39-42 Differentiate [tex]f[/tex] and find the domain of [tex]f\text{.}[/tex]
39. [tex]f(x)=\frac{x}{1-\ln (x-1)}[/tex]

Answers

Answer 1

[tex]\text{Given that,}\\\\f(x) = \dfrac x{1- \ln (x-1)}\\\\\\f'(x)=\dfrac{(1- \ln(x-1))-x\cdot \left(0-\dfrac 1{x-1} \right)}{(1- \ln(x-1))^2}\\\\\\~~~~~~~~= \dfrac{(x-1)(1- \ln(x-1))+x}{(x-1)(1-\ln(x-1))^2}\\\\\\~~~~~~~~= \dfrac{x-x\ln(x-1)-1+\ln(x-1)+x}{(x-1)(1-\ln(x-1))^2}\\\\\\~~~~~~~~= \dfrac{2x-1-(x-1)\ln(x-1)}{(x-1)(1-\ln(x-1))^2}\\[/tex]

[tex]\text{domain f(x):} ~\{x|x > 1, x\neq e+1 \}[/tex]


Related Questions

I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER

Answers

Answer:

227

Step-by-step explanation:

Since they give you the hypotenuse length of 290in and they ask you to find the length os the adjacent angle, use the cosine to find side b.

So you do tan38=b/290 then calculate.

The true answer is 226.5728 but they ask you to round.

Write 8 statements and reasons for the proof

Answers

Answer:

Step-by-step explanation:

mr jones told his students they each need half of a piece of paper calvin cut his piece of paper horizontally and mathew cut his piece of paper diagonally which student has the larger area on his half piece of paper

Answers

Answer:

Both

Step-by-step explanation:

After cutting the paper, both Calvin and Matthew have the same area. Calvin cut his into two rectangles that are each half the area of the original piece of paper. Matthew cut his paper into two equivalent right triangles that are also half the area of the original piece of paper.

Celia bought a bag of 12 goldfish for $3.

What is the cost of 1goldfish?

Answers

Answer:

0.25

Step-by-step explanation:

Answer:

0.25

Step-by-step explanation:

3÷12=0.25

12 goldfish for $3

Analyze the diagram below and complete the instructions that follow.
8

Find the value of y.
A. y = 2
B. Y=4sqrt3/3
C. y = 4
D. Y=4sqrt3

Answers

Answer:

y = 4

Step-by-step explanation:

Thewtriangle on the right side has a 90° angle and a 30°, so the third angle is 60°. That makes the triangle a 30-60-90 right angle. The short leg is half the length of the hyptenuse.

y = 8/2 = 4

Answer: C. y = 4

The direct route from Marta's apartment to work is a road that is a straight line. The road is closed for repairs. Marta had to drive 8 miles west and then 6 miles south to get to work. She returned home by the same route. How many miles would she have saved round-trip if she had taken the direct route?

Answers

She would have to take 5.29 miles to save round-trip if she had taken the direct route.

What is the Pythagoras theorem?

The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.

The direct route from Marta's apartment to work is a road that is a straight line. The road is closed for repairs.

Marta had to drive 8 miles west and then 6 miles south to get to work. She returned home by the same route.

Let's consider x to be the direct route.

By Pythagoras theorem, we can find the direct route

[tex]x^{2} = 8^{2} +6^{2} \\\\x^{2} = 64 - 36\\\\x^{2} = 28\\\\x= \sqrt{28} \\\\x= 5.29[/tex]

Thus, She would have to take 5.29 miles to save round-trip if she had taken the direct route.

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34.321 greater than 34.3211

Answers

Answer:

It's not

Step-by-step explanation:

To know this, you have to put a zero to the right.

So it'd be 34.3210, and as you can see, 34.3211 is greater

A 2-cup bottle of glass cleaner costs $9.12. What is the price per fluid ounce

Answers

Answer:

$0.57

Step-by-step explanation:

In one cup there are eight fluid ounces

To find the cost per fluid ounce all you have to do is divide the price by how many ounces]

To find ounces= 2x8=16

To find price per ounce 9.12/16= .57

In the given figure x = 145°. What theorem can be used to prove the lines p and q are parallel?

A) Same side interior angles converse theorem
B) Corresponding angles converse theorem
C) Alternate exterior angles converse theorem
D) Alternate interior angles converse theorem​

Answers

C alternate exterior angles converse theorem

When two lines are parallel the alternate exterior angles are congruent

Can y’all help me pls

Answers

Answer:Sure, what do you need help with

Step by step explanation:

Sure, what do you need help with

Find the surface area of the cylinder. Round your answer to the nearest tenth.

Answers

yo wheres the cylinder

The directions on a box of Luigi’s Pizza Mix are as follows: Spread the dough to the edges of a circular pan or a 10-inch by 14-inches rectangular pan. You will need to use the following formulas to answer the questions below. For a circle: A = πr2 where π = 3.14C = 2πr For a rectangle: A = lw P = 2l + 2w a. If you used the same amount of dough, how large a circular pan would you need to make a pizza of the same area and thickness as one made in the rectangular pan? *

Answers

The circular pan must have a radius of 6.68 inches.

How large a circular pan would you need?

The area of the circular pan just be the same as the area of the rectangular pan.

The rectangular pan is 10in by 14 in, so its area is:

A = 10in*14in = 140in^2

Then the circular pan must have an area:

A' = 3.14*r^2 = 140in^2

We can solve this for r:

r = √(140in^2/3.14) = 6.68 in

The circular pan must have a radius of 6.68 inches.

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Larissa spent $280 per month on
clothes and a total of $2,920 for food
and entertainment during the last
5 months. How much should Larissa
expect to pay for clothes, food, and
entertainment in 1 year?

Answers

Answer:

Larissa would spend a total of: $7,680 in 1 year

Step-by-step explanation:

9408, you would take the 2920 and divide it by 5, 584, and add that to 280, which is 784, multiply 784 times 12 and u get 9408

Factor the expression using the greatest common factor 16x + 12y​

Answers

Answer:

4(4x + 3y)

Step-by-step explanation:

Given expression:  16x + 12y

Factors of 16:  1, 2, 4, 8, 16

Factors of 12:  1, 2, 3, 4, 6, 12

Therefore, the greatest common factor of 16 and 12 is 4.

As the expression has two variables, the variables cannot be factored.

Therefore, factored expression:  4(4x + 3y)

16x+12y

Factor each

16x=4×4x12y=4×3y

Take 4 common as GCF

16x+12y4(4x+3y)

Brainliest for who can help!!

Answers

I think it's like this.

Hope this helps

The equation of the trend line is y = −0.36x + 12.6.
Use the equation of the trend line to predict the wind chill for a wind speed of 33 mi/h. Round your answer to the nearest degree.

Answers

Answer:

−1\°

Step by step explation:

Let

x -----> the wind speed in mi/h

y ----> the wind chill in °F

we have

y=-0.36x+12.6y=−0.36x+12.6

so

For x=38 mi/h

substitute in the linear equation and solve for y

y=-0.36(38)+12.6=-1.08\°y=−0.36(38)+12.6=−1.08\°

Round to the nearest degree

-1.08=-1\°−1.08=−1\°

urgent help please! ^^ <3

Answers

Answer:

Lower quartile = 6

Median = 8

Upper quartile = 9

Step-by-step explanation:

If you take away a number from each end of the number set one by one, you will end up with 7 and 9 in the middle. To find the median between two numbers, add them together then divide them by 2.

7 + 9 = 16

16 ÷ 2 = 8

_________________

To find the lower and upper quartiles, split the number set into two where the median is, then, find the median of those two sections.

Lower quartile: 4, 5, 6, 6, 7

Median = 6

-

Upper quartile: 9, 9, 9, 9, 9

Median = 9

So, the median of the whole set is 8, the lower quartile is 6, and the upper quartile is 9.

hope this helps!

Witch number is a common factor of 25 and 40?
A) 2
B) 4
C) 5
D) 10

I will give Brainlyest only for correct answers. :)

Answers

The answer I think is C) 5

Answer:

The answer is 5.

Step-by-step explanation:

The answer is 5 because 5x8 and 5x5.  find the greatest common factor by matching the biggest common factor of 25 and 40.This is why the answer is 5.

Step 1: 25 = 5[tex]^2[/tex]

Step 2: 40 = [tex]2^{3}[/tex] × [tex]5^{1}[/tex]

Step 3: List of positive integer factors of 25 that divides 25 without a remainder. That is 1 and 5

Step 4: List of positive integer factors of 40 that divides 25 without a remainder. 1, 2, 4, 5, 8, 10, 20

Step 5: We found the factors and prime factorization of 25 and 40. The biggest common factor number is the GCF number.

So the greatest common factor 25 and 40 is 5.

Estimate how many times larger 5*10^8 is than 24*10^6.
A) 10 times
B) 20 times
C) 50 times
D) 100 times

Answers

Answer:

10 times

Step-by-step explanation:

What is the value of x

Answers

Answer:

your answer is 20.

Step-by-step explanation:

x^2+4^2=(2+x)^2

A circle has a diameter of 32 ft. What is its circumference?
Use 3.14 for 1, and do not round your answer. Be sure to include the correct unit in your ans
0
32 ft

Answers

Given -

diameter of circle = 32ft

To find -

the circumference of the circle

Explanation -

As we know, circumference of the circle = 2πr

where r signifies the radius of the circle. And radius if half of the diameter, i.e, r = d/2

Solution -

Circumference of the circle = 2πr

r = 32/2 = 6

Substituting the value of r,

Circumference of the circle = 2 × 3.14 × 6

Circumference of the circle = 12 × 3.14

Circumference of the circle = 37.6 ft

Therefore, the the circumference of the circle is 37.6 ft.

Ayden is 1.85 meters tall. At 2 p.m., he measures the length of a tree's shadow to be 39.55 meters. He stands 35.4 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.

Answers

The height of the tree is 4.15m

We are given that

Height of Joshua, h=1.85 m

Length of tree's shadow, L=39.55 m

Distance between the tree and Joshua=35.4 m

We have to find the height of the tree.

BC=35.4 m

BD=39.55m

What is the height?

CD=BD-BC

CD=-35.4 m=4.15 m

EC=1.45 m

All right triangles are similar. When two triangles are similar then the ratio of their corresponding sides is equal.

[tex]\triangle ABD=\triangle ECD[/tex]

[tex]\frac{AB}{EC}=\frac{BD}{CD}[/tex]

Substitute the values

[tex]\frac{AB}{1.45}=\frac{39.55\times 1.45}{4.15} \\\\AB=20.39[/tex]

Hence, the height of the tree=20.39 m

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Expand: f(z) = z / (z-1) (2-z) as Laurent series for |z| < 1​

Answers

Most problems like this can be done with two tools only: partial fractions, and the result 1/(1−w)=1+w+w2+⋯ for |w|<1. So first split your function f into 1/(z−2)−1/(z−1). I will show you how to cope with one of these factors, 1/(z−2). Writing this as −1211−z/2 is tempting but no good: the "1/(1−w)" expansion will converge only for |z/2|<1, not on the regions you are supposed to care about. So you take out a factor of z−1 instead:

1/(z−2)=z−111−2/z

The final term can be expanded with the 1/(1−w) series, valid for |2/z|<1 that is |z|>2. So that does give you a Laurent series valid in the right region (once you multiply bu z−1. These methods can be used to solve all of your problems.

Partial fractions:

[tex]f(z) = \dfrac z{(z-1)(2-z)} = -\dfrac1{1-z} + \dfrac2{2-z}[/tex]

For |z| < 1, we have

[tex]\displaystyle \frac1{1-z} = \sum_{n=0}^\infty z^n[/tex]

and

[tex]\displaystyle \frac2{2-z} = \frac1{1-\frac z2} = \sum_{n=0}^\infty \left(\frac z2\right)^n[/tex]

(The latter series is valid for |z/2| < 1 or |z| < 2, but |z| < 1 is a subset of this region.)

Then

[tex]\boxed{f(z) = \displaystyle \sum_{n=0}^\infty \left(\frac1{2^n} - 1\right) z^n}[/tex]

Find the volume of the sphere. Round your answer to the nearest tenth.

Answers

Answer:

Step-by-step explanation:

Remark

All you need do is find the radius and put it into the formula V = (4/3) pi r^3.

Givens

d = 12 yards

r = d/2

Solution

r = 12 yds/2 = 6 yds

V = 4/3 pi r^3

V = 4/3 * 3.14 * 6*6*6

V = 904.32

Answer 904.4 yd^3

Patricia was having fun playing a card game. To win the game, she
needed the next two cards dealt to be yellow cards. There are 12
cards left in the deck, and three are[yellow.
What is the probability that the two cards dealt to Patricia will both
be yellow?


Answers

Answer:

25

%

Step-by-step explanation:

te puedes subcribirte a mi canal se llama navegando con incognito

The probability that the two cards dealt to Patricia will both be yellow

is 1/4.

What is the probability?

In mathematics, probability refers to the likelihood of an occurrence occurring. Simply put, how frequently the incidence occurs over a certain period of time.

Given, there are 12 cards left in the deck, and three are yellow.

To find the probability:

The probability= number of yellow cards in the deck / total number of cards in the deck.

= 3/12

= 1/4

Therefore, the probability is 1/4.

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Solve for y: 5( 3y+4) = 6( 2y-2/3)

Answers

Answer: y= -8

Step-by-step explanation:

5( 3y+4) = 6( 2y-2/3)15y+20=12y-415y-12y=-4-203y=-24y=-24/3y= -8

please help me it's urgent ​

Answers

Answer: go to the website

Step-by-step explanation:

...............................................the problem below is so hard...................................

Answers

Answer:

16 cm

Step-by-step explanation:

Circumference of a circle

We are told that the string is wound symmetrically around a circular rod.

Now, the circumference of the rod is 4 cm and length is 12 cm.

Now, circumference is also the length of a circle. Thus, one wound of the string will be equal to the circumference of the rod.

Thus, one wound = 4 cm

Since the string makes 4 turns about the rod, then;

Length of string = 4 × 4 = 16 cm

hopes this helps ya out

Which is the correct option, I’m very confused by this question?

sin2x=

Answers

Answer:

The answer is definitely Option A

Pls help i need an A my mom is going to get mad at me pls help i will give 62 points

Answers

[tex]\bold{ANSWER:}[/tex]
BOTH TABLES

[tex]\bold{EXPLANATIONS:}[/tex]

Answer:

Both of those tables show a proportional relationship between x and y.

Step-by-step explanation:

In the second table the values all equal 0.75 when divided.

In the first table the values all equal 1.25 when divided.

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