Please help!!! I would rlly appreciate it!

The critical points of the function are (0, 0) and (3/4, -9/4), To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point

To find the critical points of the function f(x, y) = 8x^3 + y^2 + 6xy, we need to find the values of (x, y) where the partial derivatives with respect to x and y are equal to zero.

Taking the partial derivative with respect to x, we have:

∂f/∂x = 24x^2 + 6y = 0.

Taking the partial derivative with respect to y, we have:

∂f/∂y = 2y + 6x = 0.

Solving these two equations simultaneously, we get:

24x^2 + 6y = 0,

2y + 6x = 0.

From the second equation, we can solve for y in terms of x:

Y = -3x.

Substituting this into the first equation:

24x^2 + 6(-3x) = 0,

24x^2 – 18x = 0,

6x(4x – 3) = 0.

Therefore, we have two possibilities for x:

1. x = 0,

2. 4x – 3 = 0, which gives x = ¾.

Substituting these values back into y = -3x, we get the corresponding y-values:

1. x = 0 ⇒ y = 0,

2. x = ¾ ⇒ y = -9/4.

Hence, the critical points of the function are (0, 0) and (3/4, -9/4).

To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point. However, since the original function does not provide any information about the second partial derivatives, further analysis is required to classify the critical points.

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only has one zero/root, and it's a quadratic, means that that only zero has a multiplicity of 2, namely is there twice, so

\(\begin{cases} x = -10 &\implies x +10=0\\ x = -10 &\implies x +10=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{( x +10 )( x +10 ) = \stackrel{0}{h}}\implies x^2+20x+100=h\)

Answer:

1.44  ⋅  10 ^8  , 6  ⋅  10 ^5

Step-by-step explanation:

hope it helps :)

The quotient of 1.44×10⁸ and 6×10⁵ in scientific notation is 240.

Quotient is a mathematical term, which is a quantity produced when two numbers are divided.

The given terms are 1.44×10⁸ and 6×10⁵.

To write quotient, divide 1.44×10⁸ by 6×10⁵.

Quotient = 1.44×10⁸/6×10⁵

               = 0.24×10³

To express 0.24×10³ in scientific notation, eliminate decimal point,

= 24×10 = 240

The quotient of 1.44×10⁸ and 6×10⁵ can be expressed as 240.

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Answer:

D

Step-by-step explanation:

(3x+2) + (3x+2) + 2x + 2x

combine

10x+4

Answer:

D.) 10x+4

Step-by-step explanation:

perimeter= all the sides added together

3x+2+3x+2=6x+4

2x+2x=4x

6x+4+4x=10+4

Answer:

4

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

\(\frac{f(b)-f(a)}{b-a}\)

Here [ a, b ] = [ 0, 4 ] , thus

f(b) = f(4) = - 4² + 8(4) - 4 = - 16 + 32 - 4 = 12

f(a) = f(0) = - 4 , then

average rate of change = \(\frac{12-(-4)}{4-0}\) = \(\frac{12+4}{4}\) = \(\frac{16}{4}\) = 4

According to the given condition, 7 yards is more than 19 feet, To compare different units of measurement, we need to convert them to the same unit.

Multiplication is an arithmetic operation that involves combining two or more numbers to get a product. It is a way of repeatedly adding a number to itself a certain number of times. The number being multiplied is called the multiplicand, while the number of times it is being multiplied is called the multiplier. The result of the multiplication operation is called the product.

To compare 7 yards and 19 feet, we need to convert them to the same unit. Since 1 yard is equal to 3 feet, we can convert yards to feet by multiplying by 3, and we can convert feet to yards by dividing by 3.

In the first answer, we converted 7 yards to feet by multiplying by 3, which gave us 21 feet. Then we compared 21 feet to 19 feet, and found that 21 feet is greater than 19 feet. Therefore, we concluded that 7 yards is more than 19 feet.

In the second answer, we converted 19 feet to yards by dividing by 3, which gave us approximately 6.33 yards (rounded to two decimal places). Then we compared 7 yards to 6.33 yards, and found that 7 yards is greater than 6.33 yards. Therefore, we concluded that 7 yards is more than 19 feet.

Therefore, according to the given condition, 7 yards is more than 19 feet, To compare different units of measurement, we need to convert them to the same unit.

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The simplest form of a fraction is when the numerator (top number) and denominator (bottom number) have no common factors.

A fraction is a mathematical expression that represents a part of a whole, where a numerator is divided by a denominator. To simplify a fraction, we must divide both the numerator and the denominator by the same number until we cannot divide any further. To simplify a fraction, you must divide both the numerator and denominator by their greatest common factor (GCF).

For example, let's simplify the fraction 24/36. The GCF of 24 and 36 is 12. So, dividing both numbers by 12 will give us the simplified fraction 2/3.

24 ÷ 12 = 2

36 ÷ 12 = 3

Therefore, the simplified fraction of 24/36 is 2/3.

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Answer:

Step-by-step explanation:

23

Tyron receives a 30% discount on a hat. Calculations of discount percent are provided below.

The discount Percentage is calculated by = \(( Discount / Price )\) × \(100\)

What information do we have,

Usual cost = $28

Discount = $ 8.40

So,

Discount percentage \(= ( 8.40 / 28 )\) × 100

= 30%

Thus, 30% is the correct answer.

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The value of c is obtained as -3.04. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

The four fundamental operations often referred to as "arithmetic operations" are said by mathematicians to be capable of expressing any real number. The four mathematical operations that produce quotient, product, sum, and difference, respectively, are divide, multiply, add, and subtract.

We are given an equation as c - (-8.37) = 5. 33.

On solving the equation, we get

⇒c - (-8.37) = 5. 33

⇒c + 8.37 = 5. 33

⇒c = 5. 33 - 8.37

⇒c = -3.04

Hence, we get the value for c as -3.04.

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Answer:

1) 1.96

2) 0.36

3) 0.0049

4) 0.0169

5) 0.16

6) 1.21

7) 0.0009

8) 0.0196

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

put 12.4* 20 and you get D

A congruent polygon refers to two or more polygons that have the same shape and size. There must be an equal number of sides between two polygons for them to be congruent.

Congruent polygons have parallel sides of equal length and parallel angles of similar magnitude. When two polygons are congruent, they can be superimposed on one another using translations, rotations, and reflections without affecting their appearance or dimensions. Concluding about the matching sides, shapes, angles, and other geometric properties of congruent polygons allows us to draw conclusions about them.

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Answer:

-4/5

Step-by-step explanation:

Because a perpendicular slope is the the opposite of the original slope.

Answer:

m=-4/5

Step-by-step explanation:

A line perpendicular simply has the negative reciprocal of the slope of the line they gave you. This means you flip it, and multiply by -1 conceptually.  

The statistical method commonly used to analyze the clustering of personality traits is called cluster analysis.

Cluster analysis is a multivariate statistical technique that aims to identify groups or clusters of similar observations or variables based on their characteristics or measurements.

In the context of personality traits, cluster analysis can be used to explore patterns of similarity or dissimilarity among individuals based on their trait profiles.

In cluster analysis, various algorithms and distance metrics are employed to determine the grouping of observations.

The goal is to create homogeneous clusters, where individuals within the same cluster are more similar to each other compared to individuals in different clusters.

The choice of algorithm and distance metric depends on the specific objectives of the analysis and the nature of the data.

Once the cluster analysis is performed, researchers can interpret and describe the identified clusters, examine the characteristics that differentiate the clusters, and investigate the relationships between the clusters and other variables of interest.

This allows for a deeper understanding of the underlying patterns and structures within the personality trait data.

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Answer:

41.04

Step-by-step explanation:

thats the answer on khan academy :3 i hope this helps

the concentration of salt be after 10 hours is 14.04 grams per liter

Given :

The relationship between the elapsed time, t. in hours, after the dilution begins and the concentration of salt in the tank is given by

\(S(t)=500e^{^{\:}\left(-\:0.25\cdot t\right)\:}\)

here 't' is the time taken . and S(t) is the concentration of salt.

We need to find the concentration of salt S(t) after 10 hours

So , we need to find S(10)

Replace 't'  with 10 in the given equation

\(S(t)=500e^{^{\:}\left(-\:0.25\cdot t\right)\:}\\S(10)=500e^{^{\:}\left(-\:0.25\cdot 10\right)\:}\\S(10)=41.04\)

the concentration of salt be after 10 hours is 14.04 grams per liter

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Answer:

I wish you luck

Step-by-step explanation:

Answer:

5 dollars

Step-by-step explanation:

Answer:

The price of an adult ticket is $5

Step-by-step explanation:

5*5=25

31-25=6

4*5=20

62-20=42

42÷7=6

There are 30 elements in the array.

A collection of elements with the same data type stored in a line of memory is known as an array. As a result, adding an offset to a base value or the address in memory where the array's first member is stored makes it easier to establish each element's position. The base value, or index 0, serves as the offset, which is the difference between the two indices.

Given in question,

int[][][]x = new char[2][5][3]

No. of elements = 2x3x5

                        = 30

Hence, there are 30 elements in the array.

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Answer:

-2 6/7 (3/7n - 2/7)

Step-by-step explanation:

Answer:

75˚

Step-by-step explanation

58+47=105

Triangle is 180˚

180-105=75

x=75

Answer:

A = 2(7) + (1/2)(4)(4 + 9) = 14 + 26 = 40 m²

Answer:

-6x+20

Step-by-step explanation:

The population means test is a type of hypothesis test used to measure cholesterol levels before and after drug therapy.

There are quantitative response variables (cholesterol levels). This is a matched pair repeated measures study for one sample. When performing a hypothesis test for a single population mean µ using the normal distribution (often called the z-test), take a simple random sample from the population. Either the population you are testing is normally distributed and/or the sample size is greater than 30.

Hypothesis tests are used to make decisions or judgments about the values of parameters such as B. Population mean. There are two approaches to performing hypothesis testing. Critical value approach and p-value approach.

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Answer:

x = -3/4 or x = 3

Step-by-step explanation:

Solve for x over the real numbers:

(-4 x - 3) (x - 3) = 0

Hint: | Find the roots of each term in the product separately.

Split into two equations:

-4 x - 3 = 0 or x - 3 = 0

Hint: | Look at the first equation: Divide both sides by the sign of the leading coefficient of -4 x - 3.

Multiply both sides by -1:

4 x + 3 = 0 or x - 3 = 0

Hint: | Isolate terms with x to the left hand side.

Subtract 3 from both sides:

4 x = -3 or x - 3 = 0

Hint: | Solve for x.

Divide both sides by 4:

x = -3/4 or x - 3 = 0

Hint: | Look at the second equation: Solve for x.

Add 3 to both sides:

Answer: x = -3/4 or x = 3

Answer:

lesser x = -3/4

greater x =3

Step-by-step explanation:

h(x) = (-4x – 3)(x – 3)

Set the function equal to zero to find the zeros

0 = (-4x – 3)(x – 3)

Using the zero product property

0 = (-4x – 3)   0=(x – 3)

Solve each  equation

3 = -4x          3 =x

-3/4=x            3 =x

lesser x = -3/4

greater x =3

The 20th prize is $4400.

It is a sequence where the difference between each consecutive terms is the same.

Example:

2, 4, 6, 8 is an arithmetic sequence.

We have,

First prize = $12,000

Successive prize worth $400 less than the preceding prize.

Now,

We can make an arithmetic sequence.

12,000, 11,600, 11,200, ...

So,

a = 12,000

d = -400

The nth term of an arithmetic sequence.

= a + (n - 1)d

So,

The 20th prize.

= 12,000 + (20 -1)400

= 12,000 - 19 x 400

= 12,000 - 7600

= 4400

Thus,

20th prize = $4400

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We get a total of 175 collars sold and 226 leashes sold for the week, and an average of 25.0 collars and 32.3 leashes sold per day.

We have,

Day       Collars      Leashes

Sunday        30          34

Monday        22          29

Tuesday        21               27

Wednesday   25          32

Thursday         17          30

Friday          26           39

Saturday          34           35

Total          175          226

Average          25.0  32.3

To complete the table, we can add up the number of collars and leashes sold each day to get the total for the week.

We can also calculate the average number of collars and leashes sold per day by dividing the total by 7.

Thus,

We get a total of 175 collars sold and 226 leashes sold for the week, and an average of 25.0 collars and 32.3 leashes sold per day.

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Answer:

50

Step-by-step explanation:

25*2= 50+25= 75

Answer:

25

Step-by-step explanation:

75-25=50/2=25

Answer:

A)

Step-by-step explanation:

Answer:

I love your profile picture

To be more precise, we can say that there exists an integer k (which is xy) such that cd = abk. This means that ab divides cd without leaving a remainder.

If a, b, c, and d are integers, where a ≠ 0, such that a ∣ c and b ∣ d, then ab ∣ cd.


To prove that ab ∣ cd, we need to show that there exists an integer k such that cd = abk.

Since a ∣ c, there exists an integer x such that c = ax.

Similarly, since b ∣ d, there exists an integer y such that d = by.

Substituting these values in cd = abk, we get axby = abk.

Dividing both sides by ab, we get xy = k.

Since xy is an integer, k is also an integer.

Therefore, we have shown that cd = abk, where k is an integer.

Hence, ab ∣ cd.



To understand why ab ∣ cd, we need to understand what it means for a ∣ c and b ∣ d.

When we say that a ∣ c, we mean that there exists an integer x such that c = ax. This essentially means that c is a multiple of a.

Similarly, when we say that b ∣ d, we mean that there exists an integer y such that d = by. This means that d is a multiple of b.

Now, let's consider ab. Since a ∣ c, we know that c = ax for some integer x. Similarly, since b ∣ d, we know that d = by for some integer y.

Multiplying these two equations, we get cd = (ax)(by) = ab(xy).

Now, we can see that ab ∣ cd because cd is a multiple of ab.

To be more precise, we can say that there exists an integer k (which is xy) such that cd = abk. This means that ab divides cd without leaving a remainder.

Therefore, we have proved that if a, b, c, and d are integers, where a ≠ 0, such that a ∣ c and b ∣ d, then ab ∣ cd.

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\(\text{Use the Pythagorean theorem:}\\\\a^2+b^2=c^2\\\\\text{Plug in and solve:}\\\\7^2+14^2=c^2\\\\49+196=c^2\\\\245=c^2\\\\\text{Square root both sides to cancel out the exponent}\\\\\sqrt{245}=\sqrt{c^2}\\\\\boxed{7\sqrt{5}=c}\\\\\)