Solve the system of equations given below.

The equations you mentioned:

1. y = xy:

To solve this differential equation, we can separate the variables and integrate both sides.

dy/y = x dx

Integrating both sides gives:

ln|y| = (1/2)x² + C

Exponentiating both sides gives the general solution:

|y| = [tex]e^{((1/2)x^2 + C)[/tex]

Taking the positive and negative values of y, we get two branches of solutions:

y = [tex]Ae^{(1/2)x^2[/tex] and y = [tex]-Ae^{(1/2)x^2[/tex], where A is an arbitrary constant.

2. xy = 2y:

Rearranging the equation, we get:

xy - 2y = 0

Factoring out y, we have:

y(x - 2) = 0

This equation has two solutions:

y = 0 and x - 2 = 0, which leads to x = 2.

3. y = [tex]e^x[/tex] - y:

Rearranging the equation, we get:

y + y = [tex]e^x[/tex]

Combining like terms, we have:

2y = [tex]e^x[/tex]

Dividing both sides by 2, we get:

y = (1/2)[tex]e^x[/tex]

4. y = (1 + y²)[tex]e^x[/tex]:

Rearranging the equation, we get:

y - y² = [tex]e^x[/tex]

Factoring out y, we have:

y(1 - y) = [tex]e^x[/tex]

This equation has two solutions:

y = 0 and 1 - y = [tex]e^x[/tex], which leads to y = 1 - [tex]e^x[/tex].

5. y = xy + y:

Rearranging the equation, we get:

y - xy - y = 0

Combining like terms, we have:

-xy = 0

This equation has two solutions:

x = 0 and y = 0.

6. y = y[tex]e^x[/tex] - 2[tex]e^x[/tex] + y - 2:

Rearranging the equation, we get:

y[tex]e^x[/tex] - y = 2[tex]e^x[/tex]- 2

Factoring out y, we have:

y([tex]e^x[/tex] - 1) = 2([tex]e^x[/tex] - 1)

Dividing both sides by ([tex]e^x[/tex] - 1), we get:

y = 2

7. y = x/(y + 2):

Rearranging the equation, we get:

y(y + 2) = x

Expanding the equation, we have:

y² + 2y - x = 0

This equation doesn't have a general solution in terms of elementary functions. It can be solved numerically or using approximation methods.

8. y = xy/(x - 1):

Rearranging the equation, we get:

(x - 1)y = xy

Dividing both sides by y and rearranging, we have:

x - 1 = x/y

Solving for y, we get:

y = x/(x - 1)

9. x²y = ylny - y:

This is a nonlinear differential equation that doesn't have a general solution in terms of elementary functions. It can be solved numerically or using approximation methods.

10. xy - y = 2x²y:

Rearranging the equation, we get:

xy - 2x²y - y = 0

Factoring out y, we have:

y(x - 2x² - 1) = 0

This equation has two solutions:

y = 0 and x - 2x² - 1 = 0, which leads to x = (1 ± √3)/2.

11. y - 3y² = x + 2y:

Rearranging the equation, we get:

-3y² + y + 2y - x = 0

Combining like terms, we have:

-3y² + 3y - x = 0

This equation doesn't have a general solution in terms of elementary functions. It can be solved numerically or using approximation methods.

12. y = (2xy + 2x)/(x² - 1):

Rearranging the equation, we get:

y(x² - 1) = 2xy + 2x

Expanding the equation, we have:

x²y - y = 2xy + 2x

Combining like terms, we get:

x²y - 2xy - y - 2x = 0

This equation doesn't have a general solution in terms of elementary functions. It can be solved numerically or using approximation methods.

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Answer:

.02

Step-by-step explanation:

The spherical coordinates for the point (0, -3, -3) are (3√2, -π/2, π/4).

(a) To change from rectangular coordinates to spherical coordinates, we use the following formulas:

rho = √(x² + y² + z²)

theta = atan2(y, x)

phi = acos(z / rho)

Given the rectangular coordinates (5, 5√3, 10√3), we can substitute the values into the formulas to find the corresponding spherical coordinates:

rho = √((5)² + (5√3)² + (10√3)²)

= √(25 + 75 + 300)

= √(400)

= 20

theta = atan2(5√3, 5)

= atan(√3)

≈ 1.0472 radians

phi = acos((10√3) / 20)

= acos(√3 / 2)

= π/6 radians

Therefore, the spherical coordinates for the point (5, 5√3, 10√3) are (20, 1.0472, π/6).

(b) Given the rectangular coordinates (0, -3, -3), we can apply the formulas for spherical coordinates:

rho = √((0)² + (-3)² + (-3)²)

= √(0 + 9 + 9)

= √(18)

= 3√2

theta = atan2(-3, 0)

= -π/2 radians

phi = acos((-3) / (3√2))

= acos(-1/√2)

= π/4 radians

Hence, the spherical coordinates for the point (0, -3, -3) are (3√2, -π/2, π/4).

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a. For the function f(x) = (x + x)(log(x) + 3x) is O(x) with the witnesses C = 7 and k = 1.

b. It is proved that f(x) = (x + x)(log(x) + 3x) is (x) with the witnesses C = 1 and k = 1.

c. The obtained witnesses C = 1, C' = 10, and k =[tex]10^C.[/tex] such that g(x)log(x) < Cg(x) whenever x > k. And g(x) = 1.

a) To show that f(x) = (x + x)(log(x) + 3x) is O(x),

find witnesses C and k such that f(x) ≤ C × x for all x > k.

Let's simplify the expression for f(x):

f(x) = 2x × (log(x) + 3x)

= 2x × log(x) + 6x²

Now, find a witness C and a value k such that f(x) ≤ C × x for all x > k.

Let's choose C = 7 and k = 1.

This means show that f(x) ≤ 7x for all x > 1.

For x > 1,

f(x) = 2x × log(x) + 6x²

< 2x × log(x) + 6x² + 7x

= 2x × log(x) + 6x² + 7x

= x(2log(x) + 6x + 7)

≤ x(2log(x) + 13x)

≤ x × 7

= 7x

This implies,

f(x) = (x + x)(log(x) + 3x) is O(x) with the witnesses C = 7 and k = 1.

b) To show that f(x) = (x + x)(log(x) + 3x) is (x),

find witnesses C and k such that f(x) ≥ C × x for all x > k.

Let us simplify the expression for f(x):

f(x) = 2x × (log(x) + 3x)

= 2x × log(x) + 6x²

Now, find a witness C and a value k such that f(x) ≥ C × x for all x > k.

Let us choose C = 1 and k = 1.

This means show that f(x) ≥ x for all x > 1.

For x > 1,

f(x) = 2x × log(x) + 6x²

> x × log(x) + 6x²

= x(log(x) + 6x)

≥ x(log(x) + x)

≥ x × log(x)

≥ x

Therefore, we have shown that f(x) = (x + x)(log(x) + 3x) is (x) with the witnesses C = 1 and k = 1.

c) To find the obtained witnesses C, C', and k .

such that g(x)log(x) < Cg(x) whenever x > k,

Examine the expression f(x) = (x + x)(log(x) + 3x) and determine the function g(x).

Let us simplify the expression for f(x),

f(x) = 2x × (log(x) + 3x)

= 2x × log(x) + 6x²

From the given condition, we have g(x)log(x) < Cg(x) rewrite this as,

log(x) < C

Since log(x) is an increasing function, if log(x) < C, it means x < [tex]10^C.[/tex]Therefore, the witness k is [tex]10^C.[/tex]

Now let us determine g(x).

Since g(x)log(x) appears in the inequality, we can take g(x) = 1.

C = 1, C' = 10, and k = [tex]10^C.[/tex] for g(x)log(x) < Cg(x) whenever x > k. And g(x) = 1.

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Answer:

Explanation:

given f(x) = 3x - 1

for f(x) = 2

3x - 1 = 2

3x = 2 + 1

3x = 3

x = 3/3

x = 1

Answer:

H0: μ = 7.0

H1: μ > 7.0

Step-by-step explanation:

The null hypothesis will equal and take up the value of the population mean value ;

The population mean value, μ is 7.0

Null hypothesis ; H0: μ = 7.0

The alternative hypothesis will align with the claim ; which will take up and side with the value and direction of the sample mean ; 7.82 micrograms/100 ml

7.82 > 7.0 (sample mean is greater Than the population mean).

Hence, the alternative hypothesis, H1 will be ;

H1 : μ > 7.0

Answer:

B. 9

Step-by-step explanation:

Proportions are just like fractions and to figure them out sometimes you can use simplification in different forms.

[tex]\frac{x}{6}[/tex] = [tex]\frac{36}{24}[/tex]

Now to get to 6, 24 had to be divided by 4...in proportions and fractions usually, the top and bottom are both simplified or proportioned to the same number or scale

36 ÷ 4 = 9

Check your answer by inserting it there to see if it works

9*4 = 36            6*4 = 24

Answer:

[tex]\boxed {\boxed {\sf B. \ 9}}[/tex]

Step-by-step explanation:

We are given this proportion:

[tex]\frac {x}{6}=\frac{36}{24}[/tex]

We want to solve for x, so we must isolate the variable using inverse operations.

It is being divided by 6. The inverse of division is multiplication, so we multiply both sides of the proportion by 6.

[tex]6*\frac {x}{6}=\frac{36}{24}*6[/tex]

[tex]x=\frac{36}{24}*6[/tex]

[tex]x=1.5*6 \\x=9[/tex]

Another way to solve is with cross multiplication. Multiply the first numerator by the second denominator, then the first denominator by the second numerator.

[tex]\frac { x}{6}=\frac{36}{24}[/tex]

[tex]24*x=6*36[/tex]

[tex]24x=216[/tex]

The variable is being multiplied by 24. The inverse of multiplication is division, so we divide both sides of the equation by 24.

[tex]24x/24=216/24\\x=9[/tex]

The value of x that makes this proportion true is 9.

The main effects of the relevant variables are 3.5x and -1.6x, while the interaction effect is 0.9x*x.

The given model for manufacturing yield, expressed as a percentage of good products, is represented by the equation ỹ = 95 + 3.5x - 1.6x + 0.9x*x. In this equation, x represents the reactor temperature, and X2 represents the air pressure.

The coefficient 3.5 corresponds to the main effect of the reactor temperature, indicating that for each unit increase in temperature, the yield is expected to increase by 3.5 percentage points.

Similarly, the coefficient -1.6 represents the main effect of air pressure, implying that for each unit increase in pressure, the yield is expected to decrease by 1.6 percentage points.

Additionally, the term 0.9x*x accounts for the interaction effect between temperature and pressure. This suggests that the combined influence of temperature and pressure on the yield is not solely determined by the sum of their individual effects. Instead, the interaction effect captures the nonlinear relationship between these variables.

To estimate the probability of the yield being higher than 96% for a temperature of 315K and pressure of 130kPa, we need to evaluate the model equation for these specific values.

Substituting x = 315 and X2 = 130 into the equation, we can calculate the corresponding yield. If the yield exceeds 96%, the estimated probability would be 100%; otherwise, it would be 0%.

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Answer:

angle 1 = 124

angle 2 = 56

angle 3 = 124

angle 4 = 56

Step-by-step explanation:

This problem is a bit like a puzzle. To make notation easier I'm going to do this:

angle 1 = a

angle 2 = b

angle 3 = c

angle 4 = d

Now, let's start with what we know from the image.

All angles added together form a circle or 360 degrees

a + b + c + d = 360

In the same regard a + d = 180, and b + c = 180

Also,

a = c

and

b = d

It also tells us angle 4 is 25 degrees greater than one fourth of angle 1. Which is written as.

d = 1/4(a) + 25

If we look at all the equations we have, we can see that two of the equations have two of the same variables:

a + d = 180

and

d = 1/4(a) + 25

Using substitution we can take the second equation substitute it for d in the first equation giving us:

a + (1/4(a) + 25) = 180

Now we just solve for a

[tex]\frac{4}{4} a+ \frac{1}{4} a + 25 = 180\\\\\frac{5}{4}a + 25 = 180 \\\\(\frac{5}{4}a + 25) - 25 = (180) -25\\\\\frac{5}{4} a = 155\\\\\frac{5}{4} a * \frac{4}{5} = 155 * \frac{4}{5}\\\\a = 124[/tex]

Therefore a, or angle 1, is 124

Since a = c, then c, or angle 3, is also 124

Since a + d = 180 and a = 124 then

d = 180 -124

d = 56

So, d, or angle 4, is 56

And because b = d then b, or angle 2, is also 56

a = 124

b = 56

c = 124

d = 56

For extra measure, we can check our work by using the first equation

a + b + c + d = 360

124 + 56 + 124 + 56 = 360

Answer:

16%

Step-by-step explanation:

(174-150)/150= 0.16

0.16*100 = 16%

Answer:

The next term will be -5.

Step-by-step explanation:

This is actually an AP with a = 11 and common difference d = -4.

Therefore next term will be -1 - 4 = -5

Answer:

Step-by-step explanation:

The numbers in this sequence come by subtracting 4 so

11, 7, 3, - 1, - 5, - 9, - 13

The quantified statement (∃x)¬D(x) can be translated into simple, everyday English as "There exists a penguin that is not dangerous."

The quantified statement (∃x)¬D(x) can be further explained in the context of penguins. Let's break it down:

The symbol (∃x) denotes the existence of an object or entity that satisfies a certain condition. In this case, it refers to a penguin that meets the condition specified afterward.

The predicate ¬D(x) can be understood as the negation of the predicate D(x), where D(x) represents the statement "x is dangerous." The negation symbol (¬) in front of D(x) indicates the opposite or negation of the statement.

Combining these elements, the quantified statement (∃x)¬D(x) asserts that there is at least one penguin for which the predicate "is not dangerous" holds true. In everyday English, this statement can be translated as "There exists a penguin that is not dangerous."

Essentially, it implies that within the domain of all penguins being considered, at least one penguin can be found that is not considered dangerous. This quantified statement allows for the possibility that not all penguins are dangerous and acknowledges the existence of non-threatening penguins.

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Answer:

-11 degrees Fahrenheit.

Step-by-step explanation:

the higher the negative number is, the colder it gets <D

Answer:

3/10 inches apart

Step-by-step explanation:

total miles based on 2" equals 33 miles can be found by solving this proportion:

2/33 = 6/x

2x = 198

x = 99

99 miles divided by 11 rest stops means each stop is 9 miles apart

now use new ratio of 1" equals 30 miles

1/30 = x/9

30x = 9

x = 9/30 or 3/10 inches

Answer:

Monthly deposit= $489.59

Step-by-step explanation:

Giving the following information:

Future Value (FV)= $180,000

Number of periods (n)= 18*12= 216

Interest rate (i)= 0.055 / 12= 0.004583

To calculate the monthly deposit, we need to use the following formula:

FV= {A*[(1+i)^n-1]}/i

A= monthly deposit

Isolating A:

A= (FV*i)/{[(1+i)^n]-1}

A= (180,000*0.004583) / {[(1.004583)^216] - 1}

A= $489.59

Answer:

are u ok tho

Step-by-step explanation:

The expected value of the given random variable is 8.3. This means that, on average, if we repeatedly sample from this random variable, we can expect the resulting values to be around 8.3.

To find the expected value of a random variable, you multiply each possible value by its corresponding probability and sum them up. In this case, we have a combination of probabilities and numerical values. Let's calculate the expected value:

Multiply each numerical value by its corresponding probability:

(0.35 * 8) + (0.3 * 9) + (0.05 * 10) + (0.1 * 11) + (0.05 * 11) + (0.15 * 11)

Perform the calculations:

2.8 + 2.7 + 0.5 + 1.1 + 0.55 + 1.65

Sum up the results:

8.3

Therefore, the expected value of the given random variable is 8.3. This means that, on average, if we repeatedly sample from this random variable, we can expect the resulting values to be around 8.3. The expected value provides a measure of central tendency for the random variable.

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The given question can be answered as follows:

True or False:

The ANOVA Test uses the entire bell. - False_

____ There are 2 types of hypotheses. - True_

____ The null hypothesis may posit that there is no significant difference between - True

Explanation:

ANOVA (Analysis of Variance) is a statistical test used to determine whether two or more population means are equivalent. It does not use the entire bell, so the statement is false.There are two types of hypotheses: the null hypothesis and the alternative hypothesis. The statement is true.The null hypothesis is used to determine if there is a significant difference between two or more sets of data. It can posit that there is no significant difference between two or more sets of data. So, the statement is true.

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The ANOVA Test uses the entire bell is a false statement.

There are 2 types of hypotheses is a true statement.

The null hypothesis may posit that there is no significant difference between the groups is a true statement.

Hence, the correct answer is: False; True; True.

The given statements can be summarized as follows: Statement 1 is that the ANOVA Test uses the entire bell. It is false.

Statement 2 is that there are 2 types of hypotheses. It is True.

Statement 3 is that the null hypothesis may posit that there is no significant difference between the groups. It is True.

Hence, the correct answer is: False; True; True.

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Answer:

$2500

Step-by-step explanation:

First, multiply the $15 for the 150 people attending, to get 2250. Next, add the last $250 to get a total cost of $2500

Hopefully this helps- let me know if you have any questions!

Answer:

i think it is 2500

Step-by-step explanation:

take 15 times the amount of people. then add the 250 fee

Answer:

Where is the question so that I can help you with it

Answer:

50

Step-by-step explanation:

this can be solved by ratio   15/x = 30/100.  Cross multiply and solve for x.  The answer is 50.

A class interval refers to option b) a division used for grouping a set of observations.

The correct answer is (b) a division used for grouping a set of observations. In statistics, when dealing with a large set of data, it is often helpful to group the data into intervals or classes to better understand the distribution. A class interval represents a range of values that are grouped together. It is defined by specifying the lower and upper boundaries of each interval.

For example, if we are analyzing the heights of individuals, we may create class intervals such as 150-160 cm, 160-170 cm, and so on. The purpose of using class intervals is to simplify the data and provide a clearer picture of the distribution. It allows us to summarize the data and identify patterns or trends within specific ranges. Therefore, option (b) is the correct description of a class interval.

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Answer:

Tens digit, x = 3

Unit digit, y = 8

Number = 38

Step-by-step explanation:

Let the 2 digit number = xy

y = x + 5 - - - (1)

10x + y = 4(x + y) - 6

10x + x + 5 = 4(x + x + 5) - 6

11x + 5 = 4(2x + 5) - 6

11x + 5 = 8x + 20 - 6

11x + 5 = 8x + 14

11x - 8x = 14 - 5

3x = 9

x = 9/3

x = 3

From (1)

y = x + 5

y = 3 + 5

y = 8

Answer:

50 units

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

Step-by-step explanation:

Step 1: Define

a = 48

b = 14

c = ?

Step 2: Solve for c

Answer:

x=-2

Step-by-step explanation:

Answer:

x = 12 the correct answer

Ok. So 14% of 18.00 can be figured out without a calculator. 18.00 / 10 = 1.80 = 10%.

(18.00 / 100) x 4 = 0.72

1.80 + 0.72 = $2.52 is the tip.

$18 + $2.52 = $20.52

⭐ Answered by Foxzy0⭐

⭐ Brainliest would be appreciated, I'm trying to reach genius! ⭐

⭐ If you have questions, leave a comment, I'm happy to help! ⭐

I hope the answer is helpful