What value of x satisfies the conclusion of the mean value theorem for f(x) = ln(x3) over the interval [1, e2]?

Answers

Answer 1

Answer:

[tex]x \approx 3.195[/tex] satisfies the conclusion of the Mean Value Theorem for [tex]f(x) = \ln x^{3}[/tex] over the interval [tex][1,e^{2}][/tex].

Step-by-step explanation:

According to the Mean Value Theorem, for all function that is differentiable over the interval [tex][a, b][/tex], there is at a value [tex]c[/tex] within the interval such that:

[tex]f'(c) = \frac{f(b)-f(a)}{b-a}[/tex] (1)

Where:

[tex]a[/tex], [tex]b[/tex] - Lower and upper bounds.

[tex]f(a)[/tex], [tex]f(b)[/tex] - Function evaluated at lower and upper bounds.

[tex]f'(c)[/tex] - First derivative of the function evaluated at [tex]c[/tex].

If we know that [tex]f(x) = \ln x^{3} = 3\cdot \ln x[/tex], [tex]f'(x) = \frac{3}{x}[/tex], [tex]a = 1[/tex] and [tex]b = e^{2}[/tex], then we find that:

[tex]\frac{3}{c} = \frac{3\cdot \ln e^{2}-3\cdot \ln 1}{e^{2}-1}[/tex]

[tex]\frac{3}{c} = \frac{6\cdot \ln e-3\cdot \ln 1 }{e^{2}-1 }[/tex]

[tex]\frac{3}{c} = \frac{6}{e^{2}-1}[/tex]

[tex]c = \frac{1}{2}\cdot (e^{2}-1)[/tex]

[tex]c \approx 3.195[/tex]

[tex]x \approx 3.195[/tex] satisfies the conclusion of the Mean Value Theorem for [tex]f(x) = \ln x^{3}[/tex] over the interval [tex][1,e^{2}][/tex].

Answer 2

Answer:

C. 1/2(e^2-1)

Step-by-step explanation:

Edge AP Cal 2022


Related Questions

George buys pizza. He eats 3/8 of pizza for lunch and 1/4 of the pizza for dinner

Answers

Answer:

Step-by-step explanation:

To find the amount he ate we just add the fractions:

3/8 +1/2 = 7/8 or 0.875

HOPE THIS HELPS!

HAVE A GR8 DAY ;-)

What is the total cost with sales tax price $17.95 tax 6%

Answers

the answer would be 16.87

Answer:

$19.03

Step-by-step explanation:

Okay, this is a standard percentage problem, so learning how to do this is necessary. First, we have to find what 6% of $17.95 is, since of is our keyword and that means to multiply, and percentages turn into decimals:

17.95 x 0.06 = 1.08

So we have our tax, then we have to add that to our original price to get the whole thing:

17.95 + 1.08 = 19.03

So the total sale price is $19.03

A test is worth 60 points. Multiple-choice questions are worth 2 points, and
short-answer questions are worth 5 points. If the test has 15 questions, how
many multiple-choice questions are there?
O A. The number of multiple-choice questions minus the number of
short-answer questions is 60.
OB. The number of multiple-choice questions times the number of
short-answer questions is 15.
C. The number of multiple-choice questions plus the number of
short-answer questions is 15.
D. The number of multiple-choice questions plus the number of
short-answer questions is 60

Answers

Answer:

C. The number of multiple-choice questions plus the number of

short-answer questions is 15.

Step-by-step explanation:

This question can be solved using a system of equations.

I am going to say that:

x is the number of multiple-choice questions

y is the number of short-answer questions.

Multiple-choice questions are worth 2 points, and short-answer questions are worth 5 points.

This means that:

[tex]2x + 5y = 60[/tex]

The test has 15 questions.

This means that:

[tex]x + y = 15[/tex].

Which means that option C is the correct answer.

Answer:

C. The number of multiple-choice questions plus the number of short-answer questions is 15.

Step-by-step explanation:

x + y = 15

What is the value of 16 • 2-2?

Answers

Answer:

= 30

Step-by-step explanation:

Two students on roller skates stand face-toface, then push each other away. Which student will always have the fastest speed

Answers

Answer:

The student with lower weight will move faster than the one with higher weight.

Step-by-step explanation:

The students are on roller skates and it is assumed that their wheels are identical. They are on a frictionless flat horizontal ground. According to Newton's Law F=ma

Mass of student 1 is 97 kg

Mass of student 2 is 61 kg

The force magnitude is assumed to be equal and acceleration is same. The student with higher weight will have lesser force exerted than the student with lighter weight.

apriquide Rd
.) Travis is planning to ride at a constant speed during an upcoming bike trip. He wants to know
how many miles he will ride after different numbers of hours.
c) Plot two points that show how far Travis
will ride after 3 hours and after 4 hours.

Answers

Answer:

3 times 30 miles and 4 times 40 miles

Step-by-step explanation:

Travis will ride at a distance of 30 miles after 3 hours and at a distance of 40 miles after 4 hours.

What is Speed?

Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.

Speed is a scalar quantity as it only has magnitude and no direction.

Given that,

Travis is planning to ride at a constant speed during an upcoming bike trip.

This implies that the slope of the graph will be a constant.

So the graph will be a straight line.

We have two points on the graph (1, 10) and (2, 20).

The starting point will be (0, 0).

Slope = (20 - 10) / (2 - 1) = 10

So the equation of the line is y = 10x.

When x = 3 hours, y = 30 miles

When x = 4 hours, y = 40 miles

Hence the points has to be marked at (3, 30) and (4, 40).

Learn more about Speed and Slope here :

https://brainly.com/question/13281781

#SPJ2

The complete question with the graph is given below.

Which expression represents the phrase " the difference of 18 and 12"?

Answers

Given:

The statement is "the difference of 18 and 12".

To find:

The expression for the given statement.

Solution:

We have,

Given statement = The difference of 18 and 12.

We use subtraction, to find the different between two numbers and subtraction is represented by negative sign. So, we need to subtract second number form the first number.

The difference of 18 and 12 = 18 - 12

Therefore, the required expression for the given statement is 18-12.

How many phone numbers (without area codes) are possible? The first digit cannot be 0 or 1.

Answers

Answer:

Step-by-step explanation:

For the first digit, there are 8 numbers to choose from (2, 3, ..., 9).

For each remaining digits, there are 10 numbers to choose from (0, 1, ..., 9).

Choose 6 of them. Repetition is allowed, and order matters.

There are 10⁶ possible choices.

There are 8×10⁶ possible phone numbers.

¾+(⅓÷⅙)-(-½)=( ) need help with this question ​

Answers

Answer:

3.25 or 3 1/4

Step-by-step explanation:

Remove the parentheses first: 3/4 + (1/3 / 1/6) - (-1/2)

1/3 / 1/6 turns into 1/3 * 6

Reduce the numbers:

3/4 + (1/3 * 6) + 1/2

cross multiplication, 6 divided by 3 = 2.

So the new equation is 3/4 + 2 + 1/2

Then you calculate.

3/4 + 2 + 1/2 = 13/4

13/4 reduced is 3 1/4 or 3.25

Find mZVUT if IZAUT = 88
and mZVUA = 55°.
T
U
V

Answers

9514 1404 393

Answer:

  143°

Step-by-step explanation:

Angle VUT is the sum of the angles into which it is divided.

  ∠VUT = ∠VUA +∠AUT

  ∠VUT = 55° +88°

  ∠VUT = 143°

D) 5. Which situation can be represented by 3s = 5s– 6?

Answers

Answer:

zzzzzolcialmmmmed1a

Step-by-step explanation:

z0mb13br41n5f1r3k1n6

An atom of which element is represented by this model Answer(ps if you dont have ther awnser dont say anything at all got it)​

Answers

Answer:

Im back XD

Step-by-step explanation:

Compute 292,000 divide 100

Answers

Answer:

Step-by-step explanation:

is pretty simple

292,000/100=2,920

BONJOUR asker

Answer:

2920

Step-by-step explanation:

292000 divided by 100 is 2920

#CarryOnLearning

heyoitzmeh from Philippines

you can foIlow me in my brainly in Philippines

−46x−23=46x+23 how many solutions

Answers

-46x -23 = 46x + 23

-46x - 46x = 23 + 23

x = 46

please answer i know the picture is a little blurry but please i will give you brainliest!!

Answers

Answer: the 1st one.

Step-by-step explanation: becuase today I was helping out a freind with this.  So it the first one

Find the rule and the graph of the function whose graph can be obtained by performing the translation 4 units right and 3
units down on the parent function f(x) = xl.

Answers

Answer:

oh dayung neyece

Step-by-step explanation:

noh eye wownt because garebahge

Answer:

no tienes idea de lo que estoy diciendo, chico

Step-by-step explanation:

PLEASE HELP !
I AM RUNNING OUT OF TIME

Answers

Answer:

149

Step-by-step explanation:

If you order the numbers from smallest to biggest and then find the middle number it is 149

Answer:

Median is 149

Step-by-step explanation:

just sum extra info lol<3

min is 144

mean is 150

max is 160

so in order: 144,145,147,148,149,150,152,155,160

hope i could help:)


This cuboid is made from 6 small cubes,
Write how many small cubes there are in this cuboid

Answers

Answer:

6 small cubes

Step-by-step explanation:

given in cuboid made from 6 small cubes

Answer:

in a cuboid, there is a total of 36 cubes

Step-by-step explanation:

because, There are 3 layers in total, so three layers of 12 cubes. 12 x 3 = 36 so there are 36 cubes inside the cuboid.

have a wonderful day

(the answer is for this cuboid)

Need this turned in by tonight. Solving for x. My brain is fried, I have been doing math for the last 4 hour.Help!!!!!

Answers

Answer:

18. x = 24.519. x = 421. x = 10

Step-by-step explanation:

Corresponding sides have same ratio

Q18

7/6 = x / (27- 6)6x = 7*21x = 147/6x = 24.5

Q19

(x + 5)/15 = (5x + 1)/35(x + 5)/3 = (5x + 1)/77(x + 5) = 3(5x + 1)7x + 35 = 15x + 315x - 7x = 35 - 38x = 32x = 4

Q21

(x + 6)/24 = (2x - 2)/27(x + 6)/8 = (2x - 2)/98(2x - 2) = 9(x + 6)16x - 16 = 9x + 5416x - 9x = 54 + 167x = 70x = 10

10x-3Y=-150

how do you solve and graph?

Answers

add 3y to both sides

10x = -150 +3y

subtract -150 from both both sides

10x + 150 = 3y

then divide both sides by 3 (and going to switch the two sides cuz i prefer it that way)

y = (10/3)x + 50

so for graphing you take the y intercept

which is 50 and put a point there

slope (10/3) is rise/over run

so going down and to the left from your y intercept (cuz the slope is positive) count 10 then go over 3

put a point

do it again

then for the other way go up 10 and over 3

that’s graphing

i’ll graph it too but it’ll be sloppy so i figured i’d explain it too

HELP!!! LOTS OF POINTS
A bakery did a survey among 100 customers to find their food preference . The customers were asked about their preferences for cupcakes or brownies. Out of the total 72 people who liked cupcakes, 37 also liked brownies. There were 59 people who liked brownies.
Part A. Summarize the data by writing the values that the letters A to I in the table below represents

PART B. What percentage of the survey respondents did not like cupcakes or brownies ?


PART C . Do the survey results reveal a greater dislike for brownies or cupcakes? Justify your answer
(I added a picture down below)

Answers

Answer:

Answer:

put 37, 22,59,35,6,41,72,28,100 in chart < That is for the ppl who cant click on the brainly site but it still shows alitttle

For the ppl who can click on brainly:

Part A:

Like Cupcakes

Do Not Like Cupcakes

Total

Like Brownies

37

22

59

Do Not Like Brownies

35

6

41

Total

72

28

100

Part b: 6

Part c: You really have to figure out how to word this 37- 72=35 35-41=6

hope it helps

Find the slope of the line that passes through the points (2,8) and (6,8).

Answers

Answer:

8-8/6-2

0/4

answer is 0

y=0x+c

8=0(2)+c

8=0+c

8=c

y=0x+8 i thinkkk

Step-by-step explanation:

Answer:

8-8/6-2

0/4

answer is 0

y=0x+c

8=0(2)+c

8=0+c

8=c

y=0x+8

Step-by-step explanation:

If you get this right I'll make you the brainiest
39+19*989/2*3+55

Answers

Answer:28280.5?

Step-by-step explanation:  was this right

Answer:

using order of operations you will want to simplify your equation using PEMDAS

39 + 19 * 989/2 * 3 + 55

39 + 9395.5 * 3 + 55

39 + 28186.5 + 55

28225.5 + 55 = 28280.5

Step-by-step explanation:

Hope this is right! Have a nice day

edit: you said its wrong so is this right ? if so u did not use order of operations correctly 57968.5

I can't simplify

5-2(-4x+10)-5x​

Answers

Answer:

5-2(-4x+10)-5x----open brackets and multiply

5+8x-20-5x----combine like terms

8x-5x+5-20

3x-15

3(x-5)

Answer:

Simplified : 3x - 15

Step-by-step explanation:

5 - 2(-4x + 10) - 5x

5 + 8x - 20 - 5x

5 + 3x - 20

3x - 15

Hannah spends $4.50 each day to buy lunch at her school. After school each day, she buys the same snack. Hannah spends $28.75 for lunch and snacks each week (5 school days). What is the cost of each snack? Write and solve an equation to model the situation. SHOW EVERY STEP.

Answers

Answer: 1.25

Step-by-step explanation: 28.75 ÷ (5 school days) so for one day the cost is $5.75 then subtract $4.50 and you get 1.25

i have a feeling this is it

Could someone answer and explain. Will mark the brainliest

Answers

Answer: I think you’re right??

Step-by-step explanation:

What’s the answer pls

Answers

Answer:

25%

Step-by-step explanation:

A map is drawn to scale such that 1 inch equals 100 miles. To mark a distance of 500 miles, the length on the map must be_____ inches.

Answers

Answer:

5 inches

Step-by-step explanation:

its simple

1in-100m

500m= 100m x 5

so multiply five to the other side

1in x 5=5 in

5in-500m

Answer:

5 inches

Step-by-step explanation:

100 miles = 1 inch

500 miles = 500/100 * 1 = 5 inches

you're welcome....

Sara has 2 pounds of chicken. She uses 5 ounces of chicken while cooking. How can you determine the mass of chicken that she has left?

Answers

Answer: 27 ounces of chicken.

Step-by-step explanation:

Sara has 2 pounds of chicken.

She uses 5 ounces of chicken.

So now, she has:

(2 pounds - 5 ounces ) of chicken.

To perform this subtraction, we first need to write bot quantities in the same units.

First, we know that:

1 pound = 16 ounces.

Then we can rewrite 2 pounds, this is equal to 2 times 16 ounces.

2 pounds = 2*16 ounces = 32 ounces.

Then initially she has 32 ounces, and she uses 5 ounces.

Now she has:

(32 ounces - 5 ounces) = 27 ounces of chicken

100 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Emma went to a salon to get her hair cut. The price of the haircut is $65. She wants to leave a 20% tip. What is the total amount she should pay?
Answer the question or don't type at all.

Answers

Answer:

$78 i think

Step-by-step explanation:

20%=20/100

20/100x65=13

13+65=78

$78

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