Write the partial fraction decomposition of the rational expression. Check your result algebraically.
Answers
Answer:
See below.
Step-by-step explanation:
First, distribute:
[tex]=\frac{1}{x(x+1)}[/tex]
Now, perform partial fraction decomposition. This is only two factors, so we only need linear functions:
[tex]\frac{1}{x(x+1)} =\frac{A}{x}+\frac{B}{x+1}[/tex]
Now, multiply everything by x(x+1):
[tex]1=A(x+1)+B(x)[/tex]
Now, solve for each variable. Let's let x=-1:
[tex]1=A(-1+1)+B(-1)[/tex]
[tex]1=0A-B=-B[/tex]
[tex]B=-1[/tex]
Now, let's let x=0:
[tex]1=A(0+1)+B(0)[/tex]
[tex]A=1[/tex]
So:
[tex]\frac{1}{x(x+1)}=\frac{1}{x}-\frac{1}{(x+1)}[/tex]
Double Check:
[tex]\frac{1}{x}-\frac{1}{(x+1)}=\frac{(x+1)}{x(x+1)}-\frac{x}{x(x+1)}[/tex]
[tex]=\frac{x-x+1}{x(x+1)} =\frac{1}{x^2+x}[/tex]
Related Questions
PLEASE HELP Which ordered pair is a solution to the system of inequalities?
y< 3x
y< 5
Answers
Answer:
I am pretty sure that it is C
Step-by-step explanation:
A 1,3 so 3 < 3 no not true
x,y
B -12,50 50< -36 Also not true
x , y
C 9 , 4 4<27 Yes 4< 5 YEPPP
D 4,10 10<12 Yes 10<5 NOOPPPPPEEEE
For the piecewise function, find the values g(-2), g(3), and g(4).
X +5, for x<3
g(x)=
6- X, for x>3
9(-2)=
g(3)=
9(4)=
Answers
Answer:
g(-2)= -2 + 5 =3 ( here we chose the function g(x)= x+5 as x< 3)
Step-by-step explanation:
g(3)= is not defined ( function is defined for x<3 and x>3 but not x=3)
g(4) = 6-4=2 ( here we chose the function g(x)= 6-x as x> 3)
write and equation to represent the following statement 28 is 12 less thank K. solve for K K =
Answers
Answer:
K = 40
Step-by-step explanation:
As they said that 28 is 12 less than K , it means that you've to add them to get the answer. So , 28 + 12 = 40 which is represented by the variable "K"
Hope it helps and pls mark as brainliest : )
Answer:
Equation : 28 = k - 12K = 40Step-by-step explanation:
28 is 12 less than k
Let's create an equation:
[tex]28 = k - 12[/tex]
Now, let's solve:
[tex]28 = k - 12[/tex]
Move variable to L.H.S and change its sign
Similarly, Move constant to R.H.S and change its sign
[tex] - k = - 12 - 28[/tex]
Calculate the difference
[tex] - k = - 40[/tex]
Change the signs on both sides of the equation
[tex]k = 40[/tex]
Hope this helps...
Best regards!!
x+15=6 What does x equal?
Answers
Answer:
x=-9
Step-by-step explanation:
6-15=-9
Answer:
-9
Step-by-step explanation:
When you add some thing to a negative that means you are actually subtract that number
A father is 60 years old and his son is half his age. How old was the boy when his father was four times his age?
Answers
Hey there! I'm happy to help!
We see that the father is 60 years old, and the son is half of that age, so this means that the son is 30 years old.
We want to see the age the son was at when the father was four times his age. We know that the father is thirty years older than him, so we can write this equation with s representing the age of the son.
s+30=4s (30 years older than the son is equal to to four times the son's age at the time)
We subtract 30 from both sides.
s=4s-30
We subtract 4s from both sides.
-3s=-30
We divide both sides by -3.
s=10
Therefore, the boy was 10 when his father was four times his age. This is because his father would have been 40 because that is 30 more years than 10, and it is four times ten!
Have a wonderful day! :D
6th grade math help me, please:D
Answers
Answer:
the answer is c...............
a warehouse had 3 shelves long enough to hold 8 boxes and high enough to hold 4 boxes. all the shelves are full how many boxes are on the shelves all together?
Answers
Answer:
8*4*3=96 boxes in total
Step-by-step explanation:
I think. I just multiplies the 3 numbers. Hope this helps (:
Answer:
8*4*3=96 boxes in total
Step-by-step explanation:
I just multiplies the 3 numbers.
13. A hole is drilled in a block of wood as shown in the sketch. The hole is 3/4 of
the total depth of the wood. The total depth of the block of wood is 13/16 in.
How deep is the hole?
Hole
Answers
The depth of hole is 0.609 inches.
Given, the total depth of the block of wood is [tex]\frac{13}{16}[/tex] inches.
Since the hole is [tex]\frac{3}{4}[/tex] of the total depth, so the depth of the hole will be,
[tex]D=\frac{3}{4} \times\frac{13}{16}[/tex]
Or, [tex]D=\frac{39}{64}[/tex]
[tex]D=0.609375 \ in[/tex]
Hence the depth of hole is 0.609 inches.
For more details follow the link:
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The measure of ∠1 is 150°. What are the measures of ∠4, ∠3 and ∠2?
Answers
Answer:
∠1 is 150°
∠2 is 30°
∠3 is 150°
∠4 is 30°
Step-by-step explanation:
∠1 is vertically opposite to ∠3 so they are equal
360° - (150° + 150°) = 360° - 300° = 60°
∠2 and ∠4 must sum to 60°
Step-by-step explanation:
From the question
∠1 is opposite to ∠ 3 and vertically opposite angles are equal
So
∠1 = ∠ 3
That's
∠ 3 = 150°∠ 3 and ∠ 4 are on a straight line and angles on a straight line add up to 180°
So to find ∠4, subtract ∠3 from 180°
That's
∠ 4 = 180 - ∠ 3
∠ 4 = 180 - 150
∠ 4 = 30°Since ∠ 4 and ∠ 2 are opposite they are also equal
That's
∠ 4 = ∠ 2
Therefore
∠ 2 = 30°Hope this helps you
There are 50 mangoes 20 of which are unriped another basket contains 40 mangoes 15 unripe if we take 1 mangoes from each basket Find the probability of getting both are ripe Find the probability of getting both are unripe Find the probability of getting one ripe and one unripe Find the probability of at least one right Find the probability of at least one uripe
Answers
Answer:
probability of getting both are unripe
= 0.15
probability of getting both are ripe
= 0.375
Probability of one ripe and one unripe
=0.234375
Probability of at least one unripe
=0.625
Step-by-step explanation:
50 mangoes 20 of which are unriped in the first basket .
Riped = 50-20= 30
Probability of unripe = 20/50
Probability of unripe= 0.4
Probability of ripe = 30/50
Probability of ripe = 0.6
40 mangoes of which 15 are unripe In the second basket
Number of riped= 40-15= 25
Probability of unriped= 15/40
Probability of unriped= 0.375
Probability of riped= 25/40
Probability of riped= 0.625
probability of getting both are unripe
= 0.4*0.375
probability of getting both are unripe
= 0.15
probability of getting both are ripe
= 0.6*0.625
= 0.375
Probability of one ripe and one unripe
= 0.625*0375
= 0.234375
Probability of at least one unripe
= 1- probability of no unripe
= 1 - probability of both ripe
= 1-0.375
= 0.625
A student earned grades of B, B, A, C, and D. Those courses had these corresponding numbers of credit hours: 4, 5, 1, 5, 4. The grading system assigns quality points to letter grades as follows: A=4, B=3, C=2, D=1, and F=0. Compute the grade point average (GPA) and round the result to two decimal places.
Answers
Answer:
Computation of Grade Point Average (GPA):
GPA = Total Weighted Points divided by total credit hours
= 45/19
= 2.37 on 4.00 Grade Average
Step-by-step explanation:
a) Data and Computations:
Courses Grade Letters Credit Hours Quality Points Weighted Points
1 B 4 3 12
2 B 5 3 15
3 A 1 4 4
4 C 5 2 10
5 D 4 1 4
Total 19 credit hours 45 Points
b) GPA = Total Weighted Points divided by total credit hours
= 45/19
= 2.37
c) The GPA for this student is the total weighted points (which is a product of the credit hours (loads) and the quality point) expressed as a ratio of the total credit hours for the courses she took. The grade point average ensures that the each point used in calculating the GPA is weighed by the credit hours allocated to the course. The resultant figure of 2.37 implies that out of 4.00 grade points, the student scored 2.37, translating to about 59%.
Which pair of non-congruent figures must be similar? two squares two parallelograms (not rectangles) two right triangles two isosceles triangles (not equilateral)
Answers
Answer:
The answer is A (Two squares)
Step-by-step explanation:
Any give square will have proportionate side lengths,as they are the same, meaning that if you dilute one square it will always be proportinate
Answer:
it is a
Step-by-step explanation:
the other person is correct. and I did the test
Please help!! Over several years, Stephon gathered data about his age and the time it took him to run two laps on the school track. The scatter plot shows the data he gathered and the line of best fit. The equation of the line of best fit is y = -2.1x + 565.6. Based on the line of best fit, approximately how long will it take Stephon to run two laps on the track when he is 192 months old?
Answers
Answer:
It will take Stephon about A: 163 seconds to run two laps when he is 192 months old.
Step-by-step explanation:
To find 163 seconds all I did was eyeball where 192 months is going to be on the x-axis and lined it up with the provided line of fit, then I ran it across the x-axis to the y-axis and I got around 163 seconds.
Given line of best fit is y = -2.1x + 565.6, where x is age in months and y is time in seconds, it take Stephon 162.4 seconds to run two laps on the track when he is 192 months old
A line of best fit is a straight line that minimizes the distance between it and some data. The line of best fit is used to express a relationship in a scatter plot of different data points.
Given in the question,
x = age in months
y = time in seconds
Here, age of child is independent and time taken to run two laps is dependent variable.
given line of best fit : y = -2.1x + 565.6
given y = 192 months
finding the value of y :
y = -2.1x + 565.6 = -2.1 * 192 + 565.6 = 162.4
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In which table does y vary inversely with x? A. x y 1 3 2 9 3 27 B. x y 1 -5 2 5 3 15 C. x y 1 18 2 9 3 6 D. x y 1 4 2 8 3 12
Answers
Answer:
In Table C, y vary inversely with x.
1×18 = 18
2×9 = 18
3×6 = 18
18 = 18 = 18
Step-by-step explanation:
We are given four tables and asked to find out in which table y vary inversely with x.
We know that an inverse relation has a form given by
y = k/x
xy = k
where k must be a constant
Table A:
x | y
1 | 3
2 | 9
3 | 27
1×3 = 3
2×9 = 18
3×27 = 81
3 ≠ 18 ≠ 81
Hence y does not vary inversely with x.
Table B:
x | y
1 | -5
2 | 5
3 | 15
1×-5 = -5
2×5 = 10
3×15 = 45
-5 ≠ 10 ≠ 45
Hence y does not vary inversely with x.
Table C:
x | y
1 | 18
2 | 9
3 | 6
1×18 = 18
2×9 = 18
3×6 = 18
18 = 18 = 18
Hence y vary inversely with x.
Table D:
x | y
1 | 4
2 | 8
3 | 12
1×4 = 4
2×8 = 16
3×12 = 36
4 ≠ 16 ≠ 36
Hence y does not vary inversely with x.
Evaluate f(x) when x= 9
f(x) = {6x² +2 if 6
112 if 9
No solution
O 110
O 12
56
Answers
Answer:
[tex] f(x) = 6x^2 +2 , -6 <x<9[/tex]
[tex] f(x) = 12 , 9 \leq x <13[/tex]
And we want to evaluate f(x=9)
And for this case the answer would be:
[tex] f(9)= 12[/tex]
Best answer:
O 12
Step-by-step explanation:
For this problem we have the following function given:
[tex] f(x) = 6x^2 +2 , -6 <x<9[/tex]
[tex] f(x) = 12 , 9 \leq x <13[/tex]
And we want to evaluate f(x=9)
And for this case the answer would be:
[tex] f(9)= 12[/tex]
Best answer:
O 12
Solve of the following equations for x: 3x = 5
Answers
Answer: 1.7
Step-by-step explanation:
5 divided by 3=1.666666667
1.6 and next 6 in line is over 5 so the 6 turns to a 7
3*1.7= 5.1 but when rounded 1 tells 5 to stay down so it = 5
What is the value of x in the triangle
Answers
Answer:
3
Step-by-step explanation:
[tex]a^{2} +b^{2} =c^{2}[/tex]
[tex]x^{2} +b^{2} =(3\sqrt{2} )^{2}[/tex]
[tex]3*3=9[/tex][tex]\sqrt{2} *\sqrt{2} =2[/tex]
[tex]2*9=18[/tex]
9*2=18
x^2=9
b^2=9
x=3
75% letter size paper and 25% legal size paper. What is the ratio of letter size paper to legal size paper
Answers
Answer:
3:1
Step-by-step explanation:
75%=[tex]\frac{75}{100}[/tex]=[tex]\frac{3}{4}[/tex]
25%=[tex]\frac{25}{100}[/tex]=[tex]\frac{1}{4}[/tex]
Angle bisectors AX and of triangle ABC meet at point I. Find angle C in degrees, if AIB = 109.
Answers
Answer:
angle C = 38 degrees
Step-by-step explanation:
Refer to attached figure (sorry, forgot to attach earlier)
Given
AIB = 109
Let
CAX = XAB = x
CBY = YBA = y
XIB = YIA = x+y ........exterior angles
XIB = YIA = 180-109 = 71 ............ sum of angles on a line
=>
x+y = 71
ACB = 180 - 2x -2y ................. sum of angles of a triangle
= 180 - 2(x+y)
= 180 - 2(71)
= 180 - 142
= 38
Find the intervals of convergence of f(x), f '(x), f ''(x), and ∫f(x) dx. (Be sure to include a check for convergence at the endpoints of the intervals. Enter your answer using interval notation.) f(x) = [infinity] (−1)n + 1(x − 8)n n8n n = 1
Answers
Answer: See solution and explanations in the attached documents
Step-by-step explanation:
See explanations in the attached documents
the product of 12 and K is 84 solve for K K =
Answers
Answer: k = 7
Step-by-step explanation:
12k=84
Divide(12)
k=7
Hope it helps <3
Answer:
7Step-by-step explanation:
The product of 12 and k is 84
let's create an equation:
[tex]12k = 84[/tex]
Divide both sides of the equation by 12
[tex] \frac{12 \: k}{12} = \frac{84}{12} [/tex]
Calculate
[tex]k = 7[/tex]
Hope this helps...
Best regards!!
Points A,B,C and D are midpoints of the sides of the larger square. If the smaller square has area 60, what is the area of the bigger square?
Answers
Answer:
80
Step-by-step explanation:
which of the following is equivalent to the expression below? log2-log14 A. LOG(1/7) B. LOG(-12) C. LOG 12 D. LOG 7
Answers
Answer:
The answer is option A.
Step-by-step explanation:
Using the properties of logarithms
that's
[tex] log(x) - log(y) = log( \frac{x}{y} ) [/tex]
log 2 - log 14 is
[tex] log(2) - log(14) = log( \frac{2}{14} ) [/tex]
Simplify
We have the final answer as
[tex] log( \frac{1}{7} ) [/tex]
Hope this helps you
Answer:
log ( 1/7)
Step-by-step explanation:
log2-log14
We know that log ( a/b) = log a - log b
log (2 /14)
log ( 1/7)
Explain how to find the range of a data set. What is an advantage of using the range as a measure of variation? What is a disadvantage?
Answers
Answer:
The range is found by subtracting the minimum data entry from the maximum data entry.
Step-by-step explanation:
The range is found by subtracting the minimum data entry from the maximum data entry.
It is easy to compute.
It uses only two entries from the data set.
Total length of a pole is 21.3 m. If 0.2m of the length of the pole is inside the ground. Find how much of its length is outside the ground
Answers
Answer:
21.1 mStep by step explanation
Total length of pole = 21.3 m
Length of pole inside the ground = 0.2 m
Let length of pole outside the ground be X,
So, according to the Question,
[tex]x + 0.2 = 21.3[/tex]
Move constant to R.H.S and change its sign
[tex]x = 21.3 - 0.2[/tex]
Calculate the difference
[tex]x = 21.1 \: m[/tex]
Hope this helps...
Good luck on your assignment...
Please help with this
Answers
Answer:
B
Step-by-step explanation:
Hi I need this question please asap.
Answers
Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 64 + x2 − y2 R = {(x, y): x2 + y2 ≤ 64}
Answers
The area of the surface above the region R is 4096π square units.
Given that:
The function: [tex]f(x, y) = 64 + x^2 - y^2[/tex]
The region R is the disk with a radius of 8 units [tex]x^2 + y^2 \le 64[/tex].
To find the area of the surface given by z = f(x, y) that lies above the region R, to calculate the double integral over the region R of the function f(x, y) with respect to dA.
The integral for the area is given by:
[tex]Area = \int\int_R f(x, y) dA[/tex]
To evaluate this integral, we need to set up the limits of integration for x and y over the region R, which is the disk cantered at the origin with a radius of 8 units.
Using polar coordinates, we can parameterize the region R as follows:
x = rcos(θ)
y = rsin(θ)
where r goes from 0 to 8, and θ goes from 0 to 2π.
Now, rewrite the integral in polar coordinates:
[tex]Area =\int\int_R f(x, y) dA\\Area = \int_0 ^{2\pi} \int_0^8(64 + r^2cos^2(\theta) - r^2sin^2(\theta)) \times r dr d \theta[/tex]
Now, we can integrate with respect to r first and then with respect to θ:
[tex]Area = \int_0^{2\pi} \int_0^8] (64r + r^3cos^2(\theta) - r^3sin^2(\theta)) dr d \theta[/tex]
Integrate with respect to r:
[tex]Area = \int_0^{2\pi}[(32r^2 + (1/4)r^4cos^2(\theta) - (1/4)r^4sin^2(\theta))]_0^8 d \theta\\Area = \int_0^{2\pi} (2048 + 256cos^2(\theta) - 256sin^2(\theta)) d \theta[/tex]
Now, we can integrate with respect to θ:
[tex]Area = [2048\theta + 128(sin(2\theta) + \theta)]_0 ^{2\pi}[/tex]
Area = 2048(2π) + 128(sin(4π) + 2π) - (2048(0) + 128(sin(0) + 0))
Area = 4096π + 128(0) - 0
Area = 4096π square units
So, the area of the surface above the region R is 4096π square units.
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A business marketing firm specializes in radio advertising. They hope to show there is a linear relationship between sales and the amount of money a client invests in radio advertising. Which hypothesis test would be most appropriate for addressing this question?
Answers
Answer: Chi-square test
Step-by-step explanation:
A Chi-square test is a test used or applied to check or see if a relationship between two categorical variables. Example
The marketing firm trying to show their client that there is a linear relationship between sales and the amount of money the client has invested in radio advertisements uses chi-square method by comparing the two variables which are Sales made and Amount spent on advert or promotion on radio.
For each sequence, find the common difference.
-6,0, 6, 12,...
8, 15, 22,29, ...
-2,-4, -6, -8,...
2,-1,-4,-7....
Please helpp
Answers
Answer:
first is 18
second is 36
third is -10
fourth is -10