Find the derivative of y with respect to x. y= ((lnx)/(2+lnx))

Answers

Answer 1

Using the known theorem [tex]\left(\frac{f}{g}\right)'=\frac{f'g-g'f}{g^2}[/tex] you get
[tex]y'=\left(\frac{\ln x}{2+\ln x}\right) '=\frac{(\ln x)'(2+\ln x)-(2+\ln x)'\ln x}{(2+\ln x)^2}=\frac{\frac{1}{x}(2+\ln x)-\frac{1}{x}\ln x}{(2+\ln x)^2}[/tex].

Therefore, [tex]y'=\frac{\frac{2+\ln x}{x}-\frac{\ln x}{x}}{(2+\ln x)^2}=\frac{\frac{2}{x}}{(2+\ln x)^2}=\frac{2}{x(2+\ln x)^2}[/tex].

Related Questions

HELP WILL MARK BRAINLIEST
Use the net to find the lateral area of the cylinder
height is 9inch and radius is 5inch

Answers

Lateral Area = 2πrl

Lateral Area = 2 x π x 5 x 9

Lateral Area = 282.74 in²

---------------------------------------------------------------------------
Answer: The lateral area of the cylinder is 282.74 in²
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Two numbers have a difference of 0.7 and a sum of 1 . What are the numbers ?

Answers

The two numbers are 0.85 and 0.15

0.85 + 0.15 = 1
0.85 - 0.15 = 0.7

hope this helps

If the APY of a savings account is 5.3%, and if the principal in the savings account is $5100 for an entire year, what will be the balance of the savings account after all the interest is paid for the year?
A. $5300.00
B. $5127.03
C. $5100.00
D. $5370.30

Answers

the answer is D. hope this helps

Answer:

Option D - $5370.30

Step-by-step explanation:

Given : If the APY of a savings account is 5.3%, and if the principal in the savings account is $5100 for an entire year.

To find : What will be the balance of the savings account after all the interest is paid for the year?

Solution :

First we find the interest he paid.

The interest formula is [tex]I=P\times R\times T[/tex]

Where, P is the principal P=$5100

R is the rate of interest R=5.3%=0.053

T is the time T=1 year

Substituting the values,

[tex]I=5100\times 0.053\times 1[/tex]

[tex]I=\$270.3[/tex]

The balance of the saving account is the sum of interest paid and principal value.

Amount = Interest +Principal

Amount = $270.3 +$5100

Amount = $5370.3

Therefore, Option D is correct.

How many 4-sequences on {0..9} do not begin with 0?

Answers

I take a [tex]n[/tex]-sequence to mean any permutation of the digits 0-9 of length [tex]n[/tex]. Furthermore, I'm assuming no number can be repeated.

If that's the case, then for any 4-sequence, the first digits place (leftmost) has 9 possible choices (1-9). Once that number is used up, we have 9 numbers left in the pool of digits, from which we select a 3-sequence. The number of possible 3-sequences would be [tex]\dfrac{9!}{3!}=60,480[/tex]. Multiply this by 9 (to account for the first digit's possibilities) and we get a grand total of [tex]\dfrac{9\times9!}{3!}=544,320[/tex] possible 4-sequences on [tex]\{0,\ldots,9\}[/tex].

There are 9000 possible 4-sequences that do not begin with the digit 0.

The question asks how many 4-sequences on the set {0..9} do not begin with 0. To solve this, we need to consider the number of possible options for each of the four positions in the sequence, knowing that the first digit cannot be 0.

For the first position, there are 9 options (1-9), since 0 is not allowed. For the next three positions, each can be any of the 10 digits (0-9), since there are no restrictions. Thus, the total number of such sequences is the product of the number of options for each position.

9 options (1st position) x 10 options (2nd position) x 10 options (3rd position) x 10 options (4th position) = 9 x 10 x 10 x 10 = 9000.

So, to find how many 4-sequences do not begin with 0, multiply the number of choices for each position: 9 (first position, cannot be 0) x 10 (second position) x 10 (third position) x 10 (fourth position), resulting in 9000 such sequences.

A cardboard sheet is cut in the shape of a triangle, with vertices at (0,0), (20,0), and (3,4) units. the thickness of the sheet is uniform. what is the x-coordinate of its center of mass?

Answers

This problem can be solved in two ways, the long way, or the short way.

1. The long way
We know that the base of the triangle is along the x-axis, and the length of the base is 20.
The centre of mass is located at 2/3 of the distance from vertex (3,4) along the median, which cuts the base at (10,0).
Therefore the centre of mass is located at
x=3+(10-3)*2/3=23/3
y=4/3

2. The short way
It turns out that the centre of mass of a triangle sheet is located at the mean of the coordinates of the three vertices, i.e.
CG=((0+20+3)/3, (0+0+4)/3)=(23/3, 4/3) as before.

If the side length of a square pyramid is triple and the slant height is divided by 5 what would be the formula to find the modified surface area

Answers

If the original side length is "s" and the original slant height is "h", the original surface area is
.. S = (base area) +(lateral area)
.. S = s² +(1/2)*(4s)*h
.. S = s(s +2h)

Now, if we make these replacements: s ⇒ 3s, h ⇒ h/5, we have
.. S' = (3s)(3s +2h/5)
.. S' = 9s² +(6/5)s*h . . . . . . . the formula for the modified area (in terms of original dimensions)

_____
Of course, in terms of the modified dimensions, the formula is the same:
.. S' = s'(s' +2h')

Noel is playing a game where he draws one playing card each out of two stacks of 5 cards. The table below shows all possible sums for the two numbers on the cards.

Answers

Noel is more likely to draw two cards with a sum that is greater than 13.

To determine which outcome is more likely, let's count the number of combinations that meet each criterion.

1. **Sum that is a multiple of 3**:

- Possible sums: 3, 6, 9, 12

- Counting the combinations:

- 3: 1 combination

- 6: 2 combinations

- 9: 3 combinations

- 12: 4 combinations

- Total combinations: 1 + 2 + 3 + 4 = 10 combinations.

2. **Sum greater than 13**:

- Possible sums: 14, 15, 16, 17, 18, 19, 20, 21, 22, 23

- Counting the combinations:

- 14: 1 combination

- 15: 2 combinations

- 16: 2 combinations

- 17: 3 combinations

- 18: 2 combinations

- 19: 3 combinations

- 20: 2 combinations

- 21: 3 combinations

- 22: 1 combination

- 23: 1 combination

- Total combinations: 1 + 2 + 2 + 3 + 2 + 3 + 2 + 3 + 1 + 1 = 20 combinations.

Comparing the total combinations, we see that there are more combinations with a sum greater than 13 (20 combinations) than there are combinations with a sum that is a multiple of 3 (10 combinations). Therefore, Noel is more likely to draw two cards with a sum that is greater than 13.

The probable question may be:

Noel is playing a game where he draws one playing card each out of two stacks of 5 cards. The table below shows all possible sums for the two numbers on the cards.

3, 6, 7, 9, 1

1 = 4, 7, 8, 10, 12

4 = 7, 10, 11, 13, 15

6 = 9, 12, 13, 15, 17

8 = 11, 14, 15, 17, 19

12 = 15, 18, 19, 21, 23

Is Noel more likely to draw two cards with a sum that is a multiple of 3 or two cards with a sum that is greater than 13?

Noel is more likely to draw two cards with a sum greater than 13, as there are 37 combinations compared to 11 combinations for multiples of 3.

To determine whether Noel is more likely to draw two cards with a sum that is a multiple of 3 or two cards with a sum that is greater than 13, we can analyze the table provided.

1. Sum that is a multiple of 3:

- There are several combinations of card values that result in a sum that is a multiple of 3. We can count these combinations from the table:

- (3, 4), (3, 7), (3, 9), (3, 12)

- (6, 7), (6, 10), (6, 12)

- (7, 8), (7, 11)

- (9, 10), (9, 13)

- (11, 12)

2. Sum greater than 13:

- We need to count the combinations of card values that result in a sum greater than 13:

- (6, 8), (6, 10), (6, 11), (6, 12), (6, 13), (6, 15), (6, 17)

- (7, 8), (7, 9), (7, 10), (7, 11), (7, 12), (7, 13), (7, 15), (7, 17), (7, 19)

- (9, 10), (9, 11), (9, 12), (9, 13), (9, 15), (9, 17), (9, 19)

- (11, 12), (11, 13), (11, 15), (11, 17), (11, 19)

- (12, 13), (12, 15), (12, 17), (12, 19)

- (13, 15), (13, 17), (13, 19)

- (15, 17), (15, 19)

- (17, 19)

After counting the combinations, we can compare the number of combinations in each category:

1. Sum that is a multiple of 3:

- Total combinations: 11

2. Sum greater than 13:

- Total combinations: 37

Comparing the totals, we can see that Noel is more likely to draw two cards with a sum that is greater than 13, as there are more combinations resulting in this outcome.

Complete Question:

Help please !!!!!!! .......

Answers

The table represents a geometric sequence because the successive y-values have a common ratio of 0.6

A geometric sequence is a sequence of numbers, where the successive values after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. In this case the common ratio is 0.6.

5 * 0.6 = 3
3 * 0.6 = 1.8
1.8 * 0.6 = 1.08

There are four steps in solving one’s personal financial challenges:

1. considering opportunity costs
2. assessing risks and returns
3. setting short- and long-term goals
4. assessing needs and wants

Which of these is the correct order of these steps?

2, 3, 1, 4

1, 2, 3, 4

4, 1, 2, 3

3, 1, 4, 2

Answers

Answer: C. 4, 1, 2, 3.

I hope this helps :)

Answer: Third option is correct.

Step-by-step explanation:

Since there are four steps in solving one's personal financial challenges:

1) First he needs to assessing the needs and wants .

2) Then, he will consider opportunity costs, i.e. next best alternative.

3) Then, he will assessing the risks and returns associated with the opportunity costs.

4) Last, but not the least, he will be setting short and long term goals.

So, The correct order of these steps is 4,1,2,3.

Hence, Third option is correct.

An experienced roofer can roof a house in 26 hours. A beginning roofer needs 39 hours to complete the same job. Find how long it takes for the two to do the job together

Answers

The way to do this is to use the formula
1/r1 + 1/r2 = 1/rt
r1 = time for roofer 1 in hours = 26 hours.
r2 = time for roofer 2 in hours = 39 hours.

1/26 + 1/39 = 1/rt
0.03846 + 0.02564 = 1/rt
0.06410 = 1/rt ****** (I've used these stars later on. Ignore them now)

You could go on one of two ways. You could put 1 one under 0.06410 and cross multiply. I'll do that first.

0.06410 / 1 = 1/rt
0.06410 * rt = 1 * 1
0.06410 * rt = 1 Now divide by the number on the left.
rt = 1/0.06410
rt = 15.6

Or you could do this. Go back to the step with the stars.
Turn both steps upside down

0.06410 = 1 / r2 Take the reciprocal of both sides.
1/0.06410 = r2
r2 = 15.6 hours for both roofers working together.

There are other ways of doing this problem. None are any quicker. The point is that your answer should come to a number below either of the workers. It makes sense. The slower worker still does some work, but the faster worker does most of it.

Final answer:

The experienced roofer and the beginning roofer together can complete the job in approximately 15.6 hours, which is found by adding their work rates and taking the reciprocal of the sum.

Explanation:

To find how long it takes for both an experienced and a beginning roofer to roof a house together, we need to sum their work rates and then find the reciprocal of that sum. We'll start by considering the work rates of both the experienced and the beginning roofer. The experienced roofer can roof a house in 26 hours, which means the roofer completes 1/26 of the job per hour. The beginning roofer completes the job in 39 hours, which is 1/39 of the job per hour.

Now, we can calculate their combined work rate:
1/26 + 1/39 = (39 + 26) / (26 * 39) = 65 / 1014 = 1/15.6

These two roofers together complete 1/15.6 of the job per hour. To find out how long it will take them to complete the job together, we take the reciprocal of this rate:
1 / (1/15.6) = 15.6 hours.

Therefore, it would take the experienced and beginning roofer combined around 15.6 hours to roof the house together.

i,ii,iii,iiii,iiiii what is the twentieth term?

Answers

I think it would be iiiiiiiiiiiiiiiiiiii since it seems to just be adding an i each time. Hope this helps.

Will someone please find the value of x for these questions

Answers

Try this solution:

12) for h=√(10²-6²)=8
then
[tex] \frac{x-6}{8} = \frac{8}{6}; \ =\ \textgreater \ \ x= \frac{50}{3} [/tex]

14) 6:11 as x:10. It means that
[tex] \frac{6}{11} = \frac{x}{10}; \ =\ \textgreater \ \ x=6*10/11= \frac{60}{11} [/tex]

A stained glass window is in the shape of an equilateral triangle. what is the measure of one interior angle of the triangle

Answers

For an equilateral triangle, the only angle for the inside can be 60 degrees.

60° x 3 (Angles) = 180°

What number fills in the blank to complete the factorization of 3x + 24?

(x + 8)

Answers

Answer:

The factor form of given expression is 3(x+8) so the required number is 3.

Step-by-step explanation:

The given expression is

[tex]3x+24[/tex]

Write the factors of each term.

[tex]3x+24=3\times x+3\times 8[/tex]

In both terms, 3 is a common factor.

Take out the common factor 3.

[tex]3x+24=3(x+8)[/tex]

The factor form of given expression is 3(x+8). The factor (x+8) is given, therefore the required number is 3.

Carlos’s hockey team has ten players, not counting the goalie.Five non goalie players need to be selected for a starting line-up.

A)How many different starting lineups are possible if positions are not assigned?

B)How many starting lineups are possible if positions are assigned?

Answers

Final answer:

There are 252 different starting lineups possible if positions are not assigned, and 30,240 starting lineups are possible if positions are assigned.

Explanation:

For part A of the question, where positions are not assigned, we can calculate the number of different starting lineup combinations by using the combination formula. Since we are choosing 5 players out of 10 without regard to order, we use:

C(n, k) = n! / (k!(n-k)!)

Where n is the total number of players to choose from, and k is the number of players we want to choose. Therefore, we have:

C(10, 5) = 10! / (5! (10-5)!) = 252

There are 252 different starting lineups possible if positions are not assigned.

For part B, where positions are assigned, we use the permutation formula because the order in which we select the players matters. This formula is:

P(n, k) = n! / (n-k)!

Since the order in which the players are chosen matters, we have:

P(10, 5) = 10! / (10-5)! = 30,240

There are 30,240 different starting lineups possible with positions assigned.

The two tables below show the success rates of several groups of businesses in a certain city. The first shows the number of businesses of several types started in Sharon’s city over the course of two years, and the number of those businesses which did not succeed and were forced to shut down within two years of opening. The second deals with separate records of successful new businesses, showing how much profit those new businesses turned over two years. Businesses on the boundary lines fall in the lower category. Type Food Retail Financial Service Opened 3,193 2,280 1,898 5,045 Closed 1,977 1,626 1,443 3,548 Up to $25k $25-50k $50-75k $75-100k Over $100k Food 945 623 601 258 114 Retail 813 548 347 188 63 Financial 316 244 195 86 51 Service 979 739 432 174 124 Using the tables as experimental data, determine which of the following situations have a probability of at least 15.00%. I. a food establishment succeeding and earning $50,000 or more II. a service establishment succeeding and earning between $25,000 and $75,000 III. a retail establishment succeeding and earning no more than $50,000 a. I only b. I and II c. II and III d. III only

Answers

The answer is D. III only. A retail establishment succeeding and earning no more than $50,000 is correct in the choices given.

Answer:

The answer is D on edge 2020.

Step-by-step explanation:

Vanessa earns a base salary of $400.00 every week with an additional 5% percent commission on everything she sells. Vanessa sold $1650.00 worth of items last week.

What was vanessas total pay last week

Answers

Vanessa’s total pay is $482.50

help please in eed answers asap

Answers

A cube has the same length for its height, width, and length. So to find the volume, we multiply:

4.2 x 4.2 x 4.2 = 74.088 cm^3

Answer:

74,088 cm³

Step-by-step explanation:

[tex]whl = V \\ \\ [4,2]^{3} = 74,088[/tex]

I am joyous to assist you anytime.

What is the product of (-1/4) x (-3/7)? Write your answer in simplest fraction form

Answers

[tex]\frac{-1}{4}\times \frac{-3}{7} = \frac{(-1)(-3)}{(4)(7)} = \frac{3}{28}[/tex]

A gardener crosses tall true-breeding pea plants with short true-breeding ones. Tall plants are dominant to short ones. He collects the seeds to grow F1 plants and then allows them to self-pollinate to form an F2 generation. Which of the following describes the traits of the offspring correctly?

Answers

The responses given are as follows;
a) Three–fourths of the F1 and one–half of the F2 plants will be tall.
b) All of the F1 and three–fourths of the F2 plants will be tall.
c) Three–fourths of the F1 and all of the F2 plants will be tall.

Let’s name tall as T and short as t
Since both are true breeding plants
Tall plants have the genotype TT and short plants have the genotype tt
Tall plants will make gametes of type T only
Short plants make gametes of type t only
After cross breeding the offspring would all be of genotype Tt as they’re made of T and t gametes
F1 generation formed have the genotype Tt
Since T is dominant all F1 plants are tall
When F1 self pollinates
F1 * F1
Tt *Tt
Gametes are
T t T t
F2 population offspring genotypes are as follows;
TT -1/4 tall
Tt -1/4 tall
Tt -1/4 tall
tt - 1/4 short
3/4 of the plants are tall
Remaining 1/4 is short

Therefore response b is correct
All f1 plants are tall and 3/4 of f2 plants are tall

Assume that the poisson distribution applies and that the mean number of hurricanes in a certain area is 5.55.5 per year.
a. find the probability that, in a year, there will be 44 hurricanes.
b. in a 5555-year period, how many years are expected to have 44 hurricanes?
c. how does the result from part (b) compare to a recent period of 5555 years in which 88 years had 44 hurricanes? does the poisson distribution work well here?

Answers

We are given
λ = mean = 5.5 hurricanes per year
and Poisson distribution applies.

P(k, λ ) = λ ^k * e^(- λ ) / k!

a) 4 hurricanes in a year
P(4,5.5)=5.5^(4)*e^(-5.5)/4!
=0.1558

b) In 55 years, the expected number of years with 4 hurricanes
= 55*0.1558 = 8.57, could be rounded to the nearest integer, 9.

c) Records show that in 55 years had 8 years had 4 hurricanes each year.
This compares very closely with the expected number 8.57.

Name all pairs of vertical angles.

Answers

4 vertical angles, these are the legs of the table
:)

solve the system of equations 6X + 5 y equals 55 + 6 x + 5 y equals 60

Answers

6x+5y=55+6x+5y
-5y. -5y
6x. =55+6x
-6x. -6x
0=55

no solution

No solution there is no solution

Simplify (- 5/8) divided by (-3/4)
A: 20/24
B: -20/24
C: -15/32
D: 15/32

Answers

[tex]-\frac{5}{8} : -\frac{3}{4}= \frac{5}{8}* \frac{4}{3} = \frac{20}{24} = \bold{\frac{5}{6} }[/tex]

The answer is A (20/24)

(-5/8) / (-3/4)

Step 1: -5/8 · 4/-3

Step 2: -5 · (-4)
______
8 · 3

Step 3: 20/24

Answer: 5/6

Your answer is 5/6

Hope I helped!

Let me know if you need anything else!

~ Zoe (Rank:'Genius')

the first term in an arithmetic sequence is 5. the foutth term in the sequence is -4. the tenth term is 22. which function can be used to find the nth term of the arithemetic sequence

Answers

Consider this option:
if the given terms are a₁=5; a₂=-4; a₁₀= -22, then

1. rule: n-th term of any arithmetic sequence is:
[tex]a_n=a_1+d(n-1), [/tex] where d - difference of this sequence.
2. using the mentioned rule
a₄=a₁+d(4-1), ⇒ -4=5+3d; ⇒ d=-3.
(a₁₀=a₁+9d=5-3*9=-22).
3. if d=-3 and a₁=5, then it is possible to make up an equation for n-th term:
[tex]a_n=5-3(n-1)=8-3n;[/tex]
a₁₀₀=8-3*100=-292.

A circle has a circumference of 361π. What is the diameter of the circle?

Answers

Circumference of a circle = πD

Given that the circumference = 361π

πD = 361π

D = 361 units

The formula to find circumference of circle is given by

[tex] C =2\pi r [/tex]

Where r is radius of circle and pi =3.14

We are given Circumference here as 361π

Plugging the value in the formula :

[tex] 361\pi =2\pi r [/tex]

r=361/2 = 180.5

radius of circle is 180.5.

We know that Diameter is double of radius.

So diameter = 2*180.5 = 361

Answer: Diameter of circle is 361.

What is the slope of the line on the graph. I need help I!!!

Answers

From just looking at the graph we can already notice that the slope is gonna be a negative since the line is going downhill.

So using the Rise Over Run we can calculate the slope, from each point the slope rises 2 and runs -6 (-2/6) then simplify to -1/3

-1/3 is your slope

Martin needs 60 meters of fence to go around a rectangular garden.
The length, l, of the garden is twice its width w.
Three of these equations give the correct value for w.

Which equation does NOT?

2 • w + 2 • 2w = 60

2 • (2w + w) = 60

w + 2w = 60

w + 2w + w + 2w = 60

Answers

w + 2w = 60 would be your answer.

Answer:

w + 2w = 60

Step-by-step explanation:

w + 2w = 60

This equation will not give you the correct value for W because W is the siez or represents the size of the smaller side, since you have 4 sides, 2 small and 2 big, the sum of this 4 sides will be the perimeter, or the total meters of fence needed, since the total meter of fence need is 60 and in the equation you just have 2 sides, the value for W will be double than the real.

solve the system of equations by substitution y=5x-13 and 5x+2y=19

Answers

y = 5x - 13 ----------- (1)
5x + 2y = 19 --------- (2)

Sub (1) into (2):

5x + 2(5x -13) = 19
5x + 10x - 26 = 19
15x = 19 + 26
15x = 45
x = 3 -------- sub back into (1)
y = 5(3) - 13
y = 15 - 13
y = 2

Ans: x = 3, y = 2

At what Kelvin temperature will a sample of gas occupy 12 liters if the same sample occupies 8 liters at 27 °C?

Question 11 options:

45.0K

450K

40.5K

405K

Answers

Since the gas it is getting compressed with a change on temperature, we consider that the pressure is constant, and of course the number of mole is constant (same gas), therefore, from the ideal gas law
P
V
=
n
R
T
we can say:
V
T
=
constant
Therefore,
V
1
T
1
=
V
2
T
2
⇒
T
1
=
V
1
×
T
2
V
2
⇒
T
1
=
12
L
×
300
K
8
L
=
450
K
A=450k

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