For a submarine cable, the range of signalling is governed by the function


f(r) = r^2 ln⁡(1/r)

where 0
Find df/dr.

Answers

Answer 1

Answer:

 [tex]\frac{df}{dr} = (-r) + log(\frac{1}{r} )( 2 r)[/tex]

Step-by-step explanation:

Explanation

Given function f(r) = r² log r  ....(i)

Apply derivatives formula

              [tex]\frac{d}{dx} UV = U^{l} V + V^{l} U[/tex]

             [tex]\frac{d}{dx}x^{n} = nx^{n-1}[/tex]

            [tex]\frac{d}{dx}log x = \frac{1}{x}[/tex]

Differentiating equation (i) with respective to 'r' , we get

                [tex]\frac{df}{dr} = r^{2} (\frac{1}{\frac{1}{r} } )\frac{d}{dr} (\frac{1}{r } )+ log(\frac{1}{r} ) 2 r[/tex]

                [tex]\frac{df}{dr} = r^{2} (\frac{1}{\frac{1}{r} } )(\frac{-1}{r^{2} } )+ log(\frac{1}{r} ) 2 r[/tex]

Final answer:-                

               [tex]\frac{df}{dr} = (-r) + log(\frac{1}{r} )( 2 r)[/tex]


Related Questions

What is the area of the region bounded by the lines x= 1 and y= 0 and the curve y=xe^x^2?

Answers

Answer:

A = 0.859

Step-by-step explanation:

We want to find the area of the region bounded by the lines x = 1 and y = 0 and the curve y = xe^(x²).

At y = 0, let's find x;

0 = xe^(x²)

Solving this leads to no solution because x is infinity. Thus we can say lower bound is x = 0.

So our upper band is x = 1

Thus,lets find the area;

A = ∫xe(x²) dx between 1 and 0

A = (e^(x²))/2 between 1 and 0

A = ((e¹)/2) - (e^(0))/2)

A = 1.359 - 0.5

A = 0.859

The lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min. If one such class is randomly selected, find the probability that the class length is between 50.8 and 51 min.

Answers

Answer: the probability that the class length is between 50.8 and 51 min is  0.1 ≈ 10%

Step-by-step explanation:

Given data;

lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min

hence, height = 1 / ( 52.0 - 50.0) = 1 / 2

now the probability that the class length is between 50.8 and 51 min = ?

P( 50.8 < X < 51 ) = base × height

= ( 51 - 50.8) × 1/2

= 0.2 × 0.5

= 0.1 ≈ 10%  

therefore the probability that the class length is between 50.8 and 51 min is  0.1 ≈ 10%  

Please help ASAP!!!!!!!!!

Answers

Answer:[tex]\boxed{24}[/tex]Solution Steps:

______________________________

1.) Plug our numbers into the formula:[tex]B[/tex] × [tex]H[/tex][tex]6[/tex] × [tex]4=24[/tex]

______________________________

HELP NOW PLSSSSS
(where the longer it takes to solve a problem and the fewer people who answer it correctly, the more difficult it is). On each subsection, question 1 will be "easy" and question 15 will be considered "difficult." However, the ascending difficulty resets from easy to hard on the grid-ins.

Hence, multiple choice questions are arranged in increasing difficulty (questions 1 and 2 will be the easiest, questions 14 and 15 will be the hardest), but the difficulty level resets for the grid-in section (meaning questions 16 and 17 will again be "easy" and questions 19 and 20 will be very difficult).

Answers

the answer is 4/.12

:)

Answer:

Hence, multiple choice questions are arranged in increasing difficulty (questions 1 and 2 will be the easiest, questions 14 and 15 will be the hardest), but the difficulty level resets for the grid-in section (meaning questions 16 and 17 will again be "easy" and questions 19 and 20 will be very difficult).

What is the question??

Jeffrey is 5 years older than his brother. If j represents Jeffrey’s age, the expression j−5 can be used to find his brother’s age. If Jeffrey is 23, how old is his brother?

Answers

If j=23 and j-5 is how old Jeffery's brother is then Jeffrey's brother is 17 years old.

So j=17

His brother is 17 because 23-5 =17

48 is 16 2/3% of what number?

Answers

Answer:

288

Step-by-step explanation:

I hope this helps <3

n − 32 5 = 10 help plz

Answers

Answer:

n=335

Step-by-step explanation:

Answer:

Step-by-step explanation:

Here you go mate

Step 1

n − 325 = 10  equation

Step 2

n − 325 = 10  simplify by adding 325 to both sides

Answer

n=335

Find the missing values of the variables. The diagram is not to scale. Show steps

Answers

Step-by-step explanation:

i assume this is the question you asked me to look at.

Well, angle 116° and y are supplementary angles

therefore,116°+y=180°

y=180°-116°=64°

Now to find x

x+y+125+72=360°

x+64+125+72=360

x+261=360

x=360-261=99°

The measure of x° is  99° and the measure of y° is 64°.

What is quadrilateral?

A quadrilateral is a polygon with four sides four angles and four vertices. Whenever we name a quadrilateral, we need to keep in mind the order of the vertices.

From the given figure,

116°+y°=180° (Sum of adjacent angles is 180°)

y°=180°-116°

y°=64°

Sum of interior angles of quadrilateral is 360°.

Here, x°+y°+72°+125°=360°

x°+64°+72°+125°=360°

x°+261°=360°

x°=99°

Therefore, the measure of x° is  99° and the measure of y° is 64°.

Learn more about the quadrilaterals here:

https://brainly.com/question/29934440.

#SPJ2

What equation is a proportion?

7/9 = 21=28
1/3 = 1/4
5/8 = 20/32
3/4 = 6/9

Answers

5/8 = 20/32
Explanation: 5 x 4 = 20 and 8 x 4 = 32

Answer:

5/8=20/32

Step-by-step explanation:

Which pair of expressions is equivalent? 2(x + 5) and 2x + 10 B. 3x – 6 + 4x + 9 and 7x + 15 0. C. 4y - 2) and 4y - 2 0 D. 5y + 12 - 3y and 2y – 12​

Answers

Answer:

A

Step-by-step explanation:

the equivalent pair of expression are 2(x+5)and 2x+10

Part A : At Mountain Park Middle school, there are 250 seventh-grade students who are not in advanced math. Let a represent the number of seventh-grade students who are not in advanced math?

Part B: How many students are NOT in advanced math?

Answers

Answer:

hard to explain

Step-by-step explanation:

Answer:I think 80 at bottom like

Step-by-step explanation:

Is 9/16 a terminating or repeating decimal plz ASAP brainley

Answers

Answer:

terminating.

Step-by-step explanation:

9/16 converted to a decimal is .5625 which is terminating

three blocks are placed together as shown below. 3.8cm 8.7cm 9.4cm​

Answers

It’s gotta be 21.9cm cause u just add them all

5(-6 + 4)=..................​

Answers

Answer:

-10

Step-by-step explanation:

5(-6 + 4)

=-30+20

=-10

Answer:

-10 or just 10 in general

Step-by-step explanation:

Solve the inequality.
X + 25 < 33
O A. x< 58
B. x < 8
C. X> 58
O
D. X > 8

Answers

Answer:

x < 8

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Step-by-step explanation:

Step 1: Define

x + 25 < 33

Step 2: Solve for x

Subtract 25 on both sides:                    x < 8

Here we see that any value x smaller than 8 would work as a solution to the inequality.

Find the value of x.
4x + 5
2x + 21, smby help me wit dis pls

Answers

Answer: x = 8

Step-by-step explanation:

4x + 5 = 2x + 21

4x + 5 - 2x = -2x + 2x +21 (Subtract 2x from both sides)

2x + 5 = 21

2x + 5 - 5 = 21 - 5 (Subtract 5 from both sides)

2x = 16

2x/2 = 16/2 (Divide both sides by 2)

x = 8

Let f(x) = 16 – x^2 , g(x) = 4 – x. Find (fg)(x) and its domain

Answers

f(4-x)=12
Domain:(-oo,oo) these are infinity symbols by the way.

Directions: Convert the following equations from standard form to slope-intercept form.
(10 points)

14. 4x + y = -1

15. 5x - 2y = 14

16. 10x - 2y = -6

17. 8x + y = 12

18. 6x - 10y = 20

Answers

y= -4x-1
y= 5/2x-7
y=5x+3
y= -8x +12
y= 3/5x-2

FinWhat is the perimeter of the triangle in the graph? Round your answer to the nearest tenth if necessary. (1 point) 8.9 8.0 12.9 8.5d the missing y-coordinate that makes the two triangles congruent. Triangle ABC: A(8,4), B(2,6), C(5, 0) Triangle MNO: M(7,4), N(1,2), O(4, y)

Answers

Answer:

man did you ever find out the answer bc I'm dying I cannot fail this test-

Answer:

12.9

Step-by-step explanation:

it is common sense

also i just took test

Please I need help like now

Answers

Answer:

it's is d

Step-by-step explanation:

seening this info

for every 2/3 of cold water there is 1/2 of vegetable Oil

to make this answer complte if if we add a another cup of water the amount that is requared  and since were adding 1/2 of oil which is 2/3 of water need adding 2/3+2/3=4/3

Hence 4/3 or D is right

Eidoskaijsizjzkxkxdkjajjsjeksjsii

Answers

Answer:

Yes, Yes, No, Yes

Step-by-step explanation:

whats the value of v 69 = 7v – 6

Answers

Answer:

75/7

Step-by-step explanation:

69=7v-6 rewrite as 69+6=7v

75 = 7v

75/7 = v

halp
A 43-foot ladder is leaning against a building and forms a 29.37° angle with the ground. How far away from the building is the base of the ladder? Round your answer to the nearest hundredth.

21.09 feet
24.20 feet
37.47 feet
49.34 feet

Answers

Answer:

37.46

Step-by-step explanation:

I think not sure tho

4) Which formulas can be used to find the area of a parallelogram and a
square? There are two possible answers. Check one.
10 pa
O A = b x h
A = 2L + 2W
A = L + L + W + W
A = bh

Answers

Answer:

O A = Bx H and A = L + L + W + W.

Step-by-step explanation:

Find the measure of angle b (15

Answers

Answer:

Angle b is 15 measure the scale

You are running a concession stand at a basketball game. You are selling hot dogs and
sodas.Each hot dog costs $1.50 and each soda costs $ 0.50. At the end of the night, you made a total of
$78.50. You sold a total of 87 hot dogs and sodas combined. You musſt report the number of hot dogs
sold and the number of sodas sold. How many hot dogs were sold and how many sodas were sold?

Answers

Answer: 52

Step-by-step explanation: Friend me and yes that is right!

please help i m clusless

Answers

Answer:

-25+? = -5

cross -5 over and it the negative sign would turn to postive sign

-25+(5)=?

Therefore answer = 20

To confirm this answer

-25+20= -5

Answer: (1) 20 (2) -15 (3) -10

Explanation:
I know it’s late but hope this helps! ^^

Factor the expression using the GCF. 44-11 I NEED HELP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

11(4-1)

Step-by-step explanation:

11 is the greatist common factor of 44 and 11 so you factor an 11 out of both terms

44/11=4

11/11=4

Therefore the answer is 11(4-1)

The population of a certain community is known to increase at a rate proportional to the number of people present at time t. If the population has doubled in 5 years, how long will it take to triple?

Answers

Answer:

[tex]t=7.85 years[/tex]

Step-by-step explanation:

We can write this rate as an ordinary differential equation.

[tex]\frac{dP}{dt}=aP[/tex]

Where a is proportional constant, P the population variable, and t the time.

[tex]\frac{dP}{P}=adt[/tex]

Integrating each side of the equation.

[tex]\int \frac{dP}{P}=\int adt[/tex]

[tex]ln(P)=at+c[/tex]

[tex]P=e^{at+c}[/tex]

[tex]P=e^{c}e^{at}=Ce^{at}[/tex]

To find C we need to use the initial condiction, it means evaluae P at t=0.

[tex]P_{0}=Ce^{0}=C[/tex]

[tex]P=P_{0}e^{at}[/tex]

Now, we use the sentence  the population has doubled in 5 years.

[tex]2P_{0}=P_{0}e^{a5}[/tex]

We can find "a" in this condition.

[tex]2=e^{a5}[/tex]

[tex]ln(2)=a5[/tex]

[tex]a=\frac{ln(2)}{5}[/tex]

[tex]a=0.14[/tex]

Finally, let's find how long will it take to triple.

[tex]3P_{0}=P_{0}e^{0.14t}[/tex]

[tex]3=e^{0.14t}[/tex]

[tex]t=\frac{ln(3)}{0.14}[/tex]

[tex]t=7.85 years[/tex]

I hope it helps you!

help me , my project is do soon .

Answers

Answer:

whats the question

Step-by-step explanation:

Other Questions
cups of water fill 4 identical water bottles. How many cups fill each bottle? If at some point in time an object has zero velocity and zero acceleration, what does that mean about its motion at the next instant what is the verb of private? Estoy escribiendo una novela de fantasa y juvenil, pero ahora nos como seguir con la historia. Consejos?I'm writing a fantasy and youth novel, but now I don't know how to go on with the story. Tips? Need help ASAP Explain why folie arcadienne is a good song plz don't answer if u don't know the answer CAN SOMEBODY WRITE ME A 500 WORD ESSAY ABOUT THE INAUGURATION THAT HAPPENED TODAY PLZZ!! Eidoskaijsizjzkxkxdkjajjsjeksjsii Which of the following environmental parameters would be important to monitor in order to ensure sustainable logging?A. The number of trees cut down versus number trees burned B. The number of new trees planted to replace those removedC. The number of trees needed to increase soil fertilization D. The number of trees removed within a single species 5(-6 + 4)=.................. help im confused!! i need to find the x Factor the expression using the GCF. 44-11 I NEED HELP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!! how do i solve this question? pls help ill give brainliest :) How many countries are in the $55,000 to $69,999 range IS AGING INVITABLE??????????? hi waht is mm in algebra maths Which best describes the importance of meiosis to living organisms? *O genetic variation and growthO growth and developmentO development and sexual reproductionO sexual reproduction and genetic variation How did the idea of nonviolence effect Diane Nash's view of segregation? Explain how a carbon atoms moves From primary consumers to secondary consumersExplain how a carbon atoms moves From consumers back to the atmosphere (2 different methods)Explain how a carbon atoms moves From consumers to fossil fuels please help thank you