How do I find 2 power series solutions about the point x0=0 for the differential equation: (1+2x) y''-2y'-(3+2X) y=0?

Answer:

tho thop

Step-by-step explanation:

If it takes 10 workers 2.5 years to build a 20 story building, it will take 2.5 sec 20 workers to build a 40 story building.

Given that a skyscraper's height and the number of workers needed to build it determine how long the project takes, We must make the time.

Allow the time t, height h, and number of workers to be ω.

Then, based on the relationship,

t = kh/ω

where k is constant.

The formula in the term of k is:

k = tω/h

Additionally, it takes 10 employees t0 2.5 years to construct a 20-story skyscraper.

Now putting the value

k = (2.5 × 10)/20

k = 25/20

k = 5/4

If a 40-story skyscraper requires 20 workers to construct, we have

t = kh/ω

t = (5/4) × (40/20)

t = 5/2

t = 2.5 sec

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The complete question is:

The time is takes to build a skyscraper is proportional to its height and inversely proportional to the number of construction workers. If it takes 10 workers 2.5 years to build a 20 story building, how long will it take 20 workers to build a 40 story building?

Answer:

a. 12f + 18 < 85

b. 5 friends

Step-by-step explanation:

f = the number of friends

Answer:

H

Step-by-step explanation:

Because 20 percent is 24 dollars off and the second option is 30 dollars off and the third is 40 dollars off and 120-40 is 80 dollars so sentence H is correct

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When 12 is subtracted from the square of a number and the result is 4 times the number, then the negative solution is -2

Consider the number as x

Square of the number = \(x^{2}\)

12 subtracted from the square of a number = \(x^{2} -12\)

4 times the number = 4x

Then the equation will be \(x^{2} -12=4x\)

Rearrange the terms and it will become a quadratic equation

\(x^{2} -4x-12=0\)

Split the middle term and solve the equation

\(x^{2} +2x-6x-12=0\)

Take common terms

x(x+2)-6(x+2) = 0

Take common term outside

(x-6)(x+2) = 0

Therefore

x = 6, -2

The negative solution is -2

Hence, when 12 is subtracted from the square of a number and the result is 4 times the number, then the negative solution is -2

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Answer:

Step-by-step explanation:

-2(3x)= -6x

Step-by-step explanation:

IF  x-4   is a factor, then putting in x = + 4    will make the polynomial = 0

5 ( 4^3) - 20 (4^2) - 5(4)  + 20   =   0    Yes...it is a factor

\(x - 4 = 0 \\ x = 4 \\ \)

substitute value of x in the function to see if it equals to zero , if not it won't be a factor of the function

\(5 {x}^{3} - 20 {x}^{2} - 5x + 20 = 0 \\ 5(4) ^{3} - 20( {4})^{2} - 5(4) + 20 = 0 \\ 5(64) - 20(16) - 20 + 20 = 0 \\ 320 - 320 - 20 + 20 = 0 \\ 0 = 0\)

so (x-4) is a factor for the function

Answer:

It's 8

Step-by-step explanation:

We can simplify 2/3 / (1/8) as follows:

2/3 / (1/8) = 2/3 * 8/1      (dividing by a fraction is the same as multiplying by its reciprocal)

           = 16/3

Therefore, the relationship between 2/3 / (1/8) and 2/3 * 8/1 is:

2/3 / (1/8) = 16/3 = 2/3 * 8/1

So the correct answer is (D) 2/3 / (1/8) = 2/3 * 8/1.

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Answer:

Area of the given fan is 763.4 cm²

Step-by-step explanation:

Area of a sector in a circle = \(\frac{\theta}{360}(\pi r^2)\)

Here, angle θ = Central angle subtended by the arc

r = Radius of the circle

Since, fan is in the form of a sector of a circle with radius = 27 cm

Measure of the central angle subtended by the arc FN = ∠FAN = 120°

Area of the fan = \(\frac{120}{360}(\pi )(27)^2\)

                         = \(\frac{729\pi }{3}\)

                         = 243π

                         = 763.407

                         ≈ 763.4 cm²

Therefore, area of the given fan is 763.4 cm²

In both cases, we reject the null hypothesis, suggesting that the mean weight is less than 20.5 pounds.

(a) Based on the sample data, we can construct a 90% confidence interval for the true population mean weight of bananas in the boxes. Using the sample mean weight of 18.86 pounds and sample standard deviation of 3.7 pounds, we get a margin of error of 1.12 pounds and a confidence interval of (17.74, 20.98) pounds. Since this interval does not include the hypothesized mean weight of 20.5 pounds, we reject the null hypothesis at the 10% level.
(b) Using a one-tailed t-test with 149 degrees of freedom and a significance level of 10%, we get a p-value of 0.013. Since this p-value is less than the significance level, we reject the null hypothesis and conclude that the mean weight of bananas in the boxes is less than 20.5 pounds.
a) Confidence interval: Using a 90% confidence level, we calculate the margin of error as (Z-score * (sample standard deviation / √sample size)) = 1.645 * (3.7 / √150) ≈ 0.442. The confidence interval is (18.86 - 0.442, 18.86 + 0.442) = (18.418, 19.302). Since the entire interval is less than 20.5, we reject the null hypothesis.
(b) P-value: We calculate the test statistic as (sample mean - hypothesized mean) / (sample standard deviation / √sample size) = (18.86 - 20.5) / (3.7 / √150) ≈ -4.52. The p-value for a one-tailed test is P(Z < -4.52) ≈ 0.00003, which is less than the significance level (0.10). Thus, we reject the null hypothesis.
In both cases, we reject the null hypothesis, suggesting that the mean weight is less than 20.5 pounds.

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I hope it helped you!!

Oof

Answer:

20x

Step-by-step explanation:

First of all, we need to always do the x first. And then subtract it I guess.

25x + (5x – 10)

30x-10

20x

Answer:

The slope is 1/2

Step-by-step explanation:

AS seen in the graph I provided you can see that the points are increasing by 1/2

Answer: False

Step-by-step explanation:

Answer:

Factor the numerator and denominator and then divide out any common factors.

Step-by-step explanation:

Answer:

7-3x

Step-by-step explanation:

You would have 7 so that would be 7 at the start of the equation. Then you would want to take away 3 at a time so it would be 3x with x representing the amount of times you take away

The mathematical model of an abstract syntax tree (AST) for a programming language's block (BL) statement typically involves representing the syntax of the statement using a tree structure.

This tree structure consists of nodes that correspond to different components of the statement, such as keywords, variables, operators, and expressions. The AST provides a way to parse and interpret the syntax of the statement, allowing for efficient compilation and execution of the code.

The model can be represented using various algorithms and data structures, such as recursive descent parsing or top-down parsing. Ultimately, the AST serves as a tool for developers to analyze, optimize, and debug their code, and is an essential component of many modern programming languages.

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to find the expected attendance, multiply the attendance by probability then add the products

6000 * 0.1 = 600

25000 * 0.2 = 5000

15000 * 0.2 = 3000

55000 * 0.5 = 27500

27500 + 3000 + 5000 + 600 = 36100

36100 * 15 = 541500 - 300000 = 241500 - 55000 = 186500

The output of this code will be the optimal values of the decision variables B, D, E, and S2 that maximize the objective function subject to the given constraints.

To solve this optimization problem using MATLAB, we can use the linprog function from the Optimization Toolbox.

First, we need to rewrite the problem in standard form, which requires converting the objective function to a minimization problem by multiplying it by -1, and expressing all constraints as linear inequalities of the form Ax <= b. In this case, we have:

Minimize: -B - 1.9D - 1.5E - 1.08S2

Subject to:

A + C + D + S0 = 100,000 -> A + C + D + S0 <= 100,000

0.5A + 1.2C + 1.08S0 - B - S1 <= 0

A + 0.5B + 1.08S1 - E - S2 <= 0

A <= 75,000

B <= 75,000

C <= 75,000

We can then use the following MATLAB code to solve the problem:

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% Define the objective function coefficients

f = [-1; -1.9; -1.5; -1.08];

% Define the constraint matrix

A = [1 1 1 1 0 0 0 0 0; 0.5 1.2 0 -1 -1 0 0 1.08 0; 1 0.5 0 -1 0 -1 1.08 0 0; 1 0 0 0 0 0 0 0 0; 0 1 0 0 0 0 0 0 0; 0 0 1 0 0 0 0 0 0; 0 0 0 0 1 0 0 0 0; 0 0 0 0 0 1 0 0 0; 0 0 0 0 0 0 0 0 1];

% Define the constraint RHS vector

b = [100000; 0; 0; 75000; 75000; 75000; 0; 0; 0];

% Define the bounds on the decision variables

lb = zeros(9,1);

ub = [75000; 75000; 75000; Inf; Inf; Inf; Inf; Inf; Inf];

% Solve the linear program

[x, fval, exitflag] = linprog(f, A, b, [], [], lb, ub);

% Print the optimal solution

fprintf('Optimal Solution:\n');

fprintf('B = %.2f\n', -fval);

fprintf('D = %.2f\n', -x(2));

fprintf('E = %.2f\n', -x(3));

fprintf('S2 = %.2f\n', -x(9));

The output of this code will be the optimal values of the decision variables B, D, E, and S2 that maximize the objective function subject to the given constraints.

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Answer:

part c is the correct answer to this question

If we sample the function x(t) = cos(75t) at the Nyquist frequency, the resulting discrete frequency would be half of the Nyquist frequency, which is equal to half of the highest frequency component in the continuous signal.

In this case, the highest frequency component in x(t) is 75 Hz, as determined by the coefficient of t in the cosine function. According to the Nyquist-Shannon sampling theorem, to accurately represent a signal, the sampling frequency must be at least twice the highest frequency component. Therefore, the Nyquist frequency in this scenario would be 2 * 75 Hz = 150 Hz.

Since we are sampling at the Nyquist frequency, the resulting discrete frequency would be half of the Nyquist frequency, which is 150 Hz / 2 = 75 Hz. Hence, when sampling x(t) at the Nyquist frequency, the resulting discrete frequency would be 75 Hz.

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If 8x ≤ g(x) ≤ 4x4 − 4x2 + 8 for all x,  x will be evaluated as lim x→1 g(x), 1 is 8.

To evaluate the limit of g(x) as x approaches 1, we must first examine the given inequality. It states that if 8x is less than or equal to g(x), and g(x) is less than or equal to 4x4 - 4x2 + 8, then this is true for all x.

Calculating the limit of g(x) as x approaches 1, we start by substituting x = 1 into the given inequality. This gives us 8(1) ≤ g(1) ≤ 4(1)4 - 4(1)2 + 8. Simplifying, this gives us 8 ≤ g(1) ≤ 8, so g(1) must be equal to 8.

Therefore, the limit of g(x) as x approaches 1 is 8.

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The first coordinate of the ordered pair is the x-value, while the second coordinate corresponds to the y-value.

Part a)

Substitute x=a and y=-4 to find an equation for a:

Solve for a:

Therefore, the value of a that makes the ordered pair (a,-4) a solution to the equation 4x-3y=10, is -1/2.

Part b)

Substitute x=3 and y=a+1:

Solve for a:

Therefore, the value of a that makes the ordered pair (3,a+1) a solution to the equation y=-5x+2, is -14.

Answer:

2(19x+40)

Step-by-step explanation:

Factors:

38: 1, 2, 19 and 38.

80: 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80.

The highest (greatest) number they have in common is 2. Therefore, the GCF is 2.

Factoring:

38/2= 19

80/2=40

2(19x+40)

Answer:

62.17 days

Step-by-step explanation:

The computation of the number of days  is shown below:

Given that

A(t)=10 × 0.5^(t ÷ 18.72)

1 = 10 × 0.5 ^ (t ÷ 18.72)

0.1 = 0.5 ^ (t ÷ 18.72)

Now consider the log in both sides

ln(0.1) = ln(0.5)^ (t ÷ 18.72)

ln(0.1)  ÷  ln(0.5) = (t ÷ 18.72)

3.321928095  = (t ÷ 18.72)

So, t = 62.17 days

With the help of log, we can easily compute it

Answer:function

Step-by-step explanation:

The line passes the graph once

SAMPLE Answer:

If the graph passes the horizontal-line test, then the function is one-to-one. Functions that are one-to-one have inverses that are also functions. Therefore, the inverse is a function.

Answer:

the answer to this is option 4.

Answer:

4, x = -17

Step-by-step explanation:

Answer: 9/10 of the book.

Step-by-step explanation:

1. Convert all of the fractions to have a common denominator. 6, 5, and 3 are all multiples of 30, so we can convert the fractions to 30ths.

1/6 = 5/30

2/5 = 12/30

1/3 = 10/30

2. Add the fractions together to find the whole amount of the book Joyce has read.

5/30 + 12/30 + 10/30 = 27/30

3. Simplify

27/30 -> 9/10

Step-by-step explanation:

1/6 + 2/5 +1/3=

nominator × with the other fraction denominator+ second fraction nominator × with first denominator / denominator ×denominator =

1/6+2/5= 1×5+2×6/6×5=5+12/30=17/30

17/30+1/3=,17×3+1×30/30×3=51+30/90=,81/90

now let's try to simplify it.

81/90 by 9=9/10