Find a general solution to the differential equation 2y''-5y'-3y=0

The provided differential equation is a first-order linear differential equation, which can be solved using an integrating factor. After solving, the particular solution satisfying the initial condition y(0)=7 is y=e^(-sin(x))(5sin(x)+7).

The differential equation provided is a first-order linear differential equation, which can be solved using an integrating factor. In this case, dy/dx + ycos(x) = 5cos(x), the integrating factor is e^(∫ cos(x) dx) = e^sin(x). Multiplying everything by the integrating factor, we get (ye^sinx)' = 5cos(x)e^sin(x).

Then we can integrate on both sides to get ye^sin(x) = 5sin(x) + C, where C is the constant of integration. To find the particular solution, we can use the initial condition y(0)=7. By substituting these values, we can solve for C. Substituting x=0 and y=7 yields C=7. Thus, the particular solution is y=e^(-sin(x))(5sin(x)+7).

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The one-way ANOVA or one – way analysis of variance is used to know whether there are statistically substantial dissimilarities among the averages of three or more independent sets. It compares the means between the sets that is being examined whether any of those means are statistically pointedly dissimilar from each other. If it does have a significant result, then the alternative hypothesis can be accepted and that would mean that two sets are pointedly different from each other. The symbol, ∑ is a summation sign that drills us to sum the elements of a sequence. The variable of summation is represented by an index that is placed under the summation sign and is often embodied by i. The index is always equal to 1 and adopt values beginning with the value on the right hand side of the equation and finishing it with the value over head the summation sign.

since you have the 75, we know that a would equal 105 for line g , since a line = 180 degrees

 so to make line f parallel with g it needs the same angles with line n as line g has

so if a = 105, then angle d would also need to be 105

 The answer is D

Answer:

x= 2 vertex: (2,4)

Step-by-step explanation:

just did the assignment

IT is A: Rewrite the expression on the left using the distributive property.

Answer:

since he missed b ill answer it for your b is 24 because when you look at the grragh  it goes from 0 then to 24 so its unit rate would be 24

Step-by-step explanation:

The unit rate of fragrance A is; $ 26, and the unit rate of fragrance B is; $ 24. Hence Fragrance A has the greater unit rate.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

According to the condition the rate of the fragrance A will be;

78/3 = 156/6

= 234/9

= 26 $ per bottle

According to the graph the price of the fragrance B will be;

24/4 = 48/2

=24 $ per bottle

Therefore, the unit rate of fragrance A is; $ 26, and the unit rate of fragrance B is; $ 24.

Hence, Fragrance A has the greater unit rate.

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The solution is $ 153

The change in the net working capital is $ 153

What is Net Working Capital?

The difference between a company's current assets and current or short-term liabilities is known as net working capital, or working capital.

Cash flow will have an operational origin, when there is a net decrease in working capital

Working Capital = Current Assets - Current Liabilities

Given data ,

Let the change in net working capital be A

Now , the equation will be

Working Capital at the beginning = Current Assets - Current Liabilities

Substituting the values in the equation , we get

Working Capital at the beginning = 316 - 220

Working Capital at the beginning = $ 96

And ,

Working Capital at the end = Current Assets - Current Liabilities

Substituting the values in the equation , we get

Working Capital at the end = 469 - 260

Working Capital at the end = $ 209

So ,

The change in net working capital A = Working Capital at the end - Working Capital at the beginning

Substituting the values in the equation , we get

The change in net working capital A = 209 - 96

The change in net working capital A = $ 153

Therefore , the value of A is $ 153

Hence , change in the net working capital is $ 153

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1 foot = 12 inches

12.8 x 12 = 153.6 inches each side

we know that

The x-intercept is the value of x when the the value of y is equal to zero

and

The y-intercept is the value of y when the the value of x is equal to zero

In the graphed function we have that

the value of x when the the value of y is equal to zero is [tex]-1[/tex]

therefore

the x-intercept is equal to the point [tex](-1,0)[/tex]

the value of y when the the value of x is equal to zero is [tex]-3[/tex]

therefore

the y-intercept is equal to the point [tex](0,-3)[/tex]

the answer is

x-intercept = (–1, 0)

y-intercept = (0, –3)

Answer:

[tex]150.72 feet^2[/tex] is the difference in the area covered.

Step-by-step explanation:

A lawn sprinkler sprays water 8 feet at full pressure, P.

A lawn sprinkler rotates 360 degree which means area covered by sprinkler is of circular shape. Since the sprinkler is in center and sprays the the water 8 feet away in all the direction while rotating.

Radius of the circle = 8 feet

Maximum pressure = P

As we know that higher the pressure higher will the force by which water will move out of the sprinkler. And with more force, sprinkler will able to spray water farther.

So we this we can say that pressure of the sprinkler is directly proportional to the radius of the circle in which water sprayed

[tex]pressure\propto Radius[/tex]

[tex]P\propto r[/tex]

[tex]\frac{P_1}{r_1}=\frac{P_2}{r_2}=constant[/tex]

[tex]P_1=P.P_2=P-50\%\times P=0.5 P[/tex]

[tex]r_1=8 feet.r_2=?[/tex]

[tex]r_2=\frac{0.5 P\times 8 feet}{P}=4 feet[/tex]

Area when , [tex]r_1= 8 feet[/tex] (Area of circle=[tex]\pi (radius)^2[/tex])

[tex]A=\pi r_1^{2}=\pi (8 feet)^2[/tex]

Area when ,[tex]r_2= 4 feet[/tex]

[tex]A'=\pi r_1^{2}=\pi (4 feet)^2[/tex]

Difference in Area = A- A'

[tex]\pi (8 feet)^2-\pi(4 feet)^2=\pi(48 feet^2)=150.72 feet^2[/tex]

[tex]150.72 feet^2[/tex] is the difference in the area covered.

According to budgeting guidelines often referred to as the 20/30/50 rule, no more than 20% of your net income should be spent on debt repayments. Therefore, the maximum amount spent on credit payments for a $1,500 monthly income should be $300.

The best practice for budgeting recommends that no more than 20% of your net monthly income should be spent on debt repayments, including credit payments. This is commonly referred to as the 20/30/50 rule. Therefore, given a monthly net income of $1,500, the maximum amount spent on credit payments should be 20% of $1,500, which equals to $300.

Here's how you would calculate it:

So, the correct answer is B. $300.

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To solve this problem, all we have to do is to use the formula below, plug in the value of the parameter λ, then calculate for the median distance. The formula is:

Median = ln 2 / λ

Substituting:

Median = ln 2 / 0.01357

Median = 51.08 m

The [tex]\( t \)[/tex]-value for a 99% confidence interval based on a sample size of 10 is 3.2498.

To find the [tex]\( t \)[/tex]-value for a 99% confidence interval estimation based on a sample size of 10, we need to use the [tex]\( t \)[/tex]-distribution table or a calculator. The [tex]\( t \)[/tex]-distribution is used when the sample size is small (typically [tex]\( n < 30 \)[/tex]) and the population standard deviation is unknown.

Given:

- Confidence level: 99%

- Sample size [tex](\( n \)): 10[/tex]

The degrees of freedom [tex](\( df \))[/tex] are calculated as:

[tex]\[ df = n - 1 = 10 - 1 = 9 \][/tex]

To find the critical [tex]\( t \)[/tex]-value for a 99% confidence interval with 9 degrees of freedom, we look for the [tex]\( t \)[/tex]-value that corresponds to the area in the tails of the distribution. For a 99% confidence interval, the area in each tail is:

[tex]\[ \frac{1 - 0.99}{2} = 0.005 \][/tex]

So we need the [tex]\( t \)[/tex]-value such that 0.5% of the distribution is in each tail.

Using a [tex]\( t \)[/tex]-distribution table or a calculator, we find the [tex]\( t \)[/tex]-value for 9 degrees of freedom and a 99% confidence interval (or 0.5% in each tail).

The [tex]\( t \)[/tex]-value for 9 degrees of freedom at the 99% confidence level is approximately:

[tex]\[ t_{0.005, 9} \approx 3.2498 \][/tex]

Thus, the [tex]\( t \)[/tex]-value for a 99% confidence interval based on a sample size of 10 is approximately 3.2498.

Answer: For 0 ≤Ф≥ 2π (where π= 180°)

∴ Ф = 22.5°, 67.5°, 112.5°, 157.5°, 202.5°, 247.5°, 292.5°, 337.5°

Step-by-step explanation:

sin(3Ф)cos(Ф) - cos(3Ф)sin(Ф) = √2/2

sin(3Ф - Ф) =√2/2

3Ф -Ф = sin∧-1{√2/2}

 2Ф = 45°

∴ Ф = 22.5°

Final answer:

The sales tax rate is found by dividing the amount of sales tax by the cost of the item before tax and then multiplying by 100. In this case, the sales tax rate is 5%.

Explanation:

To find the sales tax rate of an item, you need the amount of sales tax paid and the cost of the item before tax. The formula to calculate the sales tax rate is:

sales tax rate = (amount of sales tax \/ cost of the item before tax) \ 100

Applying the formula, we have:

sales tax rate = ($22.50 \/ $450) \ 100

sales tax rate = 0.05 \ 100

sales tax rate = 5%

Therefore, the sales tax rate for the item is 5%.

Answer:

Option B.

Step-by-step explanation:

We need [tex]2\frac{3}{4}[/tex] wheelbarrows of sand for 8 wheelbarrows of concrete.

That means ratio between sand and concrete is [tex]2\frac{3}{4}:8[/tex]

Or [tex]\frac{11}{4}:8[/tex]

Now we have to calculate the amount of sand to make 248 cubic feet of concrete.

If the amount of sand required is x cubic feet then the ratio of sand and concrete will be x : 248.

Since both the ratios should be same therefore,

[tex]\frac{x}{248}=\frac{\frac{11}{4} }{8}[/tex]

[tex]\frac{x}{248}=\frac{11}{32}[/tex]

x = [tex]\frac{11\times 248}{32}[/tex]

x = [tex]\frac{2728}{32}[/tex]

x = [tex]\frac{341}{4}[/tex]

  = [tex]85\frac{1}{4}[/tex] cubic feet

Option B will be the answer.

The student worked for 5 hours and 45 minutes before taking a lunch break, calculated by finding the difference between the clock-in time of 6:45 a.m. and the lunchtime of 12:30 p.m.

The student worked for a certain number of hours before taking a lunch break. To calculate the duration of work before lunch, we subtract the start time from the end time. The student clocks in at 6:45 a.m. and clocks out at 12:30 p.m. for lunch.

First, we convert the time worked to a 24-hour format: 6:45 a.m. remains the same but 12:30 p.m. is 12:30 in 24-hour time. Now, we calculate the time difference:

Adding up the hours and minutes, we get a total of 5 hours and 45 minutes worked before lunch.

The total surface area of the cylinder is approximately 1187.72 cm², the volume is approximately 3077.2 cm³, and the cost to cover it with gift wrap at $3 per square centimeter is $3,558.76.

The surface area of a cylinder is calculated using the formula: Surface Area = 2πr(height) + 2πr². With a diameter of 14 cm, the radius (r) is half of that, which is 7 cm. Plugging in the values, the surface area is 2π(7 cm)(20 cm) + 2π(7 cm)².

For part b, once we have calculated the surface area, we can determine the cost to cover the cylinder using the given price per square centimeter. If S represents the total surface area, the cost will be $3 times S.

The volume of the cylinder can be found with the formula V = πr²h, and using the radius of 7 cm and a height of 20 cm, we get the volume V = π(7 cm)²(20 cm).

Performing these calculations:

Using 3.14 for π, we get:

The area of the larger square is 4 times larger than the area of the smaller square. The area of the big hexagon is 12 sq. in.

The area of the larger square is 4 times larger than the area of the smaller square. This is because the area of a square is proportional to the square of its side length.

In this case, the side length of the larger square is twice the side length of the smaller square, so the area of the larger square is 2² times greater than the area of the smaller square.

Given that the area of the small hexagon is 3 sq. in, the area of the big hexagon can be found by multiplying the area of the small hexagon by the square of the scale factor:

Area of big hexagon = (scale factor)² * Area of small hexagon = 2² * 3 sq. in = 12 sq. in