Find all Singular points of the given differential equation then classify as Irregular Singular Points ISP, or Regular Singular Points, RSP.
x^2(x-2)y'' + y' + xy = 0
a. Both x = -0 and x=2 are ISP's
b. x=0 is ISP and x=2 is RSP
c. Both x = 0 and x=2 are RSP's
d. x=0 is RSP and x=2 is ISP

The sum of all the edges in the solid shape is 24 unit.

Length is a measurement οf distance οr size. It can refer tο the physical extent οf an οbject, the size οf an area, οr the amοunt οf time sοmething takes. Length is measured in units such as centimeters, meters, feet, inches, yards, miles, and sο οn. Length is an impοrtant cοncept in mathematics and physics, used tο measure distances and calculate speed and οther quantities.

The sum οf all the edges in the sοlid shape is 24. This is calculated by adding the 4 edges οf the square (4 x 1 = 4) plus the 12 edges οf the 4 equilateral triangles (12 x 1 = 12).

Therefοre, 4 + 12 = 24.

Since all the sides οf the triangles and the square are equal in length, it can be said that all the edges in the sοlid shape are equal. This means that the length οf each edge is equal tο 24/24, οr 1. This means that the length οf each edge οf the sοlid shape is 1 unit.

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Complete question:

The solid shape below is made up four equilateral triangles and a square. What is the sum of all the edges in the solid shape?​

[Given each side is 1 unit]

Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)

To rotate a point 90 degrees  clockwise about a given point,we can follow these steps -

Translate the coordinates   of the given point so that the center of rotation is at the origin.   In this case,we subtract the coordinates   of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).

Perform the rotation by swapping the x and y coordinates and changing the sign of the   new x coordinate. In this case,we  swap the x and y coordinates of (-5, 3)   to  get (3, -5).

Translate the coordinates back to their original position   by adding the coordinates of the center (0,1)  to the result from step 2. In   this case, we add (0,1) to (3, -5) to get (3, -4).

Therefore, the coordinates   of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).

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The range of values of  (f + g)(x) is for all values of x  -infinity to + infinity

The domain of a function is defined as the set of all the possible input values that are valid for the given function.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

We are Given f(x) = |x| + 9 and g(x) = –6,

Required the range of (f + g)(x)

First, calculate

(f + g)(x) = f(x) +  g(x)

Substitute values for f(x) and g(x)

(f + g)(x) = |x| + 9 - 6

(f + g)(x) = |x| + 3

The above expression shows that (f + g)(x) ≥3

Range = (f + g)(x) ≥3 for all values of x

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The volume of the figure, by splitting it into two cuboids comes to be 3300 ft³.

The volume of a cuboid is the product of its three dimensions i.e. length, breadth, and height.

Let us split the given figure into two cuboids

So, the volume of the figure will be the sum of the volume of both the cuboids.

So, the volume of the cuboid with dimensions 20 ft x 25 ft x 5ft

= 20 x 25 x 5

=2500 ft³.

The volume of the cuboid with dimensions  4 ft x 25ft x 8ft

=4 x 25x 8

=800 ft³.

So, the volume of the figure = 2500 + 800 =3300 ft³.

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Answer:

3w

Step-by-step explanation:

=16w+−13

Combine Like Terms:

=16+−13=(16+−13)=3

=3w

Hope this helps!!

Answer:

Step-by-step explanation:

This problem is on ratio, and we can use part to the whole to arrive at our answer

given that total vehicles is 210 vehicles

the  sum of the ratio of cars to trucks is = 4+3= 7

therefore applying part to the whole formula we have

for cars

4/7=x/210

cross   multiply we have

7x= 210*4

x= (210*4)/7

x= 30*4

x= 120

So in all there are 120 cars in the lot

In each diagram, line f is parallel to line g, and line t intersects both lines f and g. The given information suggests the application of certain geometric properties and relationships.

Firstly, when a transversal line (line t) intersects two parallel lines (lines f and g), it creates several pairs of corresponding angles.

Corresponding angles are congruent, meaning they have equal measures. This property can be used to determine the measures of specific angles in the diagram.

Secondly, when a transversal intersects parallel lines, it also creates alternate interior angles and alternate exterior angles.

Alternate interior angles are congruent, as well as alternate exterior angles.

By utilizing these properties and relationships, one can analyze the diagram and determine the measures of various angles.

It is important to measure angles systematically and compare them to find congruent or equal measures.

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Answer:

D. 3

Step-by-step explanation:

Assuming the model represents an equation, the following can be deduced:

On the left side of the equation, the model shows we have 3 "x's", and 6 "1's". Let this represent:

3x + 6

On the right side of the equation, we have 2 "x's" and 9 "1's". Let this represent:

2x + 9.

The model would represent the equation below:

\( 3x + 6 = 2x + 9 \)

Solve for x

\( 3x + 6 - 2x = 2x + 9 - 2x \) (Subtracting 2x from both sides of the equation)

\( x + 6 = 9 \)

\( x + 6 - 6 = 9 - 6 \) (subtracting 6 from both sides of the equation)

\( x = 3 \)

Answer:

100

Step-by-step explanation:

well you can put 5 students in each class guaranteed 5 times over so it would make sense because 5 for each class 9th-12th 5 times over again and again will eventually give you the answer of 100 5•20

If we take 5 students are in each class.

Then let minimum number of students be x

ATQ

1/20()x = 5

x = 5 × 20

x = 100

Answer: 100 people

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The definition and the solution to the points can be defined as follows:

Calculation:

For point a:

The width of the class refers to the difference between the upper and lower classes (category).

It is therefore \(\to \bold{52-50 = 2}\)

For point b:

For point c:

For point d:

                     \(=\bold{\frac{8}{(8+15+12+10+5)}}\\\\=\bold{\frac{8}{50}}\\\\=\bold{0.16}\\\\\)

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During the exponential phase, e.coli bacteria in a culture increase in number at a rate proportional to the current population. If growth rate is 1.9% per minute and the current population is 172.0 million, the population 7.2 minutes from now can be calculated using the following formula:

P(t) = P ₀e^(rt)where ,P₀ = initial population r = growth rate (as a decimal) andt = time (in minutes)Substituting the given values, P₀ = 172.0 million r = 1.9% per minute = 0.019 per minute (as a decimal)t = 7.2 minutes

The population after 7.2 minutes will be:P(7.2) = 172.0 million * e^(0.019*7.2)≈ 234.0 million (rounded to the nearest tenth)Therefore, the population of e.coli bacteria 7.2 minutes from now will be approximately 234.0 million.

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The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.

If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:

1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.

2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.

3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.

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The length of the arc KL in the given circle is 3.49 units

In a circle whose radius is R, the length of an arc defined by an angle x is given by:

Length = (x/360)*2*3.14*R

Here we know that the radius is 2 units, and the angle for the arc KL is 100°, then we can replace these values in the formula above so we get that the length of the arc is:

Length = (100/360)*2*3.14*2

Lenght = 3.49 units.

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Answer:

1 * 10^16 or 10000000000000000

Step-by-step explanation:

Answer: 1e+16 or 10000000000000000

Step-by-step explanation: Just multiply it

Answer:

Step-by-step explanation:

7/18=7/18

it cant be divided agian

1/3=1/3

it cant be divded agian

1/5=1/5

it cant be divded agian

1/10=1/10

it cant be divded agian

3 1/2=3/2

2 5/9 =10/9

i am not sure if this is what you wanted ...

Answer:

L(y) = g(x)

\(y = C_{1} e^{-4 x} + C_{2} e^{7 x} + \frac{1}{(-28)}(( x + (\frac{ -3 (1) }{28} )) + \frac{1}{14}\)

Step-by-step explanation:

Step(i):-

Given differential equation

  y'' − 3 y' − 28 y = x − 2

Operator form ( D² - 3 D - 28 )y = x -2

                         f( D ) y = Ф(x)

Auxiliary equation

                    f( m ) = m² - 3 m - 28

          ⇒  m² - 3 m - 28 =0

         ⇒  m² - 7 m +4 m - 28 =0

         ⇒ m ( m -7 ) + 4 ( m -7) =0

         ⇒ (m + 4)( m -7) =0

       ⇒ m = -4 and m =7

Complementary function

               \(y_{c} = C_{1} e^{-4 x} + C_{2} e^{7 x}\)

Step(ii):-

Particular integral

\(P.I = y_{p} = \frac{1}{f(D)} (x-2)\)

             \(= \frac{1}{D^{2}- 3 D - 28 } (x)-2\frac{1}{D^{2} - 3 D - 28} e^{0 x} )\)

           \(= \frac{1}{(-28)(1 - (\frac{D^{2}-3 D) }{-28} )} (x) + \frac{1}{0-0-28} X 2\)

           \(= \frac{1}{(-28)}( 1 + (\frac{D^{2} -3 D) }{28} )^{-1} (x) + \frac{1}{14}\)

( 1 + x )⁻¹ = 1 - x + x² - x³ +.....

  we use notation \(D = \frac{dy}{dx}\)

         \(= \frac{1}{(-28)}( 1 + (\frac{D^{2} -3 D) }{28} )+ (\frac{D^{2} -3 D) }{28})^{2} +.....) (x) + \frac{1}{14}\)

Higher degree terms will be neglected

        D(x) =1

        D²(x) =0

      \(= \frac{1}{(-28)}(( x + (\frac{ -3 (1) }{28} )) + \frac{1}{14}\)

  The particular integral

  \(y_{p} = \frac{1}{(-28)}(( x + (\frac{ -3 (1) }{28} )) + \frac{1}{14}\)

Conclusion:-

General solution of given differential equation

\(y = y_{c} + y_{p}\)

\(y = C_{1} e^{-4 x} + C_{2} e^{7 x} + \frac{1}{(-28)}(( x + (\frac{ -3 (1) }{28} )) + \frac{1}{14}\)

Answer:

the answer is 546.458333 or 546.46

Step-by-step explanation:

Given:

- 6x + 6y = -24

- 4x + 4y = -12

Simplest form of the above equation is,

- x +y = -4

y=x-4 .................. (1)

- x + y = -3

y=x-3 .................. (2)

Let us find some points for the (1) equation.y=x-4

When x=1, we get, y=-3

When x=2, we get, y=-2

When x=3, we get, y=-1

(1, -3), (2, -2), and (3, -1).

Let us find some points for the (2) equation.

When x=1, we get y=-2

When x=2, we get y=-1

When x=3, we get y=0

(1, -2), (2, -1), and (3, 0).

Hence, the graph is,

Sicne, line are parallel.

Hence, the system is inconsistent.

That is, the system has no solution.

The linear equations in the slope intercept form is,

y= x+ (-4)

y= x+ (-3)

Answer:

7 times 4 which is 28 at each fair.

Answer:

Step-by-step explanation:

The parallelogram is two congruent triangles. Area of blue triangle is ½·2·2 = 2 units²

Area of parallelogram = 4 units²

:::::

area of blue parallelogram = 4×9 = 36 units²

:::::

area of green parallelogram = 3×5 = 15 units²

Answer:

1:2.

Step-by-step explanation:

Divide both sides by 10.

You get 1:2.

Answer: my sis helped me a little so i think its right try 1,500

Step-by-step explanation:

if she gets paid 849000 a year then i would divide 849000 by 12 cause theres that meany months in a year then with that number subtract the Christmas plus witch is 5500 and thats the answer i think

What is the sum of the geometric series Σ2

Σ(3)

rounded to the nearest whole number?

Answer: O2

Answer:

Arithmetic sequence with common difference of 3.

Step-by-step explanation:

Arithmetic sequence:

The difference between consecutive terms is always the same, and this difference is called common difference.

Geometric sequence:

The quotient between consecutive terms is always the same, and this quotient is called common ratio.

In this question:

5 - 2 = 8 - 5 = 3

5/2 = 2.5 different of 8/5 = 1.6

This means that it is an arithmetic sequence with common difference of 3.

In this case we have a translation of 8 units to the left and 11 units upwards.

To find the translation, we just need to compare the two known vertices before and after the translation.

If we have a translation of a units in the x-axis and b units in the y-axis, we will get:

T(a, b)L ---> L'

We know that L = (7, -3) and L' = (-1, 8)

Then we can write:

(7 + a, -3 + b) = (-1, 8)

Then we have two equations:

7 + a = -1 ---> a = -1 - 7 = -8

-3 + b = 8 ---> b = 8 + 3 = 11

Then we have a translation of 8 units to the left and 11 units up-.

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Complete question:

"Right triangle LMN has vertices L(7, –3), M(7, –8), and

N(10, –8). The triangle is translated on the coordinate plane so the coordinates of L’ are (–1, 8).

Find the translation done"

The sum of the given series is mentioned above.

A function describes a relationship between a dependent and independent variable. Example -

y = f(x) = 5x + 9

Given are the series as shown in the figure attached.

{ 1 } -

We can write the series as -

6 + 7 + 8 + 9 + 10 + ...... + 100

It is a arithmetic sequence. We can write the sum as -

∑{ i }  = (95/2)(2 x 6 + 94 x 1)

∑{ i }  = (95/2)(12 + 94)

∑{ i }  = 95 x 53

∑{ i }  = 5035

{ 2 } -

We can write the sum as -

∑{ n } = n       {there is no 'i' term}

Therefore, the sum of the given series are mentioned above.

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A.

1. Mode: No mode. Median: 24. Mean: 30.875. Range: 50.

2. Mode: No mode. Median: 33.5. Mean: 43.9. Range: 85.

3. Mode: No mode. Median: 46. Mean: 43.571. Range: 61.

4. Mode: No mode. Median: 17. Mean: 18. Range: 28.

5. Mode: No mode. Median: 10.5. Mean: 13.5. Range: 27.

6. Mode: 15. Median: 22.5. Mean: 25.857. Range: 31.

B.

7. Mode: 4.3. Median: 4.2. Range: 2.1.

8. Mode: 18.6. Median: 18.6. Range: 0.8.

C.

9. Mode: No mode. Median: 4/9.

10. Mode: No mode. Median: 5/24.

The equation to represent the situation are as follows:

Company A;

y = 3.25x + 125

Company B;

y = 3x + 150

The miles of travel the total cost will be the same is 100 miles.

Your family needs to rent a car for a week while on vacation. Company A charges $3.25 per mile plus a flat fee of $125 per week. Company B charges $3 per mile plus a flat fee of $150 per week.

Therefore, the equation to express the situation is as follows;

Company A;

y = 3.25x + 125

Company B;

y = 3x + 150

where

The number of miles the travel will cost the same can be calculated as follows:

3.25x + 125 = 3x + 150

3.25x - 3x = 150 - 125

0.25x = 25

x = 25 / 0.25

x = 100

Therefore, the number of miles is 100 miles.

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