find the general solution of the differential equation1. dy/dx = 2x/y2. dy/dx = x(y+4)

A) First derivative for y = 3x² + 5x + 10 is dy/dx = 6x + 5; B) First derivative of for, y = 100200x + 7x is dy/dx = 100207 ; C) First derivative for y = In (9x4) is dy/dx = 4 / (3x).

A. y = 3x² + 5x + 10:

First derivative of the given equation, y = 3x² + 5x + 10 is as follows:

dy/dx = d/dx (3x²) + d/dx (5x) + d/dx (10)dy/dx

= 6x + 5

Since there are no exponents in 5x, the derivative of 5x is simply 5.

Similarly, since 10 is a constant, the derivative of 10 is zero.

B. y = 100200x + 7x:

First derivative of the given equation, y = 100200x + 7x is as follows:

dy/dx = d/dx (100200x) + d/dx (7x)dy/dx

= 100200 + 7

= 100207

C. y = In (9x4):

The given equation is, y = In (9x4).

The first derivative of this function can be obtained as follows:

dy/dx = 1 / (9x4) * d/dx (9x4)dy/dx

= 1 / (9x4) * 36x3dy/dx

= 4x3 / (3x4)dy/dx

= 4 / (3x)

Therefore, the first derivative of the given function y = In (9x4) is 4 / (3x).

A) First derivative forgiven equation, y = 3x² + 5x + 10 is dy/dx = 6x + 5; B) First derivative for given equation, y = 100200x + 7x is dy/dx = 100207 ; C) First derivative for given equation, y = In (9x4) is dy/dx = 4 / (3x).

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We can conclude that gcd(a, b) divides 15 if and only if there exist integers s and t such that as + bt = 15.

If there are integers s and t such that as + bt = 15, then we can conclude that gcd(a, b) divides 15. This is known as Bézout's identity, which states that for any two integers a and b, there exist integers s and t such that as + bt = gcd(a, b).

To see why this is true, consider the set of all linear combinations of a and b, that is, the set {ax + by : x, y are integers}. This set contains all multiples of gcd(a, b) since gcd(a, b) divides both a and b.

Therefore, gcd(a, b) is the smallest positive integer that can be expressed as a linear combination of a and b.

Now, if as + bt = 15, then 15 is a linear combination of a and b, which means that gcd(a, b) divides 15.

Conversely, if gcd(a, b) divides 15, then we can find integers s and t such that as + bt = gcd(a, b), and we can scale this equation to obtain as' + bt' = 15, where s' = (15/gcd(a, b))s and t' = (15/gcd(a, b))t.

Therefore, we can conclude that gcd(a, b) divides 15 if and only if there exist integers s and t such that as + bt = 15.

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The approximate population of the Latinos in the united states, growing at a growth rate of 2.5% per year in 2020 is 64,004,227

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the population of the latinos x years after 2010.

There were 50,000,000 latinos in the united states. at a growth rate of 2.5% per year, hence:

y = 50000000(1.025)ˣ

In 2020 (x = 10):

y = 50000000(1.025)¹⁰ = 64,004,227

The approximate population of the Latinos in the united states, growing at a growth rate of 2.5% per year in 2020 is 64,004,227

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Answer: The answer is 2^3 x 3 x 5

Step-by-step explanation: Hope this helps, give brainliest if it does!

The price for 5 pounds of honey is $13.32.

Unitary method is a mathematical technique used to solve problems related to proportions and ratios.

To find the price for 5 pounds of honey, we can use a proportion:

Price of 3 pounds of honey / 3 = Price of 1 pound of honey

We can use this equation to find the price of 1 pound of honey, and then multiply by 5 to find the price of 5 pounds of honey.

Price of 3 pounds of honey / 3 = 7.99 / 3

Price of 1 pound of honey = 2.6633 (rounded to 4 decimal places)

Price of 5 pounds of honey = 2.6633 x 5 = $13.32 (rounded to 2 decimal places)

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The average velocity from t = 2s to t = 4s would be - 48 ft/s.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that an object is thrown upward with initial velocity of 48 feet per second from a high of 120 feet. The height of the object t seconds after it is thrown is given by h(t) = - 16t² + 48t + 120.

Average rate of change of velocity with time is called average velocity. Mathematically -

v{avg.} = Δx/Δt                                                         .... Eq { 1 }

Δx = x(4) - x(2)

Δx = - 16(4)² + 48(4) + 120 - {- 16(2)² + 48(2) + 120}

Δx = - 96

Δt = 4 - 2 = 2

So -

v{avg.} = Δx/Δt = -96/2 = - 48 ft/s

Therefore, the average velocity from t = 2s to t = 4s would be - 48 ft/s.

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When two data sets are both symmetric, then the appropriate measure of center to describe them would be the mean.

The mean, also known as the average, is calculated by adding up all the values in the data set and dividing by the total number of values. It represents the "center" of the data because it balances out the values on both sides of the distribution.

The mean is a good measure of center for symmetric data sets because it captures the balance of the distribution and provides a single value that summarizes the data.

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Which measure of center should you use to describe two data sets that are both symmetric?

Answer:

To find the area of the larger triangle in part a), we can use the equation for the area of a triangle, which is A = (1/2)bh. Since the height of the larger triangle is 21 cm and the height of the smaller triangles is 3 cm, we can say that the height of the larger triangle is 7 times greater than the height of the smaller triangles. This means that the base of the larger triangle is also 7 times greater than the base of the smaller triangles.

Since the area of a triangle is directly proportional to the product of its base and height, the area of the larger triangle is 7 times greater than the area of the smaller triangles. Since the area of the smaller triangles is 4.8 cm², the area of the larger triangle is 7 * 4.8 = <<7*4.8=33.6>>33.6 cm².

For part b), we can use a similar method to find the number of smaller triangles used to form the larger triangle. Since the perimeter of the larger triangle is 32 times greater than the perimeter of the smaller triangles, the sides of the larger triangle are also 8 times greater than the sides of the smaller triangles. This means that the number of sides of the larger triangle is also 8 times greater than the number of sides of the smaller triangles.

Since the number of sides of a triangle is directly proportional to the number of triangles used to form it, the number of smaller triangles used to form the larger triangle is 8 times the number of smaller triangles used to form the smaller triangles. Since we don't know how many smaller triangles were used to form the smaller triangles, we can't determine the exact number of smaller triangles used to form the larger triangle. However, we can say that it is at least 8.

1. Set up: To set up a void function, define it with the keyword "void" in the function signature, such as void functionName(). For a value-returning function, specify the return type in the function signature, such as dataType functionName().

2. Implementation and Documentation: In the implementation of the void function, write the necessary code to perform the desired actions. For a value-returning function, include a return statement to return the desired value. Properly document the function by providing a meaningful function name, describing the purpose of the function, and specifying any input parameters and the return value (if applicable).

1. Set up: To set up a void function, use the keyword "void" in the function signature. For example:

c++

void functionName()

This indicates that the function does not return a value. For a value-returning function, specify the return type in the function signature. For example:

c++

dataType functionName()

Replace dataType with the desired data type to be returned by the function.

2. Implementation and Documentation: In the implementation of a void function, write the necessary code to perform the desired actions. This can include any sequence of statements or function calls.

For a value-returning function, include a return statement to specify the value to be returned. For example:

c++

dataType functionName()

{

   // Code to perform calculations or operations

   return result; // Replace "result" with the actual value to be returned}

In both cases, it is crucial to provide proper documentation for the function. This includes choosing a meaningful name for the function, describing the purpose or functionality of the function, specifying any input parameters and their types, and indicating the return value (if applicable). This documentation helps other developers understand and use the function correctly.

By following these steps, you can effectively set up, implement, and document void and value-returning functions in your code.

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The possible number of pounds of candy that Chau can buy, can be found to be p ≤ 10.

Chau has $70 to spend on candy and out of this amount, the value of a single candy is $ 7.

This means that the maximum number of candy that Chau can buy is :

= Amount to spend by Chau / Cost of candy

= 70 / 7

= 10 candies

This means that Chau can buy a maximum of 10 candies given the amount he has.

The inequality is therefore:

p ≤ 10

This shows that he can either buy 10 candies or less.

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The full question is :

Chau buys candy that costs $ 7 per pound. He will spend at most $ 70 on candy. What are the possible numbers of pounds he will buy? Use p for the number of pounds Chau will buy

To achieve a goal of 99.99% uptime, the SOC would allow approximately 52.56 minutes of downtime per year.

To calculate the number of minutes of downtime allowed within a goal of 99.99% uptime, we first need to determine the allowable downtime percentage.

Uptime percentage can be calculated as follows:

Uptime percentage = 100% - Downtime percentage

For a goal of 99.99% uptime, the downtime percentage would be:

Downtime percentage = 100% - 99.99% = 0.01%

To calculate the number of minutes of downtime, we need to convert the downtime percentage to minutes in a year:

Minutes of downtime = (Downtime percentage / 100) × Minutes in a year

Assuming there are 365 days in a year and 24 hours in a day (ignoring leap years), the number of minutes in a year would be:

Minutes in a year = 365 × 24 × 60 = 525,600 minutes

Now we can calculate the allowable minutes of downtime:

Minutes of downtime = (0.01% / 100) × 525,600 minutes

Minutes of downtime ≈ 0.0001 × 525,600 ≈ 52.56 minutes

Therefore, to achieve a goal of 99.99% uptime, the SOC would allow approximately 52.56 minutes of downtime per year.

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Answer: B. 13 - , r

Step-by-step explanation:

The expression that has a solution of 4 when r = 9 is:

B. 13 - r

Answer:

x=5

Step-by-step explanation:

The conclusion made by the homeowner is an example of empirical probability.

Empirical probability, also known as experimental probability, is based on observed data or experiments. In this case, the homeowner is basing their conclusion on their observation that the mail arrived before 3pm on 8 out of 14 days. This is a result of direct observation or experience, rather than being calculated using a mathematical formula or theory.

The homeowner's conclusion is not based on any theoretical probabilities or mathematical calculations, but rather on their observation of past events. Therefore, the conclusion that the probability of the mail arriving before 3pm tomorrow is about 57% is an example of empirical probability.

Therefore, the homeowner's conclusion that the probability of the mail arriving before 3pm tomorrow is about 57% is an example of empirical probability, based on their observation of past events.

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Answer:

y=-⅗x+3

Step-by-step explanation:

5y=-3x+15. Divide 5 on both sides

5. 5

y=-⅗x+15/5

y=-⅗x+3

Hope this helps :)

Answer:

not equivalent to meteorologists ratio

Step-by-step explanation:

meteorologists ratio is

rainy days : sunny days = 2 : 5

last months weather is

rainy days : sunny days

= 10 : 20 ( divide both parts by LCM of 10 )

= 1 : 2 ← not equivalent to 2 : 5

\(\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}\)

the following expression can be solved as follows ~

\( \frac{x}{3} + 1 = \frac{x}{8} + \frac{1}{11} \\ \)

Taking LCM on both the sides ,

\( \frac{x + 3}{3} = \frac{11x + 8}{88} \\ \)

On cross multiplying ,

\(( x + 3)88 = (11x + 8)3 \\ \\ \implies \: 88x + 264 = 33x + 24\)

let's now gather the like terms at either sides of the equation and solve ~

\(88x - 33x = 24 - 264 \\ \\ \implies \: 55x = - 240 \\ \\ \implies \: x = \cancel\frac{ - 240}{55} \\ \)

on further simplifying ,

\(\implies x = \frac{ - 48 }{ 11} \\ \)

hope helpful ~

The answer is 27w - 27u +36 of the given -9( -3w + 3u - 4)

Given,

In the question:

Use distributive property to remove parenthesis.

-9(-3w + 3u - 4)

Now, According to the question:

First, we know:

What does parentheses mean distributive property?

The distributive property allows us to multiply all terms in a parentheses by a number outside of it. a(b +c) = ab + ac.

We have:

-9(-3w + 3u - 4)

Solve by Distributive Property :

-9(-3w + 3u - 4)

Open the bracket:

27w - 27u +36

Hence, The answer is 27w - 27u +36 of the given -9( -3w + 3u - 4)

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Answer:

Option c, G(x) = 12x

Step-by-step explanation:

Vertical stretch occurs when a base graph is multiplied by a certain factor that is greater than 1

In the equation f(x) = mx, the m is acting as the vertical stretch or compression of the identity function.

- f(x) = x by m vertically stretches the graph of f by a factor of m units if

m > 1

- vertically compresses the graph of f by a factor of m units if

0 < m < 1.

This means the larger the absolute value of m, the steeper the slope.

Answer:

Here, the parent should pass through the origin, which is through the coordinate (0,0).

The only function that passes through this (0,0) point and is vertically stretched is only valid is:

y = 12x

The solution to the second-order initial value problem The general solution to the second-order linear differential equation ay'' + by' + cy = 0, with constant coefficients is given as;$$ y = e^{mx} $$.

This gives us the auxiliary equation Where $m_1$ and $m_2$ are the roots of this equation. Then, the general solution to the differential equation is given by;$$y = c_1 y_1 + c_2 y_2 $$.

Now, substituting y(0) = 5 and y'(0) = -2 into the general solution Therefore, the solution to the second-order initial value problem is $$y = \frac{1}{4} \left( - 5 e^{- 5 x} \cos \left(3x+\frac{13 \pi}{12}\right) - e^{- 5 x} \sin \left( 3x + \frac{13 \pi}{12}\right) \right) $$

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Answer:

14776.8

Step-by-step explanation:

Yeahh its that because its the difference and the elevation for the death valley is below sea level so if you do

x-(-y) you essentially get x+y so therefore you add the two numbers and your good (x stands for that mountain and y is for the death valley

Answer:

66 candies

Step-by-step explanation:

70-4=66

Answer:

90 counterclockwise or 270 clockwise

Step-by-step explanation:

just trust me bro lolskies

====================================================

Explanation:

Through some strange formatting error, the tickmarks are not in the proper locations. They should be to the right and slightly above the letter. They should be close by, and not far away like that.  

It looks like the purple figure is the image while the blue figure is the preimage. If that's the case, then we've applied a 90 degree counterclockwise rotation to go from blue to purple.

Notice how angle AQA' is 90 degrees as shown by the green segments in the diagram below. So are BQB' and CQC' and DQD' as well.

We could also rotate the blue figure 270 degrees clockwise to arrive at the same purple image. Note how 90+270 = 360 which is a full circle.

The slope of the line, which is 15 in this case, represents the rate of change in the height of the plant per week. In other words, for each additional week that passes, the plant is expected to grow by an average of 15 centimeters based on the data and the line of best fit.

what is slope?

In mathematics, slope is a measure of the steepness of a line. It describes the ratio of the vertical change (rise) between two points on a line to the horizontal change (run) between those same two points. In other words, slope is the change in y divided by the change in x. The slope of a line can be positive, negative, zero, or undefined, and it can be used to describe the direction and rate of change of a linear relationship between two variables.

what is variables?

In mathematics, variables are symbols or letters used to represent unknown values or quantities in equations, formulas, or mathematical expressions. They are used to denote quantities that can take on different values, and are often used in algebra to solve equations or to describe patterns and relationships between different mathematical objects. In a mathematical equation or formula, variables usually appear alongside constants, which are known values that do not change. Examples of variables include x, y, z, a, b, c, and so on.

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None of the wind gusts (17, 22, 8, 13, 19, 36, and 14) fall below -0.5 or above 35.5, there are no outliers in this data set. Therefore, the correct answer is D) none.

To identify any outliers in the data set, we can use a common method called the 1.5 interquartile range (IQR) rule.

The IQR is a measure of statistical dispersion and represents the range between the first quartile (Q1) and the third quartile (Q3) of a dataset. According to the 1.5 IQR rule, any value below Q1 - 1.5 × IQR or above Q3 + 1.5 × IQR can be considered an outlier.

To determine if there are any outliers in the given data set of wind gusts (17, 22, 8, 13, 19, 36, and 14), let's follow these steps:

Sort the data set in ascending order: 8, 13, 14, 17, 19, 22, 36.

Calculate the first quartile (Q1) and the third quartile (Q3).

Q1: The median of the lower half of the data set (8, 13, 14) is 13.

Q3: The median of the upper half of the data set (19, 22, 36) is 22.

Calculate the interquartile range (IQR).

IQR = Q3 - Q1 = 22 - 13 = 9.

Step 4: Identify any outliers using the 1.5 IQR rule.

Values below Q1 - 1.5 × IQR = 13 - 1.5 × 9 = 13 - 13.5 = -0.5.

Values above Q3 + 1.5 × IQR = 22 + 1.5 × 9 = 22 + 13.5 = 35.5.

Since none of the wind gusts (17, 22, 8, 13, 19, 36, and 14) fall below -0.5 or above 35.5, there are no outliers in this data set.

Therefore, the correct answer is D) none.

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Answer:

I think it's 160

Step-by-step explanation:

5×4(n-1)d

5×4(9-1)

20×8

=160.

Answer:

2

Step-by-step explanation:

The y-intercept is the point on the graph where the line intersects with the y-axis. Since this point must be on the y-axis the x-value must be 0. Every coordinate on the y-axis has an x-value of 0. So, to find the answer find the y-value when x=0. In this case, when x=0, y=2. Therefore, the y-intercept is 2, also written as (0,2).

Answer:

He will earn $123.25

Step-by-step explanation:

You multiply $7.26 by 17.

Answer:

l = 40 m

Step-by-step explanation:

The formula for area of a rectangle is

A = lw, where

Step 1:  Since we're given the area and width, we plug in these two values for A and w and to solve for l (length):

360 = 9l

Step 2:  Divide both sides by 9 to solve for l

(360 = 9l) / 9

40 m = l

Optional Step 3:  We can check our answers by checking that the product of 40 and 9 is 360

40 * 9 = 360

360 = 360

Answer:

sec(x) = sqrt(10)

Step-by-step explanation:

We know that tan(x) = 3.

Using the identity tan^2(x) + 1 = sec^2(x), we can solve for sec(x).

First, let's square both sides of the equation tan(x) = 3:

tan^2(x) = 3^2

tan^2(x) = 9

Next, we can substitute this expression for tan^2(x) into the identity:

tan^2(x) + 1 = sec^2(x)

9 + 1 = sec^2(x)

10 = sec^2(x)

Finally, we can take the square root of both sides to solve for sec(x):

sqrt(10) = sec(x)

Therefore, sec(x) = sqrt(10).