Solve the following initial value problem. cos2x sin x dy + (cos?x)y = 5, 7(7/3) = 4 dx

Answers

Answer 1

The solution to the given initial value problem $cos2x sin x dy + (cos?x)y = 5, 7(7/3) = 4 dx$ is $y(x) = (5/6) * (cos^2(x) - 1) + (28/9) * sin(x) + (40/9) * cos(x)$.

To solve the initial value problem, we can use the method of integrating factors. The integrating factor is found by taking the exponential of the integral of the coefficient of y with respect to x. In this case, the coefficient is cos(x). So, the integrating factor is $e^(^\int ^{ cos(x)} \, ^d^x^) = e^s^i^n^(^x^))$.

Multiplying the given differential equation by the integrating factor, we obtain:

$e^{sin(x)} * [cos^{2x} sin(x) dy + cos(x) y] = 5e^{sin(x)} dx$

By using the product rule and simplifying, we have:

$d/dx [e^{sin(x)} * y * cos^{2x}] = 5e^{sin(x)}$

Integrating both sides with respect to x, we get:

$e^{sin(x)} * y * cos^{2(x)} = \int {5e^{sin(x)}} \, dx = 5e^{sin(x)} + C,$

where C is the constant of integration.

Simplifying and solving for y, we obtain:

$y(x) = [(5/6) * (cos^{2x} - 1) + (28/9) * sin(x) + (40/9) * cos(x)] / (e^{sin(x)} * cos^{2(x)} + Ce^{-sin(x)},$

where C is the constant of integration.

To find the value of C, we can use the initial condition y(7/3) = 4. Substituting this into the equation and solving for C, we can determine the specific solution.

In conclusion, the solution to the given initial value problem is $y(x) = (5/6) * (cos^{2x} - 1) + (28/9) * sin(x) + (40/9) * cos(x)$, subject to the specified initial condition.

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Related Questions

The table shows the estimated number of lines of code written by computer programmers per hour when x people are working. A 2-column table with 6 rows. The first column is labeled people working with entries 2, 4, 6, 8, 10, 12. The second column is labeled lines of code written hourly with entries 50, 110, 160, 210, 270, 320. Which model best represents the data? y = 47(1. 191)x y = 34(1. 204)x y = 26. 9x – 1. 3 y = 27x – 4.

Answers

Based on the given data, the model that best represents the data is y = 27x - 4. This is because the data seems to have a linear relationship and can be fit by a straight line.

The other models (y = 47(1.191)x, y = 34(1.204)x, and y = 26.9x - 1.3) are all exponential models and do not fit the data as well as the linear model.
To confirm this, we can plot the data points on a graph and see that they form a linear pattern. We can also calculate the correlation coefficient between the two variables, which measures the strength of the linear relationship between them.

A correlation coefficient of 0.998 indicates a very strong positive linear relationship, further supporting the choice of a linear model.
In summary, the best model to represent the given data is y = 27x - 4, which shows a linear relationship between the number of people working and the lines of code written hourly.

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Answer: D

Step-by-step explanation:

Please Help!!!

Which graph represents the solution to negative one half m is greater than or equal to seven elevenths?

number line with closed circle on point negative 14 over 11 and arrow shaded to the right
number line with closed circle on point negative 7 over 22 and arrow shaded to the right
number line with closed circle on point negative 14 over 11 and arrow shaded to the left
number line with closed circle on point negative 7 over 22 and arrow shaded to the left

Answers

The solution set to the inequality, -1/2m ≥ 7/11, is: m ≤ -14/11.

See attachment for the graph.

How to Graph the Solution Set to an Inequality?

If the possible set of values to an inequality is "greater than or equal to" (≥), or "less than or equal to" (≤), then a closed circle is used to indicate the point on the graph.

On the other hand, an open circle is used for "< or >".

If it is "> or ≥" the shaded arrow is drawn to the right, if "< or ≤", it is drawn to the left of the inequality graph.

Given the inequality, -1/2m ≥ 7/11, solve for m:

-1/2m(-2) ≥ 7/11(-2)

m ≤ -14/11 [the sign changes because we are multiplying both sides by negative number]

The solution to the inequality is: m ≤ -14/11.

The graph is given below for m ≤ -14/11.

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Please Help!!!Which graph represents the solution to negative one half m is greater than or equal to

Answer:

Step-by-step explanation: the answer is D with the arrow pointing to the left.

Hope this helps!

If 5 dogs share equally a bag of dog treats, each dog gets 24 treats.
Suppose 8 dogs share equally the bag of treats. How many treats
does each dog get? (EXPLAIN)

Answers

This is a two-part question in which we must identify the value of one part to determine the other part’s value. Since we already know each dog gets 24 treats if shared equally by 5 dogs, we can set up an equation:

5 • 24 = 120

If 5 dogs equally share the bag of dog treats, there is a total of 120 treats. We now can apply this to the scenario of 8 dogs distributing:

120 / 8 = 15

If 8 dogs share equally the bag of treats, each dog will receive 15 treats.

The floor area in an Air Force warehouse measures 200 feet by 200 feet. What is the maximum safe floor load if the maximum weight the floor area can hold is 4000 tons?
a. 100 pounds per square foot
b. 120 pounds per square foot
c. 140 pounds per square foot
d. 160 pounds per square foot
e. 200 pounds per square foot

Answers

The floor area in an Air Force warehouse measures 200 feet by 200 feet. The maximum safe floor load is (option e) 200 pounds per square foot.

To determine the maximum safe floor load, we need to calculate the maximum weight the floor area can support per square foot.

Given that the floor area measures 200 feet by 200 feet, the total area is 200 * 200 = 40,000 square feet.

If the maximum weight the floor area can hold is 4000 tons, we need to convert tons to pounds since we're calculating the weight per square foot.

1 ton is equal to 2000 pounds, so 4000 tons is equal to 4000 * 2000 = 8,000,000 pounds.

To find the maximum safe floor load per square foot, we divide the total weight by the total area:

Maximum safe floor load = $\frac{8,000,000 \text{ pounds}}{40,000 \text{ square feet}} = 200 \text{ pounds per square foot}$

Therefore, the maximum safe floor load is 200 pounds per square foot (option e).

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Is it possible to solve 3 equations with 4 variables?

Answers

A linear system with 3 equations and 4 variables by representing it with an augmented matrix and bringing the matrix to reduced row-echelon form can be solved.

What is linear system?

A mathematical representation of a system based on the application of a linear operator is known as a "linear system" in systems theory. Ordinarily, compared to nonlinear systems, linear systems display much simpler features and properties. The automatic control theory, signal processing, and telecommunications all heavily rely on linear systems as a mathematical abstraction or idealisation.

Linear systems, for instance, are frequently used to model the propagation medium for wireless communication systems. An operator, H, that converts an input, x(t), into an output, y(t), a kind of black box description, can be used to describe a general deterministic system.

The superposition principle, or alternatively both the additivity and homogeneity properties, must be satisfied by a system to be considered linear, and only then.

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7. Write an equation of the line parallel to y = 8x - 1 that contains (-6, 2). Please write the equation
in slope-intercept form.

Answers

Answer:

you have to use the formula of a line passing through a point, so: y-y0=m(x-x0)

We also know that m=8, because it is parallel to the line y=(8=m)x -1

so: y-2=8(x+6)

and you solve it, so:

y-2=8x+48

y=8x+48+2

y=8x+50

Select the correct answer.
Answer the question based on the data in the two-way table.
Gender Below
Boy
Girl
Total
Grades
Above
Average Average
14
23
22
45
16
30
Which statement is true?
Total
37
38
75
OA. P(boylabove average grades) = P(boy)
OB. P(above average grades/boy) = P(above average grades)
P(boyjabove average grades) # P(above average grades)
D. P(above average grades/boy)=P(boy)

Answers

P(above average grades/boy) = P(above average grades). The correct option is B

What is probability ?

The likelihood that a male will have grades above average is 23/37, or roughly 62%. 38/75, or almost 51%, of students are expected to have grades above average.

Statement A is untrue since the two probabilities do not equal one another. The probability of a guy having above-average grades is not the same as the probability of a student having above-average grades, hence Statement C is also untrue. Statement D is untrue since a boy's chance of being chosen is not the same as his chance of earning above-average grades.

Given that he was chosen, the likelihood of a boy obtaining above-average grades is the same as the likelihood that he will. This is so that the likelihood that a boy will have above-average grades is unaffected by the selecting procedure.

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I need help on the picture I sent

Answers

The length of the hypotenuse is as:

a. 25 inches

b. 10.30 m

c. 26 feet

d. 12.65 cm

e. 50 mm

f. 2.24 mile

What is the Formula for a Right-Angled Triangle?

The Pythagoras formula is used to calculate the area of a right-angled triangle. It asserts that the hypotenuse's square is equal to the sum of its other two sides' squares. (Hypotenuse)² = (Base)² + (perpendicular)² is the Pythagorean formula.