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3 years ago

How do we multiply numbers

1 answer:

7 0

To multiply a number, simply take a number (Let's say 4) and another number (Let's say 3). If you multiply 4 by 3, you are simply taking the number 4, and adding it to itself 3 times (4 + 4 + 4).

I hope this makes sense, please tell me if you need some more information.

Hope this helps!

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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

Plz help me do this

MrRissso [65]

Answer:

(i) 16 (ii) 29 (iii) 76 (iv) 23

Step-by-step explanation:

i just plugged everything into the equations.

3 0

3 years ago

Micah recorded the amount of time his mom and dad spend reading bedtime stories. He plotted the data in the box plot below.

katrin [286]

Answer:

The lengths of time that his mom reads are typically longer and have more variability than the lengths of time that his dad reads.

Step-by-step explanation:

The Mom's plot is longer in ranges, therefore, she would have more variability than the dad.

4 0

3 years ago

Read 2 more answers

At a hockey game, a vendor sold a combined total of 148 sodas and hot dogs. The number of sodas sold was three times the number

AleksandrR [38]

Answer:

37 hot dogs and 111 sodas

Step-by-step explanation:

148 divided by 4= 37

148 - 37= 111

if the number of sodas was three times it would have to be broken up into three groups making the hot dogs 37 and sodas three times the amout would be 111. hope this helped sorry for any spelling mistakes

3 0

2 years ago

Read 2 more answers

60 pOINTS HELP PLEASE 4. A 20-kg child is tossed up into the air by her parent. The child is 2 meters off the ground traveling 5

Solnce55 [7]

K.E=0.5mv^2
GPE=mgh
The child has both K.E and GPE
$ke = 0.5 \times 20 \times {5}^{2} \\ ke = 10 \times 25 \\ ke = 250 \: joules$
$gpe = 20 \times 9.81 \times 2 \\ gpe = 40 \times 9.81 \\ gpe = 392.4 \: joules$
g is taken as 9.81

6 0

3 years ago