‏In Problems 1 and 2 use Euler's method to obtain a four decimal approximation of the indicated value . Carry out the recursion of ( 3 ) by hand , first using h = 0.1 and then using h = 0.05 .

y’ = x + y^2 , y(0); y(0.2)

Answers

Answer 1

I saw on your other question that you mention y (0) = 0. Let

f(x, y) = x + y ²

Now consider the recurrences in Euler's method,

[tex]\begin{cases}x_0=0\\x_n=x_{n-1}+h&\text{for }n>0\end{cases}[/tex]

[tex]\begin{cases}y_0=y(x_0)=0\\y_n=y_{n-1}+f(x_{n-1},y_{n-1})h&\text{for }n>0\end{cases}[/tex]

where h is the step size.

We then approximate y (0.2) in ...

• ... 2 steps for h = 0.1 :

[tex]\begin{cases}x_0=0\\y_0=0\end{cases}[/tex]

[tex]\begin{cases}x_1=x_0+0.1=0.1\\y_1=y_0+f(x_0,y_0)\times0.1=0\end{cases}[/tex]

[tex]\begin{cases}x_2=x_1+0.1=0.2\\y_2=y_1+f(x_1,y_1)\times0.1=0.01\end{cases}[/tex]

so that y (0.2) ≈ 0.01;

• ... 4 steps for h = 0.05 :

[tex]\begin{cases}x_0=0\\y_0=0\end{cases}[/tex]

[tex]\begin{cases}x_1=x_0+0.05=0.05\\y_1=y_0+f(x_0,y_0)\times0.05=0\end{cases}[/tex]

[tex]\begin{cases}x_2=x_1+0.05=0.1\\y_2=y_1+f(x_1,y_1)\times0.05=0.0025\end{cases}[/tex]

[tex]\begin{cases}x_3=x_2+0.05=0.15\\y_3=y_2+f(x_2,y_2)\times0.05=0.0075003125\end{cases}[/tex]

[tex]\begin{cases}x_4=x_3+0.05=0.2\\y_4=y_3+f(x_3,y_3)\times0.05=0.0150031252343798828125[/tex]

so y (0.2) ≈ 0.015.


Related Questions

A tortoise can reach speeds of 0.12 m/s. Work out the speed of a tortoise in
kilometres per hour (km/h)
T​

Answers

Answer:

yous should multiply it by 3.6;

0.12*3.6=0.432 km/h

ill mark brainlist plss help

Answers

Answer:

kilometers

Step-by-step explanation:

I hope it´s right for you

In the equation y=-x+2 first you graph...

Answers

Answer:

Step-by-step explanation:

sorry if its wrong

Which graph represents 49x2 + 4y2 + 196x – 40y + 100 = 0?

Answers

Answer:

D

Step-by-step explanation:

Answer:

its D

Step-by-step explanation:

desmos

I need help with this problem will mark the brainliest

Answers

Answer:

angle C = angle E. that my answer

Angle C equals angle e


[tex]4x + 2x = 20 \\ x + 3x = 50[/tex]
simotenus equation ​

Answers

Answer:

I think there is an error in the question, I assume it reads:

4x+2y=20

x+3y=50

If not, please make appropriate corrections to the question.

Answer: x=-4, y=18

Step-by-step explanation:

4x+2y=20

Simplify, divide by two,

2x+y=10.....................(1)

x+3y=50....................(2)

Multiply (2) by 2

2x+6y=100 ....................(2a)

Subtract (1) from (2a)

2x+6y - (2x+y) = 100 - 10

5y = 90

y=18..............................(3)

Substitute (3) into (1)

2x+(18)=10

2x = 10-18 =-8

x=-4  ............................(4)

Substitute (3) and (4) into (1) for verification

2x+y = 2(-4)+18 = 18-10 = 10   checks.

Substitute (3) and (4) into (2) for verification

x+3y=-4+3(18) = -4+54 = 50  checks.

Have a nice day!

help please my tutor is being annoying and she finally left she said i have to finish before she comes back

Answers

Answer:

2x-6

Step-by-step explanation:

I think it’s 2x-7 I’m not sure though

Incorrect 00:00 Evaluate the expression for x = 1.7. Enter your answer in the box. х2 + 3x​

Answers

Answer:

7.99

Step-by-step explanation:

x^2 +3x

Let x=1.7

(1.7)^2 +3(1.7)

2.89+5.1

7.99

Can someone help
Me with this please I will mark u brilliant

Answers

Answer:

Option 3 Is your answer

Step-by-step explanation:

Brainlist plz

A? is a graphical display of a set of data where each separate piece of data is shown as a
mark above a number line.

Answers

Answer:

dot plot a visual display in which each piece of data is represented by a dot above a number line.

Step-by-step explanation:

Question 10 (2 points)
Solve.
3x²+2=17

Answers

Answer:

x1

Step-by-step explanation:

It’s x1!!!!!!!!!!!!!!!!!!

How I find total surface area

Answers

Answer:

there's this site called ixl.com that I use to help me it works very good  I highly recommend it !

Step-by-step explanation:

The product of s and 10

Answers

Answer:

10s

Step-by-step explanation:

The product of s and 10

In mathematic, when the word "product" is used, it means multiplication.

10 × s ---> 10s *Both of them are the same.*

Hope this helps and stay safe, happy, and healthy, thank you :) !!

Answer:

The product of s and 10 = 10s

Step-by-step explanation:

The term “product” determines a multipaction problem.

The variable S is unknown within the value

so with a numerical and a algebraic number, the number comes together

Find the slope of the line that passes through (10, 10) and (1, 3).

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answers

using rule of gradient

y2 - y1 / x2 - x1

= (10 - 3) / (10 - 1)

= 7/9

Turner’s backyard deck cost $38.31 per square meter to build. The deck is 9 meters wide and 11 meters long. How much did it cost to build the deck?

Answers

Answer:

$3792.69

Step-by-step explanation:

First, we would find the area,

Area = width x length

Area = 9 x 11

Area = 99[tex]m^{2}[/tex]

Since each square meter costs $38.31, we would multiply the cost with the area,

Total Cost = 99 x 38.31

Total Cost = $3792.69

(Anyone can correct me if I'm wrong)

Write the word as an equation
2 1/2 is the same as the sum of the number w and 1/2
An equation that represents this sentence is...

Answers

The word as an equation 2 1/2 is the same as the sum of the number w and 1/2 is 2 1 / 2 = w + 1 / 2

How to write word as an equation

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

Therefore, the word as an equation 2 1/2 is the same as the sum of the number w and 1/2 is as follows;

The sum of the number w and 1/2 is w + 1 / 2.

Then, the word as an equation 2 1/2 is the same as the sum of the number w and 1/2 is

2 1 / 2 = w + 1 / 2

learn more on equation here: https://brainly.com/question/26352475

Find the solution of the system of equations.
y=1 = -x + 5 and y = 1/6-1
PLEASE HELP ME !!

Answers

x= -6
y= -2
Explanation is in photo below


h(x)=-5(x-1)^2+45
what is the maximum height

Answers

9514 1404 393

Answer:

  45

Step-by-step explanation:

The equation is that of a parabola in vertex form.

  y = a(x -h)^2 +k

where 'a' is the vertical scale factor and (h, k) is the vertex.

Comparing this to the given function, you find ...

  a = -5

  h = 1

  k = 45

The negative value of 'a' tells you the parabola opens downward, so the y-value of the vertex is the maximum value of the function: 45.

A negative number is always = the absolute value of a number

Answers

Answer:

To find the absolute value of an negative number, just take away the negative sign

The absolute value of a number can NEVER be negative

Step-by-step explanation:

For example, to find the absolute value of -22, it would be 22, since it is 22 points away from zero. To find the absolute value of -99.9, it would be 99.9.

A negative number is NOT always the absolute value of a number.

For example, the absolute value of 34 is, 34. If you plot it on a number line, it is 34 points away from zero, therefore proving a negative number is NOT always the absolute value of a number.

The absolute value of a number can NEVER be negative.

Answer:

The absolute value of a number is always POSITIVE! To find the absolute value, all you need to do is take away the negative sign!

Have a great day!

WILL GIVE BRAINLST

HAVE A AMAZING DAy !!

Answers

Answer:

u 2

and stay positive :)

Step-by-step explanation:

Hello! I do not know if you meant to put up a question, but I also hope that you have an amazing day! :)

What is the correct expanded form and value of 43?
O 4+4+4= 12
O 4.4.4=64
O 3+3+3+3= 12
O 3.3.3.3= 81

Answers

Your answer would be 4.4.4=64.

Answer:

B. 4・4・4= 46 I hope it helps.

What's the probability/area to the RIGHT of z = 1.35 ?

Answers

Answer:

Who was the first president of United States?

A Benjamin Franklin

B George Washington

C Abraham Lincoln

D John Adams

HURRY PLEASE!!!! Based on the information given, can you determine that the quadrilateral must be a
parallelogram? Explain.
Given: XN NZ and NY Z NW
X
Y
Z

Answers

Answer:

I'm going to say no.

Step-by-step explanation:

What you are given is true of a parallelogram but you still need some more information.

You would need at least one of the angles.

What is the place value of the 7 in 436.967

Answers

Answer:

thousandths

Step-by-step explanation:

What is the volume of the cone to the nearest cubic millimeter (use pi)

Answers

V= 183.2 cubic millimeter

Please help and thank you! Will mark whoever answers right the brainliest!
John will paint the walls and ceiling of the room shown. The windows measures 3 feet by 6 feet. The door measures 7 feet by 3 feet.
Part A: Describe the surfaces John will not paint.
Part B: Judy says you need to use subtraction to find the area of the surfaces John will paint. Is Judy correct? Explain.
Part C: A gallon of paint covers about 350 squared feet. How many gallons of paint will John need to buy to paint the walls and ceiling of the room? Justify your answer.

Answers

Answer:

Step-by-step explanation:

Part A. John will not be painting the floor area of that of the door or window openings.

Part B. Subtracting the areas of the floor, door, and window from the total surface area will provide the area to be painted so Judy is correct.

Part C.

We first need to find the area to be painted.

A=floor+2(wall1)+2(wall2)-window-door

A=14(7)+2(7)8+2(14)8-3(6)-3(7)

A=98+112+224-18-21

A=395 ft^2

Since a gallon of paint will cover 350 ft^2

395ft^2(gal/350ft^2)=1.13 gal

John will need approximately 1.13 gallons of paint. (Rounded to nearest hundredth of a gallon)

There are at least 5 slices of bread left in the bag. Use p as your variable

The inequality is:

Answers

Answer: p ≤ 5

Step-by-step explanation: The inequality is: p ≤ 5

Deondre drops a nickel from a balcony that is 125 meters in the air. The function y=-5t+125 can be used to represent y, the height of the coin in meters after t seconds. Write and solve an equation to find the time it will take for the coin to hit the ground. ​

Answers

The time it will take for the coin to hit the ground is 5 seconds for the given function.

What is distance?

Displacement and distance are terms used to describe how an object or person moves, but they have different meanings.

No matter where anything starts or ends, distance describes how much ground it has travelled. It is a scalar quantity with units like metres, kilometers, miles, etc. for measurement.

On the other hand, displacement describes a change in an object's or a person's location from their original position to their end position, including direction. Since it has both magnitude (the distance) and direction, it is a vector quantity. Displacement can be positive or negative depending on the direction of movement and is measured in units like metres, kilometers, miles, etc.

The given equation is  y=-5t² +125.

When the coin hits the ground the value of y = 0 thus,

y = -5t² + 125

0 = -5t² + 125

5t² = 125

t² = 25

t = ±5

Hence, the time it will take for the coin to hit the ground is 5 seconds.

Learn more about quadratic equations here:

https://brainly.com/question/29011747

#SPJ1

GIVING BRAINIEST!!!!!!What is the equation of the line that passes through 6,4 and 2,10

Answers

Answer:

y = -3/2x + 13

Step-by-step explanation:

(6,4) and (2,10)

Slope:

m=(y2-y1)/(x2-x1)

m=(10-4)/(2-6)

m=6/(-4)

m =  -3/2

Point-slope intercept:

y - y1 = m(x - x1)

y - 4 = -3/2(x - 6)

y - 4 = -3/2x + 9

y = -3/2x + 13

These figures are similar. The
area of one is given. Find the
area of the other.
3 in
area=24 m
6.17
[ ? jina

Answers

Answer:

a

Step-by-step explanation:

I’m looking for same answers
Other Questions
find the missing term of the arithmetic sequence17,____,23 Can you simplify 55/50 man drove his car a distance of 315 miles in 5 hours. If continuing at this rate is possible, he will travel ____ miles in 9 hours. what is 50% more than 40 PLZ HELP ITS EASY ITS DUE IN 5 MINUTES1. Which statement is true about DNA?a. DNA is an exact copy from parent to offspring.b. DNA is not necessary for an organism to reproduce.c. DNA contains genes that hold specific traits for an organism.d. Organisms create their own DNA sequence that is not like their parents. What are the benefits of adding a scoop of the water used to boil pasta to sauces? What does that equal I need help with 22 and 23! Asap! Please help! (ONLY TWO CAPITAL LETTERS FOR EACH)WHAT IS THE ANSWER CORRECTLY !!!!!! WILL MARK BRIANLIEST !!!!!! URGENT PLZ HELP IM ON A TIME CRUNCH Is this statement true or false? A chemical reaction is balanced when the number of atoms of each element is the same for both the reactants and the products. Answer this for 10 points What is the equation of the line that passes through the point (-6, -2) and has aslope of 1/6 ? . Traits that are due to _______ are considered to be acquired traits.A educationB nutritionC injuriesD all of these Use of Por For each of the following sentences, select the rule that describes how the word por is being used. To show movement within, through, along, or around an area To indicate a length of timeTo signify an exchangeTo express a reason or motiveTo indicate a substantiation or an action on someones behalfTo show gratitude or express an apologyTo indicate the means of communication or mode of transport With percentages multiplication and to expose per la temperatura actual en una ciudad de europa es de 4c y en en noticiero se imforma q bajara a lo largo del dia a 10c cual es la temperatura minima please help. Which statements are true about the figure? Question 9Which inequality corresponds to the graph shown? What idea Hitler propagated for the Aryans Conservation of momentum