The average of three consecutive whole numbers is 21, need help asap

To find the relative maxima and minima of the function f(x, y) = x^2 + xy + y^2 + 4x + 5y, we need to find the critical points by taking the partial derivatives with respect to x and y and setting them equal to zero.

∂f/∂x = 2x + y + 4 = 0 ...(1)

∂f/∂y = x + 2y + 5 = 0 ...(2)

Solving equations (1) and (2) simultaneously, we get:

x = -3

y = -1

To determine whether these critical points are relative maxima or minima, we need to evaluate the second partial derivatives. Calculate ∂^2f/∂x^2, ∂^2f/∂y^2, and ∂^2f/∂x∂y at the critical point (-3, -1).

∂^2f/∂x^2 = 2 ...(3)

∂^2f/∂y^2 = 2 ...(4)

∂^2f/∂x∂y = 1 ...(5)

To determine the nature of the critical point, we use the second derivative test. Since ∂^2f/∂x^2 > 0 and (∂^2f/∂x^2)(∂^2f/∂y^2) - (∂^2f/∂x∂y)^2 = 2*2 - 1^2 > 0, the critical point (-3, -1) is a relative minimum.

The function f(x, y) = x^2 - 3y^2 has only one critical point at (0, 0). To determine the type of the critical point, we use the second derivative test

∂^2f/∂x^2 = 2 ...(6)

∂^2f/∂y^2 = -6 ...(7)

∂^2f/∂x∂y = 0 ...(8)

At the critical point (0, 0), we have ∂^2f/∂x^2 > 0 and (∂^2f/∂x^2)(∂^2f/∂y^2) - (∂^2f/∂x∂y)^2 = 2*(-6) - 0^2 < 0. This indicates that the critical point (0, 0) is a saddle point.

The production capacity function is given as Y(K, L) = 2K^0.25L^0.75. To find the marginal product of labor (∂Y/∂L), we differentiate Y(K, L) with respect to L while treating K as a constant.

∂Y/∂L = 0.752K^0.25L^(0.75-1) = 1.5K^0.25L^-0.25

Given that the company hires 16 workers and rents a capital of $810,000, we can substitute these values into the derivative:

∂Y/∂L = 1.5*(810,000)^0.25*(16)^-0.25

Calculating this expression will give you the marginal product of labor.

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if the pizza was cut into 10 slices and Ivan ate 40% (percent) of it, then Ivan ate 4 slices of the pizza.

If the pizza was cut into 10 slices, then each slice represents 1/10 fraction of the pizza. If Ivan ate 40% of the pizza, he ate 0.4 of the pizza.

0.4 × 1 = 0.4

To find how many slices Ivan ate, we need to find slices.

0.4 × 10 = 4 slices.

Therefore, Ivan ate 4 slices of the pizza. Fractions are a way of expressing a part of a whole. A fraction is made up of two parts: a numerator and a denominator. Fractions are used in many different areas of math, including algebra, geometry, and calculus.

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Complete Question

Ivan , Bella , and Ian agreed to share a pizza which was cut into 10 slices. Ivan are 40% of the pizza . How many slices did he eat

The particles contain 5.199 mol. The result is obtained by dividing the number of particles by the Avogadro number.

Avogadro number is the number of particles contained in 1 mol of any substance. It is 6.022 × 10²³ particles/mol.

The number of particles of a substance can be expressed as

N = n × NA

Where

The number of particles of a substance is 3.131 × 10²⁴ particles. Find the number of moles!

With the Avogadro number, the number of moles would be

N = n × NA

3.131 × 10²⁴ = n × 6.022 × 10²³

n = (3.131 × 10²⁴) / (6.022 × 10²³)

n = 0.5199 × 10¹

n = 5.199 mol

Hence, there are 5.199 mol contained in the particles.

The answer is A.

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The given matrices are a 3x2 matrix and a 2x1 matrix, which means they can be multiplied. To perform the multiplication, we need to multiply the corresponding elements in each row of the first matrix with the corresponding elements in each column of the second matrix and add the products.

The resulting matrix will be a 3x1 matrix, which means it will have 3 rows and 1 column.

Performing the multiplication, we get:
[7 -5]   [1]    [(7x1) + (-5x2)]   [(-5)]
[2 -9] x [2]  = [(2x1) + (-9x2)] = [-16]
[1 -3]   [10]   [(1x1) + (-3x2)]   [-17]
Therefore, the resulting matrix is:
[ 1 ]
[-16]
[-17]
So, the answer to the given problem is:
[ 1 ]
[-16]
[-17]

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Answer:

The rate of the current is 2 mph.

Step-by-step explanation:

When the boat travels upstream we have:

\( v_{T_{1}} = v_{b} - v_{c} \)                      

\( \frac{x_{1}}{t_{1}} = v_{b} - v_{c} \)    

Where:

\( v_{T}\): is the total speed

\(v_{b}\): is the speed of the boat = 10 mph

\(v_{c}\): is the speed of the current

x: is the distance

t: is the time

And when the boat travel downstream we have:

\(v_{T_{2}} = v_{b} + v_{c}\)        

\( \frac{x_{2}}{t_{2}} = v_{b} + v_{c} \)                              

Since the boat takes 4 hours longer to travel 48 miles going upstream than it does to travel 24 miles going downstream we have:

\( \frac{x_{1}}{t + 4} = v_{b} - v_{c} \)   (1)

\( \frac{x_{2}}{t} = v_{b} + v_{c} \)   (2)

By adding equation (1) with (2):

\( \frac{x_{1}}{t + 4} + \frac{x_{2}}{t} = 2v_{b} \)

\( tx_{1} + (t+4)x_{2} - 2v_{b}t(t+4) = 0 \)

\( 48t + 24(t+4) - 2*10t(t+4) = 0 \)

By solving the above equation for t we have:

t = 2 h      

Now, by entering "t" into equation (2) we have:

\( \frac{24 miles}{2 h} = 10 mph + v_{c} \)  

\( v_{c} = 2 mph \)

Therefore, the rate of the current is 2 mph.

I hope it helps you!  

The statement is true. The DecimalFormat class is part of the Java API, specifically within java.text package, so it is automatically available to your programs. You can use it to format numbers in various ways, such as for displaying currency or percentages.

DecimalFormat is a concrete subclass of NumberFormat that formats decimal numbers. It has a variety of features designed to make it possible to parse and format numbers in any locale, including support for Western, Arabic, and Indic digits. It also supports different kinds of numbers, including integers (123), fixed-point numbers (123.4), scientific notation (1.23E4), percentages (12%), and currency amounts ($123). All of these can be localized.

To obtain a NumberFormat for a specific locale, including the default locale, call one of NumberFormat's factory methods, such as getInstance(). In general, do not call the DecimalFormat constructors directly, since the NumberFormat factory methods may return subclasses other than DecimalFormat. If you need to customize the format object, do something like this:

NumberFormat f = NumberFormat.getInstance(loc);

if (f instanceof DecimalFormat) {

    ((DecimalFormat) f).setDecimalSeparatorAlwaysShown(true);

}

A DecimalFormat comprises a pattern and a set of symbols. The pattern may be set directly using applyPattern(), or indirectly using the API methods. The symbols are stored in a DecimalFormatSymbols object. When using the NumberFormat factory methods, the pattern and symbols are read from localized ResourceBundles

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True. The Decimal Format class is a part of the Java API and is included in the java.text package.

It is automatically available to Java programs without the need for any additional installations or imports.

The Decimal Format class is part of the Java API, and it is automatically available to your programs.

The Java API is a collection of pre-written classes, methods, and interfaces that are part of the Java Development Kit (JDK).

These classes and methods provide a wide range of functionalities that can be utilized by Java developers to build robust applications.
The Decimal Format class, specifically, is a subclass of the Number Format class and is used to format decimal numbers according to a specific pattern.

The class provides methods to format and parse decimal numbers and can be used to specify the number of digits after the decimal point, the use of a thousand separator, and the currency symbol.
The Decimal Format class in your Java program, you simply need to import the class using the import statement, and then create an instance of the class.

For example:
import java. text. Decimal Format.
public class MyClass

{
public static void main (String [] args) {
Decimal Format df = new Decimal Format("#.00");
double num = 1234.5678
System.out.println(df.format(num));
}
}
The Decimal Format class using the import statement, and then create an instance of the class called df.

We then use the format method of the class to format the decimal number 1234.5678 with two decimal places.
The Decimal Format class is an essential part of the Java API and is automatically available to your programs.

Its inclusion in the Java API makes it easier for Java developers to format decimal numbers in their applications.

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Answer: 1/3

Step-by-step explanation:

Answer:

g(x)=3x²-7

Step-by-step explanation:

Subtract 8 from 3x²+1.

3x²+1-8=3x²-7

g(x)=3x²-7

Hope this helps!

Please mark as brainliest if correct!

The value of the given expression 3 x 2,746 is 8,238.

We are given the expression:-

3 x 2,746

We have to find the value of the given expression using place value.

According to the data given in the question, we can write,

In 2746,

The place value of 6 is 6

The place value of 4 is 4*10 = 40

The place value of 7 is 7*100 = 700

The place value of 2 is 2*1000 = 2000

Hence, we can write,

3*2746 = 3*2000 + 3*700 + 3*40 + 3*6 = 6000 + 2100 + 120 + 18 = 8,238.

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The equation of a line in Slope-Interecept form is:

Where "m" is the slope and "b" is the y-intercept.

Given the following equation:

You need to solve for "y" in order to write it in Slope-Intercept form:

You can see that its slope is:

Since the slopes of parallel lines are equal, you know that the slope of the other line is:

Substitute the coordinates of the given point and the slope into this equation:

And solve for "b". This is:

Finally, knowing the slope and the y-intercept, you can determine that the equation of this line in Slope-Intercept form, is:

\(\\ \tt\Rrightarrow 15^2\times 3^2\div \sqrt[3]{125}+9^3\)

\(\\ \tt\Rrightarrow 3^25^2\times 3^2\div 5^1+3^33^3\)

\(\\ \tt\Rrightarrow 3^45^1\div 3^6\)

\(\\ \tt\Rrightarrow 3^{-2}5\)

\(\\ \tt\Rrightarrow \dfrac{1}{3^2}5\)

\(\\ \tt\Rrightarrow \dfrac{5}{9}\)

Answer:

33.33333...%

Step-by-step explanation:

The dual for the given linear programming problems are as follows:

(i) Minimize Z' = 10a + 12b Subject to: a + 7b ≥ 3 2a + 3b ≥ 4 a + 9b ≥ 5 a, b ≥ 0.

(ii) Maximize Z' = 5a + 6b + 2c Subject to: 3a + 2b + c ≤ 1 4a + 6b + c ≤ 2 a + b ≤ 0 a, b, c ≥ 0.

In the first problem, we have a maximization problem with three variables (x, y, z) and two constraints. The dual formulation involves minimizing a new objective function with two variables (a, b) and four constraints. The coefficients of the variables and the constraints are transformed according to the rules of duality.

The primal problem is:

Maximize Z = 3x + 4y + 5z

Subject to:

x + 2y + z ≤ 10

7x + 3y + 9z ≤ 12

x, y, z ≥ 0

To find the dual, we introduce the dual variables a and b for the constraints:

Minimize Z' = 10a + 12b

Subject to:

a + 7b ≥ 3

2a + 3b ≥ 4

a + 9b ≥ 5

a, b ≥ 0

In the second problem, we have a minimization problem with two variables (y1, y2) and three constraints. The dual formulation requires maximizing a new objective function with three variables (a, b, c) and four constraints. Again, the coefficients and constraints are transformed accordingly.

The primal problem is:

Minimize Z = y1 + 2y2

Subject to:

3y1 + 4y2 > 5

2y1 + 6y2 ≥ 6

y1 + y2 ≥ 2

To find the dual, we introduce the dual variables a, b, and c for the constraints:

Maximize Z' = 5a + 6b + 2c

Subject to:

3a + 2b + c ≤ 1

4a + 6b + c ≤ 2

a + b ≤ 0

a, b, c ≥ 0

The duality principle in linear programming allows us to find a lower bound (for maximization) or an upper bound (for minimization) on the optimal objective value by solving the dual problem. It provides useful insights into the relationships between the primal and dual variables, as well as the economic interpretation of the problem.

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Answer:

Circle B area = 49π square units

Step-by-step explanation:

Circle A radius =√25 = 5 units

(1.2)(5) = 7 = radius circle B

Circle B area = 7²π = 49π square units

Answer:

=12pl+B

Step-by-step explanation:

where p represents the perimeter of the base, l the slant height and B the area of the base.

Answer:

4 + 4 sqrt 10

Step-by-step explanation:

For a pattern function f(x), you can notice that the given transformations are:

f(x) => f(x - a) + 2

which means that the function has been trasnlated 3 units to the right and 2 unit upward.

In this case, the patter function is:

y = x²

after the translation you obtain the given function in the problem:

y = (x - 3)² + 2

The graph of the previous function and the pattern function are shown below:

Answer:

13

Step-by-step explanation:

a²+b²=c²

(12)²+(5)²=c²

√12²+5²=√c²

13=c

Answer:

5^2+12^2=c^2

25+144=c^2

169=c^2

c=√169

c=13

Answer:

See below ~

Step-by-step explanation:

Rule :

Opposing angles in a cyclic quadrilateral are supplementary, which means they add up to 180°.

Q12

Q13

Answer: Quarters

Step-by-step explanation:

Answer:

B. 20

Step-by-step explanation:

First, 20% of 20 is 4.

36 decreased by 4 (36-4) is 32.

The equation is N (160%)=32    or    1.6n=32

160% because it was already 100%, and its increased by 60% (100+60)

Divide  both sides by 1.6.

You get n=20

I hope this helps!

Answer:

ST (given)

Step-by-step explanation:

The maximum area is, A = 10.392

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

y = 9-x²

first, Area = x × y

Area = x(9-x²)

Now,

the Domain: (0, 3)

Also, differentiating

A' = 0

9 - 3x² = 0

x²= 9/3

x =±3

So, the maximum area is

A= 1.732 x 6

A = 10.392

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1. f(-6) = 9 - 3(-6)^2

= 9 - 3(36)

= 9 - 108

= -99

2. f(t+2) = 5(t+2)^2 - 2(t+2)

= 5(t^2 + 4t + 4) - 2(t+2)

= 5t^2 + 20t + 20 - 2t - 4

= 5t^2 + 18t + 16

The domain of the function f(t+2) is all real numbers since there are no restrictions on t.

The function f(x) = x/(x-2) is defined for all values of x except x = 2, as division by zero is undefined. Therefore, the domain of the function is (-∞, 2) U (2, ∞).

The function f(x) = √(3-x) is defined only for values of x such that 3-x ≥ 0. Solving this inequality, we get x ≤ 3. Therefore, the domain of the function is (-∞, 3].

The equation y = -4x + 6 is in slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.

The slope of the graph is -4.

The y-intercept of the graph is 6.

To find f(-6), substitute -6 into the function f(x) = 9 - 3x^2 and perform the calculation.

To find f(t+2), substitute t+2 into the function f(x) = 5x^2 - 2x and simplify the expression.

The function f(x) = x/(x-2) has a restriction on the denominator, which cannot be equal to zero. Solve the inequality x-2 ≠ 0 to find the domain.

The function f(x) = √(3-x) has a square root, which requires the expression inside the square root to be non-negative. Solve the inequality 3-x ≥ 0 to find the domain.

The equation y = -4x + 6 is in slope-intercept form, where the coefficient of x represents the slope and the constant term represents the y-intercept.

The function values, slopes, and y-intercepts of the given equations are as follows:

f(-6) = -99

f(t+2) = 5t^2 + 18t + 16 (domain: all real numbers)

Domain of f(x) = x/(x-2) is (-∞, 2) U (2, ∞)

Domain of f(x) = √(3-x) is (-∞, 3]

Slope of the equation y = -4x + 6 is -4, and the y-intercept is 6.

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Answer:B your correct

Step-by-step explanation:the x axis is the domain so if the point is directly on the y axis the x whould be zero so the answer is -1.5

It's the one second below the question because it does not have two outcomes for x. For example in a relation x could result in y = 2 or y = -2.

Hope this helps! :)

Element that would be more effective in accepting electrons - Chlorine

Element that would be the  best insulator - As

Element that would combine with sulfur - Rb

We know that in a bonding situation, it is possible to have electrons closer to one of the bonding atoms than the other. In such case, the electron cloud is seen to be closer to a given atom. The atom to which the electron cloud is closer is said to be more electronegative.

In the periodic table electronegativity is a property that tends to increase from the left hand side to the right hand side of the periodic table.

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