Consider the data set on the number line. Determine the interquartile range. A) 7 B) 5.5 C) −2 D) −9

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

GuDViN [60]

Answer:

Euler's method is a numerical method used in calculus to approximate a particular solution of a differential equation. As a numerical method, we have to apply the same procedure many times, until get the desired result.

In first place, we need to know all the values the problem is giving:

The step size is 0.2; h = 0.2. This step size is a periodical increase of the x-variable, which will allow us to calculate each y-value to each x.
The problem is asking the solution y(1), which means that we have to find the y-value assigned for x = 1, through the numerical method.
The initial condition is y(0) = 9. In other words, $x_{o} = 0\\y_{0}=9$ .

So, if the initial x-value is 0, and the step size is 0.2, the following x-value would be: $x_{1}=0.2$ ; then $x_{2}=0.4$ ; $x_{3} =0.6; x_{4} =0.8;x_{5} =1$ ; and so on.

Now, we have to apply the formula to find each y-value until get the match of $x_{5}=1$ , because the problem asks the solution y(1).

According to the Euler's method:

$y_{1} =y_{0} +hF(x_{0};y_{0})\\y_{2} =y_{1} +hF(x_{1};y_{1})\\y_{n} =y_{n-1} +hF(x_{n-1};y_{n-1})$

Where $F(x;y)=x^{2} y-12y^{2}$ , and $x_{0} =0; y_{0} =9$ ; $h=0.2$ .

Replacing all values we calculate the y-value assigned to $x_{1}$ :

$y_{1} =9+0.2((0)^{2} 9-12(9)^{2})=-185.4$ .

Now, $y_{1} =-185.4$ , $x_{1} =0.2; h=0.2$ . We repeat the process with the new values:

$y_{2} =y_{1} +hF(x_{1};y_{1}) \\y_{2} = -185.4+0.2((0.2)^{2} (-185.4)-12(-185.4)^{2} )\\y_{2}=-82682.47$

Then, we repeat the same process until get the y-value for $x_{5} =1$ , which is $y_{5} = -1.0018$ , round to four decimal places.

Therefore, $y(1)=-1.0018$ .

7 0

3 years ago

Find the product <br> -3 x 4 x (-1)

astra-53 [7]

Answer:

12

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Help me out please?? Tysvm!

Kamila [148]

Answer:

910 mL = 0.91 L

9.1 L = 9,100 mL

0.901 kL = 901 L

91 L = 0.091 kL

90.1 L = 90,100 mL

9,010 mL = 9.01 L

Step-by-step explanation:

6 0

3 years ago

Evalute the experssion -280+12x=

Alina [70]

The answer is 23 1/3. First, you need to add 280 to both sides of the equations in order cancel out 280 and get 12x by itself. But remember whatever you do to one side of an equation, you must to do the other. So now you have 12x=280. Now divide both sides of the equation by 12 in order to get x completely isolated. 280 divided by twelve is 23 1/3.

4 0

2 years ago

Trigonometry

Natasha_Volkova [10]

Answer:

Step-by-step explanation:

For a triangle the area is

$A=\frac{1}{2}bh$

If our triangle is isosceles and the 2 congruent sides each measure 4 and they include an angle of 40 degrees, let's say that the vertex angle is 40 and the sides that are not the base each measure 4. If we drop an altitude from the vertex to the base, we cut the triangle into 2 right triangles, with the vertex angle being 20 degrees and the hypotenuse being 4. To find the base, then, which is opposite the angle, we use the sin ratio:

$sin(20)=\frac{b}{4}$ and

4sin(20) = b so

b = 1.368

But we need the whole base, and that is only half of it. So

2b = 2.736

To find the height, which is adjacent to the angle, we use the cos ratio:

$cos(20)=\frac{h}{4}$ and

4cos(20) = h so

h = 3.759

Now we have enough info to find the area of the triangle using the triangle area formula from above:

$A=\frac{1}{2}(2.736)(3.759)$ and

A = 5 meters squared.

7 0

3 years ago