Answer:
[tex]A + B + E = 32[/tex]
Step-by-step explanation:
Given
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C[/tex]
Required
Find [tex]A +B + E[/tex]
We have:
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C[/tex]
Using integration by parts
[tex]\int {u} \, dv = uv - \int vdu[/tex]
Where
[tex]u = x^2[/tex] and [tex]dv = e^{-4x}dx[/tex]
Solve for du (differentiate u)
[tex]du = 2x\ dx[/tex]
Solve for v (integrate dv)
[tex]v = -\frac{1}{4}e^{-4x}[/tex]
So, we have:
[tex]\int {u} \, dv = uv - \int vdu[/tex]
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = x^2 *-\frac{1}{4}e^{-4x} - \int -\frac{1}{4}e^{-4x} 2xdx[/tex]
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} - \int -\frac{1}{2}e^{-4x} xdx[/tex]
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} +\frac{1}{2} \int xe^{-4x} dx[/tex]
-----------------------------------------------------------------------
Solving
[tex]\int xe^{-4x} dx[/tex]
Integration by parts
[tex]u = x[/tex] ---- [tex]du = dx[/tex]
[tex]dv = e^{-4x}dx[/tex] ---------- [tex]v = -\frac{1}{4}e^{-4x}[/tex]
So:
[tex]\int xe^{-4x} dx = -\frac{x}{4}e^{-4x} - \int -\frac{1}{4}e^{-4x}\ dx[/tex]
[tex]\int xe^{-4x} dx = -\frac{x}{4}e^{-4x} + \int e^{-4x}\ dx[/tex]
[tex]\int xe^{-4x} dx = -\frac{x}{4}e^{-4x} -\frac{1}{4}e^{-4x}[/tex]
So, we have:
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} +\frac{1}{2} \int xe^{-4x} dx[/tex]
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} +\frac{1}{2} [ -\frac{x}{4}e^{-4x} -\frac{1}{4}e^{-4x}][/tex]
Open bracket
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} -\frac{x}{8}e^{-4x} -\frac{1}{8}e^{-4x}[/tex]
Factor out [tex]e^{-4x}[/tex]
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = [-\frac{x^2}{4} -\frac{x}{8} -\frac{1}{8}]e^{-4x}[/tex]
Rewrite as:
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = [-\frac{1}{4}x^2 -\frac{1}{8}x -\frac{1}{8}]e^{-4x}[/tex]
Recall that:
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C[/tex]
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = [-\frac{1}{64}Ax^2 -\frac{1}{64} Bx -\frac{1}{64} E]Ce^{-4x}[/tex]
By comparison:
[tex]-\frac{1}{4}x^2 = -\frac{1}{64}Ax^2[/tex]
[tex]-\frac{1}{8}x = -\frac{1}{64}Bx[/tex]
[tex]-\frac{1}{8} = -\frac{1}{64}E[/tex]
Solve A, B and C
[tex]-\frac{1}{4}x^2 = -\frac{1}{64}Ax^2[/tex]
Divide by [tex]-x^2[/tex]
[tex]\frac{1}{4} = \frac{1}{64}A[/tex]
Multiply by 64
[tex]64 * \frac{1}{4} = A[/tex]
[tex]A =16[/tex]
[tex]-\frac{1}{8}x = -\frac{1}{64}Bx[/tex]
Divide by [tex]-x[/tex]
[tex]\frac{1}{8} = \frac{1}{64}B[/tex]
Multiply by 64
[tex]64 * \frac{1}{8} = \frac{1}{64}B*64[/tex]
[tex]B = 8[/tex]
[tex]-\frac{1}{8} = -\frac{1}{64}E[/tex]
Multiply by -64
[tex]-64 * -\frac{1}{8} = -\frac{1}{64}E * -64[/tex]
[tex]E = 8[/tex]
So:
[tex]A + B + E = 16 +8+8[/tex]
[tex]A + B + E = 32[/tex]
what is the perimeter of this given figure
pahelp po. thank you
Answer:
14 units
Step-by-step explanation:
Side length of each square is 1 unit.
So, sum of the lengths of all the border edges = 14 units
Thus, the Perimeter of the figure = 14 units
Find the slope of the line tangent to the function y=6-3x at the point (5,0)
Answer:
-3
Step-by-step explanation:
To get the slope of the line tangent to the function y = 6 - 3x
First, we need to differentiate;
dy/dx = 0 -3x^{1-1}
dy/dx = 0 - 3x^0
dy/dx = 0 - 3
dy/dx = -3
Hence the slope of the line tangent to the function at the point is -3
Can someone please help?
Answer:
It is closer to 7,000 than 8,000
The area of the base of a cylinder is equivalent to the base of a circle? A) True. B) False
Answer:
Yes
Step-by-step explanation:
The base of both the cylinder and Circle are both circles.
Help please worth 57 points
Answer:
Always, always.
Find the exact value of tan A in simplest radical form.
PLEASE HELP
Answer:
[tex] \tan(A) = \frac{opp}{adj} \\ \tan(A) = \frac{ \sqrt{72} }{3} \\ \tan(A) = \frac{ \sqrt{36 \times 2} }{3} \\ \tan(A) = \frac{6 \sqrt{2} }{3} \\ \tan(A) = 2 \sqrt{2} [/tex]
Can someone answer the top two one and two for me please
Which does NOT have a value of 4 when
simplified?
1. 5.6x0.15 + (-3.16)
1. (-7x23) + (-43)
III. -5.6+4(3)
Answer:
3 beause when you dividend it -5.6+4(3) .
CAN SOMEONE ANSWER THIS?
tan ( 37 ) = x / 12
x = 12 * tan( 37 )
C. 20 people show up to the party, and Robert decides to give them each the
same amount of pizza. How much pizza does each person get?
Answer:
Step-by-step explanation:3/5 of the pizza
If I can buy 4 calculators for $190, how much does one cost?
I would really appreciate if someone answered.
Answer:
47.50 per calculator
Step-by-step explanation:
Take the total cost and divide by the number of calculators to get the cost of one calculator
190/4 =47.50
solve for x + 24 = -12
answer in the box
x equals_______
Answer:
x = -36
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
x + 24 = -12
Step 2: Solve for x
[Subtraction Property of Equality] Subtract 24 on both sides: x + 24 - 24 = -12 - 24[Subtraction] Simplify: x = -36How much material would it take to cover the sandbox?
Answer:
D.6,600 ft
Step-by-step explanation:
I hope it helps
Simplify the ratio
6 doctors to 27 patients
Answer:
2 doctors to 9 patients
Step-by-step explanation:
Divide each by 3. They cant be simplified more.
A rectangle has a perimeter of 14 cm and length x cm. show that the width of the rectangle is (7-x)cm and hence that the area A of the rectangle is given by the formula A= x(7-x). Draw the graph, plotting x on the horizontal axis with a scale of 2cm to 1 unit, and A on the vertical axis with a scale of 1cm to 1 unit
take x from 0 to 7. From the graph find:
a) the area of the rectangle when x = 2.25cm
b) the dimensions of the rectangle when its area is 9cm^2
c) the maximum area of the rectangle
d) the length and width of the rectangle corresponding to the maximum area
e) what shape of the rectangle has the largest area
Answer:
B
Step-by-step explanation:
the dimensions of the rectangle when its area is 9cm^2
if the sum of two consecutive odd number is 20 find the number
Answer:
Step-by-step explanation:
let a number be x
let another number be x+1
x+x+1=20
2x=20-1
x=19/2
x=9.5
therefore one number is 9.5 and another number is x+1=9.5+1=10.5
[tex]\huge{ \mathrm{ \underline{ Answer} \: \: ✓ }}[/tex]
Let the Consecutive odd numbers be x and x+2
[tex]x + x + 2 = 20[/tex][tex]2x = 20 - 2[/tex][tex]2x = 18[/tex][tex]x = 9[/tex]Therefore, the numbers are :
[tex]x = 9[/tex][tex]x + 2 = 11[/tex]______________________
[tex]\mathrm{ ☠ \: TeeNForeveR \:☠ }[/tex]
For football the KLAA south division has 6 teams. Find the number of different ways that first, second and third place can be decided. NO LINKS!!!
Answer:
20 ways
Step-by-step explanation:
by using combination rule :
6C3 = 6! /(3! × 3!)
= 6×5×4×3! / 3! × 3×2×1
= 20 ways
==========================================================
Explanation:
Order matters because we want to distinguish between first place, second place, and third place winners. So something like ABC is different from BCA.
We have 6 ways to pick a first place winner, then 5 for second place, then 4 for third place. Overall, there are 6*5*4 = 30*4 = 120 permutations
You could use the nPr formula with n = 6 and r = 3 as an alternative method
[tex]_n P _r = \frac{n!}{(n-r)!}[/tex]
The exclamation marks indicate a factorial.
A spinner with 12 equally sized slices is shown below. (The 12 slices are red.) The dial is spun and stops on a slice at random. What is the
probability that the dial stops on a red slice?
Write your answer as a fraction or a whole number.
Answer:
100/100
Step-by-step explanation:
XD
If [×] =5 what is the value of x?
Answer:
x = 5
Step-by-step explanation:
I didn't quite understand what you were asking but x should equal 5
Answer: 1 is the answer because nothing time _ will equal 5 but 1 times anything equal that number So its 1
Solve the system of linear equations by elimination. Show your work
2x-y=-3
4x + 3y = -21
Answer:
x = -3, y = -3
Step-by-step explanation:
Solve the following system:
{-y + 2 x = -3 | (equation 1)
3 y + 4 x = -21 | (equation 2)
Swap equation 1 with equation 2:
{4 x + 3 y = -21 | (equation 1)
2 x - y = -3 | (equation 2)
Subtract 1/2 × (equation 1) from equation 2:
{4 x + 3 y = -21 | (equation 1)
0 x - (5 y)/2 = 15/2 | (equation 2)
Multiply equation 2 by 2/5:
{4 x + 3 y = -21 | (equation 1)
0 x - y = 3 | (equation 2)
Multiply equation 2 by -1:
{4 x + 3 y = -21 | (equation 1)
0 x+y = -3 | (equation 2)
Subtract 3 × (equation 2) from equation 1:
{4 x+0 y = -12 | (equation 1)
0 x+y = -3 | (equation 2)
Divide equation 1 by 4:
{x+0 y = -3 | (equation 1)
0 x+y = -3 | (equation 2)
Collect results:
Answer: x = -3, y = -3
What is the greatest common factor of the two terms
24x^6 and 18x^4
30x^3y^5 and 25x^2y
24x⁶ and 18x⁴ —> 6x⁴
30x³y⁵ and 25 x²y —> 5x²y
how to find the vat on 14% of 1800
Answer:
14/100*1800
25200/100
252
Step-by-step explanation:
therefore vat=252
What is the length of x?
Answer:
9.04
Step-by-step explanation:
tan 37 = x/12
0.7536 x 12= x
x = 9.04
at what rate will £420 yield
£70 in 4 years
Answer:
4.17%
Step-by-step explanation:
Rate = interest earned / (principal x time)
70 / (4 x 420) = = 0.0417 = 4.17%
Which ordered pair belongs to the function shown by this mapping diagram?
Answer:
{(7, 3), (8, 1), (9, 1), (10, 2)}
Step-by-step explanation:
Options are missing for this given problem, however, let's find the ordered pairs that should belong to the function shown by the mapping above:
We have the x-values (inputs) on our left while the corresponding y-values (outputs) are on our right.
The ordered pairs (x, y) are as follows:
{(7, 3), (8, 1), (9, 1), (10, 2)}
What is the third quartile, Q3, of the following distribution? 10,25,18,31,16,27,5,13,32,24,15,21,18,18,24,4,8,11,11,23
Hello can someone answer this question please
1/4 = 0.25 is the largest value..
It is right answer....
A car dealer just took delivery on forty new cars. He plans to put four of these cars on display at the front of the lot. In how many ways can the dealer combine four of the forty cars if order is not important?
A. 1,096,680
B. 91,390
C. 45,695
D. 2,193,360
Answer:
B. 91,390
Step-by-step explanation:
I've had this question before, I don't like'em, but that's the answer.
Answer:
option B
Step-by-step explanation:
[tex]40C_4 = \frac{40\times 39 \times 38 \times 37}{1 \times 2 \times 3 \times 4} = 91,390[/tex]
i need this done fast
Answer: 1) V≈1244.07 in 2) V≈54286.72 ft 3) V≈23816.41 yd
Step-by-step explanation:
Consider a random variable Z which has a standard normal distribution (mu = 0, sigma = 1). Choose which of the following values would be equivalent to the following probability:
P (Z > 0.54)
A. P(Z > 0.54.
B. P(Z < 0.54).
C. 1 - P(Z < - 0.54).
D. 1 - P(Z < 0.54).
Answer:
A. P ( Z > 0.54) = 0,7054
B. P ( Z < 0.54) = 0.2946
C.1) 1 - 0.2946 = 0.7054
D.1) 1 - 0.2946 = 0.7054
Step-by-step explanation:
A) P ( Z > 0.54) = 1 - P ( Z ≤ 0.54)
P ( Z ≤ 0.54) = 0,2946 from z-table
P ( Z > 0.54) = 1 - 0,2946
P ( Z > 0.54) = 0,7054
B) P ( Z < 0.54) = 0.2946
C) 1 - P ( Z < - 0,54)
1 - 0.2946 = 0.7054
D) 1 - P ( Z < 0,54)
1 - 0.2946 = 0.7054