express 2/(1-(x^2)) into partial fractions
Answers
2/ ( 1 + x) ( 1 - x) is express into partial fractions.
With an example, what is a partial fraction?
The division of an algebraic fraction into smaller, "partial fractions," components is possible. Think about the algebraic fraction (3x+5) (2x2-5x-3). This formula can be broken down into its simplest form, [2/(x - 3)] - [1/(2x + 1)]. Partial fractions are the more straightforward pieces [2/(x - 3)] and [1/(2x + 1)].
The four categories of partial fractions are linear factors, degree 2 irreducible factors, repeated linear factors, and repeated irreducible degree 2 factors.
= 2/(1-(x^2))
= 2 / (1)² - (X)²
= 2/ ( 1 + x) ( 1 - x)
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Related Questions
Sheryl deposited RM 40,000 for 3 years and RM 30,000 for 5 years at the same rate of interest. She receives total interest of RM 13,500. What is the rate of interest?
Answers
The interest rate is given as follows:
5%.
How to obtain the balance using simple interest?The balance of an account after t years, using simple interest, that is, a single compounding per year, is given by the equation presented as follows:
A(t) = P(1 + rt).
In which the parameters of the equation are explained as follows:
P is the value of the initial deposit.r is the interest rate, as a decimal.The interest accrued is given as follows:
I(t) = Prt.
For each case, the interest accrued is given as follows:
40,000 for 3 years: I(3) = 40000 x r x 3 = 120000r.30,000 for 5 years: I(5) = 30000 x r x 5 = 150000r.The total interest was of 13,500, hence:
I(3) + I(5) = 13500.
Meaning that the interest rate is obtained as follows:
120,000r + 150,000r = 13500
r = 13500/270000
r = 0.05.
r = 5%.
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Nicole gets paid $2,900 per month. She pays $638 a month for rent. What percent of her monthly pay goes to rent?
Answers
21.931% of Nicole's monthly pay goes to rent.
percent = (638/2900) x 100
percent = 0.21931 x 100
percent = 21.931%
a rectangle with a width of 30 centimeters has a perimiter of 100 centimeters to 160 centimeters graph a compound inequality
Answers
Answer:
5 ≤ L ≤ 35
Step-by-step explanation:
Let w represent the width of the rectangle.
The perimeter (P) of the rectangle is given by:
P = 2w + 2L
Where L is the length of the rectangle.
We know that w = 30 cm and that the perimeter is between 100 and 160 cm. We can now set up our compound inequality:
100 ≤ 2(30) + 2L ≤ 160
100 ≤ 90 + 2L ≤ 160
10 ≤ 2L ≤ 70
We can now divide both sides by 2 to solve for L:
5 ≤ L ≤ 35
Therefore, the compound inequality that represents the graph of a rectangle with a width of 30 centimeters and a perimeter of 100 centimeters to 160 centimeters is: 5 ≤ L ≤ 35
If AABC= AMNO, then what corresponding angle is congruent to angle N?
Answers
Answer:
.aabc=amn0#1211
Step-by-step explanation:
nosascoOsasco n=12.8
Note: Enter your answer and show all the steps that you use to solve this problem in the spaceprovided
Answers
Given:
The point P(x,y) is given as,
\(P(x,y)=P(\frac{33}{65},y)\)The objective is to find the value of sinθ.
Explanation:
Since the terminal side of angleθ meets the unit circle, the general equation of circle can be represented as,
\(\begin{gathered} x^2+y^2=1^2 \\ x^2+y^2=1\text{ . . . .. . (1)} \end{gathered}\)The position of point P on unit circle can be represented as,
To find y:
On further solving the equation (1),
\(\begin{gathered} y^2=1-x^2 \\ y=\sqrt[]{1-x^2}\text{ . . . .. (2)} \end{gathered}\)On plugging the value of x in equation (2),
\(y=\sqrt[]{1-(\frac{33}{65})^2}\)On solving the equation for y,
\(\begin{gathered} y=\sqrt[]{1-\frac{1089}{4225}} \\ =\sqrt[]{\frac{4225-1089}{4225}} \\ =\sqrt[]{\frac{3136}{4225}} \\ =\pm\frac{56}{65} \end{gathered}\)Thus, the value of sinθ will be,
\(\sin \theta=\pm\frac{56}{65}\)Since P is in IV quadrant,
\(\sin \theta=-\frac{56}{65}\)Hence, the value of sinθ=-56/65.
I need helpppp please I don’t understand this question at alll
Answers
Answer:
17000
Step-by-step explanation:
17^1 * 10^3
17 * 10*10*10
17*1000
17000
the answer is 17,000
the exponent shows how many times you multiply the number by itself
here is an image for an explanation
hope I helped ❤
What does the fox say?
Answers
Answer:
Joff-tchoff-tchoffo-tchoffo-tchoff!
Tchoff-tchoff-tchoffo-tchoffo-tchoff!
Joff-tchoff-tchoffo-tchoffo-tchoff!
Step-by-step explanation:
Answer:
"Joff-tchoff-tchoffo-tchoffo-tchoff!
Tchoff-tchoff-tchoffo-tchoffo-tchoff!
Joff-tchoff-tchoffo-tchoffo-tchoff!"
Jan went to the mall to buy 9 crop tops but she seen 201 other and she 1,000,000,000,000,000,000,000,00 dollars
Answers
Answer: buy all the crop tops
Step-by-step explanation:
Answer:
Well with that amount of money u should most definitely buy them, if you liked the of course
Step-by-step explanation:
I'm just saying
Answer the following problems. Complete your answers by using GFESA format. (given, find, equation, solution, and answer). Write your answer on a separate sheet of paper.
a. Find the amount of charge stored on either plate of 4.4 mF capacitor
connected to a 12-volt battery.
b. If a plate separation of a capacitor is 2.2 x 10-3m, determine the area of the plates if the capacitance is 1.4 F.
c. A parallel plate capacitor is filled with an insulating material with a dielectric constant of 2.5. The distance between the plates of the capacitor is 0.0003 m. Find the capacitance of the capacitor if the area of the plate is 30 m².
Answers
a) The amount of charge stored on either plate of the capacitor is 0.0528 C. ,b) The area of the plates is 3.47 x 10⁷ m². c) The capacitance of the capacitor is 6.62 x 10⁻⁸ F.
what is capacitance ?
Capacitance is a physical property of a capacitor that represents its ability to store an electric charge. It is defined as the ratio of the amount of electric charge that can be stored on the capacitor's plates to the potential difference (voltage) between them. Capacitance is measured in farads (F)
In the given question,
:Capacitance (C) = 4.4 mF = 4.4 x 10⁻³ F
Voltage (V) = 12 V
The amount of charge (Q) stored on either plate of the capacitor.
Q = C x V
Q = 4.4 x 10⁻³ F x 12 V
Q = 0.0528 C
The amount of charge stored on either plate of the capacitor is 0.0528 C.
Capacitance (C) = 1.4 F
Plate separation (d) = 2.2 x 10⁻³m
Find: The area (A) of the plates.
Equation:
C = ε0 x (A/d)
where ε0 is the permittivity of free space and has a value of 8.85 x 10⁻¹² F/m
A = C x d / ε0
A = 1.4 F x 2.2 x 10⁻³ m / (8.85 x 10⁻¹² F/m)
A = 3.47 x 10⁷ m²
The area of the plates is 3.47 x 10⁷ m².
Dielectric constant (k) = 2.5
Plate separation (d) = 0.0003 m
Area (A) = 30 m²
The capacitance (C) of the capacitor.
C = k x ε0 x (A/d)
where ε0 is the permittivity of free space and has a value of 8.85 x 10⁻¹² F/m
C = 2.5 x 8.85 x 10⁻¹² F/m x 30 m² / 0.0003 m
C = 6.62 x 10⁻⁸ F
The capacitance of the capacitor is 6.62 x 10⁻⁸ F.
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Evarado paid $1.12 for a doszen eggs at his local grocery store. Determine the cost of the eggs
Answers
Answer:
of a single egg or?
Step-by-step explanation:
Maria is bringing her sick dog Pedro in for a series of appointments at the
veterinary clinic. Her total cost over the course of treatment will be $150 for tests
and medicine plus $30 per appointment, a.
Answers
Answer:
need help asap
Step-by-step explanation:
Compare and contrast the rates4/5mile in 8 minutes and 4 minutes to travel2/5mile.
Answers
2/5 divided by 4 is 1/10
That’s all
Hope this helps
6) Lily was going to have a party so she
bought some sweets.She bought some
cookies and brownies. Cookies were $2 and
brownies were $3. She spent $144 for a total
of 60 sweets. How many cookies and
brownies did she buy?
Answers
Let's assume the number of cookies Lily bought is represented by "C," and the number of brownies is represented by "B."
According to the problem, the cost of one cookie is $2, and the cost of one brownie is $3. Lily spent a total of $144.
We can set up two equations based on the given information:
C + B = 60 (equation 1, representing the total number of sweets)
2C + 3B = 144 (equation 2, representing the total cost in dollars)
To solve this system of equations, we can use substitution or elimination method. Here, we'll use the substitution method.
From equation 1, we can rewrite it as C = 60 - B.
Now substitute this value of C in equation 2:
2(60 - B) + 3B = 144
Simplify the equation:
120 - 2B + 3B = 144
Combine like terms:
120 + B = 144
Subtract 120 from both sides:
B = 144 - 120
B = 24
Now substitute the value of B back into equation 1 to find C:
C + 24 = 60
C = 60 - 24
C = 36
Therefore, Lily bought 36 cookies and 24 brownies.
Find the measure of angle KMU.
Answers
140 degrees
compare 2/6 and 3/4
Answers
1. x^6-2x^5+x^4/2x^2
2. Sec^3x+e^xsecx+1/sec x
3. cot ^2 x
4. x^2-2x^3+7/cube root x
5. y= x^1/2-x^2+2x
Answers
(1) The integral of the function is (1/10)x⁵ - (1/8)x⁴ + (1/6)x³ + C.
(2) The integral is (1/4)(sec x)⁴ + eˣ(sec x) + (1/2)(sec x)² + C.
(3) The integral of cot²x dx is 1/sin(x) - sin(x) + C
(4)The integral of the function \(\frac{3}{8} x^{\frac{8}{3} } - \frac{6}{13} x^{\frac{13}{3} } + 21x^{\frac{2}{3}} + C.\)
(5) The shaded area under the curve is 7.22 sq units.
What is the integral of the functions?(1) The integral of (x⁶ - 2x⁵ + x⁴) / 2x² is determined as follows;
(x⁶ - 2x⁵ + x⁴) / 2x² = (x⁴(x² - 2x + 1)) / 2x²
= (x⁴(x - 1)²) / 2x²
= (x²(x - 1)²) / 2
∫(x²(x - 1)²) / 2 dx
= (1/2) ∫x²(x - 1)² dx
= (1/2) ∫x²(x² - 2x + 1) dx
= (1/2) ∫(x⁴ - 2x³ + x²) dx
= (1/2)(1/5)x⁵ - (1/2)(1/4)x⁴ + (1/2) (1/3)x³ + C
Simplifying further:
= (1/10)x⁵ - (1/8)x⁴ + (1/6)x³ + C
(2) The integral of (sec³x + eˣsecˣ + 1) / (sec x) dx, is calculated as follows;
(sec³x + eˣsecˣ + 1) / (sec x) = (sec³x + eˣsecˣ + 1)(sec x / sec x)
= (sec⁴x + eˣsec²x + sec x) / sec x
Note; sec x as 1/cos x
= sec⁴x/cos x + eˣsec²x/cos x + sec x/cos x
= sec³x/cos x + eˣsec x + sec x/cos x
Integrate by substitution method.
u = sec x
du = sec x tan x dx.
∫(sec³x + eˣsec x + sec x/cos x) dx
= ∫(u³ + eˣu + u) du
= (1/4)u⁴ + eˣu + (1/2)u² + C
Substitute u back in terms of sec x;
= (1/4)(sec x)⁴ + eˣ(sec x) + (1/2)(sec x)² + C
(3) The integral of cot²x dx;
cot²(x) = (cos²(x))/(sin²(x))
Let u = sin(x)
du = cos(x) dx
= ∫(1-u²)/u² du
= ∫(1/u²) - 1 du
= ∫u⁻² - 1 du
= -1/u - u + C
= -1/sin(x) - sin(x) + C
(4) The integral of the function is;
∫(x² - 2x³ + 7)/∛x dx = ∫x²/∛x dx - ∫2x³/∛x dx + ∫7/∛x dx
= \(\frac{3}{8} x^{\frac{8}{3} } - \frac{6}{13} x^{\frac{13}{3} } + 21x^{\frac{2}{3}} + C.\)
(5) The shaded area under the curve is calculated as follows;
the given function;
\(y = x^{1/2} - x^{2} + 2x\)
∫y = A = \(\frac{2}{3} x^{3/2} - \frac{1}{3} x^3 \ + x^2\)
the limits = 2 and 0
A = \(\frac{2}{3} (2)^{3/2} - \frac{1}{3} (2) ^3 \ + (2)^2\)
A = 1.89 - 2.67 + 8
A = 7.22 sq units
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PLEASE HELP I NEED THIS DONE ASAP. WILL GIVE BRAINLIEST!!!
Answers
The required value probability is 0.20.
What is Probability?The probability of an event is a number used in science to describe how probable it is that the event will take place. In terms of percentage notation, it is stated as a number between 0 and 1, or between 0% and 100%. The higher the probability, the more probable it is that the event will take place.
According to question:We have given;
Total number of outcomes = 25
Number of favorable outcomes = 5
Then;
Probability = 5/25
= 1/5
= 0.20
Thus, required probability is 0.20.
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William leaves his home at 15:03 and walks for 12 minutes to Euston station.
He spends 4 minutes buying a ticket and then catches the next train to Bletchley.
What time will he arrive at Bletchley?
Train timetable
Euston
14:49 15:18 15:29
14:52
15:32 15:35
Harrow
Watford 15:01
15:30
15:41 15:44 16:11
Hemel
15:39 15:50
15:53
16:20
Tring
15:31
16:00
Q
16:14 16:41
Bletchley 15:47
16:16
16:30
Bedford 15:54 16:23 16:34 16:37 17:04
15:32 15:59
Answers
To find out what time he will arrive at Bletchley, we need to look at the arrival time for the train that departs Euston at 15:32. According to the timetable, this train arrives at Bletchley at 16:16.
William spends 12 minutes walking to Euston station and 4 minutes buying a ticket, so his total journey time is 12 + 4 + 44 = 60 minutes (since there are 60 minutes in an hour). Therefore, he will arrive at Bletchley at 16:16 + 60 minutes = 17:16.
So, William will arrive at Bletchley at 17:16.
*Answer*
15:47
Step-by-step explanation:
He left; 15:03
Walk for; 12mins
Spends extra;4min
So by my side,
I'll sum up those values we're having to find the total time that was spent
12+4= 16mins
So, at that time when he reached at the station it was 15:19 when we add those extra mins
And so I think it'll 15:47
My thought told me so though
1200-5(3x+30)=600 show the steps to solve this problem
Answers
Answer:
x=+30
Step-by-step explanation:
1200-5(3x+30)=600
We move all terms to the left:
1200-5(3x+30)-(600)=0
We add all the numbers together, and all the variables
-5(3x+30)+600=0
We multiply parentheses
-15x-150+600=0
We add all the numbers together, and all the variables
-15x+450=0
We move all terms containing x to the left, all other terms to the right
-15x=-450
x=-450/-15
x=+30
Answer:
\( \boxed{ \bold{ \huge{ \boxed{ \sf{x = 30}}}}}\)
Step-by-step explanation:
\( \sf{1200 - 5(3x + 30) = 600}\)
Distribute 5 through the parentheses
\( \dashrightarrow{ \sf{1200 - 15x - 150 = 600}}\)
Subtract the numbers: 150 from 1200
\( \dashrightarrow{ \sf{ - 15x + 1050 = 600}}\)
Move 1050 to right hand side and change it's sign
\( \dashrightarrow{ \sf{ - 15x = 600 - 1050}}\)
Subtract 1050 from 600
\( \dashrightarrow{ \sf{ - 15x = 450}}\)
Divide both sides of the equation by -15
\( \dashrightarrow{ \sf{ \frac{ - 15x}{ - 15} = \frac{ - 450}{ - 15} }}\)
Calculate
\( \dashrightarrow{ \sf{x = 30}}\)
Hope I helped!
Best regards! :D
What is the area of the circular Olympic wrestling arena if it has a diameter of 29.5 feet?
Answers
Since the Olympic wrestling arena has a circular shape, we can find the area using the following formula:
\(\begin{gathered} A=\pi r^2 \\ \end{gathered}\)Where:
\(r=\frac{diameter}{2}=\frac{29.5}{2}=14.75ft\)Therefore:
\(\begin{gathered} A=\pi(14.75)^2 \\ A\approx683.49ft^2 \end{gathered}\)Answer:
683.49 ft²
10. A pipe whose diameter measures 1 1/4 inches should have less threads per inch than a pipe with a diameter of _______ inch.
A. 3
B. 1/2
C. 1
D. 11/2
Answers
A pipe whose diameter measures 1 1/4 inches should have less threads per inch than a pipe with a diameter of 11/2 inch. So, the correct answer is (D).
To determine the correct answer, we need to compare the diameters of the two pipes and understand the relationship between pipe diameter and threads per inch.
The number of threads per inch generally decreases as the pipe diameter increases. This means that a larger pipe diameter will have fewer threads per inch compared to a smaller pipe diameter.
Given that the first pipe has a diameter of 1 1/4 inches, we need to find the pipe diameter from the options that is larger than 1 1/4 inches.
The option that meets this requirement is D. 11/2. This represents a pipe diameter of 1 1/2 inches. Therefore, a pipe with a diameter of 1 1/2 inches should have fewer threads per inch than a pipe with a diameter of 1 1/4 inches. Therefore, the correct answer is D. 11/2.
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what is 0.1 as a fraction
Answers
Answer:
1/10
Step-by-step explanation:
The type of graph used by precision teachers to track rate of learning and ensure the learner is on track for attaining fluency.
A. Line Graph
B. Scatterplot
C. Standard Celeration Chart
Answers
Standard Celebration Chart is used by precision teachers to track rate of learning and ensure the learner is on track for attaining fluency.
Since , It is a consistent display of frequency of change over time (celebration) precision teachers use it to track rate of learning and ensure the learner is on track for attaining fluency. The Standard Celebration Chart (initially called the Standard Behavior Chart) is used to observe and improve human learning and interaction. The chart shows the frequency of performance and its celebration, i.e., growth of learning across time.
Frequency, whose formula is
F = Count/Time,
Tells what happened during a specific time.
Celebration, whose formula is
C = Count/Time/Time, or Frequency/Time, tells what happens across the longer period of time – weeks, months, years, or decades.
All Standard Celebration Charts retain and present the original data in the form of frequency and celebration.
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Guys I really need your guys with this
Answers
Answer:
The correct answer is the third option: | 6 | is the distance between 0 and 6, and the distance is always positive regardless of direction.
Step-by-step explanation:
Distance is a physical measurement, which is never negative. Therefore, the absolute value of a number is never negative.
By this definition, if x is a positive number or 0, then its absolute value is x itself. If x is a negative number, then its absolute value is the additive inverse of x.
Since the absolute value is never negative, then the distance will always be positive, regardless of direction. That is why the third option is the correct answer:
| 6 | is the distance between 0 and 6, and the distance is always positive regardless of direction.
Need help with this question
Answers
Answer:
i cant see it
Step-by-step explanation:
umm
the length of a rectangle is five times the width. if the area of the rectangle is 125 square inches, find the length and width
Answers
Width: 5
25 divided by 5=5
25x5=125
Q.1
According to the Department of Food and Nutrition, the recommended daily allowance (RDA) of calcium for adults is 800 mg. A nutritionist thinks that people with income below poverty level average less than RDA of 800 mg. intakes of calcium were determined for a sample of 40 people with income below poverty level. The results are obtained in the following frequency distribution. Compute the quartiles.
Intake (mg) Frequency
101-200 1
201-300 1
301-400 9
401-500 13
501-600 10
601-700 6
Answers
The quartiles of the distribution are given as follows:
First quartile: 350.5 mg.Second quartile: 450.5 mg.Third quartile: 550.5 mg.How to obtain the quartiles of the distribution?The sample size of the distribution is of:
n = 40.
The first quartile is the value that is greater than 25% of the distribution, hence it is the value at the position which is 25% of the sample size, hence:
Position: 0.25 x 40 = 10.Value: 350.5 mg -> mid-point of the bounds of 301 and 400.The second quartile is the value that is greater than 50% of the distribution, hence it is the value at the position which is 50% of the sample size, hence:
Position: 0.50 x 40 = 20.Value: 450.5 mg.The third quartile is the value that is greater than 75% of the distribution, hence it is the value at the position which is 75% of the sample size, hence:
Position: 0.75 x 40 = 30.Value: 550.5 mg.More can be learned about the quartiles of a distribution at https://brainly.com/question/9265525
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Answer this correctly I’ll give brainalist + 10 points
Answers
Answer:
x = 43
Step-by-step explanation:
Since these angles are inside a right angle, we know their sums are complementary (they add up to 90°.)
x + x + 4 = 90
2x + 4 = 90 | Combine x's
2x = 86 | Subtract 4 from both sides
x = 43 | Divide both sides by 2
Please help
Me
I need to finish this I will give brainlest
Answers
Only the opposite edges of a rectangle's parallel and congruent angles are congruent. Although the sides and angles of a trapezoid may not always be identical, at least one set of its sides must be parallel.
what is parallel lines?In geometry, parallel lines are coplanar unlimited lines that never cross. In a particular three-dimensional space, the parallel planes represent the ones that never cross. Parallel curves are those with a constant minimum separation between them and no places of contact or intersection. In geometry, parallel lines are two lines which run in the exact same plane, evenly spaced apart, and hadn't cross. Both vertical and horizontal can be used. In commonplace items like train tracks, stacks of notebooks, and crossings for pedestrians, straight lines can be seen.
The form of Jackson's poster is best described as a rhombus. A quadrilateral with a rhombus has opposing sides that are parallel and all of its sides are equal. Additionally, it has congruent opposing angles. In addition to having parallel opposing sides, a parallelogram also has non-congruent sides and angles. Only the opposite edges of a rectangle's parallel and congruent angles are congruent. Although the sides and angles of a trapezoid may not always be identical, at least one set of its sides must be parallel.
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The constraints of a problem are listed below. What are the vertices of the feasible region?
\(x+y\leq 7\\x-2y\leq -2\\x\geq 0\\y\geq 0\)
Answers
The vertices of the feasible region is (4, 3)
What are the vertices of the feasible region?From the question, we have the following parameters that can be used in our computation:
x + y ≤ 7
x - 2y ≤ -2
x ≥ 0
y ≥ 0
Express as equations
So, we have
x + y = 7
x - 2y = -2
Subtract the equations
3y = 9
So, we have
y = 3
Next, we have
x + 3 = 7
This gives
x = 4
Hence, the vertex of the feasible region is (4, 3)
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