Find the general solution of the following differential equation 2xdx – 2ydy = x^2ydy – 2xy^2dx.

Answer:

Values of x are ±4 and ±5

Step-by-step explanation:

Let y = \(x^{2}\)

Which means: \(y^{2} = x^{4}\)

Therefore:

A quadratic equation is formed:

\(y^{2} - 41y + 400 = 0\)

The above quadratic equation can be simplified either by The Double Bubble Method or using the quadratic formula

Double Bubble Method:

\(y^{2} - 41y + 400 = 0\)

The pair of factors of 400 that add together to give 41 are 25 and 16. Use these two factors to rewritre -41y:

\(y^{2} - 25y - 16y + 400 = 0\)

Then do Factorization by grouping (i.e group the terms with common factors before factorizing):

\(y(y -25) - 16(y - 25) = 0\)

\((y - 25)(y - 16) = 0\)

The product of two expressions is zero, which means either of the two expressions is equal to Zero:

Either: \(y - 25 = 0\)

Substituting \(y = x^{2}\):

          = \(x^{2} - 25 = 0\)

         = \(x^{2} = 25\)

         = \(\sqrt{x^{2}} = \sqrt{25}\)

         ∴ x = ±5

 Or: \(y - 16 = 0\)

Substituting \(y = x^{2}\)

     \(= x^{2} - 16 = 0\)

     \(= x^{2} = 16\)

     \(= \sqrt{x^{2}} = \sqrt{16}\)

    ∴ x = ±4

∴Values of x are ±4 and ±5

Answer:

=4p^2−12p+13

Step-by-step explanation:

Let's simplify step-by-step.

4p^2−12p+13

There are no like terms.

This method is only effective when one of the equations can be solved for either x or y in terms of the other variable.

The Substitution Method is one of the methods used to solve a system of equations. This method involves solving for one variable in terms of the other in one of the equations and substituting this expression into the other equation. The following are the steps involved in using the Substitution Method:

Solve for either x or y in one of the equations:

In this step, one of the equations in the system is selected and solved for either x or y in terms of the other variable. This expression is then substituted into the other equation to obtain an equation in one variable.

Substitute the expression you got into the other equation:

The expression obtained in step 1 is substituted into the other equation to eliminate one of the variables.

Simplify and solve for the variable that remains:

The equation obtained in step 2 is then simplified and solved for the variable that remains.

Back substitute and solve for the first variable:

After finding the value of one of the variables, back substitution is performed into one of the original equations to solve for the other variable.

Check your solution:

The solution obtained in step 4 is then checked by substituting the values of x and y into both equations of the system to ensure that they satisfy both equations.

It is important to note that the Substitution Method is only effective when one of the equations can be solved for either x or y in terms of the other variable. If this is not possible, another method such as the Elimination Method can be used.

In conclusion, the Substitution Method is an effective way to solve a system of equations by eliminating one of the variables. It involves a series of steps that can be followed to arrive at the solution. However, it is important to note that this method is only effective when one of the equations can be solved for either x or y in terms of the other variable.

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Answer:

The equation is not equal

Step-by-step explanation:

\(-3*-5=16*\\15\neq 16\)

Answer:

0.7425π

Step-by-step explanation:

The area of the circle is πr² and since the diameter is 3, the radius is 1.5, and 1.5² is 2.25. Then you need to multiply the height of the pool which is 0.33, so 2.25 * 0.33 is 0.7425, but dont forget π.

Answer:

Step-by-step explanation:

2 x 8f + 2 x 9g  2 x -4

16f + 18g -8

Answer:

your questions is wrong it's 2×2-6x=56

answer= X=-9

Step-by-step explanation:

2×2-6x=56

4-6x=56

-6x=56-4

-6x=54

-X=54/6

-X=9

X=-9

Answer:

the answer is -7w

Step-by-step explanation:

-2w - 5w = -7

The missing dimension (the model diameter of the bicycle wheel) is 4.8 inches.

We can use the scale factor to create a proportion that will fix the issue:

scalefactor = 1:5

Scale factor = Actual diameter / Model diameter

Let x represent the omitted measurement (the bicycle wheel's model diameter):

2 feet / x = 5 / 1

When we multiply both parts by x, we obtain:

2 feet = 5x

Dividing both sides by 5, we get:

x = 2/5 feet

Now that we know that 1 foot = 12 inches, we can change the model's diameter to inches:

x = (12 inches/foot ) * (2/5) feet = 4.8 inches

As a result, the dimension that is lacking (the bicycle wheel's model diameter) is 4.8 inches.

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The correct statement regarding the mode of the sample is given as follows:

a. can be larger, smaller or equal to the mode of the population.

The mode of a data-set is the observation that appears the most often in the data-set.

The mode of the sample is simply the most frequently occurring value in the sample. It is not necessarily expected to be the same as the mode of the population, which is the most frequently occurring value in the entire population.

As a sample is a group taken from an entire population, the observation that appears the most in the sample can be different from the more common observation in the population,

Hence, option (a) is correct.

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Answer:

x = -1.7, or x = -17/10

Step-by-step explanation:

f(x) = 9.2 + 6x + 1 is a linear function and as such (and because the slope is not zero) has only one solution.  Combining like terms, we get

f(x) = 10.2 + 6x = 0 (you must set this equal to zero if solving for zero(s).

Then 6x = -10.2, and x = -1.7, or x = -17/10

Answer:

5 miles per hour

Step-by-step explanation:

Let the speed of Kelly is \(v_1\) miles per hour and speed of Raul is v₂ miles per hour.

Since, speed = \(\frac{\text{Distance}}{\text{Time}}\)

Kelly took 135 minutes to cover 90 miles from New York to Philadelphia.

∵ 1 minute = \(\frac{1}{60}\) hours

∴ 135 minutes = \(\frac{135}{60}\) = \(\frac{9}{4}\) hours

v₁ = \(\frac{90}{\frac{9}{4}}\)

   = \(90\times \frac{4}{9}\)

   = 40 miles per hour

Raul took 153 minutes to cover the same distance as Kelly,

∵ 1 minute = \(\frac{1}{60}\) hours

∴ 153 minutes = \(\frac{153}{60}\) = \(\frac{51}{20}\) hours

v₂ = \(\frac{90}{\frac{51}{20}}\)

    \(=90\times \frac{20}{51}\)                        

    = 35.29

    ≈ 35.3 miles per hours

v₁ - v₂ = 40 - 35.3

         = 4.7

         ≈ 5.0 miles per hours

Therefore, Kelly is 5 miles per hours faster than Raul.     

Answer:

Well, what's the question?

Answer:

none of these terms are like terms

Answer:

there is  no like terms in this expression

Step-by-step explanation:

there is "a", "b" and "ab"

you cant combine anything because they are all different

Hope this helps!!

For the following scenario where a researcher wanted to test the ratings of three different brands of paper towels with 7 reviewers each, you would utilize Friedman's rank test.

For the given scenario, the appropriate test to use would be the Friedman's rank test. This is because we have three different brands of paper towels, and each brand is rated by 7 reviewers.

The Friedman's test is used to determine if there are significant differences among the groups in a repeated measures design, where the same individuals are rated on multiple occasions. Therefore, it is the appropriate test for this scenario where the ratings are collected from multiple reviewers for each brand.

This test is also appropriate because there are more than two related groups being compared (three brands of paper towels), and the data is likely ordinal (ratings). The Wilcoxon sign rank test is typically used when comparing only two related groups.

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Answer:

d

Step-by-step explanation:

edg 2021

Answer:

d

Step-by-step explanation:

Answer: 2(x+2)=(y+3)^2

Step-by-step explanation:

Answer:

A. 2(x+2) = (y+3)²

Step-by-step explanation:

Edge

0.6004 is standard deviation of equation .

Why is there a standard deviation?

=0.6004$P(120≤X≤153)=0.6004​

The mean is μ=147, and the standard deviation is σ=16.

0.6462−0.0458=0.6004.

Thus, P(120≤X≤153)=0.6004.

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The transverse line is: Line t

The parallel lines are: m and n

From the transverse and parallel line theorem of geometry, we know that:

If two parallel lines are cut by a transversal, then corresponding angles are congruent. Two lines cut by a transversal are parallel IF AND ONLY IF corresponding angles are congruent.

Now, from the given image, we see that the transverse line is clearly the line t.

However we see that the lines m and n are parallel to each other and as such we will refer to them as our parallel lines in the given image.

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Answer:

About 4 weeks.

Step-by-step explanation: Because:  

5 1/5 divided by 1 /25 equals 3.71428571429. And that rounded down is 4.

Answer:

220

Step-by-step explanation:

hope it helps

The required when two classes are combined, the average final exam score is approximately 87.

Number of students in the first class = 20

The average score of the first class = 92

Number of students in the second class = 25

The average score of the second class = 83

Calculate the total number of students:

Total number of students = Number of students in the first class + Number of students in the second class

Total number of students = 20 + 25 = 45

Calculate the total score for both classes:

Total score for the first class = Number of students in the first class * Average score of the first class

Total score for the first class = 20 * 92 = 1840

Total score for the second class = Number of students in the second class * Average score of the second class

Total score for the second class = 25 * 83 = 2075

Calculate the combined total score:

Combined total score = Total score for the first class + Total score for the second class

Combined total score = 1840 + 2075 = 3915

Calculate the average final exam score when the two classes are combined:

Average final exam score = Combined total score / Total number of students

Average final exam score = 3915 / 45

Average final exam score = 87

Therefore, when the two classes are combined, the average final exam score is approximately 87.

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Evaluating this vector at (1, 1, 1), we get:(-i - j - k) / (3^(3/2))

(a) To find curl r^A(-yi + xj), we use the formula:

curl F = (1/r) ∂/∂θ (rF₃) - ∂/∂r (rF₂)

where F = r^A(-yi + xj) and r = (x^2 + y^2)^1/2. We have F₃ = 0 because F has no z-component, so we only need to compute F₂ and F₁. We have:

F₂ = r^A(-y) and F₁ = r^A(x)

Taking partial derivatives, we get:

∂F₂/∂r = Ar^(A-1)(-y)

∂F₂/∂θ = 0

∂F₁/∂r = Ar^(A-1)(x)

∂F₁/∂θ = 0

Plugging these into the formula for curl F, we get:

curl F = (1/r) ∂/∂θ (rF₃) - ∂/∂r (rF₂)

= (1/r) ∂/∂r (rF₂) - ∂/∂r (rF₂)

= (Ar^(A-1)(x) + Ar^(A-1)(y)) k

= Ar^(A-1)(xi + yj + zk)

So we have curl F = α r^A k, where α = A and k is the unit vector in the z-direction.

(b) To find the direction of the curl for A = -5 and A = 2, we simply need to normalize the vector Ar^(A-1)(xi + yj + zk) obtained in part (a). We have:

For A = -5: curl F = -5r^(-6)(xi + yj + zk)

= -(x/r^3)i - (y/r^3)j - (z/r^3)k

Normalizing this vector, we get:

direction = (-x/r^3)i - (y/r^3)j - (z/r^3)k / |(-x/r^3)i - (y/r^3)j - (z/r^3)k|

= (-x/r^3)i - (y/r^3)j - (z/r^3)k

For A = 2: curl F = 2r^(1)(xi + yj + zk)

= 2(xi + yj + zk)

Normalizing this vector, we get:

direction = (2xi + 2yj + 2zk) / |2xi + 2yj + 2zk|

= (1/sqrt(3))i + (1/sqrt(3))j + (1/sqrt(3))k

(c) To determine the sign of the circulation around a small circle oriented counterclockwise when viewed from above and centered at (1, 1, 1), we can use the right-hand rule.

If we curl our fingers in the direction of the circle and our thumb points in the direction of the curl of the vector field, then the sign of the circulation is positive if our palm points upwards and negative if our palm points downwards.

For A = -5, the direction of the curl is (-x/r^3)i - (y/r^3)j - (z/r^3)k. Evaluating this vector at (1, 1, 1), we get:

(-i - j - k) / (3^(3/2))

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(a) Setting do = 18,000 represents the initial loan amount borrowed for the car. (b) a36 = 0 because it denotes the balance owed at the end of the 36th month, indicating complete repayment. (c) The monthly interest rate is 0.00333 (or approximately 0.3333%). (d) At the end of the first month, before payment, the amount owed will be the initial loan amount plus monthly interest. After making the payment, the amount owed will be the previous amount owed minus the payment made.(e) Recurrence relation: an+1 = (1 + monthly interest rate) * an - b, where an is the amount owed at the end of month n and b is the payment amount made at the end of month n.(f) Solution formula: an = (1 + monthly interest rate)ⁿ* do - b * [(1 + monthly interest rate)ⁿ - 1] / monthly interest rate, where do is the initial loan amount. g) cannot be determined.

(a) We should set do = 18,000 because it represents the initial amount of money borrowed to buy the car. In this scenario, it signifies the principal or the original loan amount. By setting do = 18,000, we establish the starting point for our calculations and subsequent payments.

(b) The value of a36 is 0 because it represents the amount of money owed at the end of the 36th month, which corresponds to the end of the repayment period. At this point, all payments have been made, and the loan has been fully repaid, resulting in a balance of zero.

(c) The monthly interest rate can be calculated by dividing the annual interest rate by 12 (since there are 12 months in a year). In this case, the annual interest rate is 4%, so the monthly interest rate would be 4%/12 = 0.3333...% or approximately 0.00333 (rounded to four decimal places).

(d) At the end of the first month, before making the payment, the amount owed can be calculated by adding the monthly interest to the initial loan amount. Since it's the first month, no payment has been made yet. After making the payment, the amount owed at the end of the first month will be the result of subtracting the payment amount from the previous amount owed.

(e) The recurrence relation for the amount owed can be expressed as: an+1 = (1 + monthly interest rate) * an - b. Here, an represents the amount owed at the end of month n, and b represents the payment amount made at the end of month n.

(f) The solution formula for the recurrence relation is an = (1 + monthly interest rate)^n * do - b * [(1 + monthly interest rate)^n - 1] / monthly interest rate. Here, do represents the initial loan amount.

(g) To determine the value of b, we need more information about the specific terms of the loan, such as the number of payments to be made over the 3-year period. Without this information, it is not possible to calculate the exact value of b. The value of b will depend on the desired monthly payment amount and the number of payments.

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To determine the sample standard deviation for each sample, we need to calculate the variability within the data points.

The given data consists of two samples, one from urban homes and the other from farm homes, with concentrations of endotoxin. By using the appropriate formula, we can calculate the sample standard deviation for each sample.

To calculate the sample standard deviation, we follow these steps:

Calculate the mean (average) of each sample.

Subtract the mean from each data point and square the result.

Sum up the squared differences.

Divide the sum by the total number of data points minus one.

Take the square root of the result to obtain the sample standard deviation.

For the given data:

Urban homes (U): 6.0, 5.0, 11.0, 33.0, 4.0, 5.0, 89.0, 18.0, 35.0, 17.0, 23.0

Farm homes (F): 4.0, 14.0, 11.0, 9.0, 9.0, 8.0, 4.0, 20.0, 5.0, 8.9, 21.0, 9.2, 3.0, 2.0, 0.3

By applying the formula and performing the calculations for each sample, we can determine their respective sample standard deviations.

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Answer:

a. $76.00

b. y = 23x - 76

Step-by-step explanation:

a. If Anton earned $23 every week for twelve weeks, his total revenue would be 23 (12) = 276 dollars. He only had $200 after paying his parents back, though, so that means if you take away the $200 leftover money he got (after paying his parents back) from the $276 he earned over the 12 weeks, you'll get 276 - 200 = he borrowed $76.00 from his parents.

b. Anton is earning $23 every week, so the money, y, that he'll have after x weeks is y = 23x. But since he borrowed $76 from his parents, that much money should be subtracted from his money-making equation, leaving us with y = 23x - 76. Hope this was helpful!

The expression improper fractions to mixed numbers will be 1 ¹/₄, 2 ¹/₃, and 1 ²/₃.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expressions are given below.

(5 x 1/4), (3 x 7/9), and (2 x 5/6)

Then simplify each expression, then we have

⇒ 5 x 1/4

⇒ 1/4 + 1/4 + 1/4 + 1/4 + 1/4

⇒ 5 / 4

⇒ 1 ¹/₄

⇒ 3 x 7/9

⇒ 7/9 + 7/9 + 7/9

⇒ 7/3

⇒ 2 ¹/₃

⇒ 2 x 5/6

⇒ 5/6 + 5/6

⇒ 5/3

⇒ 1 ²/₃

The expression improper fractions to mixed numbers will be 1 ¹/₄, 2 ¹/₃, and 1 ²/₃.

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The value of the t test is 13.36, we have to conclude that there is sufficient evidence that suggests that insurance adjustment was greater than $2400.

H0: u = 24000

H1: u > 24000

we have n = 84 homes

bar x = 27500

s = 2400

Next we have to find the test statistic

The formula for this is given as

\(t = \frac{x-u}{s/\sqrt{n} }\)

When we out in the values we would have

\(t = \frac{27500-24000}{2400/\sqrt{84} }\)

This would give us the answeer of the t test as

t test = 13. 3658

We have alpha = 0.02

the degree of freedom = 84 - 1 = 83

we have to find tα/2, df

=  ±2.0865

Given that the value of the test statistic is greater than critical value we would have to then reject the null hypothesis.

Hence the conclusion that we can make is that there is sufficient evidence that suggests that insurance adjustment was greater than $2400.

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