Let f be a differentiable function such that f(3) = 2.345 and f' (x) = ln (x^2+ 1). What is the value of f (5)?
A) 3.301
B) 5.631
С) 6.950
D) 7.976

Answers

Answer 1

Use a linear approximation to [tex]f(x)[/tex] centered at [tex]x=3[/tex]:

[tex]f(x)\approx f(3) + f'(3)(x-3)[/tex]

Then

[tex]f(5)\approx2.345+\ln(3^2+1)(5-3)\approx6.95[/tex]

which makes C the most likely choice.

Answer 2

Here we want to solve the differential equation, by finding the Taylor expansion of the function and evaluation we will find that f(5) = 6.950, so the correct option is C.

Taylor series the equation:

Here we must start by doing a Taylor expansion of the function, remember that the Taylor expansion is given by:

f(x) = f(a) + f'(a)*(x - a) + ...

The series has more terms, but we can work with two to get an estimation, if we use a = 3 we get:

f(x) = f(3) + ln(3^2 + 1)*(x - 3) = 2.345 + ln(10)*(x - 3)

Now we evaluate this in x = 5 to get:

f(5) = 2.345 + ln(10)*(5 - 3) = 6.950

So the correct option is C.

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Related Questions

math I need help with it!!!!!

elana went to the store where you can scoop your own popcorn and buy as much as you want. She bought 10 ounces spicy popcorn for $2.50

how much dose popcorn cost per ounce

Answers

Answer:

each ouce is worth 25 cents

solution

in order to solve this you need to create proportions so

10 ounces

per $2.50

well you want this to be a unit rate so you would have

10 ounces  =  1 ounce

2.50                      x

to get to the unit rate, you can see that you divided 10 from 10 ounces so you would do the same to the bottom ...

2.50/10 which is equal to 0.25.

So i have a question???

What time is shown on the clock below?




A 5:455:45

B 5:005:00

C 4:454:45

D 4:09

Answers

Answer:

There is no clock I can not help you without the completed question.

B. If the parents spent a total of $400 on everything for the party, how much more did they spend in addition to what was spent in parts (a) and (b)?
Part A answer of how much they spent was 64.50
Part B the answer of what they spent was 23.88

Answers

Answer:

311.62

Step-by-step explanation:

add a and b then subtract it by 400 there is ur answer my friend

Answer:

Plz mark me brainlest!

Step-by-step explanation:

311.62 Because I added that total and I got 551.78, and that doesn't make's sesne so I founded another answer for it and it's 331.62

Answer

331.62

Hope this helps you!

Express each of these system specifications using predicates, quantifiers, and logical connectives, if necessary.

a. At least one console must be accessible during every fault condition.
b. The e-mail address of every user can be retrieved whenever the archive contains at least one message sent by every user on the system.
c. For every security breach there is at least one mecha- nism that can detect that breach if and only if there is a process that has not been compromised.
d. There are at least two paths connecting every two dis- tinct endpoints on the network.
e. No one knows the password of every user on the sys- tem except for the system administrator, who knows all passwords.

Answers

The system specification with predicates, quantifiers, and logical connectives are:

a. ∃C(x) ∀F(y) such that if F(y) is true, C(x) is true.

b. ∀U(x) (∃M(y) if ∀U(z), ∃M(w) is true, then E(x) is true).

c. ∀B(x) (∃D(y) D(y) can detect B(x) ↔ (∃P(z) ¬P(z) is true)).

d. ∀E(x, y) (∃P(z, w) and ∃P(u, v) such that P(z, w) and P(u, v) connect

E(x, y)).

e. ∀U(x) (¬P(x) is true, except for the system administrator who knows all passwords: ∀U(y) P(y) if y is the system administrator).

We have,

a.

Let C(x) be the predicate "x is a console" and F(x) be the predicate "x is a fault condition".

The specification can be expressed as:

∀F(x) ∃C(y) such that if F(x) is true, C(y) is true.

b.

Let U(x) be the predicate "x is a user" and M(x) be the predicate "x is a message".

The specification can be expressed as:

∀U(x) ∃E(y) such that if ∀U(x), ∃M(z) is true, E(y) is true.

c.

Let B(x) be the predicate "x is a security breach", D(x) be the predicate "x is a detection mechanism", and P(x) be the predicate "x is a compromised process".

The specification can be expressed as:

∀B(x) ∃D(y) such that D(y) can detect B(x) if and only if ∃P(z) such that ¬P(z) is true.

d.

Let E(x, y) be the predicate "x and y are distinct endpoints" and P(x, y) be the predicate "x and y are connected by a path".

The specification can be expressed as:

∀E(x, y) ∃P(z, w) and ∃P(u, v) such that P(z, w) and P(u, v) connect E(x, y).

e.

Let U(x) be the predicate "x is a user" and P(x) be the predicate "x knows the password".

The specification can be expressed as:

∀U(x) ¬P(x) is true, except for the system administrator who knows all passwords, which can be expressed as:

∀U(x) (x is the system administrator → P(x)).

Thus,

The system specification with predicates, quantifiers, and logical connectives are:

a. ∃C(x) ∀F(y) such that if F(y) is true, C(x) is true.

b. ∀U(x) (∃M(y) if ∀U(z), ∃M(w) is true, then E(x) is true).

c. ∀B(x) (∃D(y) D(y) can detect B(x) ↔ (∃P(z) ¬P(z) is true)).

d. ∀E(x, y) (∃P(z, w) and ∃P(u, v) such that P(z, w) and P(u, v) connect

E(x, y)).

e. ∀U(x) (¬P(x) is true, except for the system administrator who knows all passwords: ∀U(y) P(y) if y is the system administrator).

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What annual rate of interest is required to double an investment in 9 years

Answers

Answer:

8%

Step-by-step explanation:

If an investment scheme promises an 8% annual compounded rate of return, it will take approximately (72 / 8) = 9 years to double the invested money

Tomi's band has won twice as many awards as All's band. Write an algebralc expression for the number of awards Tomi's band has won. Be sure to indicate what the variable in your expression represents​

Answers

Given problem;

  Write and algebraic expression for the number of awards Tomi's band has won;

   Let the number of award Tomi's band has won = T

   Let the number of award All's band has won  = A

We know;

      Tomi's band has won twice as many awards as All's band.

       T = 2 x A

  T  = 2A

The algebraic expression is T = 2A

Absolute Value of 7 equals -7
True or false

Answers

This would be false because the absolute value of 7 is 7. If the number were -7, then 7 would be the absolute value.

Tracy goes on a 3 day and night school band trip. There is no cost for travel and each band member only pays half the cost of the hotel room. However, each person is responsible for the cost of their own meals. His portion of the hotel bill is $49 per night and Tracy leaves a 10% tip for the maid service. Before tax, Tracy spends $32 per day on eating out plus 15% of this amount in tips. If Tracy spends a total of $280.74 on the band trip, what percent tax was Tracy charged on his food?
a.
6%
b.
7%
c.
8%
d.
9%

Answers

Answer:

D

Step-by-step explanation:

The service tax that is given on the food each day is 9 %.

What does service tax mean?

The government levies a service tax on particular service transactions carried out by the service provider. Suppose x% service tax is levied on a good on $n then the total amount that is to be paid is $(n(1+x/100)).

How to solve the problem?

Let the percent service tax that is charged on food be x%.

The situation is The total expenditure is $280.74 which is $49 per day on the hotel bill for 3 days on which a 10% tip was given for the maid services each day.  

$32 was spent each day on food plus 15% of that amount was given as a tip each day.

And x% of $32 was given on tax.

Then, the equation that best represents the given situation is

280.74/3=49+(0.10)(49)+32+(0.15)(32)+(x/100)(32)

Then 93.58=90.7+(32)(x/100)

⇒32x=2.88×100

⇒x=288/32=9%

Thus, the service tax that is charged on the food each day is 9 %.

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Isabelle collects hats and shoes. After collecting 18 hats this year, she had 39 hats and 49 shoes.
Which shows how to find the number of hats she started off with at the beginning of the year?
OA. 18 x 49
ОВ.
39 - 18
OC.
18 + 39
OD
49 + 18

Answers

Answer:

39-18

Step-by-step explanation:

39-18=21

Label the endpoints to round 49.672 to the nearest hundredth

Answers

Answer:

49.67 , you're welcome !

The round-off of the decimal number nearest to the hundredth is 49.67.

What is a round-off?

When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number. For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done.

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

The given number is 49.672 will be rounded off as below:-

49.672 = 49.67

Therefore, the round-off of the decimal number nearest to the hundredth is 49.67.

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if angle two equals 130 find the measure of angle 6 and the answer is not 50 or 130 willmark brainiest​

Answers

9514 1404 393

Answer:

  130°

Step-by-step explanation:

Angles 2 and 6 are both in the northeast corner of their respective intersections, so are "corresponding" angles.

Assuming lines A and B are parallel, corresponding angles have the same measure. The measure of angle 6 is 130°.

Let U = {5, 10, 15, 20, 25, 30, 35, 40)
A = {5, 10, 15, 20}
C - (10, 20, 30, 40).
Find AUC?

Answers

Answer:

auc=5,10,15,20,30,40

Solve for the predicted values of y and the residuals for the following data.

Advertising 12.5 3.7 21.6 60.0 37.6 6.1 16.8 41.2
Sales 148 55 338 994 541 89 126 379

Answers

Answer:

Step-by-step explanation:

Given the data:

Predicted value (X):

12.5

3.7

21.6

60.0

37.6

6.1

16.8

41.2

Sales (Y) :

148

55

338

994

541

89

126

379

Using a linear regression calculator to obtain the linear model for the predicted y values

Ypred = 15.23977X - 46.29181

_Y ____Ypred ___residual(Y - Ypred)

148 ___ 144.21 ______ 3.79

55 ____10.05 _______44.5

338 ___282.89______ 55.11

994 ___868.09______ 125.91

541 ____526.72 _____ 14.28

89 ____ 46.67 _______42.33

126 ____209.74 ______ −83.74

379____581.59 ______ - 202.59

what is 300% as a decimal and as a mixed number or fraction in simplest form

Answers

Answer:

3.0

Step-by-step explanation:

3/1 = 3 = 3.0


If the area of a shape is 50 square feet and the width is 10 feet, what is the lentgth

Answers

Answer:

5 feet

Step-by-step explanation:

To find the length of the shape, we can divide the area to the width.

Formula for area is [ a = lw ].

Since we are solving for length, the formula will be [ l = a/w ]

l = 50/10

l = 5

Best of Luck!

The answer of your question is 5 feet

complete ratio for the brain thingy

Answers

Answers
20,16
75,60
2.5,2

A class has 20 students.the teacher divides them into teams of 4 students.how many teams are there?

Answers

Answer:

5

Step-by-step explanation:

20 divided by 4 equals 5

or

4 times 5 equals 20

or

4+4+4+4+4=20

or

5+5+5+5=20

The answer is 5, there are 5 teams.

7. Drag and drop each of the values below to correctly complete the inequality statement.
10
✓ 20
3.9
3

Answers

Answer:

4231

Step-by-step explanation:

Take the test

What is the LCM of 550731776 and 21381376 || SUPER URGENT, WILL GIVE BRAINLIEST TO FIRST AND CORRECT ANSWER!!!!!!

Answers

Answer: LCM = 45,997,668,663,296

Answer:

The Least Common Multiple (LCM) is: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 7 x 7 x 7 x 7 x 7 x 17 x 17 x 17 x 17 = 45997668663296

Help me represent this easy equation: For every unit of X you must produce 3 of Y

Answers

Answer:

Okay the, 3 of Y by every unit of X. Simple.

Step-by-step explanation:

convert 3.8 (8 repeating) into a fraction ​

Answers

Answer:

19/5

Step-by-step explanation:

Answer:

3 8/9

Step-by-step explanation:

I used a website

To rewrite a subtraction problem, the integer behind the subtraction sign has to be changed to its-?

Answers

Opposite sign which is an addition sign

noah receives a 5$ discount every month on his cell phone bill because he signed up for auto pay from his bank account. over the last 8 month , noah has paid a total of $ 280 for his cell phone bill. Watch would noah be charged for his cell phone bill each month if he stopped using auto pay


Answers

The answer would be he’d would have paid 320$

There are
There are
There are
altogether
The shoe store has 324 pairs of shoes and 187 pairs
of sandals. How many pairs of shoes and sandals
does the shoe store have in all?
pairs of shoes.
pairs of sandals
pairs of shoes and sandals​

Answers

Answer:

shoes 324×2 =648

sandals 187×2 = 374

so 374 + 648 = 1022 shoes and sandal pairs

PLEASE MARK AS BRAINLIEST!!!!

ITS URGENT!!

Answer:

511 pairs and 1022 footwear pieces

Step-by-step explanation:

simplify 3 to the power of 2 times 3 to the power of 5

Answers

Answer:

2187

Step-by-step explanation:

3 ^2  * 3 ^5 = 2187

please mark brainliest

The answer is 3⁷ because when you are multiplying exponents with the same base, you keep the base and add the exponents. an example of this would be  4² x 4³. To simplify the expression you ignore the base, which is 4, and add the 2 and 3 to get 4⁵. So the answer to your question is 3⁷.

why is earth called living planet​

Answers

Answer:

because there are Living organisms such as Humans, plants, cells, bacteria etc.

Answer:

well if we are living and there are animals then this is a living planet and there are plants

Step-by-step explanation:

A store buys 8 sweaters for $72 and sells them for $288. How many profit does the store make per sweater?

Answers

Answer:

$27 per sweater

Step-by-step explanation:

To solve this, all we need to do is subtract the profit made by the amount the store bought the sweaters for:

288 - 72 = 216

Now, we can divide this number by 8 to find how much profit the store made per sweater:

216 / 8 = 27

So, the store made a profit of $27 per sweater.

Hope this helps :)

Mk bud I’m your tutor so let’s do 8 x 72 which equals 576 Mk then they stood it for 288 each so let’s x it again 8 x 288 equals 2,304 so now let’s - 576 from 2,304. 2,404 - by 576 equals 1,728

Suppose a turtle walks 3/8 of a mile in 50 minutes
What is the unit rate when the turtle’s speed is expressed in miles per hour (mph)?
A) 3/20 mph
B) 5/20 mph
C) 7/20 mph
D) 9/20 mph

Answers

Answer:

I'm not really sure but I want to say A) 3/20

Solve -4(x + 10) - 6 = -3(x - 2).

Answers

Answer:

-52 I think

Step-by-step explanation:

Im pretty sure...

The answer would be x=-52

Find the area of a circle shaped swimming pool with a radius of 5 meters

Answers

Answer:

25π

Step-by-step explanation:

using the formula πr² you replace r with the radius of 5 and square that which equals 25π or approximately 3.1415 and repeating numbers.

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