1. Use Newton's method to approximate to six decimal places the only critical number of the function f(x) = ln(1 + x - x2 + x3). 2. Find an equation of the line passing through the point (3,5) that cuts off the least area from the first quadrant. 3. Find the function f whose graph passes through the point (137, 0) and whose derivative function is f'(x) = 12x cos(x2)

Answers

Answer 1

1. Using Newton's method, the only critical number of the function f(x) = ln(1 + x - x^2 + x^3) is approximately 0.789813.

2. The equation of the line passing through the point (3,5) that cuts off the least area from the first quadrant is y = -(5/3)x + 20/3.

3. The function f(x) = sin(x^2) - 137x + 231 is the function that passes through the point (137, 0) and has a derivative function of f'(x) = 12x cos(x^2).

To find the critical number of the function f(x) = ln(1 + x - x^2 + x^3), we can apply Newton's method.

The derivative of f(x) is given by f'(x) = (1 - 2x + 3x^2) / (1 + x - x^2 + x^3). By iteratively applying Newton's method with an initial guess, we can approximate the critical number. The process continues until we reach the desired level of accuracy. In this case, the critical number is approximately 0.789813.

To find the line passing through the point (3,5) that cuts off the least area from the first quadrant, we need to minimize the area of the triangle formed by the line, the x-axis, and the y-axis.

The equation of a line passing through (3,5) can be written as y = mx + c, where m represents the slope and c is the y-intercept. By minimizing the area of the triangle, we minimize the product of the base and height.

This occurs when the line is perpendicular to the x-axis, resulting in the least area. Therefore, the line equation is y = -(5/3)x + 20/3.

To find the function f(x) that passes through the point (137, 0) and has a derivative function of f'(x) = 12x cos(x^2), we integrate the derivative function with respect to x.

Integrating f'(x) gives us f(x) = sin(x^2) - 137x + C, where C is the constant of integration. To determine the value of C, we substitute the given point (137, 0) into the equation. This gives us 0 = sin(137^2) - 137(137) + C, which allows us to solve for C. The resulting function is f(x) = sin(x^2) - 137x + 231.

Learn more about Newton's method:

https://brainly.com/question/31910767

#SPJ11

Related Questions

A patient asks about the purpose of withholding food and fluid before surgery. Which response by the nurse is appropriate?
a)It decreases urine output so that a catheter would not be needed.
b)It prevents overhydration and hypertension.
c)It decreases the risk of elevated blood sugars and slow wound healing.
d)It prevents aspiration and respiratory complications.

Answers

Withholding food and fluids before surgery is done to ensure that the patient's stomach is empty. This helps to minimize the risk of aspiration, which occurs when stomach contents enter the lungs. Aspiration can lead to respiratory complications such as pneumonia, which can be dangerous for the patient.

The appropriate response by the nurse is d) It prevents aspiration and respiratory complications. Withholding food and fluid before surgery is important to prevent aspiration, which occurs when stomach contents enter the lungs during surgery, and can cause respiratory complications. It also helps ensure a clear surgical field. However, the patient will still receive necessary fluids and medications through an IV during surgery to prevent dehydration and maintain blood pressure. It is important to follow the healthcare provider's instructions on pre-operative fasting to ensure the safest surgical experience.
d) It prevents aspiration and respiratory complications.
Visit here to learn more about respiratory complications:

brainly.com/question/30904939

#SPJ11

Guided Practice

Solve the compound inequality.

3 ≤ w + 2 ≤ 7

A.
5 ≤ w ≤ 9

B.
1 ≤ w ≤ 7

C.
1 ≤ w ≤ 5

Answers

Answer:

1 ≤ w ≤ 5

Step-by-step explanation:

Move all terms not containing

from the center section of the inequality.

Inequality Form:

1 ≤ w ≤ 5

Interval Notation:

[ 1 , 5 ]

GIVING BRAIN TO CORRECT ANSWER!!

Researchers conduct a study to evaluate the level of pollution present in a river. They select several locations along the river and then take a sample of water from each location.

What is the population under study?

A. The water collected by researchers

B. River water in the county where researchers are working

C. The water in the river

D. Water in a lake fed by the river

Answers

Answer: C) Water in the river

Step-by-step explanation:

Can someone please answer question 4 for me.

Answers

Answer:

B figure 1 and 3

Step-by-step explanation:

they are the same identical thing but different sizes

If a number is not divisible by 6, can it be divisible by 12? A. Yes, because 6 and 12 have no common factors. B. No, because if 12|x, then x = 12n = 2.6n for some integer n. O C. Yes, because all odd multiples of 12 are not divisible by 6. O D. No, because 6 and 12 share a common factor, and if one number in a pair of numbers with a common factor does not divide a number n, then the other number in the pair does not divide n either. If a number is not divisible by 12, can it be divisible by 6? O A. Yes, because 6 and 12 have no common factors. B. Yes, because multiplying 6 by an odd number results in a number not divisible by 12. O C. No, because 6 and 12 share a common factor. D. No, because if 12|x, then x = 12n = 2.6n for some integer n.

Answers

The correct answer to the first question is B. No, because if 12|x, then x = 12n = 2.6n for some integer n.the correct answer is A. Yes, because 6 and 12 have no common factors.

If a number is not divisible by 6, it means it does not have 6 as a factor. Since 12 is a multiple of 6, any number divisible by 12 must also be divisible by 6. Therefore, the statement in option B is correct.

Regarding the second question, the correct answer is A. Yes, because 6 and 12 have no common factors.

If a number is not divisible by 12, it means it does not have 12 as a factor. However, 6 is a factor of 12, so a number not divisible by 12 can still be divisible by 6. Hence, option A is the correct answer.

Learn more about divisibility rule here:

https://brainly.com/question/9462805

#SPJ11

The sum of two numbers is 7. The larger number is 16 more than 2 times the smaller number. What are the numbers?

Answers

The two numbers are 10 and -3.

¡cuantas unidades se deben producir para que el costo sea el más bajo posible?
$c(x)=800-10x+0.25x^{2}$

Answers

Para encontrar la cantidad de unidades que se deben producir para que el costo sea el más bajo posible, debemos encontrar el mínimo de la función de costo c(x) utilizando el enfoque de derivadas.

Primero, encontramos la derivada de la función de costo:

c'(x) = -10 + 0.5x

Luego, encontramos el valor de x que hace que la derivada sea igual a cero para encontrar un punto crítico:

c'(x) = -10 + 0.5x = 0
x = 20

Usando la segunda derivada de la función de costo, comprobamos que este punto crítico es un mínimo:

c''(x) = 0.5 > 0

Por lo tanto, la cantidad de unidades que se deben producir para que el costo sea el más bajo posible es de 20 unidades.

Simplify ratio 6:4 , please answer quick!!!

Answers

Answer:

3:2

Step-by-step explanation:

Hi there!

6:4 = 3:2

6*2=3

4*2=2

3:2

What add this /6=25/30

Answers

Answer:5/6

Step-by-step explanation:

simplify

Consider this function. f(x) = -3x +3 Which graph represents the inverse of function f?

Answers

The inverse of the given function is y = 3-x/3. The graph is attached below.

Inverse of a function

Functions are written in terms of variables. Given the linear function

f(x) = -3x + 3

Find the inverse

y = -3x + 3

Replace the variables

x = -3y + 3

Make y the subject of formula

3y = -x + 3

y = 3-x/3

Plot the graph of the resulting function

Learn more on inverse of function here: https://brainly.com/question/3831584

#SPJ1

The data in this table represents a linear function.

What is the slope of this line?

27

13

3

72

x y
2 7
5 16
7 22
9 28

Answers

the answer is 3x :) which is the 3rd option

The equation of a line is given by:

y = mx + c

Where m is the slope.

Slope = (d - b) / (c - a)

Where (a, b) and (c, d) are the two points.

The slope of the linear function is 3.

What is an equation of a line?

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example: y = -3x - 4

Slope = -3 and y-intercept is -4.

We have,

A table that represents a linear function.

x y

2 7

5 16

7 22

9 28

We can have points such as:

(x, y) = (2, 7), (5, 16), (7, 22), and (9, 28)

We can select any two points and find the slope.

(2, 7) = (a, b)

(5, 16) = (c, d)

Slope:

= (d - b) / (c - a)

= 16 - 7 / 5 - 2

= 9 / 3

= 3

Slope = 3

Thus,

The slope of the linear function is 3.

Learn more about equation of a line here:

https://brainly.com/question/23087740

#SPJ5

which of the following describes variance? group of answer choices it is the difference between the maximum value and the minimum value in the data set it is the difference between the first and third quartiles of a data set it is the average of the squared deviations of the observations from the mean it is the average of the greatest and least values in the data set

Answers

Variance is described as the average of the squared deviations of the observations from the mean. It is a measure of the spread or dispersion of a dataset, indicating how much the individual data points deviate from the mean value.

Variance is the anticipated squared variation of a random variable from its population mean or sample mean in probability theory and statistics. Variance is a measure of dispersion, or how far apart from the mean a group of data are from one another. Descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling are just a few of the concepts that make use of variance. In the sciences, where statistical data analysis is widespread, variance is a crucial tool.

More on variance: https://brainly.com/question/14116780

#SPJ11

t/f) the matrix a and its transpose, at, have diﬀerent setsof eigenvalues

Answers

False,Any matrix A has the same eigenvalues as its transpose At.

Help me with question 21 to get brainliest

Answers

Step-by-step explanation:

We can call the original value x. In 2012, the painting's value was 1.05 x. In the beginning of 2013, the value was (1.05 x) * 0.98, and that increased to (1.05x) * 0.98 * 1.40 at the end of 2013. When we simplify, we get 1.4406 x as a value, and we know that this is equal to $52,640. We can write 1.4406x = 52640, and when we solve for x, we get x ≈ $36415.38. Hope this helps!

A ski jump is designed to follow the path given by the parametric equations: x = 3.50t² y = 20.0 +0.120t⁴ - 3.00√t⁴+1 (0≤ t ≤ 4.00 s) where distances are in meters Find the resultant velocity and the acceleration of a skier when t = 4.00 sec.

Answers

The resultant velocity and acceleration of the skier at t=4.00 sec on the ski jump path are 12.8 m/s and 45.9 m/s², respectively.

To find the resultant velocity, first find the velocity vector components using the parametric equations:

vx = 7.00t, vy = 0.48t³ - 6.00t²/√(t⁴+1)

At t=4.00 s, vx = 28.0 m/s and vy = 10.50 m/s. The resultant velocity is the magnitude of the velocity vector, given by:

|v| = √(vx² + vy²) = 12.8 m/s

To find the acceleration vector components, differentiate the velocity vector components with respect to time:

ax = 7.00 m/s², ay = 1.44t² - 12.00t/√(t⁴+1) - 6.00t³(t⁴+1)^(-3/2)

At t=4.00 s, ax = 7.00 m/s² and ay = 45.9 m/s². The acceleration vector magnitude is:

|a| = √(ax² + ay²) = 46.1 m/s².

For more questions like Vector click the link below:

https://brainly.com/question/29740341

#SPJ11

which go's to which.................................

Answers

the matches are

-2(2x+5) ≤ -7(x+4) x<=-6

4x-3x-1 x<=-1

5(x-3)9(x+1) x>=-6

3(x-4)+5 2x-9 x>=-2

What is inequality?

Generally, Inequality is a mathematical statement that compares two values or expressions and indicates whether they are equal or not equal, or which one is greater or smaller. Inequalities are expressed using symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

For example, 5 < 8 is an inequality that indicates that 5 is less than 8, and x + 3 ≥ 7 is an inequality that indicates that the value of x plus 3 is greater than or equal to 7.

Inequalities are commonly used in algebra and other branches of mathematics to represent relationships between quantities.

Answers

We will have the following:

*First: We determine the measure of angle L:

$L+M+N=180\Rightarrow L+90+67=180$$\Rightarrow L=23$

So, the measure of angle L is 23°.

*Second: We will use the measure of MN and the angle of L to determine the length of the hypotenuse:

$8=h\sin (23)\Rightarrow h=\frac{8}{\sin (23)}$$\Rightarrow h=20.47443732\ldots\Rightarrow h\approx20.5$

So, the length of the hypotenus is approximately 20.5 units.

Here is the graph that shows the scenario:

M is a right angle in triangle LMN. The measure of angle Nis 67 and the length of MN is 8.What is the

Some one help me please I’m struggling with 1-2 how do I work it out

Answers

To find volume do bxh =V

X + 2x - 4 = 14 how to solve this

Answers

Answer:

x=6

Step-by-step explanation:

x+2x-4=14

FIRST STEP;

GROUP LIKE TERMS

x+2x-4=14

x+2x=14+4

Then you add

3x=18

Then you divide both sides by 3 to find the value of x

18 can be divided by 3, 6 times so it leaves our answer as;

x=6

E Homework: 11.6 Question 5, 11.6.3 > HW Score O Point Use the product rule to find the derivative of the given function y = (2x3 + 4)(5x - 2) . y'= 0

Answers

The derivative of the function y = (2x³ + 4)(5x - 2) is y' = 40x³ - 12x² + 20. The given function is y = (2x³ + 4)(5x - 2).

We need to find the derivative of the function using the product rule.

Formula of the product rule: (fg)' = f'g + fg'

Where f' is the derivative of f(x) and g' is the derivative of g(x)

Now, let's solve the problem:

y = (2x³ + 4)(5x - 2)

Here, f(x) = 2x³ + 4 and g(x) = 5x - 2

So, f'(x) = 6x² and g'(x) = 5

Now, using the product rule, we can find the derivative of y. The derivative of y is given by:

y' = (f'(x) × g(x)) + (f(x) × g'(x))

Put the values of f'(x), g(x), f(x) and g'(x) in the above formula:

y' = (6x² × (5x - 2)) + ((2x³ + 4) × 5)y'

= (30x³ - 12x²) + (10x³ + 20)y'

= 40x³ - 12x² + 20

To learn more about function, refer:-

https://brainly.com/question/30721594

#SPJ11

a rectangular patio is 9 ft by 6 ft. when the length and width are increased by the same amount, the area becomes 88 sq ft. ginger is using the zero product property to solve the equation (6 x)(9 x)

Answers

Solving the equation (6x)(9x) using the zero product property we get the solution is x = 2.

To find the solution to the equation, we can use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. In this case, the product of (6x) and (9x) is given as 88 square feet. So, we have the equation (6x)(9x) = 88.

To solve this equation, we can first simplify it by multiplying the terms inside the parentheses. (6x)(9x) becomes 54x^2. Now our equation is 54x^2 = 88.

To isolate x, we divide both sides of the equation by 54. This gives us x^2 = 88/54. Simplifying further, we have x^2 = 22/27.

Taking the square root of both sides of the equation, we get x=±√(22/27). However, since the length and width of the rectangular patio are increased, we are only interested in the positive value of x.

Approximating the value of √(22/27), we find that x ≈ 0.832. This value represents the amount by which both the length and width of the patio should be increased to obtain an area of 88 square feet.

Learn more about factors here: brainly.com/question/14549998

#SPJ11

What is a place value chart in maths?

Answers

In mathematics, the place value chart is a tool that helps students understand the value of digits in a number. It is a visual representation of how digits are grouped and arranged to represent numbers. The place value chart is arranged in columns, with each column representing a different place value.

The place value chart starts with the ones place, also called units place. This is the rightmost column and it represents the ones digit in a number. The next column is the tens place, which represents the tens digit in a number. The hundredth place represents the hundreds digit and so on. Each column is ten times larger than the previous one.

A place value chart can be used to understand the value of a digit in a number.

Place value chart also helps to understand decimal numbers, which are numbers that have a decimal point. The decimal point separates the whole numbers from the fractional numbers. Each place to the right of the decimal point represents a smaller value.

to know more about value refer here

brainly.com/question/30145972#

#SPJ11

39 A sample of a substance with an initial mass of 963 grams is decaying
at a rate of 27% per hour.
Create a function that can be used to find y, the mass of the
substance in grams remaining after x hours.
Record your answer in the space provided.

Answers

A function that can be used to find y, the mass of the substance in grams remaining after x hours is $P(x) = 963(0.63)^x$

How to create a function that can be used to find the mass of the substance?

In Mathematics and Statistics, a population or substance that decreases at a specific period of time represent an exponential decay. This ultimately implies that, a mathematical model for any population or substance that decreases by r percent per unit of time is an exponential equation of this form:

$P(x) = I(1 - r)^x$

Where:

P(x) represents the total mass or population.x represents the time or number of years.I represents the initial value of the substance.r represents the decay rate.

By substituting given parameters into the , we have the following:

$P(x) = I(1 - r)^x\\\\P(x) = 963(1 - 0.27)^x\\\\P(x) = 963(0.63)^x$

In conclusion, we can reasonably infer and logically deduce that the decay rate is equal to 63%.

Read more on exponential functions here: brainly.com/question/28246301

#SPJ1

Jared bought 7 cans of paint. A can of red paint costs $3. 75. A can of red paint costs $2. 75. Jared spent $22 in all. How many cans of red and black paint did he buy?

Answers

Jared bought 7 cans of paint. Let the number of red paint cans that Jared bought be x. The number of black paint cans he bought would be 7 - x. A can of red paint costs $3.75 and a can of black paint costs $2.75.

He spent $22 in all. Therefore we can write:3.75x + 2.75(7 - x) = 22 Multiplying out the second term and collecting like terms gives:0.5x + 19.25 = 22Subtracting 19.25 from both sides:0.5x = 2.75Dividing by 0.5:x = 5.5Since Jared can't buy half a can of paint, we should round the answer to the nearest integer. Hence, he bought 5 cans of red paint and 2 cans of black paint. The total cost of the 5 cans of red paint would be 5 x $3.75 = $18.75.The total cost of the 2 cans of black paint would be 2 x $2.75 = $5.50.The total cost of all 7 cans of paint would be $18.75 + $5.50 = $24.25.We spent more than Jared's budget. The value of $24.25 exceeds Jared's budget of $22. Hence, there is a problem with this problem statement.

Learn more about the number here:

https://brainly.com/question/24627477

#SPJ11

Helpppppppppp plssss

Answers

Answer:

An is A and E

Plsss mark as brainliest

HURRY PLS ANSWER NOW!!

What is the area of the trapezoid?

33 in2
52.5 in2
82.5 in2
91 in2

Answers

Answer:

91 in2

Step-by-step explanation:

11+15 over 2 , times by 7 equals 91 ??

I have the answers I just need someone to work it out I’ll mark as brainlesttt

Answers

Answer:

Look Below

Step-by-step explanation:

The formula for a circle is πr².

Therefore, we can divide the area of the circle by 3.14, and then square root it. 490.63/3.14=156.25... If you square root that, you get 12.5. Same thing with the other circle. 219.45/3.14=69.888... If you square root that, you get 8.36. Now that we have the radius, we can multiply that by two to find the diameter. And we're done.

Feel free to tell me if I did anything wrong! :)

1.Which triangle are acute 2.Which triangles are obtuse 3.Which triangles are scalene 4.Which triangles are isosceles 5.Which triangles are equilateral? 6.Which are right triangles?

Answers

Answer:

1.C

2.D

3.all angles need to be different

4.A

5.E

6.B

Step-by-step explanation:

write 402 base five in words

Answers

Answer:

three thousand one hundred and two

Step-by-step explanation:

three point seven two five eight

brainiest please

if a = b and b = c then a = c. true or false

Answers

Answer: true

Step-by-step explanation:

Answer: True

Step-by-step explanation: Has to be true if a b and c are all numbers

Other Questions

how do i give answers The standard normal curve shown below models the population distributionof a random variable. What proportion of the values in the population doesnot lie between the two scores indicated on the diagram?0.15O A.0.3148B. 0.3097C. 0.3025D. 0.3234O E, 0.3310 how to wash a car inside/out Which statement best describes the contrast between Wendell and his friend anas perspective in seedfolks On June 10, Marigold Company purchased $8,150 of merchandise on account from Grouper Company, FOB shipping point, terms 3/10, n/30. Marigold pays the freight costs of $420 on June 11. Goods totaling $650 are returned to Grouper for credit on June 12. On June 19. Marigold pays Grouper Company in full, less the discount. Both companies use a perpetual inventory system. (a) Prepare separate entries for each transaction on the books of Marigold Company. (Credit account titles are automatically indented when amount is entered. Do not indent manually. If no entryls requifed, select "No Entry" for the occount titles and enter of for the amounts. Record joumal entries in the order presented in the problem.) How does Mr. Frank feel about having Mr. Dussel with them? How does Mr. Van Daanfeel about it? explain how afrikaner nationalism developed against the background of urbanization industrialisation demand of black people in the city the ""o"" in the mnemonic sport for the principles of training means how did four american presidents extend influence throughout the world between 1897 and 1917 Give two reasons why you think it is important for Muslims to pray 5 times a day What are three things that the Greeks contributed to Western European music? ........................................................... When we experience an unpleasant state of tension between two or more conflicting thoughts, we are experiencing. which best describes how a binary search works? binary searches start at the beginning and check each item as it walk through the list binary searches start at the beginning and check every other item until it finds a value greater than the search, then goes back if needed. binary searches start in the middle and eliminate half of the list in each iteration until the desired value is found. binary searches split the list in half and creates a dual process to check each half of the list at the same time. it's A I got it on edge What is the value of p in this proportion?310p=4514Enter your answer as a simplified fraction in the box. quantity theory of money is based on the classical theory. accordingly, there is a direct relationship between the price level and nominal supply. true or false A sack contains 180 oranges and 65 mangoes. Find the ratio of mangoes to oranges Hi, i need to calculate roots x1 and x2 using the vieta theorem, can anyone help me? I have found the answer (1,5 ;2), all i need is a solution on how to get this answer, the equation is in the picture, will give you brainliest if you type down the correct solution for me, thanks. I need help Como se dice: "I share"? Make sure you include the correct pronoun or it will be counted wrong