Imagine that you need to compute e^0.4 but you have no calculator or other aid to enable you to compute it exactly, only paper and pencil. You decide to use a third-degree Taylor polynomial expanded around x =0. Use the fact that e^0.4 < e < 3 and the Error Bound for Taylor Polynomials to find an upper bound for the error in your approximation.

|error| <= _________

Answers

Answer 1

Answer:

0.0032

Step-by-step explanation:

We need to compute [tex]e^{0.4}[/tex] by the help of third-degree Taylor polynomial that is expanded around at x = 0.

Given :

[tex]e^{0.4}[/tex] < e < 3

Therefore, the Taylor's Error Bound formula is given by :

[tex]$|\text{Error}| \leq \frac{M}{(N+1)!} |x-a|^{N+1}$[/tex]   , where [tex]$M=|F^{N+1}(x)|$[/tex]

         [tex]$\leq \frac{3}{(3+1)!} |-0.4|^4$[/tex]

         [tex]$\leq \frac{3}{24} \times (0.4)^4$[/tex]

         [tex]$\leq 0.0032$[/tex]

Therefore, |Error| ≤ 0.0032


Related Questions

I need you guy’s help answer thanks so much

Answers

Answer:

D

Step-by-step explanation:

inverse just means opposite so if its shown dividing it first then adding, then the inverse is multiplying then subtracting

I need help ASAP thank you

Answers

Answer:

√9 × √6

√54

√27 × √2

Step-by-step explanation:

We can obtain the answer to the question given above as illustrated below:

3√6

Recall

a√b = √(a×a×b)

Thus,

3√6 = √(3×3×6)

3√6 = √(9 × 6)

Recall

√(a × b) = √a × √b

√(9 × 6) = √9 × √6

Therefore,

3√6 = √9 × √6

Recall

√9 × √6 = √(9 × 6)

√9 × √6 = √54

Thus,

3√6 = √54

Recall

√54 = √(27 × 2)

√54 = √27 × √2

Therefore,

3√6 = √27 × √2

Therefore,

3√6 = √9 × √6 = √54 = √27 × √2

Use the substitution method to solve this system.
y = 2x+4
3x+y = 9

Answers

Answer:

x = 1; y=6

Step-by-step explanation:

y = 2x +4

3x + y = 9

Substitute 2x+4 for y in 3x+y = 9

3x + y = 9

3x + 2x+4 = 9

5x + 4 = 9

5x = 9-4

5x = 5

5x/5 = 5/5

x = 1

Substitute 1 for  x in y = 2x +4

2(1) + 4

2 + 4

= 6

Answered by Gauthmath

Answer:

x = 1, y = 6

Point: (1, 6)

Step-by-step explanation:

y = 2x + 4

3x + y = 9

Since it’s saying that y = 2x + 4, substitute y for y = 2x + 4 in the second equation.

3x + 2x + 4 = 9

Add 3x + 2x (combining like terms)

5x + 4 = 9

Subtract 4 from 9

5x = 5

Solve for x

x = 1

Use x in the first equation.

y = 2x + 4

y = 2(1) + 4

y = 2 + 4

y = 6

Therefore x = 1 and y = 6
•••••••••••••••••••••••••••••••••••••••••••••••••
Check if the work is correct!

y = 6

x = 1

6 = 2(1) + 4

6 = 2 + 4

6 = 6


3(1) + (6) = 9

3 + 6 = 9

9 = 9

Y= 3x-1
2x+6=y substitution method

Answers

Answer: (7, 20)

Concept:

There are three general ways to solve systems of equations:

EliminationSubstitutionGraphing

Since the question has specific requirements, we are going to use substitution to solve the equations.

Solve:

Given equations

y = 3x - 1

2x + 6 = y

Substitute the y value since both equations has isolated [y]

2x + 6 = 3x - 1

Add 1 on both sides

2x + 6 + 1 = 3x - 1 + 1

2x + 7 = 3x

Subtract 2x on both sides

2x + 7 - 2x = 3x - 2x

[tex]\boxed{x=7}[/tex]

Find the value of y

y = 3x - 1

y = 3(7) - 1

y = 21 - 1

[tex]\boxed{y=20}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

pls help! I need the answer quickly! thank you!

Answers

The perimeter of a triangle is the summation of the three sides of the triangle. Base on the assumed values, the length of side BD is 2.

For [tex]\triangle ACD[/tex], the sides are: AC, AD and CD

So, the perimeter is:

[tex]P_{\triangle ACD} = AC + AD + CD[/tex]

For [tex]\triangle ABD[/tex], the sides are: AB, AD and BD

So, the perimeter is:

[tex]P_{\triangle ABD} = AB + AD + BD[/tex]

The difference in the perimeters is:

[tex]P_{\triangle ACD} - P_{\triangle ABD} =1 + \sqrt 3[/tex]

So, we have:

[tex](AC + AD + CD) - ( AB + AD + BD) =1 + \sqrt 3[/tex]

Open brackets

[tex]AC + AD + CD - AB - AD - BD =1 + \sqrt 3[/tex]

Evaluate like terms

[tex]AC + CD - AB - BD =1 + \sqrt 3[/tex]

Make BD the subject

[tex]BD = AC + CD - AB - (1 + \sqrt 3)[/tex]

The solution cannot be completed because the side lengths of [tex]\triangle ACD[/tex] and [tex]\triangle ABD[/tex] are not given; so, I will assume the following values.

[tex]AC =2; CD = 1; AB = \sqrt 3[/tex]

[tex]BD = AC + CD - AB - (1 + \sqrt 3)[/tex] becomes

[tex]BD = 2 + 1 + \sqrt 3 - (1 + \sqrt 3)[/tex]

Open bracket

[tex]BD = 2 + 1 + \sqrt 3 - 1 - \sqrt 3[/tex]

Evaluate like terms

[tex]BD = 2[/tex]

Base on the assumed values, the length of side BD is 2.

Read more about perimeters at:

https://brainly.com/question/6465134

I need help with this question

Answers

Answer:

7

This question is tying to introduce an idea that

eventually becomes a calculus question ....

(4^2 + 3(4)) - (0^2+3(0))

             4 - 0

28 - 0       = 7

   4

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

1. Approach

The average rate of change can simply be defined as the slope of a line that passes through any two points on a coordinate plane. In this situation, one is given a function, and one is asked to find the rate of change over an interval.

Given function: [tex]f(x)=x^2+3x[/tex]

Intervale, [tex][0, 4][/tex]

This can be done by evaluating the endpoints of the interval by substituting them into the function. Then writing the resulting the form of a point on the coordinate plane ([tex]x, y[/tex]). Finally, one can find the slope of the line that passes through the points by using the following slope formula,

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Where ([tex]x_1,y_1[/tex]) and ([tex]x_2,y_2[/tex]) are coordinate points.

2. Find the points

With the function (f(x)), substitute the end points of the itnerval ( [0, 4] ) into the function to generate coordinate points,

[tex]f(x)=x^2+3x[/tex]

[ 0, 4 ]

[tex]f(0)=(0)^2+3(0)\\=0 + 0\\ =0[/tex]

Point: (0, 0)

[tex]f(4)=(4)^2+3(4)\\= 16 + 12\\ = 28[/tex]

Point: (4, 28)

3. Find the average rate of change,

Now substitute the points the formula to find the slope, then simplify to evaluate

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

(0, 0), (4, 28)

Substitute,

[tex]\frac{y_2-y_1}{x_2-x_1}\\\\=\frac{28-0}{4-0}\\\\=\frac{28}{4}\\\\= 7[/tex]

The average rate of change is 7.

GIVING 25 POINTS AND BRAINIER IF ANSWERED!

What is one thing you would not do when finding the question in a word problem?
A. Look for a problem similar to the word problem you are trying to solve.
B. The question may not be directly stated.
C. So you can understand what the facts are in the word problem.
D. To define your strategy or game plan to solve the word problem.

Answers

The answer to your question is A

Answer:

B. The question may not be directly stated.

The perimeter of a park is 300 feet the length of the park is 50 feet longer than the width. Find the length

Answers

Answer:

55.41 feet

Step-by-step explanation:

Let the width be x.

ATQ, (x+50)*x=300, x=5*srt(37)-25=5.41. Length is 55.41 feet

14feet 23feet round each measurement to the nearest ten

Answers

10ft
20ft
I hope that’s correct ☺️
Answer:

14 feet and 23

Step-by-step explanation:

It’s already rounded to the nearest tenth

The chi-square test statistic is χ2 = 18.68 and the P-value is between 0.0025 and 0.005. What conclusion should the researcher make? Use α = 0.05.

Answers

We don't know what the exact p-value is, but we are told that it's as large as 0.005 which is smaller than alpha = 0.05

Since the p-value is smaller than alpha, this means we reject the null hypothesis.

The way you can remember this is "if the p-value is low, then the null must go". By "low", I mean "smaller than alpha".

Recall that the p-value is the probability of observing that specific test statistic, or larger. So the chances of chi-squared being 18.68 or larger is a probability between 0.0025 and 0.005; there's a very small chance of this happening. The p-value is based entirely on the assumption that the null is correct. But if the null is correct, then the chances of landing on this are very small. We have a contradiction that basically leads to us concluding the null must not be the case. It's not 100% guaranteed of course, but it's fairly strong evidence.

In short, the p-value being smaller than alpha = 0.05 means we reject the null.

In order to accept the null, the p-value must be 0.05 or larger.

Which proportion would you use to solve the following problem?

A map has a scale of 1 cm : 5 km. Determine how far apart two cities are if they are 4 cm apart on the map.
A.
B.
C.
D.

Answers

Answer:

20 km

Step-by-step explanation:

We can use ratios to solve

1 cm          4 cm

--------  = ------------

5 km          x km

Using cross products

1 * x = 4 * 5

x = 20

20 km

Answer:

1/5 = 4/x

Step-by-step explanation:

Each cm on the map represents 5 km. If it shows 4 cm apart of the map, you can use the proportion 1 cm : 5 km = 4 cm : x km.

rewrite 7/10 and negative 2/5

Answers

0.7 and -0.4 is you wanted them as decimals

Will give brainliest answer

Answers

Answer:

14 hours

Step-by-step explanation:

Take any two consecutive high tides and to find their x coordinatey and sub them..

Hi. I need help with part b thank you so much if you can do so

Answers

9514 1404 393

Answer:

  Yes, that distance is the hypotenuse of a right triangle whose sides are known

Step-by-step explanation:

The diagram seems to show the path of the ball as being two segments that are at right angles to each other. Then the direct-line distance to the hole from the tee is the hypotenuse (part A) of the triangle.

Since the leg lengths are known, the Pythagorean theorem can be used (part B) to find the length of the hypotenuse. (The answer to Part B is also the answer to Part C.)

Find f(-2) if f(x) =x^4 +2x^2-1

Answers

Answer:

Plug -2 in for x of f(x)

--> -2^4 + 2(-2)^2 - 1

---> 23

f(-2) = 23

Find the missing side of the right triangle.

Answers

Answer:

√65

Step-by-step explanation:

you have to use the pythagoras theorem to find x which is the hypotenuse

x²=7²+4²

x²=49+16

√x²=√65

x=√65

I hope this helps

__ (5 + 4) = 2 * 5 + 2 * 4

PLEASE EXPLAIN HOW YOU GOT THE ANSWER

Answers

Answer:

x = 2

Step-by-step explanation:

→ Simplify

x × ( 9 ) = 10 + 8

→ Further simplify

9x = 18

→ Divide both sides by 9

x = 2

Solve this inequality: 14 <-7x

Answers

Answer:

x > -2

Step-by-step explanation:

14 <-7x

or, 14/-7=-7x/-7

or, -2 < x

What's the value of n if 13+19= n+25

Answers

32=n +25n= 32-25 = 7

.

.

..

.

.............

Answer:

[tex]13+19=n+25[/tex]

[tex]n+25=13+19[/tex]

Add 13+19= 32

[tex]n+25=32[/tex]

Now Subtract 25 from both sides

[tex]n+25-25=32-25[/tex]

[tex]n=7[/tex]

OAmalOHopeO

What are the common factors of 24 and 60

Answers

2 and 3 are the common factor of 24 and 60

Now there is a square city of unknown size with a gate at the center of each side. There is a tree 20 b from the north gate. That tree can be seen when one walks 14 bu from the south gate, turns west and walks 1775 bu. Find the length of each side of the city.

Answers

Answer:

The length of each side of the city is 250b

Step-by-step explanation:

Given

[tex]a = 20[/tex] --- tree distance from north gate

[tex]b =14[/tex] --- movement from south gate

[tex]c = 1775[/tex] --- movement in west direction from (b)

See attachment for illustration

Required

Find x

To do this, we have:

[tex]\triangle ADE \sim \triangle ACB[/tex] --- similar triangles

So, we have the following equivalent ratios

[tex]AE:DE = AB:CB[/tex]

Where:

[tex]AE = 20\\ DE = x/2 \\ AB = 20 + x + 14 \\ CB = 1775[/tex]

Substitute these in the above equation

[tex]20:x/2 = 20 + x + 14: 1775[/tex]

[tex]20:x/2 = x + 34: 1775[/tex]

Express as fraction

[tex]\frac{20}{x/2} = \frac{x + 34}{1775}[/tex]

[tex]\frac{40}{x} = \frac{x + 34}{1775}[/tex]

Cross multiply

[tex]x *(x + 34) = 1775 * 40[/tex]

Open bracket

[tex]x^2 + 34x = 71000[/tex]

Rewrite as:

[tex]x^2 + 34x - 71000 = 0[/tex]

Expand

[tex]x^2 + 284x -250x - 71000 = 0[/tex]

Factorize

[tex]x(x + 284) -250(x + 284)= 0[/tex]

Factor out x + 284

[tex](x - 250)(x + 284)= 0[/tex]

Split

[tex]x - 250 = 0 \ or\ x + 284= 0[/tex]

Solve for x

[tex]x = 250 \ or\ x =- 284[/tex]

x can't be negative;

So:

[tex]x = 250[/tex]

Factor the following expressions completely. Show and check all work on your own paper.
x^2+169

Answers

Is not factorable over real numbers, but if you want to use imaginary numbers then it would be (x+13i) (x-13i)

Answer with rational numbers: Not Factorable


Answer with imaginary numbers: (x-13i)(x+13i)


A building security code has 2 numeric
digits, O through 9, followed by 2 letters.
What is the probability that the first digit
is 9 and the last letter is A?

Answers

Answer:

Step-by-step explanation:

First number is 1/10

Last letter is 1/26

The second digit is 1/9

The first letter is 1/25

1/10 * 1/26 * 1/9 * 1/25

0.00001709

This assumes no duplication is allowed,

If there are duplications

then 1/10 * 1/10 * 1/26 * 1/26

0.000014782

find the surface area of the prism HURRY HURRY

Answers

Answer:

should be 192

Step-by-step explanation:

9. Find the value of the trigonometric ratio tan C​

Answers

Hi there!

[tex]\large\boxed{tanC = 40/9}[/tex]

tan = O / A, or the opposite side over the adjacent side.

From the diagram, we can see that the opposite side = 40 and the adjacent side = 9, so:

tan C = 40 / 9

Answer:

tan C = 40/9

Step-by-step explanation:

According to SOH - CAH - TOA, tan = opposite over adjacent.

In the picture, the opposite of tan C is 40 and the adjacent is 9.

So, tan C = 40/9

P.S. - Answer above is also correct.

simplify the following without using calculator

√50 + √98​

Answers

Answer:

The exact answer is 12*√2, if you need approximately answer it is 12*1.4= 16.8

Step-by-step explanation:

√50 + √98​ ​= √(25*2)+√(49*2)= √25√2+√49*√2= 5√2+7*√2=12*√2

how many degrees are there in the angle made by the heart hand and the minute hand of a clock when it is 9 o'clock​

Answers

both angles are 90 degrees

A physician orders Diflucan oral suspension 200 mg now followed by 100 mg daily for a total of two weeks. How many 35 mL bottles of Diflucan 10 mg/ml suspension are needed to fill this prescription?

Answers

Answer:

Step-by-step explanation:

Total amount = 200 mg + (13 days)×(180 mg)/day = 2620 mg

One 35 mL bottle contains (35 mL)×(10 mg)/mL) = 350 mg of medication.

(2620 mg)×(1 bottle)/(350 mg) ≈ 7.5 bottles

8 bottles are needed.

A restaurant operator in Accra has found out that during the lockdown,if she sells a plate of her food for Ghc 20 each,she can sell 300 plates but for each Ghc5 she raises the price,10 less plates are sold. A.Draw a table relating 5 different price levels with their corresponding number of plates sold.

B.Use the table to find the slope of the demand

C.Find the equation of the demand fraction.

D.Use your equation to determine the price in Ghc if she sells one plate of food to maximize her revenue

Answers

The demand equation illustrates the price of an item and how it relates to the demand of the item.

The slope of the demand function is -1/2The equation of the demand function is: [tex]R(x) = (300 - 10x) \times (20 + 5x)[/tex]The price that maximizes her revenue is: Ghc 85

From the question, we have:

[tex]Plates = 300[/tex]

[tex]Price = 20[/tex]

The number of plates (x) decreases by 10, while the price (y) increases by 5. The table of value is:

[tex]\begin{array}{cccccc}x & {300} & {290} & {280} & {270} & {260} \ \\ y & {20} & {25} & {30} & {35} & {40} \ \end{array}[/tex]

The slope (m) is calculated using:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

So, we have:

[tex]m = \frac{25-20}{290-300}[/tex]

[tex]m = \frac{5}{-10}[/tex]

[tex]m = -\frac{1}{2}[/tex]

The equation of the demand is as follows:

The initial number of plates (300) decreases by 10 is represented as: (300 - 10x).

Similarly, the initial price (20) increases by 5 is represented as: (20 + 5x).

So, the demand equation is:

[tex]R(x) = (300 - 10x) \times (20 + 5x)[/tex]

Open the brackets to calculate the maximum revenue

[tex]R(x) =6000 + 1500x - 200x - 50x^2[/tex]

[tex]R(x) =6000 + 1300x - 50x^2[/tex]

Equate to 0

[tex]6000 + 1300x - 50x^2 =0[/tex]

Differentiate with respect to x

[tex]1300 - 100x =0[/tex]

Collect like terms

[tex]100x =1300[/tex]

Divide by 100

[tex]x =13[/tex]

So, the price at maximum revenue is:

[tex]Price= 20 + 5x[/tex]

[tex]Price= 20 + 5 * 13[/tex]

[tex]Price= 85[/tex]

In conclusion:

The slope of the demand function is -1/2The equation of the demand function is: [tex]R(x) = (300 - 10x) \times (20 + 5x)[/tex]The price that maximizes her revenue is: Ghc 85

Read more about demand equations at:

https://brainly.com/question/21586143

how do i convert 134five to base ten

Answers

Answer:

44

Step-by-step explanation:

1×5² + 3×5¹ +4×5⁰

25+15+4

44

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