3x-9x^2
Factorised fully

The linearized equation for the non-linear equation z = x² + 4xy + 6xy² in the region defined by 8 ≤ x ≤ 10, 2 ≤ y ≤ 4 is given by :

z ≈ 244 + 20(x - 8) + 128(y - 2).

When using the linearized equation to calculate the value of z at x = 8, y = 2, the error is 0.

1.1. To linearize the equation in the given region, we need to find the partial derivatives of z with respect to x and y:

∂z/∂x = 2x + 4y

∂z/∂y = 4x + 6xy

At the point (x₀, y₀) = (8, 2), we substitute these values:

∂z/∂x = 2(8) + 4(2) = 16 + 8 = 24

∂z/∂y = 4(8) + 6(8)(2) = 32 + 96 = 128

The linearized equation is given by:

z ≈ z₀ + ∂z/∂x * (x - x₀) + ∂z/∂y * (y - y₀)

Substituting the values, we get:

z ≈ z₀ + 24 * (x - 8) + 128 * (y - 2)

1.2. To find the error when using the linearized equation to calculate the value of z at x = 8, y = 2, we substitute these values:

z ≈ z₀ + 24 * (8 - 8) + 128 * (2 - 2)

= z₀

Therefore, the linearized equation gives the exact value of z at x = 8, y = 2, and the error is 0.

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Answer:

I can help you.

Step-by-step explanation:

1. Laptop models with at least 8 GBs of RAM: [List of laptop models]. 2.Manufacturers that make laser printers: [List of manufacturers]. 3.Manufacturers that make PCs but not Laptops: [List of manufacturers]. 4. Manufacturer(s) of the cheapest Laptop(s): [List of manufacturers].

1. To find the laptop models with at least 8 GBs of RAM, we can refer to various sources such as manufacturer websites, online retailers, and technology review websites. These sources provide detailed specifications for laptops, including RAM capacity. By filtering the available options based on the RAM requirement, we can compile a list of laptop models that meet the criteria.

2. Laser printers are commonly manufactured by several companies. Some prominent manufacturers known for producing laser printers include HP, Canon, Epson, Brother, Xerox, Lexmark, and Samsung, among others. These companies have established themselves in the printing industry and offer a wide range of laser printers suitable for various purposes, such as home use, small office settings, and large-scale commercial printing.

3. Manufacturers that make PCs but not laptops primarily focus on desktop computer systems. While many laptop manufacturers also produce desktop PCs, some companies specialize in manufacturing desktop computers exclusively. Some notable examples of manufacturers that predominantly make PCs but not laptops include Dell, Lenovo, HP (Hewlett-Packard), Acer, ASUS, and Apple. These companies offer a diverse range of desktop PCs catering to different user requirements, such as gaming PCs, workstations, and all-in-one computers.

4. Determining the manufacturer(s) of the cheapest laptop(s) requires comparing the prices of various laptop models from different manufacturers. Price comparisons can be made by referring to online retailers, technology review websites, and marketplaces that provide up-to-date pricing information. The list of manufacturers producing the cheapest laptops may vary over time due to factors like promotional offers, discounts, and market competition. It is recommended to conduct a thorough price analysis across multiple sources to identify the manufacturer(s) offering the most affordable laptops based on current market conditions.

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The function f(x) = x² + x changes by 0.9 when x goes from x=4 to x=4.1.

The instantaneous rate of change of a function at a certain position is referred to as the derivative of a function. The derivative provides the precise slope of the curve at a given location.

Given that the change goes for x = 4 to x = 4.1.

That is x + Δx = 4.1.

Substitute the value of x = 4:

4 + Δx = 4.1

Δx = dx = 0.1

The function is f(x) = x² + x.

Differentiate the function with respect to x:

dy/dx = 2x + 1

Substitute the value of x = 4.

dy/dx = 2(4) + 1

dy = 9 dx

Substitute the value of dx = 0.1.

dy = 9(0.1) = 0.9

Hence, the function f(x) = x² + x changes by 0.9 when x goes from x=4 to x=4.1.

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True. A vector in space can be described by specifying its magnitude and its direction angles. The magnitude of a vector represents its length or size, while the direction angles determine the orientation of the vector with respect to a reference axis system.

In three-dimensional space, a vector can be decomposed into its components along the x, y, and z axes. By using trigonometric functions, the direction angles of the vector can be determined. The direction angles are typically measured with respect to the positive x-axis, the positive y-axis, and the positive z-axis.

Once the magnitude and direction angles of a vector are known, the vector can be fully described. This description allows for precise calculations and analysis of vector quantities, such as displacement, velocity, and force, in various physical and mathematical contexts.

It's worth noting that there are alternative ways to describe vectors, such as using Cartesian coordinates or unit vectors. However, specifying the magnitude and direction angles provides a convenient and comprehensive representation of a vector in space.

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The average number of customers awaiting repairs is 2.38.The system utilization is 60.73%. The repairman is out on calls for the entire eight-hour day. The probability of two or more customers in the system is approximately 0.5072.

a. To find the average number of customers awaiting repairs, we can use Little's Law, which states that the average number of customers in the system (including both being repaired and waiting) is equal to the average arrival rate multiplied by the average time spent in the system. The average arrival rate is given as 1.7 requests per eight-hour day. The average time spent in the system can be calculated as the sum of the average repair time and the average waiting time. The average repair time is given as 2.8 hours per call. Since repair time is exponentially distributed, the average waiting time can be calculated as half of the average repair time (which is equal to the mean of the exponential distribution). Therefore, the average waiting time is 2.8/2 = 1.4 hours per call.

Now we can calculate the average number of customers awaiting repairs: Average number of customers = Average arrival rate * Average time spent in the system

= 1.7 * 1.4

= 2.38 (rounded to 2 decimal places)

b. System utilization is the proportion of time the repairman is busy with repairs. It can be calculated as the product of the average service time (1/mean service rate) and the average arrival rate. The mean service rate can be calculated as the inverse of the mean repair time: 1/2.8 = 0.3571 calls per hour.

System utilization = Average arrival rate * Average service time

= 1.7 * 0.3571

= 0.6073 (rounded to 2 decimal places)

c. The amount of time during an eight-hour day that the repairman is not out on a call can be calculated as the total time minus the time spent on calls.

Total time = 8 hours

To calculate the time spent on calls, we need to consider the average repair time and the number of repairs made during the day. Since repair time is exponentially distributed, the number of repairs follows a Poisson distribution with a mean of (average arrival rate * repair time). The number of repairs made during the day can be calculated as (average arrival rate * repair time * 8 hours).

Time spent on calls = Number of repairs * Average repair time

Number of repairs = average arrival rate * 8 hours = 1.7 * 8

Time spent on calls = (1.7 * 8) * 2.8 = 38.08 hours

Amount of time the repairman is not out on a call = Total time - Time spent on calls

= 8 - 38.08

= -30.08 hours

d. The probability of two or more customers in the system can be calculated using the formula for the probability of the number of arrivals in a given interval, which follows a Poisson distribution.

P(2 or more customers) = 1 - P(0 customers) - P(1 customer)

\(= e^{(-1.7)} * (1^0 / 0!)\)

≈ 0.1828

\(= e^{(-1.7)} * (1.7^1 / 1!)\)

≈ 0.3100

P(2 or more customers) = 1 - 0.1828 - 0.3100

≈ 0.5072 (rounded to 4 decimal places)

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Answer:

The answer is y= -1x+8

Step-by-step explanation:

y=mx+b

m= -1

y-y=m(x-x1)

y-5=-1(x-3)

y-5=-1x+3

+5 +5

y=-1x+8

The equation in point slope form of the line passes through the point (3,5) and has a slope of m=-1 is y= -1x+8.

Point Slope Form:
The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables. Depending on the facts at hand, there are different ways to find a line's equation. A straight line is represented using its slope and a point on the line using point slope form. This means that the point slope form is used to find the equation of a line whose slope is "m" and which passes through the points (x 1, y 1). The equation of a straight line can be expressed in various ways.

Point Slope Formula in Math:

y − y1= m (x − x1)

where,

(x, y) is a random point on the line(which should be kept as variables while applying the formula).

(x1, y1) is a fixed point on the line.

m is the slope of the line.

y=mx+c

m= -1

y-y1=m(x-x1)

y-5=-1(x-3)

y-5=-1x+3

  y= -1x+8

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Step-by-step explanation:

hi hlo hshsvbzbzbsbbzbsbsbsb

Answer:

It is 36

Step-by-step explanation:

Answer:

2. Polynomial

3. Not a polynomial

4. Polynomial

5. Polynomial

Step-by-step explanation:

The mean and standard deviation of the probability distribution is:

Y will be 0.4899 and 0.699 respectively.

A mathematical function called a probability distribution explains the likelihood of many alternative values for a variable. Graphs or probability tables are frequently used to represent probability distributions.

A probability distribution is a mathematical function used in probability theory and statistics that estimates the likelihood that various possible outcomes of an experiment will occur. In terms of its sample space and event probability, it is a mathematical description of a random phenomena.

According to the given question,

From the given probability distribution, it should be noted that the probability distribution for y will be:

Y                   0        1.         2

Probability 0.63.   0.25.   0.12

The mean of Y will be:

Mean = (0 × 0.63) + (1 × 0.25) + (2 × 0.12)

Mean = 0 + 0.25 + 0.25

Mean = 0.49

The variance will be 0.4899.

Therefore, the standard deviation will be:

standard deviation = ✓0.4899

Standard Deviation = 0.699.

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Answer:

Tim has -8 points.

Step-by-step explanation:

15 - 23

Another way to solve for this is reversing the order the numbers are shown:

23 - 15

Just remember the answer will be negative because Tim is losing more points than he originally had.

-8

The probability that a student who has an A is a male is 60%.

To find the probability that a student who has an A is a male, we need to calculate the ratio of the number of male students with an A to the total number of students with an A.

Given that there are 19 students in total, and 6 of them are female, we can determine that there are 19 - 6 = 13 male students. Out of these male students, 7 do not have an A. Therefore, the number of male students with an A is 13 - 7 = 6.

Now, we know that there are 10 students in total who have an A. Therefore, the probability that a student with an A is a male can be calculated as the ratio of the number of male students with an A to the total number of students with an A:

Probability = Number of male students with an A / Total number of students with an A

Probability = 6 / 10

Probability = 0.6 or 60%

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The surface area of the composite figure is 748 cm^2.

To find the surface area of a composite figure, we need to calculate the surface areas of each individual component and then add them together.

Let's break down the composite figure into its components:

There is a rectangular prism with dimensions 5 cm, 6 cm, and 4 cm. The surface area of a rectangular prism can be calculated using the formula: 2lw + 2lh + 2wh, where l, w, and h are the length, width, and height respectively. So, the surface area of this rectangular prism is: 2(5)(6) + 2(5)(4) + 2(6)(4) = 60 + 40 + 48 = 148 cm^2.

There is a triangular prism with dimensions 20 cm (base), 12 cm (height), and 6 cm (slant height). The surface area of a triangular prism can be calculated by finding the areas of the two triangular bases and the three rectangular faces. The area of each triangular base is (1/2)(20)(12) = 120 cm^2, and the area of each rectangular face is (20)(6) = 120 cm^2. Therefore, the total surface area of the triangular prism is: 2(120) + 3(120) = 240 + 360 = 600 cm^2.

To find the surface area of the composite figure, we add the surface areas of the rectangular prism and the triangular prism: 148 cm^2 + 600 cm^2 = 748 cm^2.

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Answer:

Step-by-step explanation:

y/3 + 1 = 7/15

y/3 = 7/15 - 1

y/3 = -8/15

y = -8/15 × 3

y = -8/5

hope this helps

plz mark as brainliest!!!!!!!!!

The number of child tickets were sold that day are 73.

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.

We are given that;

Cost of child admission= $5.30

Cost of adult admission= $8.70

Now,

Let's assume that "c" represents the number of child tickets sold, and "a" represents the number of adult tickets sold. We can create two equations based on the given information:

c + a = 163 (equation 1: the total number of tickets sold)

5.30c + 8.70a = 1169.90 (equation 2: the total sales)

We can use equation 1 to solve for "a" in terms of "c":

a = 163 - c

Substituting this expression for "a" into equation 2, we get:

5.30c + 8.70(163 - c) = 1169.90

Simplifying and solving for "c", we get:

5.30c + 1418.10 - 8.70c = 1169.90

-3.4c = -248.20

c = 73

Therefore, by algebra the answer will be 73.

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Different logs measure different physical properties of the formation that are related to porosity, and the relationship between the log measurement and porosity can be expressed through equations.

The different logs used to obtain porosity and their principles of measurement, quantities measured, and relation to porosity.
There are three main types of logs used to obtain porosity: neutron logs, density logs, and sonic logs.
Neutron logs: These logs measure the hydrogen content in a formation, which is directly related to porosity. The tool emits neutrons that interact with hydrogen atoms, and the resulting gamma rays are measured. The count rate decreases with increasing porosity. The neutron log can be expressed as:
Porosity = (neutron log reading - matrix reading) / (fluid reading - matrix reading)
Density logs: Density logs measure the bulk density of a formation, which can be related to porosity. The tool emits gamma rays that interact with the formation, and the scattered gamma rays are measured. The bulk density decreases with increasing porosity. The density log can be expressed as:
Porosity = (matrix density - bulk density) / (matrix density - fluid density)
Sonic logs: Sonic logs measure the travel time of sound waves through a formation, which can be related to porosity. The tool sends an acoustic wave and measures the time it takes to travel a specific distance. The travel time increases with increasing porosity. The sonic log can be expressed using Wyllie's time-average equation:
Porosity = (sonic log reading - matrix reading) / (fluid reading - matrix reading)
In summary, neutron logs measure hydrogen content, density logs measure bulk density, and sonic logs measure travel time of sound waves. These measurements can be used to calculate porosity using the respective equations provided.

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i) The expected value of a Poisson random variable X with parameter λ is given by E(X) = λ.

To show this, we start with the definition of the expected value for a discrete random variable:

E(X) = ∑(x * P(X = x))

For a Poisson random variable, the probability mass function is given by P(X = x) = (e^(-λ) * λ^x) / x!, where λ is the parameter.

Substituting this into the expected value formula, we have:

E(X) = ∑(x * (e^(-λ) * λ^x) / x!)

Rearranging the terms, we get:

E(X) = λ * e^(-λ) * ∑(x * λ^(x-1) / (x-1)!)

Using the property that ∑(x * λ^(x-1) / (x-1)!) = λ, we can simplify the expression:

E(X) = λ * e^(-λ) * λ = λ * e^(-λ) = λ

Therefore, the expected value of a Poisson random variable X with parameter λ is λ.

ii) The variance of a Poisson random variable X with parameter λ is given by Var(X) = λ.

To show this, we use the formula for variance:

Var(X) = E(X^2) - (E(X))^2

We have already shown that E(X) = λ. Now, we need to calculate E(X^2).

E(X^2) = ∑(x^2 * P(X = x))

Substituting the Poisson probability mass function, we have:

E(X^2) = ∑(x^2 * (e^(-λ) * λ^x) / x!)

Expanding the sum and simplifying, we find:

E(X^2) = λ * (λ + 1)

Now we can calculate the variance:

Var(X) = E(X^2) - (E(X))^2

= λ * (λ + 1) - λ^2

= λ + λ^2 - λ^2

= λ

Therefore, the variance of a Poisson random variable X with parameter λ is λ.

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Answer:

Step-by-step explanation:

You want to know the amount borrowed at 10%, 12%, and 14% if the total borrowed was $21000, the total interest was $2580, and the total of amounts borrowed at 10% and 14% was double the amount borrowed at 12%.

The relations give rise to three equations. If we let x, y, z represent the respective amounts borrowed at 10%, 12%, and 14%, we have ...

  x + y + z = 21000 . . . . . . total borrowed

  0.10x +0.12y +0.14z = 2580 . . . . . . total interest

  x + y = 2z . . . . . . . . . . . relationship between amounts

Writing the last equation as ...

  x -2y +z = 0

we can formulate the problem as a matrix equation and use a solver to find the solution. We have done that in the attachment. It tells us the amounts borrowed are ...

__

Additional comment

Recognizing that the amount at 12% is 1/3 of the total, we can use that fact to rewrite the other two equations. The interest on the $7000 at 12% is $840, so we have ...

These two equations have the solution shown above. (It is usually convenient to solve them by substituting for x in the second equation.)

<95141404393>

Answer:

two hours after the snow started melting, the depth of the snow would be 8 inches.

Step-by-step explanation:

The melting can be represented by a linear function of the snow depth (D(t)) as a function of time (t). We consider that the initial value is: 11 inches deep at time = 0 (zero). and then decreasing at a rate of 1.5 inches per hour (that is a negative slope = -1.5).

\(D(t)=11-1.5\,t\)

Therefore, 2 hours after the snow started melting, one would have:

\(D(2)=11-1.5\,(2)=11-3=8\,\,inches\)

He run on Thursday is 3.75 miles.

Algebra helps in converting a mathematical statement into an equation. We know if we have ‘more’ or ‘sum’ in the given sentence we use addition operation (+) . Similarly If we have ‘less’ or ‘difference’ we use subtraction (−) . If we have a ‘quotient’ we use division operation (÷) . To define more generalized terms; we use algebra. It is a very vast branch of mathematics and is used in all the branches of mathematics like polynomial, linear equations, graphs, etc. and in daily life too.

Now, Gavriel ran 5 miles on Wed

and,  On Thursday, he ran 3/4 as far.

We have to find the how far did he run on Thursday.

On Thursday , The distance will be:

=> 5 × 3/4

=> 15/4

=> 3.75 miles

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Answer:

4th option OR last option

Step-by-step explanation:

Ok so I think it means hexagon not heptagon since I have never heard of heptagon. Just confirm that with your teacher if it is hexagon or heptagon.

Hexagon = 6 sides

This means that it is not second option. Nor it is the third option since it said that it should be more than 6 sides. Now we are left with 1st and 4th option. It also mentioned that all opposite sides should be parallel. Looking at the first option, not all sides are parallel. Some are big and some are small. This remains with the last option which is the 4th option.

Hope this helps, thank you !!

The volume of a rectangular prism is given by the product of its length, width, and height, which is V = l * w * h, where l is the length, w is the width, and h is the height.

We are given that the volume of the prism is 3w^3 + 14w^2 + 8w. We can use this information to find the height of the prism by dividing the volume by the product of the length and width.

We know that the length of the prism is 2 more than three times the width (l = 3w + 2). Therefore, the product of the length and width is l*w = (3w + 2) * w = 3w^2 + 2w

Now we can divide the volume by the product of the length and width to find the height of the prism:

V / (l * w) = (3w^3 + 14w^2 + 8w) / (3w^2 + 2w) = 3w + 14 + 8/3w^2 + 2w

So, the height of the prism is 3w + 14 + 8/3w^2 + 2w

Which is a simplified expression for the height of the prism, in terms of the width.

Step-by-step explanation:

we all know that the teacher bought 25 tickets for the children and 5 for the adult children's tickets cost 4 shillings so we'll have to take 25 times for and adult tickets cost $6 so we'll have to take 5 * 6 will get 30 and 25 * 4 will get 100 total is equals to 130 so the teachers spent $130 buying the tickets hope this helps you.

Answer:

]1:2:3:5]

Step-by-step explanation:

I'm not sure

A coordinate grid with one line that passes through the points 0,1 and 4,0 and another line that passes through the points 0,-1 and 1,-3.

The system of linear equations given is:

y = (-1/3)x + 1

y = -2x - 3

We can determine the solution to this system by finding the point of intersection of the two lines represented by these equations.

By comparing the coefficients of x and y in the equations, we can see that the slopes of the lines are different.

The slope of the first line is -1/3, and the slope of the second line is -2. Since the slopes are different, the lines will intersect at a single point.

To find the point of intersection, we can set the two equations equal to each other:

(-1/3)x + 1 = -2x - 3

By solving this equation, we find that x = 3.

Substituting this value back into either equation, we can find the corresponding y-value.

Using the first equation, when x = 3, y = (-1/3)(3) + 1 = 0.

Therefore, the point of intersection is (3,0), which lies on both lines.

The graph that shows the solution to the system of linear equations is the one with a coordinate grid where one line passes through the points (0,1) and (4,0), and another line passes through the points (0,-1) and (1,-3). This graph represents the intersection point (3,0) of the two lines, which is the solution to the system of equations.

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The first angle is 76 and the second angle is 14. You can check this by doing 14+5=19 and then multiply that by 4.

Answer:

-6

Step-by-step explanation:

yw

Answer:

The television tower is 132 feet high.

Step-by-step explanation:

Let h be the height of the television tower. Set up and solve this proportion.

\( \frac{3}{5} = \frac{h}{220} \)

\(5h = 660\)

\(h = 132\)

Answer:

14.8 or round up to 15 burgers

Step-by-step explanation: