lies up with the others.

21.250

- 1.509

______________

19.741

Answer:

Chau drove 13.96 miles while he was using the truck

Step-by-step explanation:

Answer:

294 miles!!!!!!

Step-by-step explanation:

Answer:

$189.74

Step-by-step explanation:

Since the sales tax is 6%,

179x0.06=10.74

Add to the starting price, 179.00+10.74=189.74!

I hope this helped!

Answer:

false

Step-by-step explanation:

i hope this helps

Answer:

15(1/16)  square feet

Step-by-step explanation:

3 1/2 = 7/2

4 1/3= 13/3

7/2 x  13/3  =  91/6  =  15(1/6)

Answer:

the answer in the blank is 9

Step-by-step explanation:

Answer:

52 cm

Step-by-step explanation:

Using pythagoras theorem

hypothenuos² = adjacent² + opposite²

\( {x}^{2} \: = \: {48}^{2} + {20}^{2} \\ {x}^{2} \: = \: 2304 + 400 \\ {x}^{2} \: = \: 2704 \\ x \: = \: \sqrt{2704} \\ x \: = \: 52cm\)

Answer:

Equation of the parabola: 12y−72=(x−4)212y−72=(x−4)2 or y=x212−2x3+223y=x212−2x3+223.

Vertex form: y=(x−4)212+6y=(x−4)212+6.

No intercept form.

Vertex: (4,6)(4,6).

Focus: (4,9)(4,9).

Eccentricity: 11.

Directrix: y=3y=3.

Latus rectum: y=9y=9.

The length of the latus rectum: 1212.

Axis of symmetry: 

Step-by-step explanation:

from parabola calculator-eMathHelp

I hope it helps.

Step-by-step explanation:

y = 200  - 3 *x  has slope = -3   this is downward sloping from L to R

Answer:downward sloping

Step-by-step explanation:

negative slope

Answer:

Positive, Linear, Strong, no

Step-by-step explanation:

I got it right :)

Answer: The relationship between height and vertical jump distance is negative positive, linear, and strong.

There are no unusual observations.

Step-by-step explanation:

Edge

Answer:

A

Step-by-step explanation:

tell me if im wrong

The correlation coefficient of the security X and Y returns is closest to 0.67, indicating a moderate positive correlation between the two securities.

The correlation coefficient of the security X and Y returns is closest to 0.67. This can be calculated by dividing the covariance of the returns by the square root of the product of the variances of X and Y.

The correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges between -1 and 1, with values close to 1 indicating a strong positive correlation, values close to -1 indicating a strong negative correlation, and values close to 0 indicating a weak or no correlation.

In this case, the given covariance is 10, the variance of Security X's returns is 13%, and the variance of Security Y's returns is 17%. To calculate the correlation coefficient, we use the formula:

Correlation coefficient = Covariance / (\(\sqrt{}\)(Variance_X) * \(\sqrt\)(Variance_Y))

Plugging in the values, we get:

Correlation coefficient = 10 / (\(\sqrt\)(13%) * \(\sqrt\)(17%)) ≈ 0.67

Therefore, the closest option is 0.67, indicating a moderately strong positive correlation between the returns of Security X and Security Y.

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The correct answer is S = {A, D, D, I, T, I, O, N}.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

The sample space is the set of all possible outcomes of an experiment or event.

In this case, the experiment is choosing one card from a set of eight labeled cards.

The sample space for this experiment is the set of all possible cards that can be chosen.

In the given problem, there are eight cards labeled A, D, D, I, T, I, O, N.

The sample space is the set of all possible cards that can be chosen, which is {A, D, D, I, T, I, O, N}.

This is because each card is distinct and can be chosen independently of the others.

Therefore, the correct answer is S = {A, D, D, I, T, I, O, N}.

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Answer: A( A,D, D,I, I,N,O,T)

Step-by-step explanation:

Order does not matter!!

The required simplified solution of the given expression is given as 53.1.

Given that,
To determine the simplified solution to the expression -[4.2-3(2.1)]/{0.2}² + 1.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
=  -[4.2-3(2.1)]/{0.2}² + 1
Simplifying
= 52.5 + 1
= 53.5

Thus, the required simplified solution of the given expression is given as 53.1.

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Answer:

The team lost 9 matches

Step-by-step explanation:

Given

\(Matches = 30\)

\(Lost = \frac{3}{10}\) of the matches

\(Draw = 3\)

Required

Determine the number of matches lost

From the question, we have:

\(Lost = \frac{3}{10}\) of the matches

Mathematically, this is:

\(Lost = \frac{3}{10} * Matches\)

Substitute 30 for Matches

\(Lost = \frac{3}{10} * 30\)

\(Lost = \frac{3* 30}{10}\)

\(Lost = \frac{90}{10}\)

\(Lost = 9\)

The team lost 9 matches

45,000 square feet  is the largest area that can be enclosed.

What is rectangle?

The largest area will always be a square.

600/4=150 feet on each side but one side is not needed

put this 150 feet not needed with the opposite 150 feet to get 300 feet

you have a rectangle 150 by 300 by 150 by the river

         = 150 * 300 =  45,000 square feet

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The complete question is -

You have 600 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and the width of the plot that will maximize the area. What is the largest area that can be enclosed?

Answer:

x = 48°

Step-by-step explanation:

x + x + 84° = 180°

2x = 180° - 84°

2x = 96°

x = 96°/2

x = 48°

Answer:

84+2a=180

2a=180-84

= 96

2a=96/2

=48

So, each angles are 48 degrees.

If my answer is wrong, please inbox me! ≧ω≦

The structures indicated by the map patterns of Mesozoic (green) and Cenozoic (yellow) rocks can provide insights into the geological history and tectonic activity of the area.

The presence of linear or curvilinear patterns in the map may suggest the occurrence of faults or fractures in the rocks. Faults are fractures along which rocks on either side have moved relative to each other. These structures can be associated with the movement of tectonic plates and the deformation of the Earth's crust.

Additionally, the map patterns may reveal the presence of folds in the rocks. Folds are bending or flexing of rock layers caused by compressional forces in the Earth's crust. They can result in the formation of anticlines (upward folds) and synclines (downward folds) that can be observed in the map patterns.

The interpretation of the map patterns in terms of specific structures requires careful analysis and additional geological data. Field observations, cross-sections, and geophysical techniques are often employed to gain a better understanding of the geological structures present in the area.

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Answer:

Rs.12500

Step-by-step explanation:

18% = saved

100 - 18 = 82%(used salary)

82% = 10250

100% = ?

100 × 10250 = 1025000

1025000 ÷ 82 = Rs.12500

Answer:

23˚

Step-by-step explanation:

If x = 10, then angle VYZ = 157 by basic algebra. Knowing that VYZ and WYZ are supplementary angles, we can do 180-157 to find angle WYZ. 180-157 = 23˚

Answer:

Montrer que a ≡ b (mod n) si et seulement si a et b laissent le même reste quand ... 7k + 3 ou la forme x = 7k + 4, alors x2 − 2 est un multiple entier de 7.

Step-by-step explanation:

The angle bisector of ∠A can be constructed by the following steps below.

So, AO is the angle bisector of the ∠A in the following figure.

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It is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

In the given scenario, it is not completely true that based only on the r and p values listed above, you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

Let's first understand what is meant by the term "moderator.

"Moderator: A moderator variable is a variable that changes the strength of a connection between two variables. If there is a statistically significant bivariate relationship between the amount of texting during driving and the number of accidents, scientists investigate whether this bivariate relationship is moderated by age.

Therefore, based on the values of r and p, it is difficult to determine if age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

As we have to analyze other factors also to determine whether the age is a moderator or not, such as the sample size, the effect size, and other aspects to draw a meaningful conclusion.

So, it is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

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Answer:

gimme a sec

Step-by-step explanation:

To form a triangle, the set of line segments must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, we need to check if the given line segments 8 cm, 4 cm, and 3 cm meet this requirement.

We can start by checking if the sum of the two smaller sides (3 cm and 4 cm) is greater than the largest side (8 cm). 3 cm + 4 cm = 7 cm, which is less than 8 cm. Therefore, these three line segments cannot form a triangle.

In general, for a set of line segments to form a triangle, the largest side must be smaller than the sum of the other two sides. In this case, the line segment of 8 cm is too long compared to the other two sides, which makes it impossible to form a triangle.

In conclusion, there are no line segments that meet the requirements to form a triangle with lengths of 8 cm, 4 cm, and 3 cm.

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The area of the given square pyramid is:

total area = 1,100 inches squared.

On the second image, we can see that the pyramid is conformed of a square base and 3 triangles.

To get the surface area of the pyramid, we can just get the area of each of these simpler parts.

The base is a square of 22 in by 22 in, then the area of the base is:

B = (22in)*(22 in)  = 484 in^2

For each triangle, the area will be:

A = (base side)*(height)/2

A = (22in)*(14in)/2 = 154 in^2

And we have 4 of these triangles, then the total area of the pyramid will be:

total area = B + 4*A = 484in^2 + 4*(154 in^2) = 1,100 in^2

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Answer:

\(\textsf{1.} \quad x^2-2x-1\)

\(\textsf{2.} \quad -3x^4-5x^3+14x^2+20x-8\)

\(\textsf{3.} \quad -\dfrac{5}{2}\)

Step-by-step explanation:

Given functions:

\(\begin{cases}f(x) = x^2 - 4\\g(x) = x + 2\\h(x) = -3x + 1\end{cases}\)

Question 1

The composite function (f + g - h)(x) means to add functions f(x) and g(x) then subtract function h(x):

\(\begin{aligned}(f+g-h)(x) & = f(x)+g(x)-h(x)\\& = (x^2-4)+(x+2)-(-3x+1)\\& = x^2-4+x+2+3x-1\\& = x^2+3x+x-4+2-1\\& = x^2+4x-3\end{aligned}\)

Question 2

The composite function (fgh)(x) means to multiply functions f(x), g(x) and h(x):

\(\begin{aligned}(fgh)(x) & = f(x)\cdot g(x) \cdot h(x)\\& = (x^2-4)(x+2)(-3x+1)\\& = (x^2-4)(-3x^2-5x+2)\\& = -3x^4-5x^3+2x^2+12x^2+20x-8\\& = -3x^4-5x^3+14x^2+20x-8\end{aligned}\)

Question 3

The composite function (f/g)(h)(1/2) means to substitute the value of function h(x) when x = 1/2 into function f(x) and function g(x) and divide the former by the latter:

\(\begin{aligned}\left(\dfrac{f}{g}\right)(h)\left(\dfrac{1}{2}\right) & = \dfrac{f\left(h\left(\dfrac{1}{2}\right)\right)}{g\left(h\left(\dfrac{1}{2}\right)\right)}\\\\& = \dfrac{f\left(-3\left(\dfrac{1}{2}\right)+1\right)}{g\left(-3\left(\dfrac{1}{2}\right)+1\right)}\\\\& = \dfrac{f\left(-\dfrac{1}{2}\right)}{g\left(-\dfrac{1}{2}\right)}\\\\& = \dfrac{\left(-\dfrac{1}{2}\right)^2-4}{\left(-\dfrac{1}{2}\right)+2}\\\\& = \dfrac{-\dfrac{15}{4}}{\dfrac{3}{2}}\\\\& = -\dfrac{5}{2}\end{aligned}\)