To find the Taylor polynomial t3(x) for the function f(x) = xe^(-4x) centered at a = 0, we need to find the first four derivatives of f(x) at x = 0, evaluate them at x = 0, and use them to construct the polynomial.
The first four derivatives of f(x) are:
f'(x) = e^(-4x) - 4xe^(-4x)
f''(x) = 16xe^(-4x) - 8e^(-4x)
f'''(x) = -64xe^(-4x) + 48e^(-4x)
f''''(x) = 256xe^(-4x) - 256e^(-4x)
Evaluating these derivatives at x = 0, we get:
f(0) = 0
f'(0) = 1
f''(0) = -8
f'''(0) = 48
f''''(0) = -256
Using these values, we can construct the third-degree Taylor polynomial t3(x) for f(x) centered at x = 0:
t3(x) = f(0) + f'(0)x + f''(0)x^2/2! + f'''(0)x^3/3!
t3(x) = 0 + 1x - 8x^2/2 + 48x^3/3!
t3(x) = x - 4x^2 + 16x^3/3
Therefore, the third-degree Taylor polynomial for the function f(x) = xe^(-4x) centered at a = 0 is t3(x) = x - 4x^2 + 16x^3/3.
To know more about Taylor polynomial refer here:
https://brainly.com/question/31419648
#SPJ11
Factor ab + bc+ b² + ac.
A. (a + b)(b + c)
B. (a + c)(b + c)
C. b(a + b)(b + c)
Answer:
A. (a + b)(b + c)
Step-by-step explanation:
b( a + b ) + bc + ac
b( a + b ) + c ( b + a )
= (a + b)(b + c)
hope it helps!
Answer:
A
Step-by-step explanation:
a(b+c)+bc+bb
a(b+c)+b(c+b)
(b+c)(a+b)
how many cubes with a .25 inch side length will fit in a rectangular prism with a volume of 35.62
Answer:
142.48
Step-by-step explanation:
this i think is the answer
Find the median of the data set represented in the following stem-and-leaf plot.
62
63
64
67
Answer:
67
Step-by-step explanation:
Cement costs $76 per cubic yard. What is the cost of cement for a sidewalk that is 4 in. Thick, 3ft wide,and 40 ft. Long?
Answer:
112.46 yd³
Step-by-step explanation:
1 inch = 0.0278 yds
1 feet = 0.333 yd
Thickness = 4 inches = (4 * 0.0278) = 0.1112 yds
Width = 3 feets = (3 * 0.333) = 0.999 yds
Length = 40 feets = (40 * 0.333) = 13.32 yds
Volume of sidewalk :
Thickness * Width * Length
0.1112 * 0.999 * 13.32 = 1.479702816 yd³
1 yd³ of cement = $76
Cost :
1.479702816 yd³ * $76
= 112.457414016
= 112.46 yd³
A square has an area of 64 square units. If its sides were only half as long, what would its area be?
Answer:
16
Step-by-step explanation:
the sides now are 8x8
1/2 of that is 4x4 and 4x4=16
kayden mixed two solutions together which causes a chemical reaction and the solution becomes warm. which statement best describes what has happened
A. energy has been transformed from one form to another
B. energy has been created, where it did not exist before
C. the chemicals energy of the solution had been described
D. more energy has been created than has been destroyed
According to law of conservation of energy, the statement which best describes what has happened is that energy has been transformed from one form to another.
What is law of conservation of energy?According to law of conservation of energy, it is evident that energy is neither created nor destroyed rather it is restored at the end of a chemical reaction .
Law of conservation of mass and energy are related as mass and energy are directly proportional which is indicated by the equation E=mc².Concept of conservation of mass is widely used in field of chemistry, fluid dynamics.
Law needs to be modified in accordance with laws of quantum mechanics under the principle of mass and energy equivalence.This law was proposed by Julius Robert Mayer in the year 1812.
Learn more about law of conservation of energy,here:
https://brainly.com/question/29775341
#SPJ3
1. Use the number line to help you decide which statement is true.
Answer:
2/5 < 1/2
Step-by-step explanation:
First, find the LCM for both denominators because you can't multiply 2 to get to 5. The LCM of 5 and 2 are 10, so you put that as their denominator. Then you have to think what you multiplied by 5 or 2 to get 10. For 2/5, you multiplied 5 by 2 to get 10, so multiply the numerator by 2 too. For 1/2, you multiplied 2 by 5 to get 10, so multiply the numerator by 5. Now, you will have 4/10 and 5/10. It's pretty obvious that 5/10 is bigger than 4/10, so the correct answer is 2/5 < 1/2
I think I have the answer but, I really need help with the steps!
Answer:
simplify to:
6-32768/-60
simplify more
-32762/-60
take away the negatives
32762/60
simplify the fraction
16381/30
keep going till you get the answer
If you answer correctly I will give you brainlest 5 stars and a thank you
A baseball field has four bases that form the shape of a quadrilateral. If someone invented a
new game similar to baseball that had four extra bases in the field, what type of polygon would
the bases form?
Apentagon
Boctagon
Chexagon
Ddecagon
2.5 pounds of grapes cost $2.25 what is the cost per pound
Answer:
$0.9 per pound
Step-by-step explanation:
$2.25 divided by 2.5
Answer:
$0.9 per pound
Step-by-step explanation:
$2.25 divided by 2.5
divide the cost of the item by its weight in pounds
cos4A+sin4A-2cos2Asin2A=(2cos2A-1)2 prove it.
cos4A-sin4A=2cos2A-1
proved below.
Step-by-step explanation:
Given:
cos^4A-sin^4A=2cos^2A-1
LHS=cos^4A-sin^4A
=[cos^2A]^2-[sin^2A]^2
=[cos^2A+sin^2A][cos^2A-sin^2A]
=[1][cos^2A-(1-cos^2A)] [ cos^2A+sin^2A=1]
=[cos^2A-1+cos^2A]
=2cos^2A-1
=RHS.
Horse kg of grass in 12 days how much how much does he eat in 9 days
Step-by-step explanation:
The horse eats 9/12 in 9 days.
is there anyone who can help with this????
Answer:
C equals 48
Step-by-step explanation:
You add the two angles you have and take that answer and subtract it from 180 and that is the missing angle measure
B.e b.i.g b.r.a.i.n a.t a.l.l t.i.m.e!
(Be big brain at all time!)
B I G B R A I N :-))
You have 0.2 liter of an acid solution whose acid concentration is 16 moles per liter. You want to dilute the solution with water so that its acid concentration is only 12 moles per liter. Use the given model todetermine howmany liters of water you should add to the solution.
Answer: 0.067 litres of water
Step-by-step explanation:
The mode is:
Concentration of new solution = Moles of acid in original solution / (Volume of original solution + Volume of water added)
Assume volume of water added is w.
12 = 16 (0.2) / (0.2 + w)
(0.2 + w) * 12 = 3.2
0.2 + w = 3.2 / 12
w = (3.2 / 12) - 0.2
w = 0.067 litres of water
The amount of water you should add to the solution is 0.067 liters.
Given
You have 0.2 liters of an acid solution whose acid concentration is 16 moles per liter.
You want to dilute the solution with water so that its acid concentration is only 12 moles per liter.
The concentration of new solution;You can also use the solution dilution calculator in order to calculate the concentration of ions in a diluted solution.
The amount of water you should add to the solution is given;
[tex]\rm Concentration \ of \ new \ solution =\dfrac{\text{Moles of acid in original solution } }{\text{Volume of original solution + Volume of water added}}\\\\12=\dfrac{16(0.2)}{0.2+w}\\\\12 (0.2+w)=16(0.2)\\\\2.4 +12w=3.2\\\\12w=3.2-2.4\\\\12w=0.8\\\\w=\dfrac{0.8}{12}\\\\w=0.067[/tex]
Hence, the amount of water you should add to the solution is 0.067 liters.
To know more about concentration click the link given below.
https://brainly.com/question/882576
Please help me I am struggling I’m only in 6th grade doing harder math
Answer:
-7a+11
Step-by-step explanation:
someone help me pls 10 points
Answer:
x=-5
Step-by-step explanation:
I NEED HELP ASAP!!!!!!!!
Step-by-step explanation:
[tex]slope = \frac{rise}{run} = \frac{y2 - y1}{x2 - x1} \\ = \frac{ - 7 - 13}{5 - ( - 3)} \\ = \frac{ - 20}{8} \\ = \frac{ - 2 \times 10}{2 \times 4} \\ = \frac{ - 10}{4} \\ = \frac{ - 2 \times 5}{ 2 \times 2} = \frac{5}{2} [/tex]
A high school sponsored a badminton tournament. After each round, one-half of the players were eliminated. If there were 64 players at the start of the tournament, which equation models the number of players left after round 3?
(1) y=64(1-.5)^3
(2) y=64(1+.5)^3
(3) y=64(1-.3)^.5
(4) y=64(1+.3)^.5
Answer:
(1) y = 64(1 - .5)^3
Step-by-step explanation:
(1) y = 64(1 - .5)^3
If you are eliminated half, then you are removing 50% or .5 of the teams. The number of teams is getting smaller, so eliminate the choices with "+". The exponent refers to the number of rounds.
This is an easy one to check: 64, 32, 16, 8. There are 8 teams after three rounds.
y=64(1 - .5)^3
y= 64(.5)^3
y= 64(.125)
y= 8
ASAP please help me correct this if it is wrong
Answer:
I believe the answer for the first one is -3, 3, number 3 would be 12
Step-by-step explanation:
Because if you are dilating by 1/3 then you will be dividing by 3, so if your point A coordinates are -9,9 then that divided by 3 is -3,3
Number 3 is 12 because your total of units from point D to C is 18 and it says to dilate by scale factor of 2/3 which again means to divide by 2/3 making your new length 12 units.
(100 POINTS!!!) PLEASE HELP ME!!! FIRST TO ANSWER WILL GET BRAINLIEST! 14:40 LEFT!
Answer:
the third one
Step-by-step explanation:
Answer:
that would be c
Step-by-step explanation:
Sarah’s parents purchased a refrigerator for $320. If sales tax is 7% of the cost, how much tax did Sarah’s parents pay for the refrigerator
Answer:
22.4
Step-by-step explanation:
7% of the cost is 22.4
Answer:
$22.40
Step-by-step explanation:
Let's convert the 7% sales tax into a decimal, which should be 0.07Multiply the sales tax (as a decimal) by the cost of the refrigerator ($320). You should get $22.40Edit: Read something wrong, I fixed it, sorry.
Adam made note of all the bicycles and cars he could see parked or locked on a
certain city block. All the cars had exactly four wheels, and all the bicycles had exactly
two wheels. How many wheels were on the block if there were 15 bicycles and 7 cars?
How many wheels were on the block if there were x bicycles and y cars?
Answer
68 bicycles.
Let there be x bicycles, then there are (93 - x) tricycles.
From the given values:
2x + 3(93 - x) = 211
2x + 279 - 3x = 211
-x = 211 - 279 = -68
x = -68/-1 = 68.
Hence, the wheels were on the block if there were [tex]x[/tex] bicycles and [tex]y[/tex] cars are [tex]x=68[/tex] bicycles.
What is the simplification?
Simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving. '
Here given that,
Adam made note of all the bicycles and cars he could see parked or locked on a certain city block. All the cars had exactly four wheels, and all the bicycles had exactly two wheels.
Suppose that there are [tex]x[/tex] bicycles, then there are [tex](93 - x)[/tex] bicycles.
So,
[tex]2x + 3(93 - x) = 211\\2x + 279 - 3x = 211\\-x = 211 - 279 = -68\\x = \frac{-68}{-1}\\x= 68.[/tex]
Hence, the wheels were on the block if there were [tex]x[/tex] bicycles and [tex]y[/tex] cars are [tex]x=68[/tex] bicycles.
To know more about the simplification
https://brainly.com/question/11589761
#SPJ2
The length of a driveway is 18 yards what is it in feet?
Answer:
Step-by-step explanation:
18yd(3ft/yd)=54ft
Answer:
Hello! :) have a good day!
54 feet
Antwan drew the circle graph below
describing his time spent at school in 1
day. His teacher said that the number of
hours listed were correct, but that the
central angle measures for the sectors
were not correct. What should be the
central angle measure for the Core
subject sector?
A. 72°
B. 80°
C. 160°
D. 200°
E. 288°
What is the circumference of a circle with a diameter of 9 inches.
Answer:
28.26 inches
Step-by-step explanation:
Given
diameter (d) = 9 inches
circumference (c)
= π d
= 3.14 * 9
= 28.26 inches
I NEED HELP ASAP PLEASE
Answer:
1679616
Step-by-step explanation:
6*6
36*36*36*36
Answer:
[tex]6^{8}[/tex]
Step-by-step explanation:
[tex](6^{2})^{4} = 6^{2*4} = 6^{8}[/tex]
what is the classification of the triangle by its angles and by its sides??
ANSWER ASAP!!! PLS
Answer:
right triangle
Step-by-step explanation:
whenever there is a box in the corner it means its 90° and 90° is a right angle.
can someone help pls 10 points
Answer:
A. 4x - 6 = -3x + 5
Step-by-step explanation:
you just have to take the first equation and substitute that in, in the second equation.
hope that helps. have a good day!
plz help just look at the picture
Answer:
120
Step-by-step explanation:
Answer:
the answer is C) 120
Step-by-step explanation: