Help me please I'm not sure if im right

Use Euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the initial-value problem y' = x2y − 1 2 y

irina [24]

Answer:

Therefore the value of y(1)= 0.9152.

Step-by-step explanation:

According to the Euler's method

y(x+h)≈ y(x) + hy'(x) ....(1)

Given that y(0) =3 and step size (h) = 0.2.

$y'(x)= x^2y(x)-\frac12y^2(x)$

Putting the value of y'(x) in equation (1)

$y(x+h)\approx y(x) +h(x^2y(x)-\frac12y^2(x))$

Substituting x =0 and h= 0.2

$y(0+0.2)\approx y(0)+0.2[0\times y(0)-\frac12 (y(0))^2]$

$\Rightarrow y(0.2)\approx 3+0.2[-\frac12 \times3]$ [∵ y(0) =3 ]

$\Rightarrow y(0.2)\approx 2.7$

Substituting x =0.2 and h= 0.2

$y(0.2+0.2)\approx y(0.2)+0.2[(0.2)^2\times y(0.2)-\frac12 (y(0.2))^2]$

$\Rightarrow y(0.4)\approx 2.7+0.2[(0.2)^2\times 2.7- \frac12(2.7)^2]$

$\Rightarrow y(0.4)\approx 1.9926$

Substituting x =0.4 and h= 0.2

$y(0.4+0.2)\approx y(0.4)+0.2[(0.4)^2\times y(0.4)-\frac12 (y(0.4))^2]$

$\Rightarrow y(0.6)\approx 1.9926+0.2[(0.4)^2\times 1.9926- \frac12(1.9926)^2]$

$\Rightarrow y(0.6)\approx 1.6593$

Substituting x =0.6 and h= 0.2

$y(0.6+0.2)\approx y(0.6)+0.2[(0.6)^2\times y(0.6)-\frac12 (y(0.6))^2]$

$\Rightarrow y(0.8)\approx 1.6593+0.2[(0.6)^2\times 1.6593- \frac12(1.6593)^2]$

$\Rightarrow y(0.6)\approx 0.8800$

Substituting x =0.8 and h= 0.2

$y(0.8+0.2)\approx y(0.8)+0.2[(0.8)^2\times y(0.8)-\frac12 (y(0.8))^2]$

$\Rightarrow y(1.0)\approx 0.8800+0.2[(0.8)^2\times 0.8800- \frac12(0.8800)^2]$

$\Rightarrow y(1.0)\approx 0.9152$

Therefore the value of y(1)= 0.9152.

4 0

3 years ago

Find the values of x for which the combined function h(x) = is undefined if f(x) = 5x + 1 and g(x) = x2 - 9.

Rama09 [41]

We need to know the definition of the "combined function" h(x). I'm going to guess--by looking at answers--that the function is $h(x)=\frac{f(x)}{g(x)}$ making it

$h(x)=\frac{5x+1}{x^2-9}$

This function is undefined wherever the denominator is equal to 0 (division by zero is undefined). Factor the denominator.

$h(x)=\frac{5x+1}{(x+3)(x-3)}$

The two values of x that make the denominator 0 are 3 and -3, otherwise written $x=\pm 3$ .

5 0

2 years ago

What is the value of 3-6(z-2) if z=-2

krek1111 [17]

Answer:

27

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Step-by-step explanation:

Step 1: Define

3 - 6(z - 2)

z = -2

Step 2: Evaluate

Substitute in z: 3 - 6(-2 - 2)
(Parenthesis) Subtract: 3 - 6(-4)
Multiply: 3 + 24
Add: 27

6 0

2 years ago

Read 2 more answers

Anna is saving to buy some souvenirs on a family vacation. She has already saved $125, and she saves another $2 from her

FinnZ [79.3K]

We can assume that the y-intercept for this equation is 125, because that would be how much Anna already has saved before she begins saving money from her allowance. Then, we know that Anna adds $2 to her savings each day from the problem, so we know that the slope will be positive 2 then.

Equation:

y = 2x + 125

Graph:

Attached below

Hope this helps!! :)

6 0

2 years ago

Read 2 more answers

Last year, ginger cost $15 per kilogram. Due to a harvest shortage this year, the price of ginger has to increase by 15% per kil

Anastaziya [24]

<h3>Answer: 17.25 dollars</h3>

=======================================================

Explanation:

15% of 15 = 0.15*15 = 2.25

The cost has increased by $2.25 which means the cost per kilogram is now 15+2.25 = 17.25 dollars

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As a slight shortcut, we can multiply the old cost (15) by the multiplier 1.15 to get the same result:

1.15*15 = 17.25

This method allows us to chain together many percentage increases, and it also allows us to include percentage decreases as well. Note how 1.15 is basically the result of 100% + 15% = 1.00+0.15 = 1.15

4 0

2 years ago

Help me please I'm not sure if im right​

Help me please I'm not sure if im right