What are all the zeros of the polynomial function?
[tex]f(x)=3x^3-5x^2-10x-6[/tex]

Answer:

0

Step-by-step explanation:

Untuk menyelesaikan masalah ini, kita perlu menyelesaikan sistem persamaan linear dua variabel pertama dan sistem persamaan linear tiga variabel:

Sistem Persamaan Linear Dua Variabel:

2x + 3y = 8 ... (1)

-4x + 6y = 8 ... (2)

Untuk menyelesaikan sistem persamaan ini, kita dapat menggunakan metode eliminasi:

Langkah 1: Kalikan Persamaan (1) dengan 2 dan Persamaan (2) dengan 1. Kita memperoleh:

4x + 6y = 16 ... (3)

-4x + 6y = 8 ... (4)

Langkah 2: Tambahkan Persamaan (3) dan Persamaan (4). Kita memperoleh:

12y = 24

Langkah 3: Bagi kedua sisi dengan 12. Kita memperoleh:

y = 2

Langkah 4: Substitusikan y = 2 ke dalam Persamaan (1) atau (2). Kita memperoleh:

2x + 3(2) = 8

2x + 6 = 8

2x = 2

x = 1

Jadi, solusi dari sistem persamaan linear dua variabel adalah (x, y) = (1, 2).

Sistem Persamaan Linear Tiga Variabel:

x - z = -4 ... (5)

x + y + z = ?

2x + 3y = 8

Untuk menyelesaikan sistem persamaan ini, kita dapat menggunakan metode substitusi:

Langkah 1: Substitusikan x = 1 dan y = 2 dari sistem persamaan linear dua variabel ke dalam Persamaan (3). Kita memperoleh:

2(1) + 3(2) = 8

2 + 6 = 8

8 = 8

Langkah 2: Substitusikan x = 1 dari sistem persamaan linear dua variabel ke dalam Persamaan (5). Kita memperoleh:

1 - z = -4

z = 5

Langkah 3: Substitusikan x = 1 dan z = 5 ke dalam Persamaan (6). Kita memperoleh:

1 + y + 5 = ?

y = -6

Jadi, solusi dari sistem persamaan linear tiga variabel adalah (x, y, z) = (1, -6, 5).

Maka nilai x + y + z adalah:

x + y + z = 1 + (-6) + 5 = 0

Jadi, nilai x + y + z adalah 0

Answer:

To determine which is cheaper, we need to consider the total cost for a certain amount of time. Let's say we want to paint a picture that will take 5 hours to complete.

For Paint by Numbers:

Flat rate = $100

Hourly rate = $16/hour x 5 hours = $80

Total cost = Flat rate + Hourly rate = $100 + $80 = $180

For Paint it Right:

Flat rate = $38

Hourly rate = $24/hour x 5 hours = $120

Total cost = Flat rate + Hourly rate = $38 + $120 = $158

Therefore, Paint it Right is cheaper for this particular job. However, if the amount of time required for the job is different, the cost comparison may change.

Erin will need to purchase 48ft² of tile for her kitchen island.

In order to calculate the square footage of tile needed for Erin’s kitchen island, we will use the formula for the area of a rectangle: A = lw, where A is the area, l is the length, and w is the width.

The first step is to measure the length and width of the island. Let’s assume that the length is 16ft and the width is 3ft.

Next, we will use the formula to calculate the area of the island: A = lw

A = 16ft x 3ft

A = 48ft²

Finally, Erin will need to purchase 48ft² of tile for her kitchen island.

To double check our calculations, we can also calculate the area of each individual side of the island. For example, the area of the 16ft side is 16ft x 2ft = 32ft². The area of the 3ft side is 3ft x 7ft = 21 ft². When we add the areas together, 32ft² + 21ft² = 53ft². Since 53ft² is greater than 48ft², it is clear that calculating the area of the entire island is the correct solution.

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The proportional relationship defined by the table is given as follows:

y = 2x.

A proportional relationship is defined according to the equation presented as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

From the table, when the input variable x is increased by one, the output variable y is increased by 2, hence the constant of proportionality is given as follows:

k = 2.

Meaning that the equation is given as follows:

y = 2x.

The graph of the relation is given by the image presented at the end of the answer.

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Devon needs to save at least $162.50 per month for the next four years to have enough money to pay for his first year tuition at state university.

To calculate the minimum amount of money Devon must save to have enough money to pay for his first year tuition, we need to take into account the amount of money he has available now and the amount he plans to save each month for the next four years.

First, we can calculate the total amount of money Devon will have available for his first year of tuition by adding the $5,200 his parents will give him to the amount he plans to save over the next four years. If he saves the same amount each month, he will save $x per month for 48 months, which gives him a total of $48x. Therefore, the total amount of money he will have available is:

Total = $5,200 + $48x

We want to find the minimum amount of money he must save to have enough to pay for his first year tuition, which is $13,000. So we set up an equation:

$5,200 + $48x = $13,000

Solving for x, we get:

$48x = $13,000 - $5,200

$48x = $7,800

x = $7,800 / $48

x ≈ $162.50

Therefore, Devon needs to save at least $162.50 per month for the next four years to have enough money to pay for his first year tuition at state university.

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Using percentages we know that the population after 25 years would be 12.4 billion which is 12,40,00,00,000.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred.

A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.

The symbol "%" is frequently written after the number to indicate percentages.

Now, we know that:

The population is 8 billion.

The increasing percentage is 2.2%.

Then, the population after 25 years would be:

= 8000000000/100 * 2.2

= 17,60,00,000

Now, after 25 years:

= 17,60,00,000 * 25

= 4,40,00,00,000

Total population after 25 years:

4,40,00,00,000 + 8000000000 = 12,40,00,00,000

Therefore, using percentages we know that the population after 25 years would be 12.4 billion which is 12,40,00,00,000.

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Converting into whole number:

a. 5 5/10 = 5 1/2

b. 4 5/10 = 4 1/2

c. 5

d.  4/8 = 1/2

To convert a fraction into a whole number, you need to perform the division indicated by the fraction and express the result as a mixed number or a whole number.

Example: 55/10 means that 55 is divided by 10. When we divide 55 by 10, we get 5 with a remainder of 5. Therefore, we can express 55/10 as a mixed number: 5 5/10. However, we usually simplify the mixed number by reducing it to its lowest terms, which in this case is 5 1/2.

Similarly, we can convert the other fractions into whole numbers:

45/10 = 4 5/10 = 4 1/2

20/4 = 5

4/0.8 can be simplified first by dividing both the numerator and denominator by 0.8, which gives 5. Then we can express 5 as a fraction with a denominator of 10 by multiplying both the numerator and denominator by 2, which gives 5/10. Finally, we can reduce this fraction to its lowest terms, which is 1/2. Therefore, 4/0.8 = 1/2.

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It would  take 5 people to paint the same wall is 1 hour and 20 minutes or 1:20.

It is clear that workers twice as fast as people when painting the same surface. This means that John will always draw twice as much area as people at any given time if they are working at the same time. So if they plan well and finish painting the room at the same time, John will paint twice as much area as people.

There is only one possibility:

3 people = 4 hours

Divide by 3.

1 person = 4/3 or 1 1/3 hours

There are 60 minutes in 1 hour. Multiply 1/3 by 60.

(1/3)× 60 = 60/3 = 20

1/3 of an hour is 20 minutes.

It would take 1 person 1 hour and 20 minutes to paint the wall

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Answer: 56

Step-by-step explanation:

66 x 2 = 132

132-76 = 56

(76+52) divided by 2 = 66

Hence the mean score for class B is 56.

The probability that a random sample of 55 students has a mean age of less than 19.2 age years is 0.3866 and the probability that a random sample of 55 students has a mean age between 18.8 and 23 years is 0.27808.

a. To find P(x < 19.2), we need to find the area under the normal distribution curve to the left of x = 19.2. We can use the formula for z-score to standardize the value of x:

z = (x - μ) / δ = (19.2 - 20.9) / 5.9 = -0.2881

Looking up the area to the left of z = -0.2881 in a standard normal distribution table or using a calculator, we find that the probability is approximately 0.3869. So P(x < 19.2) is 0.3866.

b. To find P(18.8 < x < 23.0), we need to find the area under the normal distribution curve between x = 18.8 and x = 23.0. Again, we can standardize the values of x and use a standard normal distribution table or calculator:

z1 = (18.8 - 20.9) / 5.9 = -0.3559

z2 = (23.0 - 20.9) / 5.9 = 0.3559

Looking up the area between z1 = -0.3559 and z2 = 0.3559 in a standard normal distribution table or using a calculator, we find that the probability is approximately0.27808. So P(18.8 < x < 23.0) is 0.27808.

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The table for the function d = 3t is

t (hours) d = 3t (miles)

0 0

1 3

2 6

The equation of the function is given as

d= 3t

The above is a linear function

To make a table for the function d = 3t, we can choose some values of t and then calculate the corresponding values of d using the given equation.

Since the equation represents distance traveled at a rate of 3 miles per hour, we can assume that t represents time in hours and d represents distance in miles.

Let's choose some values of t and calculate the corresponding values of d:

t (hours) d = 3t (miles)

0 0

1 3

2 6

3 9

4 12

5 15

The graph is attached

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a) The probability of drawing a red marble is 1/4.

b) There is a 3/8 chance of drawing an odd-numbered stone.

c) There is a 7/16 chance of drawing a red or odd-numbered marble.

d) The odds of drawing the blue, even-numbered marble are 3/8.

(a) The ratio of red marbles to all other marbles in the jar represents the likelihood of drawing a red marble.

(4) red marbles are present.

(4) + (12) = (16) marbles total

As a result, there is a 4/16 or 1/4 chance of drawing a red marble.

(b) The proportion of odd-numbered marbles to all marbles in the jar determines the likelihood of drawing an odd-numbered marble.

6 odd-numbered marbles make up the total (red marbles numbered 1 and 3, and blue marbles numbered 1, 3, 5, and 7)

There are 16 marbles in total.

The likelihood of drawing an odd-numbered stone is therefore 6/16 or 3/8.

(c) The likelihood of drawing a red or odd-numbered marble is calculated as the product of the odds of drawing each type of marble, less the likelihood of drawing a red or odd-numbered stone (i.e., marble number 1).

a red marble's chances of being drawn = 1/4

Probability of drawing an odd-numbered marble = 3/8

Probability of drawing a marble that is both red and odd-numbered = 1/16

Therefore, the probability of drawing a red or odd-numbered marble is (1/4) + (3/8) - (1/16) = 7/16.

(d) The proportion of blue and even-numbered marbles to all other marbles in the jar determines the likelihood that a blue and even-numbered marble will be drawn.

Six blue and even-numbered marbles make up the total (blue marbles numbered 2, 4, 6, 8, 10, and 12)

Total number of marbles = 16

Probability of drawing the marble is blue and even-numbered = 6/16 or 3/8

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Answer:

There are 60 seconds in a minute, so to convert meters per minute to meters per second, we need to divide by 60.

90 meters per minute ÷ 60 = 1.5 meters per second

Therefore, the car's speed is 1.5 meters per second.

Step-by-step explanation:

Step-by-step explanation:

There are 60 in a minute, so to convert meters per minute to meters per second, we need to divide by 60

90 meters per minute ÷ 60 = 1.5 meters per second

The surface area of the pyramid is 105.6 square feet.

To find the surface area of this pyramid, we need to calculate the area of all its faces and add them up.

Since all sides of our hexagon are equal, we can simplify this formula to:

Surface Area of Hexagon = 6 x (3√3 / 2) x (Side length)²

Total Surface Area = Surface Area of Base + Surface Area of Triangular Faces

Total Surface Area = 6 x (3√3 / 2) x (Side length)² + 6 x (Side length x 15) / 2

We can simplify this expression further by factoring out 6 x (Side length)² from both terms:

Total Surface Area = 6 x (Side length)² x [(3√3 / 2) + 15]

To find the surface area of a right hexagonal pyramid with equal-length sides and triangular faces of height 15 ft, we use the formula above:

Total Surface Area = 6 x (Side length)² x [(3√3 / 2) + 15]

When the value of side length is 1, then total surface area is

=> Total Surface Area = 6 x (1)² x [(3√3 / 2) + 15] = 105.6 square feet.

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Answer:

2,7c-3,6c =-9+4,5

-0,9c=-4,5

c=5

Answer:

c=5

Step-by-step explanation:

2.7c-4.5=3.6c-9

     +4.5         +4.5

2.7c = 3.6c -4.5

-3.6c  -3.6c

-0.9c = -4.5

-0.9c/-0.9= -4.5/-0.9

c= 5

The true statement about the function notation are:

The definition of the graph is given as

The distance vs time graph

This is represented by F = d(t)

The function notation would be determined to be true or false by observation

This is so because the graph is not drawn to scale

Using the above as a guide, we have the following:

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A. IQR or B. IQR is the correct response since Sunny Town is symmetrical or Sunny Town is asymmetrical.

The pattern of data distribution across various values or intervals is referred to as a distribution. The form, centre, and dispersion of a set of data can be described and examined in this manner.

We need to measure the fluctuation of the temperature data in both locations in order to decide which place has the most stable temperature. The interquartile range (IQR), which quantifies the spread of the middle 50% of the data, is the ideal measure of variability for this application.

As a result, depending on how the distributions are shaped, the answer is either A. IQR because Sunny Town is symmetric or B. IQR because Sunny Town is skewed. The IQR would be a suitable tool to gauge the data's spread if Sunny Town's temperature data were symmetric. The IQR would also be useful to measure the spread of the data if Sunny Town's temperature data were skewed. Therefore, the range would not be a suitable indicator of variability if the temperature data from either location were not skewed.

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Answer: 18d

Step-by-step explanation:

To find the greatest common factor (GCF) of the terms in the polynomial 18d^4e^2 − 45d^2 + 36d, we need to factor each term into its prime factors and then identify the common factors with the highest exponent for each variable.

The prime factors of each term are:

18d^4e^2 = 2 x 3^2 x d^4 x e^2

45d^2 = 3^2 x 5 x d^2

36d = 2^2 x 3^2 x d

To find the common factors, we need to look for factors that appear in all terms. The common factors with the highest exponent for each variable are:

2^1, 3^2, and d^1.

Therefore, the GCF of the terms in the polynomial is:

2 x 3^2 x d = 18d

Hence, the GCF of the terms in the polynomial 18d^4e^2 − 45d^2 + 36d is 18d.

All the answers related to null hypothesis are explained below.

Null hypothesis is used to test if there is any statistical significance between the two groups being compared.

1. The null hypothesis is that there is no difference in the number of counseling sessions attended by men and women.

2a. For a two-tailed .05test, you would reject the null hypothesis if the absolute value of the t-statistic is greater than the critical value of 1.96.

2b. For a one-tailed .05test, you would reject the null hypothesis if the t-statistic is greater than the critical value of 1.645.

2c. For a two-tailed .01test, you would reject the null hypothesis if the absolute value of the t-statistic is greater than the critical value of 2.58.

2d. For a one-tailed .01test, you would reject the null hypothesis if the t-statistic is greater than the critical value of 2.33.

3. Rejecting the null hypothesis means that the data is statistically significant and you are confident that the difference in the number of counseling sessions attended by men and women is not due to chance.

4. For a two-tailed test, a Type I error occurs when the null hypothesis is rejected when it should not have been. For a one-tailed test, a Type I error occurs when the null hypothesis is rejected when the difference between the two groups is not greater than the critical value.

5. Conceptually, something is considered to be statistically significant when it is unlikely that the observed results were due to chance.

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From the given information provided, the area of the square room with rectangular section is 72 square feet.

Let's assume that the rectangular section of the floor that is tiled has length "L" and width "W". Since the area of the rectangular section is 18 square feet, we have:

L × W = 18

Since the room is square, its length and width are equal, let's say it's "x". Then, the area of the room is x².

Since the rectangular section is a part of the room, we have:

L ≤ x and W ≤ x

Therefore, we can find the minimum possible value of x by assuming that L = W = √18 (the sides of the rectangle are equal, and equal to the square root of 18), which gives:

x = √18 + √18 = 2√18

So, the area of the room is:

x² = (2√18)² = 4(18) = 72 square feet

Question - A contractor tiles a rectangular section of floor in a square room. The tiles covers 18sq. feet. What is the area of room?

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According to the trigonometric functions, the answer is A. StartFraction 12 Over 13 EndFraction.

What are trigonometric functions?

Trigonometric functions are mathematical functions that relate the angles of a right triangle to the ratios of its sides. There are six primary trigonometric functions:

Sine (sin): the ratio of the opposite side to the hypotenuse of a right triangle.

Cosine (cos): the ratio of the adjacent side to the hypotenuse of a right triangle.

Tangent (tan): the ratio of the opposite side to the adjacent side of a right triangle.

Cosecant (csc): the reciprocal of the sine function, i.e. the ratio of the hypotenuse to the opposite side of a right triangle.

Secant (sec): the reciprocal of the cosine function, i.e. the ratio of the hypotenuse to the adjacent side of a right triangle.

Cotangent (cot): the reciprocal of the tangent function, i.e. the ratio of the adjacent side to the opposite side of a right triangle.

To find sin(K), we need to use the definition of sine which is the opposite side over the hypotenuse:

sin(K) = opposite / hypotenuse

In this case, the opposite side is LM and the hypotenuse is KM. We are given that KM = 13 and LM = 12, so we can plug these values into the formula:

sin(K) = 12/13

Therefore, the answer is A. StartFraction 12 Over 13 EndFraction.

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the error interval will be [15.29, 15.3).

What is error?

Error is the difference between an actual value and an estimate, or approximate, representation of that value in applied mathematics. The discrepancy between the population's average and the average of a sample taken from that population is a frequent example in statistics. The discrepancy between an irrational number's true value and the values of rational expressions like 22/7, 355/113, 3.14, or 3.14159 serves as an example of round-off error in numerical analysis. A truncation error happens when an infinite series is ignored for all but a small number of terms. For instance, the sum of the infinite series can be used to express the exponential function ex.

Find the error interval of 15.29:

[15.29, 15.3)

Hence the error interval will be [15.29, 15.3).

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The total value of the remaining inventory is  $5,000. So correct option is B.

Inventory refers to the stock of goods or materials that a business or organization has on hand for the purpose of selling, manufacturing, or producing. It can include finished goods ready for sale, work in progress, or raw materials waiting to be processed or used. Proper management of inventory is essential to ensure that a business can meet customer demand while minimizing costs associated with carrying excess inventory or stockouts. Inventory management techniques involve tracking inventory levels, determining optimal reorder points, and controlling the flow of goods in and out of the inventory.

Using the FIFO method, we assume that the first jackets purchased are the first ones sold, so the value of the remaining inventory is calculated as follows:

The first 30 jackets are from the beginning inventory and cost $175 each.

The next 16 jackets (out of the 25 purchased in March) cost $150 each.

The next 10 jackets (out of the 35 purchased in June) cost $125 each.

The last 0 jackets (out of the 30 purchased in September) cost $100 each.

So the total value of the remaining inventory is:

30 x $175 + 16 x $150 + 10 x $125 + 0 x $100 = $5,000

Therefore, the answer is B. $5,000.

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The expression can be written as the sum of two terms as 74.5 + 0.5d

Mathematical expressions are combinations of numbers, variables, and operators (such as +, -, ×, ÷, =) that represent a mathematical relationship or computation.

To write the given expression as the sum of two terms simplify the expression by multiplying and adding or subtracting like terms.

Here we have

The expression 75 + 0.5(d - 1) represents the fine for an overdue library book, where d is the number of days overdue.

Simplify expression as shown below

=> 75 + 0.5(d - 1)

= 75 + 0.5d - 0.5

= 0.5d + 74.5  

Now the expression is in the form of the sum of two terms

Therefore

The expression can be written as the sum of two terms as 74.5 + 0.5d

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The length of the shaded arc is 68.71 metres squared.

The arc of a circle is defined as the part or segment of the circumference of a circle. Therefore, the length of the bolded arc can be found as follows:

length of an arc = ∅ / 360 × 2πr

where

Therefore,

r = 26 / 2 = 13 m

∅ = 360 - 57 = 303 degrees

length of an arc = 303 / 360 × 2 × 3.14 × 13

length of an arc =  24736.92 / 360

length of an arc = 68.7136666667

length of an arc = 68.71 metres squared

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There are 24 different possible ways a resident can receive an advertisement in the mail.

The counting principle states that if there are "a" ways to do one thing, and "b" ways to do another thing, then there are "a × b" ways to do both things. In this case, we need to multiply the number of different types of advertisements for each week to find the total number of different possible ways a resident can receive an advertisement in the mail.

Week 1: 2 different types of advertisements (postcard or leaflet)
Week 2: 3 different types of advertisements (flyer, catalog, or calendar)
Week 3: 2 different types of advertisements (brochure or poster)
Week 4: 2 different types of advertisements (business card or coupon)

Total number of different possible ways = 2 × 3 × 2 × 2 = 24

Therefore, there are 24 different possible ways a resident can receive an advertisement in the mail.

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Emila gοt a tοtal οf 2 + 7 = 9 marbles.

Let's first find οut which bags each friend gοt. Since each friend tοοk twο bags, we can subtract the marbles each friend gοt frοm the tοtal number οf marbles in the twο bags tο find οut the number οf marbles in the οther bag.

Amina gοt 5 marbles, sο the tοtal number οf marbles in her twο bags must be 1 + 4 οr 2 + 3. Let's assume she gοt bags with 1 and 4 marbles.

Then, the bags left fοr the οther friends are:

Bag 2: Breanna οr Chyna

Bag 5: Breanna οr Chyna

Bag 6: Deiοn οr Emila

Bag 7: Deiοn οr Emila

Bag 8: Available tο any friend

Bag 9: Available tο any friend

Bag 10: Available tο any friend

Breanna gοt 7 marbles, sο the tοtal number οf marbles in her twο bags must be 3 + 4. Therefοre, Chyna gοt bags with 2 and 5 marbles.

Chyna gοt 9 marbles, sο the tοtal number οf marbles in her twο bags must be 4 + 5. Therefοre, Deiοn gοt bags with 1 and 8 marbles.

Deiοn gοt 15 marbles, sο the tοtal number οf marbles in his twο bags must be 6 + 9. Therefοre, Emila gοt bags with 2 and 7 marbles.

Therefοre, Emila gοt a tοtal οf 2 + 7 = 9 marbles.

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To get the transformation's Jacobian, we must first compute the partial derivatives of each new variable with respect to each old variable: x/u = 0, x/v = 6 + 0 = 6, and x/w = 0 + 12w = 12w.

∂y/∂u = 8u ∂y/∂v = 0 ∂y/∂w = 8w + 0 = 8w z/u = 9 plus 0 = 9 z/v = 0 plus 18v = 18v z/w = 0 As a result, the transformation's Jacobian matrix is: [(x,y,z)/(u,v,w)] = J = \s[ 0 6 12w ] [ 8 0 8w ] [ 9 18v 0 ] A transformation's Jacobian is a matrix of partial derivatives that illustrates how changing the old variables impacts changing the new variables. We have three new variables x, y, and z in the provided transformation, which are functions of three old variables u, v, and w. To get the transformation's Jacobian, we must compute the partial derivatives of x, y, and z with respect to u, v, and w. We discover that x's partial derivative with respect to u is zero, x's partial derivative with respect to v is six, and x's partial derivative with respect to w is twelve. Likewise, y's partial derivative with regard to u.

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The height of ladder is approximately 26.9 feet tall.

In order to get the length of the hypotenuse, divide the non-hypotenuse side that is close to the angle by cos(). If you prefer, you can multiply this length by tan() to obtain the length of the side that is perpendicular to the angle.

Let's tackle this issue using the Pythagorean theorem.

According to the Pythagorean theorem, the sum of the squares of the leg lengths in a right triangle equals

The length of the slide is the other leg, the distance from the ladder's bottom to its base is one leg, and the ladder itself is the hypotenuse.

b² = 18² + 20²

b² = 324 + 400

b² = 724

b = √(724)

b ≈ 26.9

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