What is the derivative of ln(x∧2+1) at x=1 ?

Answers

Answer 1

The derivative of ln(x^2+1) at x=1 is 2/2 = 1.

To find the derivative of ln(x^2+1), we can use the chain rule. Let's denote the function as y = ln(u), where u = x^2+1. The chain rule states that if y = ln(u), then dy/dx = (1/u) * du/dx.

First, let's find du/dx. Since u = x^2+1, we can differentiate it with respect to x using the power rule, which states that d/dx (x^n) = n*x^(n-1). Applying the power rule, we get du/dx = 2x.

Now, we can substitute the values into the chain rule formula. dy/dx = (1/u) * du/dx = (1/(x^2+1)) * 2x.

To find the derivative at x=1, we substitute x=1 into the derivative expression. dy/dx = (1/(1^2+1)) * 2(1) = 1/2 * 2 = 1.

Therefore, the derivative of ln(x^2+1) at x=1 is 1.

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Related Questions

how to multiply fractions with the same denominator

Answers

when multiplying fractions , multiply across the numerator and denominator

you dont need common denominators

example

\(\frac{1}{2}*\frac{4}{5}=\frac{1*4}{2*5}\)

Hope this helps : -)

- Jeron

f(x) = x^2 - 4x + 4 in standard from.

Answers

Answer:

Step-by-step explanation:

ax + bx +c = 0

x^2 + (-4) x = 4

what is the value of 8^-1/3

Answers

Answer:

2

Step-by-step explanation:

cube root of 8

The average of 20 numbers is 75. The number 86 was incorrectly read as 68 while calculations. Find the correct average

Answers

The answer is in the photo

Answer:

79.7

Step-by-step explanation:

average = 20x75=1440

wrong average68+86=154

correct average 1440+154/20=79.7

hope this is correct.

simplify the following
√2×√18

Answers

root 2 x root 18 is root 36
the square root of 36 is 6
so your answer is 6
hope that helps!

what is closet to the lateral surface area of a cylinder with a height of 12 inches and a radius of 3 inches

Answers

The formula for the lateral surface area of a cylinder is 2πrh, where r is the radius and h is the height. Plugging in the given values, we get:

Lateral surface area = 2π(3)(12) = 72π
Rounded to the nearest whole number, the lateral surface area of the cylinder is 226.


To find the lateral surface area of a cylinder, you can use the formula:

Lateral Surface Area (LSA) = 2 × π × radius × height

Given that the height of the cylinder is 12 inches and the radius is 3 inches, you can plug these values into the formula:

LSA = 2 × π × 3 × 12

LSA = 6 × π × 12

LSA ≈ 6 × 3.14 × 12

LSA ≈ 226.08 square inches

So, the lateral surface area of the cylinder is closest to 226.08 square inches.

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Explain how to find the asymptotes of the function h(x) = 4 +
(5/x)
(I know the horizantal one is 4 and the vertical one is 0, but
explain how to find it)

Answers

Asymptotes are lines that a curve approaches but does not intersect. A curve may have vertical, horizontal, or slant asymptotes or none at all. Asymptotes are critical features of the curve since they are used to help graph the function.

We will use the following steps to find asymptotes of the function h(x) = 4 + (5/x):

Vertical Asymptotes:Vertical asymptotes occur when the denominator is equal to zero. So for the function

h(x) = 4 + (5/x), the denominator x cannot be equal to 0.

Therefore x = 0 is the equation of the vertical asymptote.Horizontal Asymptotes:

Horizontal asymptotes occur when the value of y approaches a constant as x becomes extremely large.

For the function h(x) = 4 + (5/x), we need to take the limit as x approaches infinity and as x approaches negative infinity respectively.

(i) As x approaches infinity,y = 4 + 0= 4(ii) As x approaches negative infinity,y = 4 + 0= 4.

Therefore, the equation of the horizontal asymptote is y = 4.

Finally, the vertical asymptote equation is x = 0, and the horizontal asymptote equation is y = 4 for the function h(x) = 4 + (5/x).

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You are remodeling your kitchen. You've contacted two tiling companies who
gladly told you how long it took their workers to tile a floor of a similar size.
Jim completed half the floor in 9 hours. Pete completed the other half of the
floor in 5 hours. If Pete can lay 35 more tiles per hour than Jim, what equation
would you use to find the rate that Jim can lay tiles? Let x represent Jim's
rate.
A. 5x - 9(x-36)
B. 5x - 91% +35)
C. 9x - 5(x-36)
D. 9x - 5(x +35)

Answers

Answer:

The correct answer would be D

9x=5(x=35)

Step-by-step explanation:

If this doesn't help I can fix it. I'm sorry in advance if it is incorrect.

Charlie is studying the time it takes members of his company to travel to the office.

He stands by the door to the office from 0840 to 0850 one morning and asks workers, as they arrive, how long their journey was.

State the sampling method Charlie used.

Answers

Charlie could have used quota sampling instead of non-random sampling.

What are sampling methods?Sampling means selecting the group that you will actually collect data from in your research. For example, if you are researching the opinions of students in your university, you could survey a sample of 100 students

Given is that Charlie is studying the time it takes members of his company to travel to the office. He stands by the door to the office from 08 : 40 A.M. to 08 : 50 A.M. one morning and asks workers, as they arrive, how long their journey was.

Charlie could have used quota sampling instead of non-random sampling. He could have selected a sample that reflects the characteristics of the whole population.

Therefore, Charlie could have used quota sampling instead of non-random sampling.

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{COMPLETE QUESTION IS -

Charlie is studying the time it takes members of his company to travel to the office.

He stands by the door to the office from 0840 to 0850 one morning and asks workers, as they arrive, how long their journey was.

State and briefly describe an alternative method of non-random sampling Charlie could have used to obtain a sample of 40 workers.}

Select the correct answer from each drop-down menu.

The scatter plot shows the association between the population of various states in the United States and the number of cellular phone users in those states.

The association between the population and the number of cellular phone users is
and . If you were to add the following data to the scatter plot, the association would be

.
Population Cellular Phones
State A 23 million 16 million
State B 12 million 10 million

Select the correct answer from each drop-down menu.The scatter plot shows the association between the

Answers

As per the scatter plot the association between the population of various states in the US and the number of cell phone users is strong, weak, and moderate. Thus option One is correct.

What is a scatter plot?

A scatter plot is a scatter graph that shows and compares the individual values and correlates them with the variables.

Here the case of cell phones in the US is shown as strong as the line is positively correlated and more than half of the people use cell phones thus it's moderate.

Find more information about the scatter plot.

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Answer:

strong

positive

the same

Step-by-step explanation: read the question instead of just copying and pasting into another tab its really simple. Strong because all the dots are really close to each other, positive becasue the dots are leading up, and the same because its literally the same if you put them 2 dots on

EDMENTUM this will correct

brebjfhewiufhuhrehoiwhewiueweobnwqjkfrjoighrf.

Answers

Duristegesbebewsnakawyhoenvefegsysrwiwhwbkkfiren

PLZZZZZZZZZ HELP!!!!!!!!!!
How many angle measurements do you need to figure out the measurements of all the labeled angles in the figure below?


A

1


B

2


C

3


D

4

PLZZZZZZZZZ HELP!!!!!!!!!! How many angle measurements do you need to figure out the measurements of

Answers

Answer:

it’s A

Step-by-step explanation:

i took it on flocabulary

Answer:

lolzz i just got that question. it's A

Step-by-step explanation:

hope ya have a good day

What does the word “flip” tell you to do in “keep change flip” for dividing fractions a) change the place of the numbers numerator and the denominator for the first fraction b) change the places of the numbers in the numerator and the denominator for the second fraction c) change the places of the numbers in the numerator and the denominator for both fractions d) change the ÷ between the fractions

Answers

Answer:

b) change the places of the numbers in the numerator and the denominator for the second fraction

Step-by-step explanation:

In the phrase "keep change flip":

You "keep" the first fraction.

"Change" the division sign into a multiplication sign.  

"Flip" (or switch) the places of the numerator and denominator in the second fraction.

Example:

\(\frac{1}{2}\) ÷ \(\frac{1}{3}\)

\(\frac{1}{2}*\frac{3}{1}=\frac{3}{2}=1.5\)

Hope this helps.

To KeianaLol thanks :)

To KeianaLol thanks :)
To KeianaLol thanks :)
To KeianaLol thanks :)
To KeianaLol thanks :)
To KeianaLol thanks :)

Answers

Answer:

PAGE 1

3.) d

4.) e

PAGE 2

5.) a

6.) e

PAGE 3

1.) b

2.) d

PAGE 4

7.) Graph C

8.) Graph B

PAGE 5

9.)  Dilation with the center at the origin and a scale factor of 2.

10.) Dilation with the center at the origin and a scale factor of 1/3.

Step-by-step explanation:

PAGE 1

3.)  d

b/c the rule for x-axis is (x,y) --> (x, -y)

One of the points is (1, 1) ==> (1, -1)

4.) The rule for y-axis is (x, y) --> (-x, y)

A(-5, 3) --> A'(5, 3)

B(2, 6) --> B'(-2, 6)

C(-1, -7) --> C'(1, -7)

PAGE 2

5.) The rule for x-axis is (x,y) --> (x, -y)

A(-5, 3) ---> A'(-5, -3)

B(2, 6) ---> B'(2, -6)

C(-1, -7) ---> C'(-1, 7)

6.) The rule for 90 degrees clockwise is (x, y) --> (y, -x)

B(3, 4) ---> B'(4, -3)

PAGE 3

1.) On the transitions right is positive and left is negative

So 2 units to the right = +2

And 9 units down = - 9

So (x, y) --> (x + 2, y - 9)

2.) A is wrong b/c that translation is (x, y) ---> (x + 3, y -3)

B is wrong b/c the translation is (x, y) ---> (x + 3, y + 3)

C is wrong b/c the translation is (x, y) ---> (x - 3, y + 3)

D is correct b/c the translation is (x, y) --->(x -3 , y -3)

A(6, 6) --> A'(3, 3)   B(7, 4) --> B'(4, 1)    C(4, 4) --> C'(1, 1)

PAGE 4

7.) The rule for 90 degrees rotation counterclockwise is (x, y) --> (-y, x)

The correct graph would show A(-3, 3) ----> (-3, -3)

The only graph that shows this is Graph C

8.) The rule for 180 degrees rotation is (x, y) ----> (-x, -y)

The correct graph would show A(-3, 3) ----> A'(3, -3)

Graph B is the only one that ALL the angles follow this rule

PAGE 5

9.) It is Dilation with the center at the origin and a scale factor of 2.

B/c --> A(3, 3) ---> A'(6, 6)     B(2, 0) ---> B'(4, 0)    C(5, 2) ---> C'(10, 4)

(3*2= 6, 3*2=6)     (2*2= 4, 0*2= 0)      (5*2= 10, 2*2= 4)

10.) It is Dilation with the center at the origin and a scale factor of 1/3

B/c ---> A(-3, 6) --> A'(-1, 2)   B(12, 3) ----> B'(4, 1)   C(-6, -6) ---> C'(-2, -2)

(-3*1/3= -1, 6*1/3= 2)         (12*1/3= 4,  3*1/3= 1)        (-6*1/3= -2, -6*1/3= -2)

Hope this helps ya!!!

At a college the scores on the chemistry final exam are approximately normally distributed, with a mean of 77 and a standard deviation of 10. The scores on the calculus final are also approximately normally distributed, with a mean of 83 and a standard deviation of 14. A student scored 81 on the chemistry final and 81 on the calculus final. Relative to the students in each respective class, in which subject did the student do better?
a. None of these
b. Calculus
c. Chemistry
d. There is no basis for comparison
e. The student did equally well in each course

Answers

The student's z-score in chemistry (0.4) is larger than their z-score in calculus (0.143),  student did better in chemistry relative to the students in the chemistry class. Therefore, the answer is (c) Chemistry.

To determine in which subject the student did better relative to the students in each respective class, we can compare the z-scores for the student's scores in chemistry and calculus.

For the chemistry final:

Mean (μ) = 77

Standard Deviation (σ) = 10

Student's Score (x) = 81

The z-score for the chemistry score can be calculated using the formula:

z = (x - μ) / σ

z_chemistry = (81 - 77) / 10 = 0.4

For the calculus final:

Mean (μ) = 83

Standard Deviation (σ) = 14

Student's Score (x) = 81

The z-score for the calculus score can be calculated using the same formula:

z = (x - μ) / σ

z_calculus = (81 - 83) / 14 = -0.143

Comparing the absolute values of the z-scores, we can see that |z_chemistry| = 0.4 and |z_calculus| = 0.143. The larger the absolute value of the z-score, the better the student performed relative to the class.

In this case, the student's z-score in chemistry (0.4) is larger than their z-score in calculus (0.143), indicating that the student did better in chemistry relative to the students in the chemistry class. Therefore, the answer is (c) Chemistry.

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A cylinder has a radius of 2.5meters. Its volume is 37.5\pi cubic meters. What is the height of the cylinder?

Answers

Answer: height = 1.91 m

Step-by-step explanation: Using the formula

V=πr2h

Solving for h

h=V

πr2=37.5

π·2.52≈1.90986m

Data where the difference between data values has meaning but there is no defined starting point

Answers

Examples of such data include stock prices, economic indicators, and meteorological data such as temperature, wind speed, and barometric pressure.

These types of data often have a trend or pattern, but the difference between the data points has meaning and does not necessarily have a defined starting point.

1. Data where the difference between data values has meaning but there is no defined starting point can be defined as data that is not linearly dependent.

2. Examples of such data include stock prices, economic indicators, and meteorological data. These types of data often have a trend or pattern, but the difference between the data points has meaning and does not necessarily have a defined starting point.

3. Stock prices, economic indicators, and meteorological data all have different scales and can move in different directions, making it difficult to track the exact difference between data points.

4. Despite this, these types of data still allow for meaningful analysis and can be used to make predictions and draw conclusions.

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the aspect ratio of a wide screen tv is 2.39:1. what is the length of the diagonal of a wide screen tv screen with an area of 150 in??

Answers

The length of the diagonal of a wide screen TV with an area of 150 inches and an aspect ratio of 2.39:1 is approximately 11.25 inches.

Aspect ratio refers to the proportional relationship between the width and height of an image or screen. In the case of a wide screen TV, the aspect ratio is 2.39:1, which means that for every 2.39 units of width, there is 1 unit of height.

To find the length of the diagonal of a wide screen TV with an area of 150 inches, we need to use the Pythagorean theorem, which states that the square of the length of the diagonal is equal to the sum of the squares of the width and height.

First, we need to find the width and height of the TV screen. We can do this by setting up the equation:

2.39x^2 = 150

where x is the width of the screen. Solving for x, we get:

x = √(150/2.39) = 10.87 inches

Now we can find the height by dividing the width by the aspect ratio:

h = 10.87 / 2.39 = 4.55 inches

Using the Pythagorean theorem, we can find the length of the diagonal:

d^2 = 10.87^2 + 4.55^2 = 126.68

d = √126.68 = 11.25 inches

Therefore, the length of the diagonal of a wide screen TV with an area of 150 inches and an aspect ratio of 2.39:1 is approximately 11.25 inches.

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A firm is evaluating a proposal which has an initial investment of $35,000 and has cash flows of $10,000 in year 1, $20,000 in year 2, and $10,000 in year 3. The payback period of the project is ________.

Answers

The payback period of the project is 2 years.

The payback period is a financial metric used to evaluate the time it takes for an investment to recoup its initial cost. It measures the length of time required for the cash inflows from the investment to equal or surpass the initial investment amount. In this case, the initial investment is $35,000, and the cash flows are $10,000 in year 1, $20,000 in year 2, and $10,000 in year 3. To calculate the payback period, we need to determine in which year the cumulative cash inflows will equal or exceed the initial investment.

By adding the cash flows year by year, we can see that at the end of year 1, the cumulative cash inflow is $10,000. By the end of year 2, the cumulative cash inflow becomes $30,000 ($10,000 from year 1 + $20,000 from year 2). Finally, at the end of year 3, the cumulative cash inflow reaches $40,000 ($10,000 from year 3).

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1/3 + 5 3/4
HELP!! PLEASE!!!

Answers

The answer is 73/12.

Answer:

\(6 \frac{1}{12}\)

Step-by-step explanation:

1) Use Least Common Denominator or (LCD)

LCD = 12

2) Make the denominators the same as the LCD.

\(5 + \frac{1 times 4 }{3 times 4 } + \frac{3 times3}{4times 3}\)

3) Simplify. Denominators are now the same.

\(5 + \frac{4}{12} +\frac{9}{12}\)

4)  Join the denominators.

\(5+ \frac{4+9}{12}\)

5)  Simplify.

\(5+\frac{13}{12}\)

6) Convert 13/12 into a mixed number.

\(5+ 1 \frac{1}{12}\)

7)  Simplify.

\(6 \frac{1}{12}\)

Decimal Form: 6.083333

a person jogs eight complete laps around a quarter-mile track in a total time of 12.5 min. determine the total distance in meter (1 mile

Answers

8 laps time 1/4 mile is 2 miles .

Average speed in miles per hour:

2 mi / 12.5 min * 60 min/hour = 9.6 mph

Average velocity is zero, since velocity is directional and the person jogged around a track. [I mention that in case this was set up as a trick question.]

But if we're really looking for average speed in m/s we can easily convert:

A mile is about 1.6 km, so it's about 1600 m.

(2 mi * 1600 m/mi) / (12.5 min * 60 s/min) = 1800 / 750 = 2.4 m/s

The directional speed of an item in motion, as measured by a specific unit of time and observed from a certain point of reference, is what is referred to as velocity.

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What did she do wrong? What can she do to prevent this?

What did she do wrong? What can she do to prevent this?

Answers

Answer:

y = 8x + 14  (8x is WRONG)

This is how it is supposed to be

y - 2 = 6x + 12

y = 6x + 14

She must combine like terms, not unlike terms

A line with a slope of -2 passes through the point (4, 7). Write an equation for this line in point-slope form.
Y-7= fill in the answer (x- fill in the answer)

Answers

Answer:

\(\boxed {\boxed {\sf y-7= -2 (x-4)}}\)

Step-by-step explanation:

We have a point and the slope, so we can use the point-slope formula.

\(y-y_1=m(x-x_1)\)

Where m is the slope and (x₁, y₁) is the point the line passes through.

We know the slope of the line is -2 and the point it passes through is (4, 7).

m= -2 x₁= 4y₁= 7

Substitute the values into the formula.

\(y-7= -2 (x-4)\)

We are asked to write the equation in point-slope form, so this is our final answer.

The equation of the line in point-slope form is: y-7= -2 (x-4)


help i’ll give Brain :(

help ill give Brain :(

Answers

Answer:

1, 4 and 5

Step-by-step explanation:

yup one, four, and five

The independent variable of a boxplot is:
O a reference stream
O continuous
O the Oregon ∣BI
O categorical

Answers

The independent variable of a boxplot is categorical. This means that variable used to create boxplot consists of distinct categories rather than continuous numerical values. The boxplot allows to visualize and compare the distribution of a quantitative variable across different categories .

In statistical analysis, the independent variable is the variable that is manipulated or controlled in order to observe its effect on the dependent variable. In the case of a boxplot, the independent variable is typically a categorical variable. This means that it consists of distinct categories or groups that are not inherently ordered or continuous.

For example, in a study comparing the heights of individuals from different countries, the independent variable would be the country itself, which is a categorical variable. The heights of individuals would be the dependent variable, and the boxplot would show the distribution of heights for each country.

By using a boxplot, we can easily compare the distribution of a quantitative variable across different categories or groups and identify any differences or patterns that may exist. It provides a visual summary of the minimum, first quartile, median, third quartile, and maximum values within each category, allowing for easy comparisons and identification of outliers.

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Ideally, an attack urface i ___

1. Open and defended. 2. A mall a poible. 3. Frequently updated. 4. A large a poible

Answers

Ideally, an attack urface is defined as A large a possible Entries

What is An Attack Surface ?

The entire number of potential points of entry for unauthorised access into any system is known as the attack surface. It includes every endpoint and vulnerability that can be used to launch a security attack. The total region of a system or organisation that is vulnerable to hacking is often referred to as the attack surface.

Concept:

The attack surface of any system refers to all possible points of entry for unauthorised access. Each endpoint and security hole that can be exploited to launch a security attack are included.

The attack surface is vast and complicated for the majority of modern enterprises. There are numerous potential cyber security concerns due to the rising number of gadgets, web apps, and network nodes.

Despite their best efforts, IT leaders are only able to see a portion of the security dangers that their company faces.

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The ordered pairs in the table below represent a linear function
Х
y
2
6
9
8
What is the slope of the function?

Answers

Answer:

2/7

Step-by-step explanation:

Assuming the table is

x         y

2          6

9           8

We have points ( 2,6) and (9,8)

We can use the slope formula

m = ( y2-y1)/(x2-x1)

   = ( 8-6)/(9-2)

   = 2/7

The number of pounds can be safely loaded onto an elevator, x, can be represented by the inequality x _> 1,200. Which number line correctly represents the inequality.

Sorry i can't show u the diagram just try i will give u alot of points

Answers

The number line correctly represents the inequality, shown in the graph.

What is a number line?

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

Here,
The inequality x ≥ 1,200 represents the number of pounds that can be safely placed onto an elevator.

So the number line is given as x ≥ 1200, a shaded line beyond the integer 1200 on the number line.

Thus, the number line accurately depicts the inequality depicted in the graph.

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The number of pounds can be safely loaded onto an elevator, x, can be represented by the inequality x

The line segment between (9,6) and (-2,-1) is bisected at (3.5,2.5). Find the y-intercept of the perpendicular bisector.

Ans: y-intercept = (0, _____)

Answers

Answer:

Y-intercept is (0,8)

Step-by-step explanation:

Firstly, we need to get the equation of the line segment

We have the general equation as;

y = mx + b

m is the slope and b is the y-intercept

So for the slope between (9,6) and (-2,-1); we have

m = (y2-y1)/(x2-x1)

m = (-1-6)/(-2-9) = -7/-11 = 7/11

Mathematically, when two lines are perpendicular, their slopes have a product of -1

Let the slope of the second line be m

m * 7/11 = -1

7m = -11

m = -11/7

The equation of the second line is;

y = mx + b

y = -11x/7 + b

The line passes through the point (3.5,2.5)

So,

2.5 = -11/7(3.5) + b

2.5 = -5.5 + b

b = 2.5 + 5.5

b = 8

so the y-intercept of the perpendicular bisector is 8

Luke is designing a scale model of a clock tower. The design of the front of the tower is shown below. What will be the area of the front face of his model? 2,500 square millimeters 10,000 square millimeters 12,500 square millimeters 15,000 square millimeters

Answers

The image of the front of the tower is missing, so i have attached it.

Answer:

Option B - 10,000 square millimeters

Step-by-step explanation:

From the image attached, we see that the dimensions of the front of the tower are;

Length; L = 200 mm

Width; w = 50 mm

Now, this front face takes the shape of a rectangle.

Area of rectangle = Length x width

Thus, plugging in the values of length and width, we will get;

Area of front face = 200 x 50

Area of front face = 10,000 square millimeters

Luke is designing a scale model of a clock tower. The design of the front of the tower is shown below.

Answer:

12,500 mm^2

Step-by-step explanation:

50 x 200 = 10,000 mm

(300 - 200 = 100) 100 x 50 x 1/2 = 2,500 mm

10,000 + 2,500 = 12,500 mm^2

Other Questions
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