By using Taylor's method of order two, we can approximate the solution for the initial-value problem y = 1 + (t - y)[tex]^2[/tex], 2 ≤ t ≤ 3, y(2).
How can we approximate the solution using Taylor's method of order two for the given initial-value problem?To approximate the solution for the given initial-value problem using Taylor's method of order two, we need to follow a step-by-step process. Let's break it down:
1. Identify the function and its derivatives
The initial-value problem is defined as: y = 1 + (t - y)[tex]^2[/tex], 2 ≤ t ≤ 3, y(2). Here, y represents the unknown function, and t is the independent variable. We need to find an approximation for y within the given time interval.
2.Express the function as a Taylor series
Using Taylor's method, we express the function y as a Taylor series expansion. In this case, we'll use the second-order expansion, which involves the function's first and second derivatives:
y(t + h) ≈ y(t) + hy'(t) + (h[tex]^2[/tex])/2 * y''(t)
3.Calculate the derivatives
Next, we need to calculate the first and second derivatives of y(t). Taking the derivatives of the given equation, we have:
y'(t) = -2(t - y)
y''(t) = -2
4. Substitute the derivatives into the Taylor series
Now, we substitute the derivatives we calculated into the Taylor series equation from Step 2:
y(t + h) ≈ y(t) + h * (-2(t - y)) + (h[tex]^2[/tex])/2 * (-2)
Simplifying further:
y(t + h) ≈ y(t) - 2h(t - y) - hc[tex]^2[/tex]
5. Set up the iteration process
To obtain an approximation, we iterate the formula from Step 4. Starting with the initial condition y(2) = ?, we substitute t = 2 and y = ? into the formula:
y(2 + h) ≈ y(2) - 2h(2 - y(2)) - h[tex]^2[/tex]
6. Choose a step size and perform iterations
Choose a suitable step size, h, and perform the iterations. In this case, let's choose h = 0.1 and perform iterations from t = 2 to t = 3. We'll calculate the approximate values of y at each step using the formula from Step 5.
7. Perform the calculations and update the values
Starting with the initial condition, substitute the values into the formula and calculate the new approximations iteratively:
For t = 2:
y(2.1) ≈ y(2) - 2h(2 - y(2)) - h[tex]^2[/tex]
For t = 2.1:
y(2.2) ≈ y(2.1) - 2h(2.1 - y(2.1)) - h[tex]^2[/tex]
Repeat this process until you reach t = 3, updating the value of y at each iteration.
By following these steps, you can approximate the solution for the given initial-value problem using Taylor's method of order two. Remember to adjust the step size and number of iterations based on the desired accuracy of the approximation.
Learn more about Taylor's method
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FIND THE DOMAIN AND RANGE!!!!
what r passing marks out of 40
Answer:
36/40 - A, 32/40 - B, 28/40 - C, and 24/40 - D
Step-by-step explanation:
Answer:
18 is ur answer
thank youI need help it's geometry
Step-by-step explanation:
[tex] \sin(45) = \frac{x}{5} \\ \frac{1}{ \sqrt{2} } = \frac{x}{5} \\ x = \frac{5}{ \sqrt{2} } = 3.535[/tex]
[tex] \sin(45) = \frac{y}{5} \\ y = \frac{5}{ \sqrt{2} } = 3.535[/tex]
Answer:
[tex]\frac{5\sqrt{2} }{2 }[/tex]
Step-by-step explanation:
x=y
45-45-90 equation is x-x- x square root of 2
How many solutions does this system of equations have?
Answer:
One solution.
A system of linear equations has one solution when the graphs intersect at a point.
I hope it's helpful!
What is the domain of all of these points?
(8, 2), (12,9), (16, 16), (20, 23)
Answer:
8, 12, 16, 20
Step-by-step explanation:
those are the domains
Which of the following nets is for a pyramid?
2nd one
hope it helps you
The net of the pyramid is given by figure B
What is the surface area of the pyramid?The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid
Surface Area of Pyramid = B + ( 1/2 ) ( P x h )
Given data ,
A net is a two-dimensional representation of a three-dimensional shape that, when folded along the edges, forms the shape of the solid.
In the case of a pyramid, the net consists of a polygonal base and triangular faces that meet at a common vertex.
The number of triangular faces depends on the type of pyramid (triangular, square, pentagonal, etc.).
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pls help me it is inportant
Answer:
(5.x)+(5.2)
Step-by-step explanation:
Hope it helps you......
Answer:
nah
Step-by-step explanation:
what is the decimal word form of 120.95?
(−3⋅10^3 )⋅(4⋅10^6)=???
Answer:
-1.19164 x 10^8
Step-by-step explanation:
f(x) = -3x + 3
f(-2) = [?]
Help
is this the answer you're looking for? I'm sorry I'm confused
HELP I NEED HELP ASAP
Answer:
C
Step-by-step explanation:
Answer:
exponential;increase
Step-by-step explanation:
answer is C
What number is 40% of 15? Round to the nearest hundredth
Answer:
6Step-by-step explanation:
10% of 15 = 1.5x4=6solve the equation 3(x + 1) + 6 = 33.
Answer:
155
Step-by-step explanation:
If the mean of 5 numbers is 10 and the mean of other 15 numbers is 20 , what is the combined mean of both 20 numbers
9514 1404 393
Answer:
17.5
Step-by-step explanation:
The sum of the 5 numbers is 5·10 = 50.
The sum of the 15 numbers is 15·20 = 300.
The sum of all 20 numbers is then 50+300 = 350, so their mean is ...
mean = sum/number = 350/20 = 17.5
The combined mean of the 20 numbers is 17.5.
4k squared = 100 solve for k
Answer:
k = 5
Step-by-step explanation:
4k^2 = 100
4k^2/4 = 100/4
k^2 = 25
k=5
An account earns simple interest.
$1500 at 4% for 5 years
a. Find the interest earned.
$
b. Find the balance of the account.
Answer:
a) $300 in interest
b) $1800 account total
Step-by-step explanation:
Interest = Principal x Rate x Time
I = 1500(.04)(5)
I = 300
A = P + I
1800 = 1500 + 300
Find the ratio of 580 ml to 1.12 I to 104 ml
Answer:
580 : 1120 : 104
Step-by-step explanation:
1.12 ml -> 1120 ml
hence,
580 : 1120 : 104
Plz help me! I need an answer right away
is the answer 84.2??? if not pls explain THANK U ITS GEOMETRY
SOMEONE PLEASE HELP
and please explain it so I won't get confused further on
Help Please................
Answer:
split then d the trinangle with the base and the height and do the rectangle as length times width
Step-by-step explanation:
Answer: 1152
Step-by-step explanation:
Please Help! Ill give brainliest no fakes PLEASE!!
Answer:
4 and then 15
Step-by-step explanation:
second one: 6:4
last one: 15:10
Select all that apply. Select the formulas that give the amount P in the account after the first period.
Options :
a.) P=1.005Po
b.) P=1.02Po
c.) P=Po(0.02/4)
d.) P=Po(4.02/4)
e.) P=Po(1+ 0.02/4)
Answer:
a.) P=1.005Po
d.) e.) P=Po(1+ 0.02/4)
Step-by-step explanation:
From the compound interest formula:
P = P0(1 + r/n)^t
Rate = 2% = 2/100 = 0.02
n = Number of compounding times per period, quarterly ; n = (12 /3) months
P = P0(1 + 0.02/4)^1
P = p0(1 + 0.02/4)
Simplifying further :
P = P0(1 + 0.005)
P = p0(1.005)
The tree frog population in your back yard doubles every two weeks. Currently, there are 10 frogs in your back yard. Assuning that there are 4
weeks in a month how many tree frogs will there be in 3 months?
Answer:
there would be 40,960 tree frogs i think
Step-by-step explanation:
Answer:
640 tree frogs
Step-by-step explanation:
If 1 month = 4 weeks
3 months = 12 weeks (3x4)
After 2 weeks the frogs double to 20
After 4 weeks the frogs double to 40
6 weeks, it doubles to 80
8 weeks, it's 160
10 weeks it's 320
12 weeks, it's 640
please helppppppp
give u 10 pts
Answer:
y = x / -4
Step-by-step explanation:
Hope that helps!
12 (X + 2) - 4x = 4( 2X + 11 ) -20
Solve for X
Answer:
Step-by-step explanation:
12 (x + 2) - 4x = 4 (2x + 11) - 20
12 + 24 - 4x = 8x + 44 - 20
36 - 4x = 8x + 24
36 - 24 = 8x - 4x
12 = 4x
---- ----
4 4
3 = x
-x = -3
x = 3
Can someone help w/ this math problem plzz
Answer:
its C
Step-by-step explanation:
6 tubs hold 125 gallons in all how much does each run hold
Answer:
125/6= 20.8 gallons
Help fast please. I will give brainliest.
Answer:
Q5 ) A 80 UNITS²
pls give me brainliest
Pls pls pls pls help
Step-by-step explanation:
To prove that two lines are perpendicular, when all we have are those two lines, we can use the Linear Pair Perpendicular Theorem - If two straight lines intersect at a point and form a linear pair of equal angles, they are perpendicular.
Our diagonals intersect at point O, so we'd need to show the two linear angles formed at that intersection point are equal, and we can do that with triangle congruency.
A rhombus is a parallelogram, so we will use what we already know about parallelograms - that the diagonals bisect each other.
It is then easy to show that the triangles ΔAOD and ΔAOB are congruent using the Side-Side-Side postulate, and from that that ∠AOD ≅ ∠AOB.
And now, since ∠AOD and ∠AOB are a linear pair, we use the Linear Pair Perpendicular Theorem - If two straight lines intersect at a point and form a linear pair of equal angles, they are perpendicular.
PROOF
(1) ABCD is a rhombus //Given
(2) AB=AD //definition of rhombus
(3) AO=AO //Common side, reflexive property of equality
(4) BO=OD // A rhombus is a parallelogram, a parallelogram's diagonals bisect each other
(5) △AOD≅△AOB //Side-Side-Side postulate.
(6) ∠AOD ≅ ∠AOB //Corresponding angles in congruent triangles (CPCTC)
(7) AC⊥DB //Linear Pair Perpendicular Theorem
The converse of this is also true: if a parallelogram's diagonals are perpendicular, it is a rhombus.