The fourth-degree Taylor polynomial of f(x) is [tex]27/(160 * 5^{(5/2)}).[/tex]
How can we determine the coefficient of [tex](x - 2)^4[/tex] in the fourth-degree Taylor polynomial of f(x)?To find the coefficient of[tex](x - 2)^4[/tex]in the fourth-degree Taylor polynomial of the function f(x), we need to compute the derivatives of f(x) up to the fourth derivative and evaluate them at x = 2.
Given that f(x) has the third derivative [tex](4x + 1)^{(3/2)}[/tex], we can start by calculating the first four derivatives:
[tex]f'(x) = 3(4x + 1)^{(1/2)}\\f''(x) = 6(4x + 1)^{(-1/2)}\\f'''(x) = -12(4x + 1)^{(-3/2)}\\f''''(x) = 36(4x + 1)^{(-5/2)}\\[/tex]
Next, we evaluate each derivative at x = 2:
[tex]f'(2) = 3(4(2) + 1)^{(1/2)} = 15^({1/2)} = \sqrt15\\f''(2) = 6(4(2) + 1)^{(-1/2)} = 6/\sqrt15\\f'''(2) = -12(4(2) + 1)^{(-3/2)} = -12/(15^{(3/2)})\\f''''(2) = 36(4(2) + 1)^{(-5/2)} = 36/(15^{(5/2)})\\[/tex]
Finally, we use these values to calculate the coefficient of [tex](x - 2)^4[/tex] in the fourth-degree Taylor polynomial, which corresponds to the fourth derivative:
coefficient =[tex]f''''(2) * (4!) / (4)^4[/tex]
Simplifying the expression:
coefficient =[tex](36/(15^{(5/2)})) * 24 / 256[/tex]
coefficient =[tex](9/(5^{(5/2)})) * 3 / 32[/tex]
coefficient [tex]= 27/(160 * 5^{(5/2)})[/tex]
Therefore, the coefficient of [tex](x - 2)^4[/tex] in the fourth-degree Taylor polynomial of f(x) is [tex]27/(160 * 5^{(5/2)}).[/tex]
Learn more about Taylor polynomials
brainly.com/question/30481013
#SPJ11
Order the angles in each triangle from smallest to largest.
Find the surface area of the
triangular prism.
10 ft.
3 ft.
3 ft
Given:
The figure of a triangular prism.
To find:
The surface area of the triangular prism.
Solution:
We know that, a triangular prism contains 2 congruent triangular surface and 3 rectangular surface.
Triangles have base 3 ft and height 2 ft.
Area of a triangle is
[tex]Area=\dfrac{1}{2}\times base\times height[/tex]
[tex]A_1=\dfrac{1}{2}\times (3)\times (2)[/tex]
[tex]A_1=3[/tex]
Area of congruent triangles are congruent. So,
[tex]A_1=A_2=3\text{ sq. units}[/tex]
Now the three rectangular surface have dimensions 10 by 3, 10 by 3 and 10 by 3 because the triangles are equilateral and the length of the prism is 10 ft.
Area of a rectangle is
[tex]Area=Length\times width[/tex]
[tex]A_3=10\times 3[/tex]
[tex]A_3=30[/tex]
Dimensions of all three rectangles are same, therefore there areas are equal.
[tex]A_3=A_4=A_5=30[/tex]
Now, the total surface area of the prism is
[tex]A=A_1+A_2+A_3+A_4+A_5[/tex]
[tex]A=3+3+30+30+30[/tex]
[tex]A=96[/tex]
Therefore, the total surface area of the prism is 96 sq. ft.
Please help me! 20 points!
Enter your answer and show all the steps that you use to solve this problem in the space provided.
What is the simplest form of the radical expression?
(in attachment)
A gymnast scores a total of 125 points in the first 4 meets of the season. At this rate, how many points will she score by the end of 14 meets
Answer:
i dont know but will u date me
Step-by-step explanation:
I need some help please
Answer:
10x - 5
Step-by-step explanation:
Perimeter is found by adding up all the side lengths.
(2x-4) + (5x+6) + (3x-7) = 10x - 5
You select a marble at random and then put it back. If you do this eight times, what is the best prediction possible for the number of times you will pick a red marble?
Answer:
1/8
Step-by-step explanation:
Maria ha invitado a 18 de sus compañeros de clase a su fiesta de cumpleaños .Si en total tiene 30 compañeros ,¿que porcentaje de la clase ha ido a su fiesta?
Answer:
59.9%
Step-by-step explanation:
100/30 = 3.3
3.3*18 = 59.9%
i’m so confused by this does anyone have this figured out
Answer:
you have to find the angels
Step-by-step explanation:
Perry's bikes rent bikes for $18 plus $4 per hour. Lea paid $42 to rent a bike for how many hours did she rent the bike?
Answer:
10.5 hours!
Step-by-step explanation:
13. Town officials are putting a pathway around a pool as shown below.
(4x+3)
pool
(2x-5) ft
deck
a) Determine the perimeter of the pool in terms of x. Write your answer in simple form and
include units. Show or explain your work.
b) Determine the area of the pool in terms of x. Write your answers as a trinomial and include
units. Show or explain your work.
Answer:
ghcfgnxfgxgfmvjbnjghjbnmxfhcgxfgcxgchmvjm
Step-by-step explanation:
good day
plz I need help on this really bad :(
Answer:
x+3y=4x+y
Step-by-step explanation:
8r2 in fraction form
8r^2 eight r squared hope this is right
It is the simplest fraction form
What is the volume of this?
Answer:
270 m³
Step-by-step explanation:
[tex]A_{triandle}[/tex] = [tex]\frac{5*12}{2}[/tex] = 30 m²
[tex]V_{triangular prism}[/tex] = 30 × 9 = 270 m³
What is the next term of the geometric sequence?
20, -10,5,
Answer:
0
Step-by-step explanation:
Answer: -2.5
Step-by-step explanation:
Ming's school is selling tickets to a play. On the first day of ticket sales the school sold 8 adult tickets and 1 student ticket for a total of $95. The school took in $71 on the second day by selling 2 adult tickets and 7 student tickets. Define two variables for this situation. Write a system of equations to represent this situation. What is the price each of one adult ticket and one student ticket?
Answer:
Your answer.
8x + y = 95.........(1)
2x + 7y = 71........... (2)
Y = 95-8x........ (3)
Put this value in eq 2
Then x = 11
Put x value in eq 3
Y = 7
Thank you. And give my answer as Brainlist answer. Follow me for more
Step-by-step explanation:
What multiplication fact could help me find out 24 ÷ 8 ?
Answer:
Step-by-step explanation:
That would be 8 x 3. It would help because 24/8 = 3.
In the figure shown the sum of the measures yxz and wxv is 75 degrees . what is the measure of zxw
Answer: 105 = WXZ
Step-by-step explanation:
180 = WXZ + 75
subtract both sides by 75 and you get WXZ is equal to 105
I'm not 100% sure, lmk if I'm wrong
how to the medium in the dot line????!! I don't want my mom to be mad at my grade please!!!!!!
Thank you whoever helps me!
Answer: To find the median, count the dots from left to right until you find the middle value.
Step-by-step explanation:
Ok so first it's not a dot line it's a dot plot. Second, let's define what a medium is. The medium is the "middle" of a sorted list of numbers. To find the Median, place the numbers in value order and find the middle number. Example: find the Median of {13, 23, 11, 16, 15, 10, 26}. The middle number is 15, so the median is 15. Tip to find the median from a list of value ordered numbers every time cross a number from each side. For example, if you cross 13 from above also cross 26 and if you cross 23 then also cross 10.
Back to your original question of how to find the medium on a dot plot you need to take all the numbers from your dotted line put them in order even if they are repeated and then cross each one on each side from right to left. Also remember if you cross out all the numbers right and left and end up with two numbers left then take them and add them and then divide by 2 and that will be the median.
An example is attached on here in order to help you understand what I am saying. Hope this helps. Your welcome and I hope you make your mama proud.
There are 9 counters in a bag.
7 of the counters are green.
2 of the counters are blue.
Ria takes at random two counters from the bag.
Work out the probability that Ria takes one counter of each colour.
Was wondering if anyone knows the answer to part A and B for this question?
Answer:
no idea
Step-by-step explanation:
Answer:
k so from my opinion
I think the answer is gonna be a
¿Sera cierto que existe una fraccion con numerador 20 equivalente a la fraccion 100/55?Justifica tu respuesta
Answer:
si porq si porq si si dices si es si
PLZ HELP ME & ANSWER CORRECTLY!!!!! NEED ANSWER ASAP!!!!!
Mica and Joy are standing at corner A of the rectangular field shown below.
Mica walks diagonally across the field, from A to corner C. Joy walks from corner A to corner B, and then to corner C. To the nearest hundredth of a mile, how much farther did Joy walk the Mica?
Answer:
0.54 miles more
Step-by-step explanation:
1. Find the Diagonal. d=w2+l2=1.252+0.752≈1.45774
2. 3/4+1 and 1/4=2 miles
3. 2 miles-1.46 estimate.
4. Solution...0.54
Tyler has $415 in his savings Tyler has $415 in his savings account account. He earns $45 a week mowing lawns. Write and solve an equation.using b for the variable to find how many weeks will he to work to have $1315 saved?
Answer:
20 weeks
Step-by-step explanation:
1315$-415$=900$
900/45=20
Hence 20 weeks
Answer: 45b
Step-by-step explanation: Divide 1315 with 45xb.
a²-a² what is the answer
Answer:
a² - a² = 0
hope it helps
Answer:
a ² - a ²= 1 a ² - 1 a ² = 0
you understand ?
Which of the following is equivalent to 3^-8 × 3^4
3^-4
3^-2
3^-12
3^-32
Please help:
Find the class width of this graph
Answer:
The biggest one is 32 to 38
Step-by-step explanation:
hope it helps
Factor the following expression completely.
2x^2y-18y
Answer:
Since both terms are perfect squares, factor using the difference of squares formula,
a2-b2=(a+b)(a−b) where a=x and b=3.2y(x+3)(x−3)
Step-by-step explanation:
hope this helps!!!
-3/4x=-5
Please help fast!!!
Answer:
x=3.75
Step-by-step explanation:
-3/4x=-5
x-3 x-3
4x=15
/4 /4
x=3.75
Answer:
x = 3.75
Step-by-step explanation:
-3/4x = -5
(-3/4) -3/4x = -5(-3/4)
x = 3.75
there are 16 appetizers available at a restaurant. From these, janet is to chose 13 for her party. How many groups of 13 appetizers are possible
Answer:
560
Step-by-step explanation:
The best way to do this is to write it out, but with large ones like this you should use the equation:
C(n,r) = n!/(r!(n-r)!),
where:
C(n,r) is the number of combinations;
n is the total number of elements in the set; and
r is the number of elements you choose from this set.
Find the length of y
Answer:
25 cm
Step-by-step explanation: