Given that {x, x3} is a fundamental set of solutions of x2y’’ -3xy’ + 3y = 0, find the general solution of x2y’’ + 3xy’ + 3xy = 4x7

The number of solutions that are there for this system of equation is: C. no solution.

In order to solve the given system of equations, we would apply the substitution method. Based on the information provided above, we have the following system of equations:

3x + 6y = 0      .......equation 1.

x + 2y = 0         .......equation 2.

By making x the subject of formula in equation 2, we have the following:

x = -2y           .......equation 3.

By using the substitution method to substitute equation 3 into equation 1, we have the following:

3(-2y) + 6y = 0

-6y + 6y = 0 (No solution).

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The solution is: the triangles are,

obtuse

acute

The Law of Cosines tells you the largest angle C will be found from ...

 C = arc cos((a² +b² -c²)/(2ab))

where c is the longest side of the triangle.

For the purpose of classifying the triangle as acute, right, or obtuse, you need only look at the sign of the argument of the arcos function. Since all side lengths are positive, this means you only need to look at the sign of the "form factor" a²+b²-c².

When f = a²+b²-c² is negative, the cosine is of an angle larger than 90°, so the triangle is obtuse. When it is 0, the angle is 90°, so a right triangle. (That condition is recognizable as related to the Pythagorean theorem.) When f > 0, the triangle is acute.

In the attached spreadsheet, we have done these calculations by summing the squares of all three sides, then subtracting twice the square of the longest side. (This makes the formula fairly simple.) It shows ...

 Triangle 1: f < 0 — obtuse triangle

 Triangle 2: f > 0 — acute triangle

In summary, you can compute a form factor ...

 f = a² +b² -c² . . . . . . . triangle with side lengths a, b, c with c longest

f < 0 — obtuse

f = 0 — right

f > 0 — acute

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complete question:

picture attached

The critical points are 2xy + y + 16 = 0 and 2x + xy + y = 0

Let's first find the partial derivative of f with respect to x, denoted as ∂f/∂x. To do this, we treat y as a constant and differentiate f with respect to x:

∂f/∂x = (∂/∂x)(x + y)(xy + 16)

Using the product rule of differentiation, we get:

∂f/∂x = (1)(xy + 16) + (x + y)(y) = y + xy + 16 + xy = 2xy + y + 16.

Similarly, let's find the partial derivative of f with respect to y, denoted as ∂f/∂y:

∂f/∂y = (∂/∂y)(x + y)(xy + 16)

Using the product rule again, we have:

∂f/∂y = (x + y)(1) + (x + y)(x) = x + xy + x + y = 2x + xy + y.

To find the critical points, we need to set both partial derivatives equal to zero and solve the resulting system of equations:

2xy + y + 16 = 0 ...(Equation 1)

2x + xy + y = 0 ...(Equation 2)

To solve the system of equations, we can use various methods such as substitution or elimination. Let's use elimination to solve equations 1 and 2 simultaneously:

Multiply equation 1 by 2 to eliminate the 2xy term:

4xy + 2y + 32 = 0 ...(Equation 3)

Now, subtract equation 2 from equation 3:

4xy + 2y + 32 - (2x + xy + y) = 0

Simplifying the equation:

4xy + 2y + 32 - 2x - xy - y = 0

3xy + y - 2x + 32 = 0

Now, rearrange the terms:

3xy - 2x + y + 32 = 0 ...(Equation 4)

We have obtained a new equation (equation 4) that relates x, y, and their coefficients.

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Therefore, the probability that the sample mean cholesterol level is greater than 206 is approximately 0.012 or 1.2%.

To calculate the probability that the sample mean cholesterol level is greater than 206, we need to know the population mean and standard deviation, as well as the sample size and distribution. Assuming that the population mean is known to be 200 and the standard deviation is 10, and that we have a sample size of 50 with a normal distribution, we can use the central limit theorem to approximate the distribution of the sample mean.
The formula for the z-score is z = (x - μ) / (σ / sqrt(n)), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Plugging in the values, we get z = (206 - 200) / (10 / sqrt(50)) = 2.24. We can use a standard normal distribution table or calculator to find that the probability of getting a z-score of 2.24 or greater is about 0.012. Therefore, the probability that the sample mean cholesterol level is greater than 206 is approximately 0.012 or 1.2%.

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The Central Limit Theorem allows us to use the sample mean to estimate the population mean even when the population distribution is unknown. The standard deviation of the population, sigma, is an important factor in determining the spread of the sample means.

The statement you are referring to is known as the Central Limit Theorem. It states that when sampling from a population with an unknown distribution, if the sample size is sufficiently large (usually n>30), the sample mean will follow an approximately normal distribution regardless of the shape of the population distribution. This is particularly useful in statistics because it allows us to make inferences about the population mean based on the sample mean.

The standard deviation, sigma, plays an important role in the Central Limit Theorem because it determines how spread out the population is. If sigma is small, the sample means will be tightly clustered around the population mean, while if sigma is large, the sample means will be more spread out.

In conclusion, the Central Limit Theorem allows us to use the sample mean to estimate the population mean even when the population distribution is unknown. The standard deviation of the population, sigma, is an important factor in determining the spread of the sample means.

1. When sampling from a population with an unknown distribution, mean mu, and standard deviation sigma,

2. If the sample size (n) is sufficiently large,

3. The sample mean (x bar) will have approximately a normal distribution.

The CLT(central limit theorem) is a vital tool in many areas of statistical analysis, as it provides a foundation for making inferences about populations based on sample data, even when the original population distribution is unknown or non-normal.

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The arc length traveled by the handle of the wrench is 0.825 meters.

When a wrench rotates, the handle moves along an arc due to its angular displacement.

To calculate the arc length traveled by the handle, we can use the formula:

Arc length = Radius [tex]\times[/tex] Angular displacement.

In this case, the length of the wrench is given as 0.33 meters, which acts as the radius.

The angular displacement is provided as 2.5 radians.

Plugging in these values, we have:

Arc length = 0.33 meters [tex]\times[/tex] 2.5 radians.

To calculate the product, we multiply the length of the wrench (0.33 meters) by the angular displacement (2.5 radians):

Arc length = 0.33 meters [tex]\times[/tex] 2.5 radians = 0.825 meters.

Therefore, the arc length traveled by the handle of the wrench is 0.825 meters.

This means that as the wrench rotates through an angle of 2.5 radians, the handle moves along an arc with a length of 0.825 meters.

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The solution of the equation is x = -3 and x = 1

From the information given, we have that the quadratic equation is expressed as;

2x² + 4x-6=0

Using the factorization method , we have the multiply the coefficient of x squared by the constant value in the expression, we get;

2(-6) = -12

Now, find the pair factors of this product whose sum is 4, we have;

+6 - 2

Substitute the values

2x² + 6x - 2x - 6 = 0

Group in equation in pairs

(2x² + 6x) - (2x -6) = 0

factorize the terms

2x(x + 3)- 2(x + 3) = 0

Then, we have;

x = 2/2 = 1

x = -3

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An ordered field is a set F with two binary operations, addition (+) and multiplication (⋅), and a binary relation, the order relation (≤), that satisfy certain axioms.

In an ordered field, we have the following properties: commutativity, associativity, distributivity, identity, inverses, transitivity, totality, antisymmetry, and the order-preserving nature of addition and multiplication.
To prove that every ordered field has no smallest positive element, we use a proof by contradiction. Suppose there exists an ordered field F and a smallest positive element ε > 0 in F. In an ordered field, the product of two positive elements is positive, and since ε is the smallest positive element, we must have ε² > ε.
However, due to the properties of ordered fields, we can perform the following manipulations: ε² > ε implies ε² - ε > 0, which in turn implies ε(ε - 1) > 0. Since ε is positive, we can conclude that ε - 1 must also be positive. Therefore, ε > 1.
But now, we have another positive element, 1, which is smaller than ε, contradicting our assumption that ε is the smallest positive element in the ordered field. This contradiction proves that no ordered field can have a smallest positive element, as any potential candidate would lead to the discovery of an even smaller positive element.

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The dotplot depicts that Only 12% of the values of x were 64.7 or greater. Because this is such a small percentage it would be surprising to get a sample mean of 64.7 or larger in an SRS of size 20 from a Normal population with μ = 64 and σ = 2.5.

The dotplot shows that only 12% of the simulated sample means were 64.7 or greater. This means that it is unlikely to get a sample mean of 64.7 or greater if the population mean is actually 64. In other words, the evidence suggests that the population mean height is greater than 64 inches.

The dotplot shows the distribution of the sample means of 250 simulated samples of size 20. The population mean is 64 and the population standard deviation is 2.5.

The fact that only 12% of the simulated sample means were 64.7 or greater means that it is unlikely to get a sample mean of 64.7 or greater if the population mean is actually 64.

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The flow of the velocity field along the straight line path from (0,0) to (1,1) is 55/3.

To find the flow of the velocity field along a path from (0,0) to (1,1), we need to integrate the velocity field along that path.

Let's consider two different paths: a straight line path and a curved path.

Straight Line Path:

For the straight line path from (0,0) to (1,1), we can parameterize the path as x(t) = t and y(t) = t, where t varies from 0 to 1.

The velocity field is given as [tex]f = 5y^2 \times 9i + (10xy)j.[/tex]

To find the flow along this path, we need to compute the line integral of the velocity field along the path.

The line integral is given by:

Flow = ∫C f · dr,

where C represents the path and dr represents the differential displacement vector along the path.

Plugging in the parameterized values into the velocity field, we have:

[tex]f = 5(t^2) \times 9i + (10t\times t)j = 45t^2i + 10t^2j.[/tex]

The differential displacement vector,[tex]dr,[/tex] is given by dr = dx i + dy j.

Since dx = dt and dy = dt along the straight line path, we have dr = dt i + dt j.

Therefore, the line integral becomes:

Flow = ∫[tex](0 to 1) (45t^2 i + 10t^2 j) . (dt i + dt j)[/tex]

= ∫[tex](0 to 1) (45t^2 + 10t^2) dt[/tex]

= ∫[tex](0 to 1) (55t^2) dt[/tex]

= [tex][55(t^3)/3] (from 0 to 1)[/tex]

= 55/3.

So, the flow of the velocity field along the straight line path from (0,0) to (1,1) is 55/3.

Curved Path:

For a curved path, the specific equation of the path is not provided. Hence, we cannot determine the flow of the velocity field along the curved path without knowing its equation.

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The probability of drawing exactly two pairs from a deck of cards containing four aces, four kings, four queens, and four jacks is approximately 0.3623 or about 36.23%.

To have exactly two pairs in a five-card hand, we need two cards of one rank, two cards of another rank, and one card of a different rank.

The number of ways to choose two ranks out of four for the pairs is (4 choose 2) = 6.

For each pair, we can choose two cards out of four in (4 choose 2) = 6 ways.

Finally, we can choose one card from the remaining 44 cards in (44 choose 1) ways.

Therefore, the number of ways to get exactly two pairs is:

6 x 6 x (44 choose 1) = 1584.

The total number of ways to draw five cards out of 16 is (16 choose 5) = 4368.

Therefore, the probability of drawing exactly two pairs is:

P(exactly two pairs) = (number of ways to get exactly two pairs) / (total number of ways to draw five cards)

= 1584 / 4368

= 0.3623 (rounded to four decimal places).

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Answer:

Step-by-step explanation:

hope this helps . Please mark my answer as best

The volume of the prism in the image attached is 27cm³. This type of prism is called Trapezoidal.

The attached image shows a Trapezoidal prism. To calculate the volume of the prism, we need to multiply the area of the base by the height.

Given dimensions:

Top width = 2 cm

Base width = 4 cm

Length = 6 cm

Height = 1.5 cm

To find the area of the base, we need to consider the average of the top width and base width.

average width = (2 + 4)cm / 2 = 6 cm / 2 = 3 cm.

The area of the base (A) can be calculated as follows:

A = Length × Width = 6 cm × 3 cm = 18 cm²

Now, we can calculate the volume (V) of the prism:

V = A × Height = 18 cm² × 1.5 cm = 27 cm³

Therefore, the volume of the prism is 27 cm³

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The expression that shows the equivalent of the given equation above would be = 16X⁶y⁶. That is option C.

An expression is said to be equivalent to another if when simplified gives the other expression of which it is being compared with.

The given expression;

= (4x³y³)²

Then open up the brackets to simplify the given expression. But, (2n³)² = 4n³*²

= 4n⁶

= 16X⁶Y⁶.

Therefore, in conclusion it is 16X⁶y⁶ that is equivalent to the given expression such is written as (4x³y-³)².

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The logit algorithm estimates the probability of each category.

In logistic regression with a dependent variable with three categories, the logit algorithm estimates the probability of each category relative to a reference category. There are different ways to define the reference category, but one common approach is to use the lowest category as the reference.

Suppose the dependent variable has three categories, labeled as 1, 2, and 3. The logit algorithm estimates the log odds of each category relative to the reference category (category 1), given a set of predictor variables. Let's denote the log odds of category 2 and category 3 relative to category 1 as logit_2 and logit_3, respectively.

The logistic regression model with three categories can be written as:

logit(p_2 / p_1) = β_0 + β_1 x_1 + β_2 x_2 + ... + β_k x_k

logit(p_3 / p_1) = γ_0 + γ_1 x_1 + γ_2 x_2 + ... + γ_k x_k

where p_1, p_2, and p_3 are the probabilities of category 1, category 2, and category 3, respectively, and x_1, x_2, ..., x_k are the predictor variables.

To obtain the probabilities of each category, we need to exponentiate the log odds and normalize them to sum up to 1. Specifically, we have:

p_1 = 1 / (1 + exp(logit_2) + exp(logit_3))

p_2 = exp(logit_2) / (1 + exp(logit_2) + exp(logit_3))

p_3 = exp(logit_3) / (1 + exp(logit_2) + exp(logit_3))

These equations show how the logit algorithm estimates the probabilities of each category in logistic regression with three categories. Note that the logit algorithm assumes that the relationship between the predictor variables and the log odds of each category is linear, and it estimates the coefficients β and γ using maximum likelihood estimation.

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First, divide 231 by 5 to find the average rate of speed per hour

231/5=46.2

And that's it! Mr. Alanzo was driving at an average rate of 46.2 miles per hour.

Hope I solved your problem, if not please stated what I did wrong and maybe I can fix it  ૮ ˶ᵔ ᵕ ᵔ˶ ა

Answer:

The correct answer is B.

Step-by-step explanation:

The value of the expression 2³/2³ is 1.

This is because 2³ (or 2 raised to the power of 3) is equal to 8, and 8 divided by itself is always equal to 1.

In other words, when you have the same base number in both the numerator and denominator of a fraction, you can simply cancel out those numbers and the result is 1.

So, 2³/2³ simplifies to 8/8, which is equal to 1.

Therefore, the correct answer is B.1.

As n increases, the partial sums Sn appear to be increasing rapidly towards infinity.

The common ratio (r) of the given geometric series can be found by dividing any term by its preceding term.

r = 16/12 = 1.33

So, the first term (a1) is 12 and the common ratio (r) is 1.33.

The formula for the partial sum of an infinite geometric series is:

[tex]S_n = a_1\dfrac{(1-r^{n})}{(1-r)}[/tex]

where a₁ is the first term, r is the common ratio, and n is the number of terms being added.

Now, we can find the partial sums for n=1,2,3,4, and 5:

S1 = 12(1 - 1.33¹)/(1 - 1.33) = -10.56

S2 = 12(1 - 1.33²)/(1 - 1.33) = -1.76

S3 = 12(1 - 1.33³)/(1 - 1.33) = 52.32

S4 = 12(1 - 1.33⁴)/(1 - 1.33) = 496.56

S5 = 12(1 - 1.33⁵)/(1 - 1.33) = 4388.16

As n increases, the partial sums Sn appear to be increasing rapidly towards infinity.

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To find the highest and lowest temperatures encountered by the ant as it traverses the circle of radius 7 centered at the origin, we need to parameterize the circle and then find the maximum and minimum values of the temperature function T(x, y) along the circle.

First, we can parameterize the circle of radius 7 centered at the origin using polar coordinates:

x = 7cosθ

y = 7sinθ

where θ is the angle measured counterclockwise from the positive x-axis.

Substituting these expressions into the temperature function, we get:

T(θ) = 4x^2 - 4xy + y^2 = 4(7cosθ)^2 - 4(7cosθ)(7sinθ) + (7sinθ)^2

= 49(2cos^2θ - 4cosθsinθ + sin^2θ)

= 49(cosθ - 2sinθ)^2

Now, we can find the maximum and minimum values of T(θ) by finding the maximum and minimum values of the function f(θ) = cosθ - 2sinθ, since T(θ) is a square of f(θ).

To find the maximum and minimum values of f(θ), we can take its derivative with respect to θ and set it equal to zero:

f'(θ) = -sinθ - 2cosθ = 0

Solving for θ, we get θ = arctan(-2), which is in the second quadrant. Since f''(θ) = -cosθ + 2sinθ is negative at this value, we know that this is a maximum value of f(θ).

Therefore, the highest temperature encountered by the ant is T(θ) = 49(cosθ - 2sinθ)^2 evaluated at θ = arctan(-2), which gives T_max = 245.

Similarly, the lowest temperature encountered by the ant is T(θ) = 49(cosθ - 2sinθ)^2 evaluated at θ = arctan(-2) + π, which gives T_min = 49.

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The sum of the terms 2, 4, 6, ..., 60 can be written in sigma notation as: ∑(2k), k = 1 to 30. Here, the Greek letter sigma, ∑, represents the sum of the terms that follow it.

The expression (2k) represents the k-th term of the sequence, where k takes values from 1 to 30. By plugging in k = 1, we get the first term of the sequence, 2. Similarly, by plugging in k = 2, we get the second term of the sequence, 4, and so on. Finally, by plugging in k = 30, we get the last term of the sequence, 60. Therefore, the sum represented by the above sigma notation is the sum of the terms 2, 4, 6, ..., 60.

In general, if we want to find the sum of the first n even numbers, we can use the following sigma notation:

∑(2k), k = 1 to n

By plugging in k = 1, we get the first even number, 2. Similarly, by plugging in k = 2, we get the second even number, 4, and so on, up to the n-th even number, which is given by plugging in k = n. Thus, the sum represented by this sigma notation is the sum of the first n even numbers.

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A regression line is referred to as the line of best fit because it is a line that is drawn through a scatter plot of data points to show the general trend or pattern of the data. The line is "best" in the sense that it is the one that minimizes the distance between the line and the data points.

In other words, the regression line is the line that comes closest to passing through as many of the data points as possible while still maintaining a relatively small amount of distance between the line and the points.

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The probability that the randomly selected sample will have less than 97.5% of the units that can hold at least 400 lbs of weight before breaking is 2.4249.

What is the binomial distribution?

In probability theory and statistics, the discrete probability distribution of the number of successes in a series of n separate experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome: success or failure, is known as the binomial distribution with parameters n and p.

Here, we have

Given: For one product, 98% of all the units made at a particular factory can hold at least 400 lbs. of weight before breaking to check the product, quality control selects a random sample of 300 units made at the factory and determines whether or not the product can hold at least 400 lbs.

p = 0.98

q = 1 - p = 1 - 0.98 = 0.02

n = 300

Using the binomial distribution,

Standard deviation = σ = √npq = √300 × 0.98 × 0.02 = 2.4249

Standard deviation = σ = 2.4249

Hence, the probability that the randomly selected sample will have less than 97.5% of the units that can hold at least 400 lbs of weight before breaking is 2.4249.

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The value of 2a₃ - 3b₃ is -29/3.

To find the value of 2a₃ - 3b₃, we shall find the third term of the arithmetic sequence and the third term of the geometric sequence.

Firstly, the third term of the arithmetic sequence:

We shall first determine the common difference (d) - the value that is constant, added to each term to get the next term.

Given:

a₁ = 3

a₂ = -1

The common difference (d):

d = a₂ - a₁

d = -1 - 3

d = -4

Next, the third term of the arithmetic sequence (a₃):

a₃ = a₂ + d

a₃ = -1 + (-4)

a₃ = -5

Secondly, the third term of the geometric sequence:

Here, we can get each term by multiplying the previous term by a common ratio (r).

Given:

a₁ = 3

a₂ = -1

The common ratio (r):

r = a₂ / a₁

r = -1 / 3

Then, the third term of the geometric sequence (b₃):

b₃ = a₂ * r²

b₃ = -1 * (-1/3)²

b₃ = -1 * (1/9)

b₃ = -1/9

Finally, we find the value of 2a₃ - 3b₃:

2a₃ - 3b₃ = 2(-5) - 3(-1/9)

2a₃ - 3b₃ = -10 + 3/9

2a₃ - 3b₃ = -10 + 1/3

2a₃ - 3b₃ = -30/3 + 1/3

2a₃ - 3b₃ = -29/3

Therefore, the value of 2a₃ - 3b₃ is -29/3.

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Question completion:

Your question is incomplete, but most probably your full question is:

The first two terms of a sequence are a₁ = 3 and a₂=-1. Let a₃ be the third term when the sequence is arithmetic and let b₃ be the third term when the sequence is geometric. What is the value of 2a₃-3b₃?

Answer:

a≥3

Step-by-step explanation:

Answer:

Part A: 120000000 is the difference

Part B: A 8 minutes, 20 seconds

Step-by-step explanation:

I'm an expert

The double integral ∬_R((x−2y)/(3x−y))dA over the parallelogram R is equal to 40ln(2).

(a) To simplify the double integral, we can make a change of variables by letting u = x - 2y and v = 3x - y. This allows us to rewrite the integrand as (u/3v), and the region R becomes a rectangle in the uv-plane enclosed by the lines u = 0, u = 4, v = 1, and v = 8.

(b) To evaluate the double integral using the change of variables u = x - 2y and v = 3x - y, we need to first find the Jacobian of the transformation. Taking the partial derivatives, we have:

∂u/∂x = 1, ∂u/∂y = -2, ∂v/∂x = 3, ∂v/∂y = -1

The Jacobian is then:

J = ∂u/∂x * ∂v/∂y - ∂u/∂y * ∂v/∂x

 = (1 * (-1)) - (-2 * 3)

 = -5

Now we can rewrite the double integral as:

∬_R (u/3v) dA = ∬_R (u/3v) |J| dudv

Substituting in the limits of integration for the new variables u and v, we have:

∫_1^8 ∫_0^4 (u/3v) |-5| dudv

= 5/3 * ∫_1^8 ∫_0^4 (u/v) dudv

= 5/3 * ∫_1^8 ln(4) dv

= 5/3 * (8ln(4) - ln(1))

= 5/3 * 8ln(4)

= 40ln(2)

Therefore, the double integral ∬_R((x−2y)/(3x−y))dA over the parallelogram R is equal to 40ln(2).

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The volume of the cylinder is 72π cubic inches.

We have,

The formula for the volume of a cylinder is given by V = πr²h,

Where r is the radius of the base and h is the height or length of the cylinder.

Given that the radius r = 3 in and the height h = 8 in, we can substitute these values in the formula and calculate the volume as follows:

V = πr²h

V = π(3 in)²(8 in)

V = π(9 in²)(8 in)

V = 72π in³

Therefore,

The volume of the cylinder is 72π cubic inches.

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The probability of drawing exactly 3 black balls out of 5 is 0.2846, or approximately 0.2846 rounded to four decimal places.

To find the probability of drawing exactly 3 black balls out of 5, we need to use the binomial probability formula, which is:

P(X=k) = (n choose k) * p * (1-p)ⁿ⁻ᵏ

where P(X=k) is the probability of getting k successes, n is the number of trials, p is the probability of success, and (n choose k) is the number of ways to choose k items out of n.

In this case, n = 5, k = 3, p = 5/14 (the probability of drawing a black ball on the first draw is 5/14, and this probability decreases with each subsequent draw), and (n choose k) = 5 choose 3 = 10 (the number of ways to choose 3 black balls out of 5).

Plugging these values into the formula, we get:

P(X=3) = (5 choose 3) * (5/14)³ * (9/14)²

= 10 * 0.0752 * 0.3778

= 0.2846

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The coordinates where the fountain will be located is (2, 1/2)

From the question, we have the following parameters that can be used in our computation:

The center town forms a parallelogram with the vertices

A = (0, 4); B = (6, 1); C = (4, -3); D = (-2, 0)

The corner points when placed on a coordinate grid can be calculated using

Mid-point = 1/2(x1 + y1, x2 + y2)

So, we have

Center = 1/2 * (0 + 4, 4 - 3) or

Center = 1/2 * (6 - 2, 1 + 0)

Evaluate

Center = (2, 1/2) or Center = (2, 1/2)

Hence, the coordinates where the fountain will be located is (2, 1/2)

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Answer: 4sr+17r−2s4+17−2

Step-by-step explanation: simplify 18r - 3s-r + 4s1r+s

then multiply by one and get 18r-3s-r+4sr+s.

then combine like terms and get 17r-3s-r+4sr+s.

combine like terms again and end up with 17r-2s+4sr

you then want to rearrange the terms to 4sr+17r-2s

and you have your answer .