Divide the difference between 70 and 20 by 25.

Given the ODE,

(x² - 4)y" + 3xy + y = 0, we need to find the power series solution about x = 0 in the form of y = Σⁿ₀ Cn(x - 0)ⁿ.

Let us substitute y = Σⁿ₀ Cn xⁿ, y" = Σⁿ₂ Cn (n)(n - 1)xⁿ⁻², and y' = Σⁿ₁ Cn (n)xⁿ⁻¹ in the given ODE.

So, we get, Σⁿ₂ Cn (n)(n - 1)xⁿ + Σⁿ₀ Cn (x² - 4) Σⁿ₁ Cn (n)xⁿ⁻¹ + Σⁿ₀ Cn xⁿ = 0

Therefore, Σⁿ₀ [Cn {(n)(n - 1) + (n + 2)(n + 1) - 1} + 3Cn⁻¹ (n + 1) - 4Cn₋₂] xⁿ = 0

Comparing the coefficients of xⁿ,

we have the recurrence relation as below: Cn {(n)(n - 1) + (n + 2)(n + 1) - 1} + 3Cn⁻¹ (n + 1) - 4Cn₋₂ = 0=> Cn {(n² - 1) + (n² + 3n + 2) - 1} + 3Cn⁻¹ (n + 1) - 4Cn₋₂ = 0=> Cn (2n² + 3n) + 3Cn⁻¹ (n + 1) - 4Cn₋₂ = 0

As the ODE is a regular singular point, the radius of convergence is 2.

So, the required power series solution is: y = C₀ (x - 0)⁰ + C₁ (x - 0)¹ + Σⁿ₂ Cn xⁿ where Cn is given by the recurrence relation Cn (2n² + 3n) + 3Cn⁻¹ (n + 1) - 4Cn₋₂ = 0.

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Answer:

Step-by-step explanation:

Lets verify one-by-one:

a)

b)

c)

d)

As we see in three cases we get rational number but the smallest one is 3, this indicates the answer is option b.

perimeter = 2(x - 6y) + 2(8x² - x - 4y)

2x - 12y + 16x² - 2x - 8y

= 16x² - 20y units

If positive integer x has 3 prime factors and 8 total factors, then (n+1)^3 total factors will x^n have where n is a positive integer

      In the question given that positive integer x has 3 prime factors and 8 total factors

      To find How many total factors will x^n have where n is a positive integer

The formula used the total number of factors of a positive integer

            x = (a+1) (b+1) (c+1)…  where a, b, c are prime factors of x.

Substituting the values from the given information:

          x = p*q*r (where p, q, and r are prime numbers)

     Total number of factors of  x = (1+1) (1+1) (1+1)

      A total number of factors of  x = 2 * 2 * 2

     The total number of factors of x = 8

If x has 3 prime factors, then the other factor could be 1x = p*q*rx^1

                                                                                               = p*q*r(1+1) (1+1) (1+1)

                                                                                               = 8

      factors  x^2 = p^2*q^2*r^2(2+1) (2+1) (2+1) = 27

      factors  x^3 = p^3*q^3*r^3(3+1) (3+1) (3+1) = 64

      factors x^n = p^n*q^n*r^n(n+1) (n+1) (n+1)

     Number of factors = (n+1)^3

              Hence the number of factors in x^n is (n+1)^3.

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The possible value of x which the two triangles are similar is x=60°.

What do you mean by triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Method:

Given that two angles of the triangle are specified, the triangles can be

similar for only one value of x.

According to the given data in the question,

The two triangles are similar when we have;

x + 10° = 2x - 50°

Which gives;

2x - x = 50° + 10° = 60°

x = 60°

Checking gives;

x + 10° = 2·x - 50° = 70°

Two angles of the first triangle are 70° and 60°

Then, the third angle of the first triangle is (180° - (70° + 60°)) = 50°

The three angles of the first triangle are therefore; 70°, 60° and 50°.

Two angles of the second triangle are 70° and 70°.

The third angle of the second triangle is (180° - (70° + 70°)) = 40°

The three angles of the second triangle are therefore; 70°, 70° and 40°

Therefore, the two triangles are similar by AAA similarity.

The two triangles are similar when, x = 60°

When x = 50°, we have;

x + 10° gives;

50° + 10° = 60°

∴ ∠(x + 10°) = 60°

The two angles of the first triangle are; 60° and 50°

The third angle on the second triangle is 180° - (60° + 50°) = 70°

On the second triangle, we have;

2·x - 50° gives;

2 × 50° - 50° = 50°

∴∠(2·x - 50°) = 50°

Therefore, the two angles of the second triangle are 70° and 50°

The third angle on the second triangle is 180° - (70° + 50°) = 60°

Therefore, the two triangles are not similar when x = 50°

Similarly, the two triangles are not similar when x + 10° = 50°

Hence, the possible value of x which the two triangles are similar is x = 60°.

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Therefore, the current height of the bean plant is 165 centimeters.

Addition is a basic mathematical operation that combines two or more numbers or quantities to give a total or a sum. In other words, it is the process of finding the total when two or more values are combined. It is denoted by the plus symbol (+). For example, in the expression 5 + 3, 5 and 3 are the addends, and the sum or total is 8. Addition is one of the four basic arithmetic operations, the others being subtraction, multiplication, and division. It is widely used in many areas of mathematics, as well as in everyday life situations such as counting objects or adding up a shopping bill.

Here,

The current height of the bean plant can be found by adding the growth of 15 centimeters to its previous height of 1.5 meters, after converting meters to centimeters:

1.5 meters = 150 centimeters

Current height = previous height + growth

Current height = 150 cm + 15 cm

Current height = 165 cm

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When using regression analysis to estimate the index model for a stock, the slope of the regression line is an estimate of the β of the asset.

The beta (β) of an asset measures the sensitivity of the asset's returns to changes in the market as a whole. A beta of 1 indicates that the asset's returns move in lockstep with the market, while a beta greater than 1 indicates that the asset's returns are more volatile than the market and a beta less than 1 indicates that the asset's returns are less volatile than the market.

On the other hand, α (alpha) is a measure of the excess return of an asset relative to its expected return, given its beta. α is not estimated by the slope of the regression line, but rather by the intercept of the regression line.

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Answer:

Q1) 104m²

Q2) 121 in.²

Step-by-step explanation:

Q1)

GIVEN :-

TO FIND :-

GENERAL FORMULAES TO BE USED IN THIS QUESTION :-

SOLUTION :-

Area of the triangle = \(\frac{1}{2} \times 8 \times 6 = 24m^2\)

Area of the rectangle = \(10 \times 8 = 80m^2\)

Area of the figure = (Area of the triangle) + (Area of the rectangle)

                              = 24m²+ 80m²

                              = 104m²

Q2)

GIVEN :-

TO FIND :-

GENERAL FORMULAES TO BE USED IN THIS QUESTION :-

SOLUTION :-

Area of the triangle = \(\frac{1}{2} \times 3 \times 7 = \frac{21}{2} = 10.5 \; in.^2\)

Area of the trapezium = \(\frac{1}{2} \times (6 +7) \times 17 = \frac{221}{2} = 110.5\; in^2\)

Area of the figure = (Area of the triangle) + (Area of the trapezium)

                              = 10.5 in.² + 110.5 in.²

                              = 121 in.²

Step-by-step explanation:

\( \tt{9 {x}^{2} - 12x + 4}\)

Here, the second order of polynomial ax² + bx + c is factorized and expressed as the product of two linear factors. First, we have to find the two numbers that adds to 12 and if we multiply those numbers , we get 36 ( The two numbers should be 6 and 6 ).

⟶ \( \tt{9 {x}^{2} - (6 + 6)x + 4}\)

⟶ \( \tt{9 {x}^{2} - 6x - 6x + 4}\) { Distribute x through the parentheses )

⟶ \( \tt{ \underbrace{9 {x}^{2} - 6x}} \: - \underbrace{6x + 4}\)

⟶ \( \tt{3x(3x - 2) - 2(3x - 2)}\)

⟶ \( \tt{(3x - 2)(3x - 2)}\)

⟶ \( \tt{ {(3x - 2)}^{2} }\)

\( \pink{ \boxed{ \boxed{ \tt{ Our \: final \: answer : \boxed{ \underline{ \tt{{(3x - 2)}^{2} }}}}}}}\)

Hope I helped ! ♡

Have a wonderful day / night ! ツ

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Answer:

150

Step-by-step explanation:

Answer: 150!

Step-by-step explanation:

i did the edge test, i got it right. trust me, i dont lie. :)  have a nice day<3

proof:

Answer:

x=1,9

Step-by-step explanation:

First, we expand the equation into the form ax^2+bx+c=0

2(x-5)^2=32

2(x^2-10x+25)-32=0

2x^2-20x+18=0

x^2-10x+9=0 (divide both sides by 2)

(x-1)(x-9)=0

x=1,9

Answer: 111.1 m

Step-by-step explanation:

(30*2)/60 = 1 km ( the tunnel length is 1 Km.)

1 Km = 1000 m.

1000/9 = 111.1 m.

They were sold 160 cars altogether that week.we can find by using percentage formula.

A percentage is a number or ratio that can be expressed as a fraction of 100. To show that a number is a percent. we use the percent symbol (%) beside the number.It is a portion of a whole expressed as a number between 0 and 100.

To find a percentage we can divide the portion of the whole by the whole itself and multiply by 100.. The formula used to calculate the percentage is: (value/total value)×100%.

Now we have

he sold at monday and tuesday=22+18=40

Let a number is x Then we get

25% of x = 40

25/100 *x =40

             x= 4000/25

             x=160

Hence he sold 160 cars at that week.

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Answer:

E

Step-by-step explanation:

Answer:

A., E.

Step-by-step explanation:

0.70 and 0.71 are greater than 0.68 but less than 0.72.

(hope this helps!)

Answer: Part A: The graph shows a negative relationship between the temperature of the city and the number of popsicles sold. As the temperature increases, the number of popsicles sold decreases.

Part B: To make the line of best fit, we need to draw a line that comes closest to the data points. We can find the slope and y-intercept of the line by using two of the data points on the graph. Let's choose the points (90, 20) and (40, 10).

Slope = (change in y) / (change in x) = (20 - 10) / (90 - 40) = 0.2

To find the y-intercept, we can use the slope-intercept form of a line: y = mx + b, where m is the slope and b is the y-intercept. Let's use the point (90, 20) and plug in the slope we just found:

20 = 0.2(90) + b

b = 2

Therefore, the approximate slope of the line of best fit is 0.2 and the approximate y-intercept is 2.

Step-by-step explanation:

To get a number point 1 is impossible for any of the team to reach at the end of the described tournament.

As given in the question,

Total number of footballs teams = 3

Each team plays once with other team

Let three teams are Team1, Team2, and Team3

Team1 plays with Team2 and Team3

Team2 will play with Team3

Winning points = 3

Losing team points = 0

Withdraw teams points = 1

To reach in finals suppose Team1 plays with Team2 and Team3 and win

Points of team1 = 3 + 3

                         = 6points

As team plays once with other team , Team1 is out of the game.

Team2 and Team3 play with each other

To reach at the end of the tournament one team has to win let it be Team2

Points of Team2 = 3

Points of Team3 = 0

No withdraw game is possible to reach into finale.

Therefore, point 1 is impossible for any team to reach at the end of the tournament.

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The equation of a straight line passing through the given point and slope is y - y1 = m(x - x1).

What is the simple definition of slope?

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

Let the given point be (x1,y1).

slope be m.

we know that,

Line equation passing through point is:

y - y1 = m(x - x1)

where m = slope and (x1,y1) = given point.

Therefore The equation of a straight line passing through the given point and slope is  y - y1 = m(x - x1).

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Answer: 59

Step-by-step explanation: angle 3 is equal to angle 6 and to find angel 3 do 180-121

The original figure is formed by the points:

To first make a reflection in the x-axis, we must follow the rule:

So, let's use this transformation with each point:

Finally, we're asked to transform these previous points using a reflection in the y-axis. To do this we must use the following rule:

So, using this rule for the points already reflected in the x-axis:

Finally, plot these points:

The expression which is equivalent to -10 is the option b, -3 - 7.

Explanation:

We can use subtraction and addition of integers to get the value of the given expression. We can write the given expression as;

-3 - 7 = -10 (-3 - 7)

The addition of two negative integers will always give a negative integer. When we subtract a larger negative integer from a smaller negative integer, we will get a negative integer.

If we add -3 and -7 we will get -10. This makes the option b the correct answer.

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Answer:

208

Step-by-step explanation:

4*30 = 120

(15-4) * 8 = 88

88 + 120 = 208

Answer:

208 cm

Step-by-step explanation:

Solving right side first. 8*15=120

Take out 8cm from 30. 30 - 8 = 22

22*4= 88

88 + 120 = 208

Check work I found the total area and the white rectangle.

15*30=450 which in total area

15-4=11 11 is the left/right side of the white rectangle

30-8=22 22 is the top/bottom side of the white rectangle.

22*11= 242

208+242=450

Answer:

what is the question

Step-by-step explanation:

The number of days in which Meena would be able to complete the work alone is 24 days.

In order to determine the number of days in which Meena would be able to complete the work alone, we would have to assign variables to the amount of time taken by Mala, Meena, and Vinay, and then translate the word problem into an algebraic equation as follows;

Note: Combined work rate = 1/x + 1/y + 1/z

Based on the information provided, we have the following equations that models the work rate by each person;

1/(x + y) = 10 ⇒ 1/10 = x + y    ........equation 1.

1/(y + z) = 12 ⇒ 1/12 = y + z    ........equation 2.

1/(x + z) = 15 ⇒ 1/15 = x + z    ........equation 3.

x + y + y + z + x + z = 1/10 + 1/12 + 1/15

2(x + y + z) = 15/60

2(x + y + z) = 1/4

x + y + z = 1/8

From equation 2, we have:

x + (y + z) = 1/8

x + 1/12 = 1/8

x = 1/8 - 1/12

x = 1/24

x = 24 days.

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We know that:

- She has some of it complete, but the robot still needs 3 arms and 6 wheels.

- Patty has saved up $68, which is enough to buy the parts she needs.

- Arms costs $13 and wheels costs $4

We must find how much money is left after making the purchase.

To find it we must subtract the money spent on the purchase from the money saved.

- money spent:

Is the money spent when she buys the arms and the wheels

So, the money spent is equal to $63

- money saved

Is the money Patty has saved.

Patty has saved up $68.

Finally, subtracting the money spent on the purchase from the money saved

ANSWER:

After Patty buys the parts, $5 is left.

Answer:

It seems you forgot to add the picture.....

If you put it in the comments i will try to solve it...

Stay safe and have a Merry Christmas!!!!!!! :D

The df value for inference about the slope in a regression analysis with n observations is n-2.

In a regression analysis, we use data from n observations to estimate the relationship between two variables. The df, or degrees of freedom, is the number of values in the final calculation that are free to vary. In simple linear regression, we estimate two parameters: the intercept and the slope.

Therefore, when calculating the df for inference about the slope, we subtract the two estimated parameters from the total number of observations (n). So, the df value for the slope is n-2. This is important because it impacts the test statistic and the confidence intervals for the slope in our regression analysis.

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